AIRCRAFT ENGINE DESIGN

BY

JOSEPH LISTON, M.E.

A.ssociate Professor of Aeronautical Engineering Purdue University; Member S.A.E,

First Edition Third Impression

McGRAW-HTLL BOOK COMPANY, Tnc.

NKW YORK AND LONDON

1942

AlIl.CK,AF'r KNOINTEl

Cop-YKIOHT, 194S, BY a'III‘3 McObaw-Uibxi I^ook: Oombaxy, Ixr;.

PlilNTEll^ IN TmES XJJSria’KI> S'TAa’JEiS Cjr AMEiltlOA

AZZ rights reserved^ I'^his hooh^ or parts thereaf, rriCLyiriid he prixiuced in any farm 'wiihoni jjrr7nissiari af the publishers.

"rHK MAPI.K BR.KHS OOlVfPAXY

Y<> rk:

I* A .

PREFACE

This text has been assembled to aid technicaj students in bridg- ing the gap between the point (a) where they have a fairly com- plete knowledge of the fundamentals of mathematics^ mechanics, and machine design and (b) the point where they are sufficiently familiar with the application of these fundamentals to the design of aircraft engines to enable them to be of value to the aircraft- engine building industry.

Usually students entering this field of study are totally lacking in the experience so essential to deciding a logical order of proce- dure of engine design. They also lack the accumulated informa- tion upon which experienced designers can call for making the innumerable assumptions that .must precede or parallel the analyses of various parts. Hence, an outline of procedure and a considerable accumulation of more or less rational data have been included. However, it is pointed out that although the Suggested Design Procedure is one way of carrying through the analysis, it is not the only way, or even the best possible way in a particular instance. Students are usually encouraged to select a ^^con- ventionaU’ type of engine for a first design because there are more signposts’^ to guide them, but this should not be mis- interpreted as implying a negative attitude toward new ideas and possible improvements over present practice. Rather, it is based on the belief, founded largely on teaching experience, that a student cannot very well design an improved or unconventional engine until he is familiar with the shortcomings and weaknesses of conventional engines.

The author is greatly indebted to the various stated sources for illustrative data, and in each case he has endeavored to give proper credit. The author is also indebted to G. D. Angle, P. M. Heldt, various staff technicians at Wright Field, the NAG A, the engine industry, and his associates at Purdue, particularly Dean A. A. Potter, Prof. G. A. Young, and especially Prof. K. D. Wood for valuable suggestions, criticisms, and assistance.

Lafayette, Indiana, JosnPH LiSTON.

April, 1942.

CONTENTS

Page

Preface v

Chapter

1. Requirements, Possibilities, and Limitations 1

Sources of Power — Basic Requirements and Limitations — Gov- ernment Requirements — References — Problems.

2. Outline op the Project 14

Selection of the Potential Market — Selection of Rated Power — Preliminary Specifications — ^Justification of Values in Example 1 — Preparation of Design Data and Drawings — Suggested Design Procedure.

3. Gas-pressure Forces 26

Forces in the Cylinder — Construction of the Indicator Card — Example — Gas-pressure-Crank-angle Diagrams — Example — References — Suggested Design Procedure — Problems.

4. Analysis of the Crank Chain 36

Forces Due to the Reciprocating Parts — Piston Velocity and Acceleration — Example — Piston Displacement, Velocity, and Acceleration for Articulated Rods — Inertia Forces Due to Reciprocating Parts — Example — Torque or Turning Effort per Cylinder — Example — Torque Reaction — Total Engine Torque — Example — Torque Variation with Number of Cylinders and Cylinder Arrangement — Suggested Design Procedure — Refer-

5. Analysis of Bearing Loads 58

Crankshaft Bearing Loads — Resultant Force on the Crankpin — Example — Crankpin Bearing Loads — Example — Crankshaft Dimensions — In-line and V-engine Crankshafts — Example — Radial-engine Crankshafts — Resultant Forties on Main Bearings — Example — Relative Wear Diagrams — Suggested Design Proce- dure—Referen cos.

6. Design of Reoiproiating Parts 88

Design Requircnnents and TJmitations- Functions of the Piston — Piston Materials — Piston Dimensions — Piston Rings— Piston

vii

viii CONTENTS

Chapter . Pauh

or Wrist Pins — Knuckle or Pink Pins — Connecting-rod Shank Stresses — Connecting-rod Cap Jiolta — Ck>nriecting-rod lOncls — Articulated Rods — Connecting-rod Materials — liearings and Bearing Metals — Suggested Design Procedure — Refercnices.

7. Crankshaft Vibration and Balance 110

Fundamental Nature of Vibration — Engine Balance — Variation in Engine Torque — Flexibility of the Oankshaft in Torsion — Types of Crankshaft Balance — Unbalanced Rotating Parts — Unbalanced Reciprocating l\irts — Reciprocating Balance in Multicylinder Engines — Counterbalancing — Exaniphi — Sug- gested Design Procedure — References.

8. Crankshaft Detaii^s and Reduction Gearing 145

Crankshaft Details — Reduction Gearing — Gear Materials and Dimensions — Example of Single-reduction Gearing Calcnilation — Example of Planetary-reduction Gearing Calfuilation — -Special Gears — Reduction-gear liearing Loads — Iltuictiion Tor<pie Meas- urements— Thrust-bearing Details — Suggested Design Proccidure — Problems — Ileferences.

9. Cylinders and Valves 173

Functions of the Cylinder — Types of Cylinder Ck>nstruction — Cylinder Materials — The Cylinder Barred — C'ooling Fins and Baffles — Valve Requirements and Materials — Brc^aihing (Capac- ity and Valve Size — Valve Details — Th(‘ CCornhuHtion (,’Chanibei* — Suggested Design Procedure — Problems — R(‘f<jr(inc(^s.

10. Valve Gear 212

Usual Valve-gear Arrangements — Valve Timing — Valv(‘ C.ains and Followers — Tangent Cams — Exampl<‘ <>f I'angenl-carn Calculations — Mushroom Cams — Exanqdcis of Mushrooru-cain Calculations — Holknv-fac^cd ( -aius — Riidial-(uigine ( *ain Kings- - Example of Radial-engine Cam C Calculations — C -am Ramps—

Cam Spacing — C-arn lA>ads — Exaini)h‘ of C -am-Ioad ( 'ah'ulat ions — Camshaft Stiffm^ss — Cam and Followau* Details — Push Pods and Rocker Arms — Valve Springs— hlxaniph^ of Valve-spring (Cal- culations— Vhil\a;-gear Details — Suggested 1 If^sign Procf‘rlun* —

Pro bid ri s — I i.e f c re rices.

11. The Crankcase, Superchargers, and Acc'Esscfues 279

Crankcase Materials and Arrangenumts — (‘rankca.srj Details —

Oil Pumps — Blowers and Supercliargc-rs— .Snp(‘r(‘hargf*r Ikiwfu' Reqiiircmients — Iinpedler Sperai — Impeller Drdails— I )ifTus(‘rs — Supercharger Drives — Accessoriris — Carhured-ors and Kmd Pumps — Magnetos, Starters, and Geiienitors— ^racdiorncd.ers, and

CONTENTS . ix

Chapter Page

Miscellaneous Accessories — Accessory Drive Details — Suggested Design Procedure — Problems — References.

APPENDICES

List of Tables in' Appendices 321

List op Figures in Appendices 321a

1. Technical Data on Aircraft Engines and Engine Parts. . . 322

2. Properties of Aircraft-engine Materials 440

3. Useful Design Formulas 460

Index 483

AIRCRAFT ENGINE DESIGN

CHAPTER 1

REQUIREMENTS, POSSIBILITIES, AND LIMITATIONS

1-1, Sources of Power. — The source of power for all present- day aircraft is the internal-combustion engine. So far, this type of prime mover is the only on^e that has proved capable of meeting all the exacting requirements of powered flight success- fully. Other prime movers such as steam plants have been considered and even tried experimentally in a few instances, but none has, to the writer’s knowledge, survived to the production stage.

1-2. Basic Requirements and Limitations. — Some of the more important basic requirements of the airplane engine are

1. Adequate power.

2. Very low weight-power ratio.

3- High specific power output.

4. High thermal efficiency.

5. Compactness,

6. Reliability and long life.

7- Relative ease of maintenance.

8. Reasonable initial cost.

9. Ability to operate under adverse conditions.

Considering these items briefly:

1. Historians now generally agree that the first successes in powered flight were delayed several years because of lack of a suitable engine. Present large aircraft designers are continually clamoring for more and more powerful engines. Reductions in parasite drag have contributed markedly to the improvements in i:)erformance attained during the last 10 years, but further improvement from this source appears to be following thc^ law of diminishing returns.

1

2

AIRCRAFT ENGINE DESIGN

The power necessary for any given proposed airplane is usually determined from an estimate of parasite drag, combined with wing drag and propeller chai*acteristics. This enables the designer to estimate the brake horsepower necessai'y for the maximum speed at which he desires to fly.

From the fundamental relations of drag, velocity, horsepower, and propeller efficiency, the maximum brake horsepower required for any given airplane may be expressed by

P =

D XVrr

)

2

T

37577

where P == brake horsepower needed at Tmux.

D == drag, lb.

Cd = coefficient of drag ffor the entire airplane), p = mass density.

/S = a representative area (usually the wing area) eoi’~ responding to C/>.

Vmax == maximum speed of the airplane, m.p.h,

7} == propeller efficiency.

Letting S = /, the total equivalent flat-plate ai*ea of the airplane (= /parasite + /wins profue) of = unit3q assuming standard density, and collecting constants,

At maximum speed, the wings will be at or very near an angle of attack at which the wing drag is a minimum. If thf? cor- responding wing-drag coefficient is inereascMl to unity, the drag equation will still hold if S is decrease<l b^^ tlH‘ inveu'se ratio. The new value of area is called flat-plate area of minimum wing- profile drag and may bo designated In symbols,

or

C Jj ruin _

C'/.(= 1)

from which

“ C l> mia X ^

REQUIREMENTS, POSSIBILITIES, AND LIMITATIONS 3

Since the minimum difeg coefficient of most airfoils is very near 0*01, == 0.01/3, approximately. Then for estimating power

requirements, *

where P = brake horsepower needed at Fmax-

Sv = square feet of parasite fiat-plate area of C 1.0.

/S = wing area, sq. ft. rj = propeller efficiency.

T'max = maximum speed of the airplane, m.p.h.

Example. — A company plans to develop an engine for military student- training planes of the following general characteristics: Well streamlined biplanes with retractable landing gear and cowled engines, 2,500 to 3,500 lb. gross weight, wing loadings around 12 td 16 lb. per sq. ft., and top speeds of 130 to 140 m.p.h. Approximately what rated engine horsepower should the company design for?

Solution. — Assuming mean values, /S == 3,000/14 = 214 sq. ft.y/jj = about 6 sq. ft. (Fig. 1-1), and tj will probably be about 80 per cent. Therefore

^ 6 4- 0.01 X 214 / 140\3

^ — 0:1 (so) “

Correlation of brake hc^sepower, wing area, and maximum speed for existing planes can be used as a basis of estimating brake horsepower necessary. This has been done for 68 Ameri- can airplanes (Fig. 1-2). These planes included all types from light sport planes to large flying boats, and as is indicated in the figure, fair correlation exists. The slope of the mean line (Fig. 1-2) is 2.56, and from its equation

P = (1-3)

where the symbols are the same as in Eq. (1-2). Equation (1-3) is useful in approximating the maximum brake horsepower, but Eq. (1-2) is more accurate and should be used when J-p and rj are known or can be determined.

2. The weight-power ratio is an important criterion to the value of an engine for airplane use. Figure 1-3 shows the wcight-

* Equation (1-2) gives reasonably close values c)f brake horsepower, but some additional minor factors should be considered for pre(use (‘alculations. See reference 1, Chap. 1, reference 2, p. 122, and N ACA l^cch. Kept. 408.

AIRCRAFT ENGINE DESIGN

power ratios for 36 repi'esentative Anerican engines. Th(3 position of any given engine with respect to the mean line may be taken as a measure of the degree of excellence of the design. However, excessively low weight-power ratios are usually

O 1000 2000 3000 4000 5000 6000 7000 8000 9000 10,000 Gross weighty lb-

Fig. 1-1. — Flat-pUite ocpii valent of parasites druK of airpiaiu'S.

Class 1. Cantilever monoplane with retracta)>le ehassi.s, fuH<*Ia|L'e,

well-cowled engine, and no external l>racing.

Class 2. (a) Cantilever or wire-liraced monoplane wif.lr can til<*v(*r or wirc- braced chassis, wheel pants, streamlined fiistUage, tmgine cowl or ring. (6) Biplane or externally braced monoplane witli retra<d.ahle chassis, streamlim* fuselage, engine cowl or ring.

Class 3. Biplane or externally braced monoplane with Htrt*amlin<r fuHelag<‘, engine cowl or ring.

Class 4. Airplanes having excessive parasite drag. {From FivU ArrfHuiuficn Manual 04.)

attained either with the aid of very higii octanci fuc^ls or at a sacrifice in operating life. For exainphb ra(*ing (‘iigiiu^s have very low weight-power ratios, but thc^y nKiuin^ spc^cial fuels and usually have a very short life IxdAvcHui <>vc‘rhauls.

Nevertheless, it is essential that the wciight b(‘ low, as additional plane weight sirnpfy means loss useful load. Figure 1-4 shows

REQUIREMENTS, POSSIBILITIES, ANU LIMITATIONS 5

the weight of engines iri terms of gross weight of the plane for 22 American aircraft in the gross weight range between 1,000

Mdxfmum speed, m.p.h.

Fig. 1-2. — Variation of maximum speed with brake horsepower per square foot , of wing area for 68 American airplanes.

0 100 200 300 400 500 600 700 800

Brotke horsepower

Fig. 1 -3-— Specific woiglit for 36 Ain<M*ican airci*aft (Migines.

and 4,000 1}>. 44i(‘ jxjvvm* loadings for tyinc‘al American air])lan('S

in the 1,000- to 4,000-11). class are shown iii Fig. 1-5.

6

AIRCRAFT ENGINE DESIGN

The effect of power loading on maximum speed is shown in Fig. 1“6. Points well below the trend line are evidence of ineffective aerodynamic cleanliness. Points far above may be due to unusually good streamlining or to excessive optimism on the part of the manufacturer.

3. From the relation b.hp. = Pj?Z/yiJV'en/33,000, it is apparent that power output is a function of size, speed, and pressure.

Gross weight, lb.

Fia. 1“4. — Proportion of engine weight to gross weight for 22 Aineri{nin airplanes in the 1,000- to 4,0a0-lV>. class.

24

J-22

fezo

Ql.

14 12 10 8

1000 1500 2000 2500 3000 3500 4000

Gross weiqht. Ib.

Fio. 1-5. — Power loadings for 22 American airplanes in the 1,000- to 4,000-lh. • class.

Rigid weight limitations obviously control tho size of engine that may be used, and the speed is limited very largely by the propeller eflRcicncy. Reduction gears may l)c uscmI wh<‘re tho added complexity and cost per horsepower is warranterl. With reduction gearing, speed limitations are imposed Ijy the valve gear and by crankpin loa<lings. Increase in the effective work-

	o	o
	^						—
				o
				o
			c
								ro — b			^ -
				I" o

REQUIREMENTS, POSSIBILITIES, AND LIMITATIONS

ing pressure is one of the most valuable methods of increasing the specific power output. Some increase in b.m.e.p. (== Pb) can be obtained by increasing the compression ratio (Fig. 1-7^). Greater increases are possible by supercharging (Fig. 1-7^). The

70 90 110 130 150 170 190 210

Maxirnum speed, m.p.h .

Fig. 1-6. — Power loading vs. maximum speed for 22 American airplanes.

Fro. 1-7A. — EiETect of compression ratio on performance. {S.A.E. Journal^ Y ol.

41, No. 4, October, 1937.)

limits on both of these methods are fixed by the ability of the fuel to withstand detonation, i.e., by the octane number of the fuel to be used, and by the maximum allowable cylinder pressures. Higher maximum pressures mean heavier cylinder construction, hence increased specific weight. This incidentally,

AIRCRAFT ENGINE DESIGN

is an important obstacle to successful use of the Diesel-type aircraft engine. Figure 1-8 shows the b.m.e.p. vs. brake horse- power for 42 American engines. The b.m.e.p. was taken from manufacturer's data; the b.m.e.p.,^,^ was determined (see Table Al-13) from b.m.e.p. = 1/0.75 X 0.9 X b.m.e.p.c^,,i«i„^.

Pig. 1-7B, — Effect of octane number on performance. {S.A.E. Journal, Vol. 41,

No, 4, October, 1937.)

140

a> 1 30 ,> .=

1:2,00

a>

i 90 80.

Fig. 1-8. — Brake rneaii effective pressure at cruisiiiK horvSC‘i>o w(‘r for 42 Amerir-aii aircraft erii^ines. AT, not supercharged; 0, super<‘h:tre:e<i, A -- 1 ; 1 })lo\ver.

The effect of supercharging on b.m.e.p. and horsf*pf>\vor is shown in Figs. 1-9A and 1A)B. Figure 1-10 shows th(* limita- tions placed on b.m.e.p. by the octanes munlxn*. In this figui*<*, points above the mean line EF indi{*ate good (‘oinhust ion- chamber and cooling design. Points far Ix^Iow this line indi- cate either poor design or use of uniu‘C(*ssarily (^xpemsive* fu(‘ls. Specified octane number vs. compression ratio for 23 Aineri{*an aircraft engines is shown in Fig. 1-1 1 .

. B

yJL

r

P

Cruj: Q

j/'n?.

(. L .

--0

o

g.M;

3^

”5:^^

o

ed

X

X

o >

fsup

icfrgK

^ c>upercnargecf ^ 7 to / biqwer j

100 200 300 400 500 600

Broike horsepower

Brake mean effeciive pressure Ib.per sa.in. (Corn to 103*’ F.)

9

10

AIRCRAFT ENGINE DESIGN

It should be borne in mind, however, that increase in the manifold pressure, the amount of supercharge, also is

limited by the octane number of the fuel. This largely accounts for the variation in octane-number rec|uirements of different engines having the same compression ratio.

Compression rcjitio

Fig. 1-11. — Octane-number reQxiirements of 2S American aircraft enginoH.

0.72

. 0.68 t-

0.64

-c 0.60

■f 0.56 <u

°:o.sz

0.48

to

£ 0.44 0.40

4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0 7.2 Compression ratio

Fig. 1-12. — Effect of corniircssion ratio on specific futrl cToiisuinpt ion for 22

American aircraft <;np'iiieH.

	c
	V..
	> c	o Ob						" o
			o						!
								*0

4. Fuel economy is important in ain'raft (Migines not only from a fuel-cost standpoint but also because the (dTeet is euinuhit iv(>, since the fuel has to be carried. Fuel raU^s attaiiu‘d in oj)f;ration are affected by the percentage of ratofl powcn* iiscul and 1)3^ th<i adjustment of the mixture control. Receiitly, much attention has been focused on economical mixtures owing in part to the

REQUIREMENTS, POSSIBILITIES, AND LIMITATIONS 11

use of exhaust-gas analyzers as a means of indicating good mixture adjustment. However, limitations are imposed by permissible cylinder temperatures. Higher compression ratios (Fig. 1-12) are a means of improving economy, but this necessi- tates more expensive fuels or resort to ^^fuel cooling by richer mixtures. Currently attained economy of operation is indicated in Fig. 1-13. These values represent manufacturers' guarantees rather than best possible performance, however.

5. Engine compactness is essential to low parasite drag, but for direct cooling (air cooling), limitations are imposed by the necessity of getting rid of a very large amount of heat through

Fig. 1-13. — Fuel rate for 25 American aircraft engines.

the fins per unit of time. In liquid-cooled engines, the problem is merely shifted from the engine to the radiator. All the heat liberated in the cylinder except that converted into work must ultimately be removed and given up to the surroundihg air. Thermal efficiencies vary from 25 to 35 per cent; hence 65 to 75 per cent of the heat energy in the fuel must be disposed of at a rate sufficient to prevent temperature rises above allowable limits. It is apparent that improving the thermal efficiency simplifies the cooling problem. In the larger sizes of engines, cooling becomes a limiting factor to cylinder dimensions.

Weight limitations are also closely related to compactness. Obviously, the more elongated and spread out an engine is, the more difficult it becomes to keep the specific weight within allowable limits. In this respect, radial engines are generally conceded to have some advantage over other types.

12

AIRCRAFT ENGINE DESIGN

6. In commercial operation, reliability is of great importance. Forced landings and crashes with resulting ]u^\vs[ )apej* headlines are about the best negative publicity an airline can have. More directly, they are tremendously expensive in both equipment and personnel.

In military work, reliability is equally important. Failure of equipment at a crucial moment may mean the difference between victory and defeat. The old saying Because of a nail the horseshoe was lost, etc., down to the loss of the Army^' is just as applicable to the working parts of an airplane engine. In the air, no item, however minor, is entirely unimportant.

Operating life between overhaul periods directly bears on the revenue-producing ability of aircraft engines. For a given schedule of operations, the longer the life between major servic- ing periods, the fewer reserve engines necessary and the less the nonrevenue-producing investment. Skille(l-lal)or requirements are also a major item of cost in keeping ecpiipment in serxdce.

7. The relative ease of maintenance is determined vc^ry largely by the simplicity of design and by the iisc^ of standard parts in so far as possible. Manufacture to vcny close dimensional limits is essential to reliability, but it also aids in |;)cn'mitting thci interchangeability of ])arts on like engines. RcMluction in the repair-parts inventory is most desirable.

8. In the ultimate, the iisofulnc\ss of all commercial i)roduc*ts is determined by tlicdr cost. Regardless of the pc^rfection of th(^ design and manufacture, the ])rodu(*t cannot comp(d,e if it is too costly. In the case of the air})lane (mginc^, th(^ raw mateanals iron, nickel, aluminum, etc*., in thcnr initial stab^s are r(dativ<‘ly inexpensive. Fabrication is the major itcnn, and that is largt^Iy determined by complexity of the design. Idnj simpl(\st design that will meet the recpiiremcuits is generality the most satisfactory when all items arc3 considered.

9. Ability to operate undcu* adverse conditions is probably more important in the aircraft engine than in any oth(‘r typ(" of prime mover. In addition to tlu^ rc'fiuircuncnit (jf unfaJling reliability, the engine is called u})on to op(n*at(^ in widcdy v'arying positions and extreme altitudes. These r(ic|iiir(^m(aits di(*tatc dual ignition, a dry-sump crankcase, sj)ecial c.aii)urc*tor design, and numerous other special features that are rcilatively much less important in engines for land or marine craft.

REQUIREMENTS, POSSIBILITIES, AND LIMITATIONS 13

1-3^ Government Requirements. — Primarily for the purpose of maintaining reasonable safety standards, the Federal Civil Aeronautics Authority has been given extensive control over American aviation. In the engine field, the control consists in forbidding the use of engines not approved by the CAA.

To receive approval, an engine must successfully pass a number of exacting tests and meet certain Other requirements. Hence, it is important for the designer to i^now the nature of these requirements. Current requirements for approval of engines are known as Civil Air Regulations, Part 13, Aircraft Engine Airworthiness.’^ In addition, the CAA has prepared Civil Aeronautics Manual 13, Aircraft Engine Airworthiness” which is ^ intended to interpret, explain and suggest methods of compliance with the regulations. ...” Both of these publica- tions should be available to the designer.

References

1. Wood: Airplane Design.”

2. Wood: “Technical Aerodynamics.’^

Problems

1. An airplane of aerodynamic cleanness halfway between class 1 and class 2 (Fig. 1-1), has a gross weight of 2,250 lb., a landing speed of 47 m.p.h. with flaps, and a maximum lift coefficient of 2.19. What brake horsepower is developed by the engine when the plane is flying at its maximum speed of 162 m.p.h.? (Assume the propeller efficiency at maximum speed is 83 per cent.)

2. For a wing area of 180 sq. ft., a wing loading of 15 lb. per sq. ft., a pro- peller efficiency of 81 per cent, and a maximum speed of 150 m.p.h., what equivalent flat-plate area of parasite resistance is implied in Eq. (1-3)? To what class of airplane does this correspond (Fig. 1-1)? If the wing load- ing were 10 lb. per sq, ft., what class of airplane would be implied?

3. a. What values oi f /S are implied by Eq. (1-3) at values of P/S of 0.3, 1.0, and 3.0 if the propeller efficiency is assumed to be 80 per cent?

h. What kinds (classes) of 5,000-lb, airplanes do the above (part a) P/S values represent if the wing loadings are 12 lb. per sq. ft.?

4. a. For values of f /S of 0.015, 0.025, 0.035, and 0.045, find the value of

K in the equation P = aS

b. Plot curves of

(%^Y-

e

Assume rj =0.8.

' ( ^ for the vahu^s of K found in part

logarithmic paper using P/S as the ordinate and E,„ax as the abscissa. 8u{)oriniposc‘ thc^ mean .liric^ in Fig. 1-2 f<jr coinjjarative piirposc^s.

6. Plot Fig. 1-3 on logarithmic, j^aper, and dc^terininci an cxprc^ssioii for varijition of sp(‘cific weight with size {i.e., b.hp.).

CHAPTEH 2

OUTLIISTE OF THE PROJECT

2-1. Selection of the Potential Market. — The logical fii\st step in designing an airplane engine is to determine the siise, i.e,^ the performance desired. This will, of course, depend upon the use to which the engine will be put and the type, size, and performance of the plane that the engine will powei*. For practically all engines, with the possible exception of d(%signs for special racing purj^oses, the ultimate object is to bxiild a unit that can be sold profitably and that will produce results in competition with other engines sufficient to attract furtlun* orders. The decision of first cost vs. operating cost,, rc^l lability, and operating life must be made in ordcjr to esta))lish a '^policy in selecting materials, dimensions, compression ratios, acces- sories, etc.

For instance, an engine designed for the low-cost light plains would incorporate good materials sufficient for reasonable! reliability, but the designer could not spe^'ify tiie v(n*y best known high-strength alloys because that would pusli the cost above competitive levels. Instead, lui would be o])ligc‘d to us<^ heavier sections of l<*ss expensive materials to provide tluj necessary strength, and that would increase the w<fight per liorsci- power. To keep the cost down, he wx^ulcl be oblig(Ml to omit special features such as superchargers and aiitomati(! mixturfi controls and, in extreme cases, x^essibly rc^diudion gc^aring or the dry-sum|3 crankcase type of lu]>rication. To enable tlie purchaser of the engine to use Jow-cost fuc^ls, the* ch^signen’ will have to keep the compression ratio down, and tliis will nuian a sacrifice in performance.

On the other hand, if an engine is to be dosigne^d for a high- performance military plane, first cost (within r(‘ason) Ix^coimvs secondary and every means at the disposal of th(^ dc^sigiux* should be used to attain maximum power with rcasona})k^ (H'onorny. For use in a large transport i)lane, first cost is important, Imt

14

OUTLINE OF THE PROJECT

15

not to the extent of a light-plane engine. Low weight per horse- power is essential, and fuel economy is vital. This will mean the use of stronger alloys, higher compression ratios, and greater supercharging. The resulting higher first cost will be justified by reduced operating and maintenance cost and by the ability to increase the specific pay load.

Obviously the potential market for the engine must be well defined before the design is begun.

2-2. Selection of Rated Power. — The market having been selected, the rated power may be decided upon. Here again cost vs. performance enters. For instance, any given airplane will operate with quite a range of engine sizes. The engine builder must decide whether he can make more money by building an engine that will appeal to the user who is willing to sacrifice high speed for lower operating cost, or vice versa. This decision is in no essential different from that which must be made by the manufacturers of any other product. Essentially, the decision becomes ^^will the company cater to a large market with small profit per unit or to a more limited market with greater profits per unit?'' At best, by the very nature of things, some factors must be left to chance.

2-3- Preliminary Specifications. — Preliminary specifications may now be drawn as indicated in Table 2-1. In general, for each item the decision of what value to use is largely a compro- mise between the best possible value and the one that will keep costs within allowable limits. Here the accumulated experience of the designer becomes very important.

The fundamental principles of the basic sciences are very useful in the design of complex machines, but derived formulas are either not available or are too complicated to be practical in many of the more intricate parts. Hence, empirical rules based on accumulated experience must be used. Many of these rules are merely the judgment of the designers based on methods that have been found to be satisfactory. To a con- siderable extent, they are the results of the trial-and-error method.

Unfortunately, progress is slow in the school of experience, and for the beginner, the way forward is anything but clear. Spe- cifically, if the inexperienced designer of airplane engines is to short-eut the long winding road, he must rely heavily upon

16

AIRCRAFT ENGINE HER ION

landmarks established by others. He must has(‘ his dec-isions regarding the major portion of the items ui)OM tlu^ findings and experiences of his predecevssors. In proceeding with the design, the student should assume the attitude that his ''company^' is going to spend a lot of money on his recommendations. If hci departs too widely from convention, he is shifting the project from an investment to a gamble.

This recommended adherence to convention shouhl not bci construed as a reactionary attitude toward new irndhcxls and progress. Rather, it is based on the belief that im|>rov(une!it in an existing art cannot very logically 1)0 made until cur- rent methods, limitations, and shortc^omings are tlioroughly understood.

2-4. Justification of Values in Example 1. — 1, 2. B<»lection of values for Table 2-1 probably can be best discusscul by means

TaBHC 2-1. GjbJNnRAU Bpiooific-\tioxs

Specification Item lOxaiiiph^ 1

1. Brake horsepower:

a. Maximum for take-off 125 at s<?a level

b. Cruising 04

c. Maximum except take-off 125

2- Revolutions per minute:

a. For take-off 2,000

b. For cruising 1,800

c. For maximum except take-off iip 2,000

3- Octane number of fuel used:

a. For take-off 73

6- Cruising and max irn urn except take-off.. 73

4. B.rn.e.p., 11). per stp in.:

a. Maximum for take-off 120

b. Cruising 100

c. Maximum except lakt^-off 120

5. Compression ratio 5.3

6. Type of cycle (two or four strf>ke) 4

7. Type of cooling*; Air

8. Arrangcuneiit of cylinders Ra<liiil

9. Nurriher of cylinders and tfuiativc sizcj i’’'iv(‘ -I j.^ by 5:?.v< in.

10. Ck)nnoctinj^ rotl — (!rank (A/ffJ ratio -1/1

11. Valve arranfrement ()verh(*a(l, incIiiuMi,

in head, rocker and pusli rods

12. Method C)f sup(‘rcdiarp;ing N<jac

13. Ignition sysUun Ilual magnetos

14. Reduction-g(^ar ratio. 1:1

W'lKa;

a nns,

OUTLINE OF THE PROJECT

17

of the example. In this particular case, the engine company’^ plans to build a unit for the medium-light plane class. Usual power loadings in this class (1,500 to 2,500 lb. gross weight) range from 10 to 20 lb. per hp. (Fig. 1-5) with a fair average at about 16 for a 2,000-lb. plane. Hence the engine will have to develop 2,000/16 = 125 b.hp. at full throttle and rated speed. This rating is based on sea-level performance since, for the purpose intended, most of the operation will be at relatively low altitudes.

Some engines are given a special horsepower rating for take-off above that which they can safely develop for extended periods. Under these conditions, take-off horsepower is for limited periods of a. few minutes only, as the engine would overheat if operated continuously at take-off horsepower. A special take-off high- octane fuel may be used when take-off power is developed. Under these special conditions, item Ic may be considered as the maximum safe horsepower for extended operation. For the example, however, the added cost of providing for extra take-off power, i.e., high supercharge and special fuel, is not considered justifiable, and item la is specified as equal to the maximum full- throttle power for continuous operation.

The specified speed of 2,000 r.p.m. is selected because (a) propeller efficiencies drop rapidly at speeds above this figure and (6) reduction gearing would add too much to the cost of the engine. From Fig. 1-6, the corresponding top speed of the plane may be assumed to approximate 135 m.p.h.

There is an increasing tendency in the aviation industry toward designing the engine to fit a specific plane. When potential sales warrant such a procedure, the power of the engine is determined by the particular requirements of the plane. In such cases, sufficient data will be available to permit the use of Eq. (1-2).

The cruising horsepower (Table A 1-1 3) should be about 75 per cent of the take-off horsepower, and the corresponding cruising speed will be about 90 per cent of takc-ofi speed, hence the selection of 94 cruising hp at 1,800 r.p.m.

3. To avoid the extra cost of premium fuels, an octane numbeu* of 73 is specified.

4. Brake mean efft^ctive ])ressures in the 75- to 150-h]). ((*ruis- ing) class range around 100 lb. i:)er sep in. (Fig. 1-8). For a

18

AIRCRAFT ENGINE DESIGN

73 octane number fuel, a higher value might be used (Fig. 1~10), but it might be difficult to attain without supercharging (see item 12, Table 2-1). Since b.m.e.p. may be expressed by the relation

p _ b.hp. X 33,000

^ LAN on

the b.m.e.p. for take-off conditions is

Pb (take-off) =

b.hp. (take-off) b.hp. (cruising)

r.p.m. (cruising r.p.m. (take-off)

X Pb (cruising)

or

Pb (take-off) == X X 100 = 120 lb. per sq. in.

Referring to Fig. 1-10, it is seen that this value is still within the range of 73 octane number fuel. Hence, a sj^ecial fuel for take-off will not be necessary.

5. Compression ratio is limited by the octane numbcn* of the fuesl, and for a knock rating of 73, a value of 5.3 for the CIZ should be satisfactory (Fig. 1-11).

6. Two-stroke-cycle engines for aircraft are still largely in the experimental stage; hence much greatcu' assuran(*e of su(?cc‘ss will be had by adhering to the more conventional four-stroke- cycle principle.

7. Direct air cooling eliminates the cost of radiators an<l troublesome piping. The al)sence of any water-cookMl engin(\s ii% the power class in which this (uigine fiilLs (liable AI-1) is good evidence that previous attemi)ts at w^ater or licjuid cooling have not been a]>le to meet the coini>etition of the air-(*ooled engines. Profiting by the experiences of others is a good way to avoid rod ink on the ledgers.

8. As regards arrangement of cylindcirs, doable A 1-1 indicat(‘s that radials predominate in the powc^r (dass iind(U' (a)iisid(‘ration. However, the inverted in-line eiiginci is also in coiisid(*raldo evidence, and the fiat-opposed or 180-(k^g. V-cnigiiui has much to recommend it for certain typess of installations siH*h as in tlui wings of bimotored ships. In the final dcicision, the company designer will probably ])o infhH‘iic(^<l by thci prosid(nd/s id(‘as on cylinder arrangement, but for the present purposes, it is of int(‘r(‘st to list some of the important items as follows :

OUTLINE OF THE PROJECT

19

Item	Air-cooled radial	Air-cooled in-line	Air-cooled opposed
Crankcase	Compact and rigid	Must be heavier for necessary rig- idity	Intermediate for same powered en- gine
Cylinders	! All equally ex- posed to cooling air 1	Careful cowling necessary to cool rear cylinders ad- equately	Some cowling to deflect air on rear cylinders except in the smallest sizes
Crankshaft. . . ,	: Short and rigid, heavily loaded crankpin. Coun- terweights neces- sary	Heavier for neces- sary stiffness. Usually no coun- terweights	Intermediate for same powered en- gine
Valve gear. . . .	Push rod and rocker arm limit speed of geared engine	Overhead cam- shaft may be used, less noisy, less maintenance, but tends to limit valve size	Push rods and rocker arms or two overhe a^d camshafts
Parasite drag. .	Considerable even with cowling, es- pecially in wing engines. Nose engines increase fuselage drag be- i cause of slip 1 stream	Less frontal area, but necessary air scoop for cooling adds to total drag I	More adaptable for cowling in wing, but cooling-air scoop adds to to- tal drag
Visibility in sin- gle-engine tractor-type plane	' Relatively ob- : structed i	Excellent for in- verted type	Better than radial

Many other items, varying in importance between the types, will come to mind, but the foregoing comparison is sufficient to indicate that none of the three arrangements of cylinders is outstandingly superior. For example 1, a radial has been vselected.

9. Firing order in a single-bank radial very nearly dictates an odd number of cylinders. The greater the number of cylinders, the greater the overlap of power impulses, hence the smoother the torque curve ; but fewer cylinders means a smaller number of parts and usually lower cost. Increasing the number of cylinders beyond seven in a single-bank radial increases the over-all

20

AIRCRAFT ENGINE DESIGN

diameter and parasite drag. Fewer and larger cylinders arc more difficult to cool, since for a given cooling-fin design, the volume increases as the cube of the dimensions, whereas the surface area of the cylinder increases only as the scjuare. How- ever, this will probably not be a limiting factor so soon as torque- curve variation in the size of engine under consideration. For the example, 5 cylinders have been selected as the compromise of the logical possibilities, 3, 5, or 7.

From the relation.

b.hp.

PhLA N,.n 33,000

the displacement per cylinder is

%

^ ^ 125 X 33,000 X 12

U = iZDA = 27idd

120 X X 5

= 82.5 cu. in. for the exam phi

Ratios of stroke to bore vary rather widely (Talkie Al-1), and they are quite often dictated by the desire to incn^asci tlui numl>er of interchangeable parts in models of similar design l>ut difTercmt power output. A low stroke-bore ratio rciduces tlui ovc^r-all diameter, hence the parasite resistan(*e, but it incrcniscvs the distance the heat has to flow to escape from the* c(‘nt(a’ of tluj piston. This generally means a heavier piston and a grciattir weight of reciprocating parts. A strokc‘-l)orfi ratio of 1 .2 is tentatively selected as reprcisenting good })nicti(*(i. ddiis will permit the later development of a large*!' (‘ngiru^ in whir'h many of the parts in the ])r(^sent model c*an he* us(*d. Ida* larg{*r unit will doubtless have larger diameter cyliudei's, but by using a fairly high stroke-bore ratio in the present niodc*!, a r(*asonabI{^ stroke-bore ratio can still be had in thc^ larg(*r mod(*l with flu* same crank-arm radius. The cylin<ler dimensions are found from

D

d- X

h27r

"”4" ■ '

d = S =

/82.5 X

V 1.2 X TT J

4.45 in., bore

1.2 X 4.45 = 5.34 in., strokti

As cylinder dimensions are usually sptH'.ificHl to tin* n(*arcst (*ight,h of an inch, the bore and stroke may be tak(*n as 412 by

OUTLINE OF THE PROJECT

21

Referring to Table A1--1, it is seen that these values compare favorably with bore and stroke values for similar sizes of engines.

10. Ratios of center- to-cen ter length of connecting rods to crank-arm radii (L/R ratios) vary from about 3.3 or less to as high as 4.5. The longer the connecting rod in proportion to the crank radius, the less the angularity between the connecting-rod axis and the cylinder center line, hence the less the side pressure, i.e., friction against the cylinder wall. But large values of L/R mean greater over-all transverse dimensions of the engine, hence greater parasite drag. A compromise value of L/R ^ 4: has been selected for Example 1.

11. For a radial engine, rocker arms and push rods are about the only feasible means of transmitting the cam-follower motion to the valves. Inclined valves in the head are specified to permit maximum valve port openings and as direct a flow as possible for the gases. To attain the b.m.e.p. specified, a high volumetric efficiency will be necessary, but two intake valves per cylinder would be objectionable because of complexity and cost.

12. Gear-driven centrifugal blowers are conventional for supercharging radial engines, but supercharging is omitted in this example to keep down the cost. To attain equal mixture distribution to the various cylinders in a radial engine, a centrif- ugal-type blower directly connected to the rear end of the crank- shaft is desirable. For later more powerful models, this blower may be converted to a supercharger by gearing it for a speed higher than the crankshaft r.p.m.

13. Two magnetos are specified for safety and reliability and to conform with government requirements. Dual ignition will also increase the power output slightly.

14. A reduction gear between the propeller and crankshaft will not be necessary (1:1 indicates direct drive) as no appreci- able loss in propeller efficiency will be had at the crankshaft speed specified.

2-6. Preparation of Design Data and Drawings. — Design data to be of value must not only be accurate but also be in logical form and neatly prepared. A jumbled aiTay of illegible calcula- tions and incomplete penciled drawings is of little value no matter how accurate. Your employer will judge the quality of your work by its neat appearance in the same general way that you are influenced toward a new car by the appeal of streamlined

22

AIRCRAFT ENGINE DESIGN

contours and glLstening finish. In (uther case, the quality of the product may or may not be high, but to soli it, it must look right. The inner quality will determine the repeat orders.

DESIGN DATA ‘ FOR A

200 HP. 6CYL.

IN LINE AIR COOLED AIRPLANE ENGINE

Designer TITLE PAGE

Fig. 2“1. — Suggested arrangement

h

Table o*f Contents Section

L GenercJil SDeclfs'cations

Coi) Table---' p. 2

(b) Reasons for

selections «p. 3

(c>

2. Gas pressure > tions

(a> Assumed data- p. 1 ^ (b) Card data p.3

etc.

TABLE OF CONTENTS PAGE title a.n<i tai>le-of-eontenlH pagew.

Mot rg in fines S Ize	Width	“nc ( Height	>- Blueprint
letter	i nches	inches	to be
A	8'/2	11	Folded
B	15 72	11
B’	22 72	11
C	15 72	22
D	22 72	• 22
D*	31	22
E	Any	36	Rolled
			TITLE BLOCK

Width d

Fig. 2-2.— “American vSociety of Mechanical IhigiiKMTH recoin ni<*ti<lcd drMwtng- papor Bvzi'i arul arrangfonent.

It is recommended that design notes ancl completed drawings be kept in a standard l)y 11 -in. three-ring notctiook. ddu*

first page of the notebool^ should be a tith^ sh<‘(‘t, the sc^cond a table of contents (Fig. 2-1), and each section cd* the work should

OUTLINE OF THE PROJECT

23

be identifiable by a small tab attached to the first sheet of the section. This tab should have a title or section number con- forming to the title and section number in the table of contents. Subtitles should follow each section title, and their location in the section should be by section page number. Each drawing should be identifiable by a suitable designating letter or number

Fia. 2-4. — Suggested method of folding drawings for insertion in design note- book. An alternate method of folding so that the title block shows when folded is standard practice with many companies.

and title both on the drawing and in the table of contents. In all cases, tabulated data, calculations, and graphical construc- tions should be titled, accompanied by adequate explanations, and, as applies, by sample calculations.

Whenever ]:K)ssi])le, drawings should be on standard sizes of l)aper and in all cases properly titled (Fig. 2-3). For insertion in the notebook, drawings should be blueprinted and folded as

24

AIRCRAFT ENGINE DESIGN

indicated in Fig. 2-4. Drawings should be complete. A drawing returned by the production department for lack of adequate dimensions or other data is a direct reflection on the engineering department and the designer. Repeated offenses usually result in the individuahs failure to receive promotion.’’

Suggested Design Procedure

1. Select the class of plane for which an engine is to be designed. Tabu- late the approximate weight, performance, parasite drag (if available), and other pertinent data.

It is recommended that, for undergraduate students, the selection be con- fined to the medium- or light-plane class as large planes require engines of more cylinders, greater complexity, etc., and this greatly increases the detail work necessary in designing the engine without adding proportionately to the fundamental knowledge gained. Also in most undergraduate courses, the time available for the design work is insufficient for those added details.

2. Prepare a table of general specifications similar to Table 2-1.

Adhere closely to current practice in deciding upon the type of engine to

be designed. Confine the selection to (a) a single-bank radial of preferably not more than seven cylinders, (6) an in-line type of not more than six cylinders, or (c) a V type of not more than eight cylinders.

In limiting the selections to the preceding types, it is not the purpose to suppress originality or potential inventive genius, but rather to require the selection of a problem that the beginner can have a fair chance of completing. As an instance of the pitfalls of allowing unlimited selections, a case is recalled in which a student was permitted, in his first undergraduate course in engine design, to select any type of engine he desired, and, without know- ing of the difficulties ahead, he selected a three-lobe-cam engine. Almost immediately, innumerable questions arose concerning logical values for this detail and proper sizes for that part. Without precedent to guide him, he soon became hopelessly lost and little was accomplished. The inexperienced designer will have problems enough with a conventional type of engine. Later, when he has acquired experience, he can depart from the conven- tional if he chooses.

3. Justify each specification item by reference to current practice wherever possible and by reference to the allowable cost decided upon.

Hasty selection of the general specifications is false economy of time, as specifying impossible values may mean the repeating of a great deal of tedious calculation farther on.

4. Make a line layout of (a) a transverse section and (&) a longitudinal section through the engine at the cylinder center lines. Show the location and desired sizes of the principal parts. Indicate desired dimensions of important parts, positions of center linOvS, etc‘.., but do not try to nuik(; a complete detailed drawing* at this stage of the design. (ffieck clos(wt posi-

* In preparing this preliminary layout, the dcsigne'r may be likened to a topographer preparing a map of a little known region. The first step is to

OUTLINE OF THE PROJECT

25

tion of connecting-rod center line to lower end of cylinder. (Cylinder must extend down approximately as far as the lowest position of the bottom of the piston skirt.) Check all features of desired arrangement to be reasonably certain of adequate mechanical clearance of parts. Inspect available blue- prints, drawings, engine parts, etc., of similar designs for assistance in selecting logical sizes for the various parts.

This preliminary layout drawing should be developed with the idea in mind that it is the general arrangement desired. At best, some detail changes will be necessary before the final design is completed, but if too radical an arrangement is attempted, major changes may have to be made. This will greatly increase the work necessary later. Hence, it is very desirable to give careful study to the proposed arrangement. The layout need not be blueprinted at this stage, but it should be to a large enough scale to permit close study and on standard-size paper properly titled (size D or Ej Fig. 2-2, is recommended).

5. When items 1 to 4 have been completed and put in proper form (Par. 2-5), submit for checking and approval. Keep a record of the man-hours required on each item.

bound the region as accurately as possible and to insert the position of important features such as rivers, lakes, and mountain chains (f.c., major dimensions, center lines, etc.). Obviously, the details will have to be added gradually as the information becomes available, but it should be borne in mind that unnecessary carelessness or poor judgment in the preliminary lay- out will result either in doubtful .accuracy of the finished product or a great deal of time-consuming revision that might have been partly avoided.

The successful designer also has something in common with the success- ful artist who, in preparing the layout for a painting, is able to visualize in his mind’s eye the appearance of the finished product. It takes years of practice to perfect this ability, but the greatest attainments always have been made by men (engineers as well as artists) who put everything they had into every job at the beginning as well as at the height of their careers.

CHAPTER 3

GAS-PRESSURE FORCES

3-1. Forces in the Cylinder. — Forces on the piston represent a combination of gas pressure and inertia forces. These forces are usually determined separately at increment angular positions of the crankshaft, plotted as unit or total force against crank angle, and then, by adding ordinates, a curve of the net force parallel to the cylinder axis is obtained. As the dimensions of the various parts of the engine are largely determined by the stresses resulting from the maximum forces, it is obviously necessary to investigate the case causing these extreme condi- tions, i.e., full throttle and highest speed.

3-2. Construction of the Indicator Card. — For the gas-pressure forces, it is necessary to construct an indicator card representing full-throttle conditions. Very elaborate procedures have been developed for analyzing the phenomena in engine cylinders with the idea in mind of more closely approaching actual condi- tions. However, even with the most complex of these methods, some discrepancies exist and must be accounted for by a ^^card factor.^^ It is believed that simpler methods of determining values for the indicator card, although admittedly less rational, are more practical and may be applied just as effectively by using a somewhat larger card factor. In short, instead of endeavoring to account for variable specific heats, dissociation, chemical equilibrium, heat flow back and forth between the gases and the cylinder, and then applying a small card factor, use values for the exponents of compression and expansion consistent with actual measured results from engines that have been indicated, calculate the pressures and volumes by the older and much simpler thermodynamic relations of the modified “air-standard’' cycle, and then apply a slightly larger card factor. The values for plotting may be found avS follows:

Determine the i.m.e.p. from

b.m.e.p.

GAS-PRESSURE FORCES

27

where i.m.e.p. = indicated mean effective pressure, lb. per sq. in. b.m.e.p. = brake mean effective pressure at maximum horsepower (= take-off horsepower), lb. per sq. in.

= mechanical efficiency at take-off horsepower. The absolute pressure at the end of expansion may be found from^’^

X (3-2)

where Pd = pressure at end of expansion, lb. per sq. in. abs.

n = exponent of the compression and expansion curves. R = compression ratio.

Fd = card factor representing the ratio of actual to theoretical card areas.

Pa = pressure at the beginning of compression, lb. per sq. in. abs.

^ Pd (3-3)

= Pa X (3-4)

where Pc = pressure at the beginning of expansion, lb. per sq. in. abs.

Pb = pressure at the end of compression, lb. per sq. in. abs.

Cylinder volumes corresponding to the foregoing pressures may be found by combining the relations

(3-5)

^ = R (3-6)

where Va = cylinder volume at the beginning of compression, cu. in.

Also

= clearance volume, cu. in.

D == piston displacement for one cylinder, cu. in.

Va == Vd and Vb = Vc

where Vd = cylinder volume at the end of expansion, cu. in.

Vc = cylinder volume at the beginning of e.xpansion, cu. in.

28

AIRCRAFT ENGINE DESIGN

Intermediate pressures along the compression line may be found from

P 1,2,3, etc. —

PbV

(3-7)

V 1,2,3, etc. being found by measuring along the abscissa or volume line to scale. Similarly, intermediate pressures along the expan- sion line may be found.

An alternate method of finding intermediate pressures is to plot points PaVa, PbVb, PcTc, and PdVd on logarithmic cross- sectional paper and connect successive points by straight lines. Pressures corresponding to any intermediate volumes may be read directly from the ordinate scale.

Fig. 3-1. — Graphical construction of a PV^ — constant line.

A graphical method of plotting compression and expansion lines is illustrated in Fig. 3-1. For instance, to construct a compression line, lay off coordinates OV and OP and locate point Select o: and such that (1 + tan a)” = 1-1- tan /3.

Draw OH, making the angle cki with OF, and OL, making the angle ^ with OP. Erect a line perpendicular to OF at F^. Construct angle OF^a equal to 45 deg. Erect a line through a perpendicular to OF. Construct P^fe perpendicular to OP. Construct angle hPiO equal to 45 deg. Draw a line through Pi parallel to OF. The intersection of the perpendicular line through a and the horizontal line through Pi locates point PiFi- Construct angle OF ic equal to 45 deg. Erect a line through c perpendicular to OF. Extend the horizontal line through Pi to d. Construct

GAS-PRESSURB FORCES

29

angle dP2.0 equal to 45 deg. Draw a line through parallel to OV. The intersection of the perpendicular line through c and the horizontal line through P^ locates point P2I 2. Proceed in the same way to locate points P3V3, P^V^, etc., and connect the points thus located with a smooth curve. The equation of the curve is PV"^ — a constant.

3-3- Example. — Construct an indicator card for the engine selected in Example 1, Table 2-1.

Procedure. — The b.m.e.p. for take-off horsepower represents maximum conditions. Mechanical efficiency will be that for full load and speed. For

Fig. 3-2. — Logarithmic plot for determining indicator-card data.

these conditions, the mechanical efficiency may be taken as equal to 85 per cent (Fig- A 1-2). qdien

120 ,

i.in.e.p. ^ n^*

The average exponent of compression and expansion may be taken as n = 1.3, the card factor Fr> = 0,9, and the pressure at the beginning of compression. Pa. = 90 per cent of atmospheric pressure (for a nonsuper- charged engine) Then, for the example,

Pd X 4rA + 0-9 X 14.7 = 72.7 lb. per sq. in. abs.

Let Pn — 73 Ib. per sq. in. abs.

= 73 X 5.3'*3 = 635 Ih. per sq. in. abs.

Pb — 13.2 X 5.3^ 3 = 115 lb. per sq. in. abs.

lISc Lib

B'lore

30

AIRCRAFT ENGINE DESIGN

The displacement per cylinder is

D = 4.52 X 0.785 X 5.375 = 85.5 cu. in.

Hence

Vb ■ - = 19.9 cu. in. = Va

0.0 — 1

Va = 85.5 + 19.9 = 105.4 cu. in. = Vd

Plotting the four points thus determined on logarithmic paper and connect- ing gives Fig. 3-2. Table 3-1 is obtained by selecting intermediate volumes and reading the corresponding pressures. The completed indicator card

Table 3-1. — Indicator-card Data from Fig. 3-2 ^

Volumes, cu. in.	Compression-line pressures, lb. per sq. in. abs.	Expansion-line pressures, lb. per sq. in. abs.
105.4	13.2	73
100	14	76
95	14.95	82
90	16	87.5
85 *	17.1	94
80	18.4	100
75	20	no
70 •	22	121
65	24.5	132
60	27	148
55	30	165
50	34.5	187
45	39	215
40	1 46	250
35	55	295
30	66	365
25	85	460
22	100	550
19.9	115	635

(Fig. 3-3) is constructed from the data in Table 3-1. Tlie area of this cai-d to the scale drawn is 6.23 sq. in., the length is 4.1 in., and the spring scale is 100 lb. per in. of ordinate, hence

i.m.e.p. (theoretical) = — — =152 lb. per sq. m.

The i.m.e.p. for the assumed actual conditions was 141 lb. per sq. in. Therefore, the card factor should be

GAS-PEB^SURE FORCES

31

Fb ■ 0.925

This value checks the originally assumed value of 0.9 reasonably well.

In superimposing the actual card by rounding the corners of the theo- retical card, Pmax may be taken as about 75 per cent of Actuall^^,

maximum cylinder pressures vary over a considerable range and depend upon numerous factors, including ignition timing, air-fuel ratio, etc. When a low-octane fuel is used^ the maximum pressures are much higher owing to detonation of a part of the charge. In extreme cases of knocking, these pressures can cause serious damage in an engine.

Tig. 3-3. — Indicator card for Kxamplc 1 (Table 3-1).

The pressure near the end of the expansion line will drop owing to opening the exhaust valve before bottom dead center (point K.V.O.* Fig. 3-3). Usually the pressure will not have expanded to exhaust-stroke pressure until the piston has moved an appreciable distance on the exhaust stroke. This justifies rounding the “toe” of the card.

If the spark occurs too early, the pressure will rise above the compression line before top dead center is reac^hed. This is undesirable, but a greater loss will occur due to Pmax being farther from top chaid (‘enter if tlie spark is retarded too much. Hence, some rounding of tli(^ card near the end of the compression strc^ke should he made.

The area of the superimposed “actual” card is 5.73 sq. in. for the exaniph', and

32

AIRCRAFT ENGINE DESIGN

F. II .0.92

This again checks the originally assumed value reasonably well.

Gas -pressure-Crank -angle Diagrams.^ — -To utilize the gas-pressure data from the indicator card, it is necessary to convert to a pressure-crank-angle basis. This may be done most conveniently by a graphical construction as illustrated in Fig. 3-4. With reference to this figure, the constructed indicator card is 'tacked to a drawing board and the atmospheric line or a line

Fig. 3-4. — Graphical method of converting the pressure-volume card to a pressure-crank-angle basis.

parallel to it is extended as shown. The length of the card parallel to the atmospheric line is directly proportional to the stroke of the piston. Hence, by using this length as a base, all other dimensions may be scaled down accordingly. The atmos- pheric line may be considered as the center line of the cylinder, and the extension will pass through the center of the crankshaft.* The location of this center may be found by scaling down the connecting-rod length to the scale of the card using the relation

This is true except in offset-cylinder engines, but the construction may be modified readily for such cases.

GAS-PRESSURE FORCES

where S = length of indicator card, in.

S' = piston stroke, in.

Zj' = center-to-center length of the engine connecting rod, in.

L = center-to-center length of the connecting rod to the scale of the card, in.

Point O, Fig. 3-4, is distant from point PeVe by the amount L -p R where R = S/2. B3^ using O as a center, construct a

j< — Expomsion — >j-<s — Exhausf In'iake >-^-Compression

E 3200 9 2400

0 40 80 120 160 200 240 280 320 360 400 440 480 520 560 600 640 680 120 Crank angle, deg.

Fig. 3-5. — Gas-pressure— crank-angle diagram for Example 1 (Table 2-1).

circle of radius R and divide the upper half into 10-deg. incre- ments with the aid of a protractor. Set a compass to length L, and using the 10-deg. increment points.?/, ?/i, 2/2; etc., strike arcs intersecting the atmospheric line on the card at x, Xi, Xo, etc. The X points represent piston positions corresponding to crankpin positions y. Erect ordinates at the x points, and read the pressures at the intercepts with the card lines directly from the ordinate scale. Convert the pressures to total force by multiply- ing each by the area of the piston, and plot against crank angle as an uniformly spaced abscissa. As atmospheric pressure is at all times acting on the under side of the piston, the effective gas pressure thrust on the piston is represented ])y the gage pressure. Hence, it is necessary to convert the ordinate-scale readings to

34

AIRCRAFT ENGINE DESIGN

gage readings. This is most easily done by shifting the ordinate scale.

3-5. Example. — Construct a gas-force-crank-angle diagram for the engine selected in Example 1, Table 2-1.

Procedu7'e. — Before locating crank-angle positions on the card (Fig. 3-3), it is necessary to determine the (scale) center-to-center length of the connect- ing rod from the L/R ratio. By using the selected value of L/R — 4 (Table 2-1), scaling down as explained in Par. 3-4, and making the graphical construction, the crank-angle positions were located as shown on Fig. 3-3. Ordinates erected to the compression and expansion lines from these points gave the data from Table 3-2, and these data were used to construct Fig. 3-5.

Table 3-2. — Gas-pbessxjre, Cbakk-angle Forces from Fig. 3-3 Area of Piston = 15;9 sq. in.

Crank angle, deg.	Pres- sure from card, lb. per sq. in. abs.	Pres- sure, lb. per sq. in. gage	Total net force on piston, lb.	Crank angle, deg.	Pres- sure from card, lb. per sq. in. abs.	Pres- sure, lb. per sq. in. gage	Total net force on piston, lb.
/ ^	150	135	2,145	/ 360	16	1.3	20.65
/ 10	380	365	5,800	S \370	14.5	-0.2	- 3.18
I 20	430	415	6,600	;380	13	-1.7	-27
1 30	420	405	6,440	^ i	i
1 40	340	325	5,160	(530	13	-1.7	-27
1 50	272	257	4,090	>540	13.2	-1.5	-23.8
1 60	218	203	3,225	/ 550	13.5	— 1.2	-19.1
g ] 70	180	165	2,620	I 560	13.8	-0.9	-14\3
§ ) 80	152	137	2,180	1 570	14	-0.7	-11.2
a \ 90	130	115	1,830	1 580	14.5	-0.2	- 3.18
jlOO	112	97	1,540	1 590	15	0.3	4.76
jlio	100	85	1,350	1600	17.5	3	47.6
|120	91	76 '	1,220	g l^io	20	5	79.5
I 130	85	70	1,120	‘i ;620	22	7	112
f 140	78	63	1,000	S / 630	24	9	143
1 150	68	53	842	S j 640	29	14	222
\ 160	59	44	700 .	O 1650	34	19	302
\ 170	50	35	556	1660	39	24	382
)l80	35	20	318	1670	48	33	525
^ (l90	28	13	206.5	I 680	61	46	781 •
g )200	20	5	79.5	1 690	80	65	1 ,032
^210	18	3	47.7	1 700	105	90	1 ,430
^ /220	16	1.3	20.65	\ 710	135	120	1 ,920
\ i	1	i		\720	150	135	2,145

GAS-PRESSURE FORCES

References

1. Univ. III., Eng. Expt. Sta., Bull. 160.

2. Hersey, Eberhardt, and Hottel: Thermod^mamic Properties of the Work- ing Fluid in Internal Combustion Engines, S.A.E. Jour., Vol. 39, No. 4, October, 1936.

3. A.S.I.C. 421.

4. Angle: Engine Dynamics and Crankshaft Design/'

Suggested Design Procedure

1. For the engine selected for your design, construct a full-throttle—fuU- speed theoretical indicator card.

If the design is to be supercharged, the effects of the altered inlet pressure must be considered in following the preceding examples.

2. Round the corners of the theoretical card to form the actual card, and determine the card factor.

3- From the actual card thus obtained, determine the indicated horse- power of the engine. Apply the assumed mechanical efficiency, and check the brake horsepower obtained with the originally assumed value of brake horsepower. If a reasonably close agreement is not had, recheck the work for errors.

4. Using data obtained from the actual card, construct a total 7iet gas- force— crank-angle (uniform angular spacing) diagram.

5. When items 1 to 4 have been completed and put in proper form, submit for checking and approval. Keep a record of the man-hours required for each item.

Problems

1. Using the basic relations of thermodynamics as applied to the modified air standard Otto cycle, prove that the pressure at the end of the expansion stroke will be as in Eq. (3-2).

2. Referring to Fig. 3-1, prove that when (1 -f- tan a)” — (1 tan jS) the resulting curve has the equation PV^ — a constant.

CHAPTER 4

ANALYSIS OF THE CRANK CHAIN

4-1. Forces Due to the Reciprocating Parts, — In converting the reciprocating motion of the piston into the rotating motion of the crankshaft; the inertia forces of the reciprocating parts play an important part in determining the net turning effort. These parts must be started from rest, accelerated to high veloc- ity; slowed to rest; accelerated again; and stopped a second time during each revolution. At the speed at which airplane-engine crankshafts turn, this process causes quite high inertia forces. Analysis of these forces will be first considered for a single- cylinder engine.

4-2. Piston Velocity and Acceleration.*

In Fig. 4-1, P represents the piston-pin center, C is the crank- pin center, M is the center of crankshaft, L is the center-to-center

length of the connecting rod in inches, and R is the crank radius in inches (= 1/2 the stroke). For any given displacement {S) in inches from head-end dead center:

S = L + R — L cos 4> — R cos 6 CD = L siiL <j> = R sin B R . '

sm (j) = Y" sin 9

cos <j> =

sin2 <3i = ^ sin^ $ ~ - sin^ 6

' A more complete method of analysis is to be found in reference 3.

36

ANALYSIS OF THE CRANK CHAIN

37

Therefore

S = L + R — (1/2 — sin^ R cos d

The velocity corre|pondmg to ;S is

. d$

(4-1)

F = — = - (1/2 -

/It O

y = i2sin.^ +

T — R sin d I 1 “h

]

I R- sin2 e'p- X 2R^ sin 9 cos ^ ^ + R- sin 6 cos 9 1 d9

(1/2 — i^2 gij^2

jK cos ^

{L^- ~R^- sin2 ^

*2

In any practical engine, for a given condition of operation, the angular velocity of the crankshaft is very closel^^ uniform. Therefore, dd/dt = ^ttN where N is in revolutions per minute. Substitution of 2TrN in the preceding expression gives V in inches per minute. Dividing by 12 X 60 gives velocity in feet per second.

2TrNR sin ^ ^ , R cos 6

r x,p.s. - 12 X 60 (1/2 -

= 0.00873 iViC sin 0 I 1 + (4-2)

‘ (Z/2 — R- sm2

The acceleration in feet per sec. 2 corresponding to Ff.p.a. is

dV

^ = 0.00873iVi? -^sin

dt

-Isii

Z/2 — R- siii“ 9

L-

sin“

dd

2R- sin 9 cos 6

dt

A = 0.00873iV2^:

do

dt

cos 6 1 ^

\Ld — R~ sin‘- dt j

(Z/2 __ R2 sin^

38

AIRCRAFT ENGINE DESIGN

but cos^ d — sin^ 6 = cos 20,

. ^ ^ 2 (sin 0 cos ^)2(sin 0 cos S) sin^ 20

sm2 6 cos^ 0 = ^ = -g —

do

dt

= 2TrN radians per min.

radians per sec.

Therefore,

A = 0.060914iV2i2 [ cos

cos 20

(Z.2 ^ w cos2 OY'^ sin- 26 4:(L'^ — sin^

J

ft- per sec.=^ (4-3)

The preceding formulas for velocity and acceleration [Eqs. (4-2) and (4-3)] would be cumbersome to use, and the following substi- tutions can be made without appreciable error:

Let

L = (L^ - sin2 6)^

Then,

== 0.00873A7'i2 sin 9(1 + Z cos 9)

= 0.00873iVi2 (sin 9 + 2 2_sin|^s 0

but 2 sin 6 cos 0 = sin 26.

Therefore,

= 0.00873iV'E(sin 6 + sm 20) (4-4)

The term (sin 0 + 3-^2^ sin 26') is called the piston-velocit]/ factor. In determining the piston velocity at various crank positions, the calculations may be simplified considerably by taking the value of the piston-velocity factor from Table 4-1. For the acceleration,

A = 0. 0009 14iV^i7 (cos 6 Z cos 26 + ]y'^Z^ sin^ 26)

But the last term sin'^'2d is small and can be neglected with-

out appreciable error.

Therefore,

A = 0.00091 4iV'^i? (cos 6 A- Z cos 20) ft. per sec.^ (4-5)

The term (cos 0 Z cos 26) is called the piston-acceleration factor. Table 4-2 is a convenient aid in determining the piston acceleration at various crank angles.

ANALYSIS OF THE CRANK CHAIN

39

Table 4-1. — TANaENTiA'i^- force and Piston-velocity Factors Values for (sin 6 -(- J-iZ sin 29)

0	1/^	0
3.50	3.75	4.00	4.25	4.5
0	0.000	0.000	0.000	0.000	0-000	360
	0.112	0.110	0.109	O.IOS	0. 107	355
10	0.223	0.219	0.216	0.214	0.212 •	350
15	0.330	0.326	0.322	0.318	0-314	345
20	0.434	0.428	0.422	0.417	0.413	340
25 1	0.532	0.525	0.518	0.513	0.508	335
30	0.624	0.616	0.608	0.602	0.596	330
35	0.708	0.699	0 . 691	0.684	0.678	325
40	0.784	0.774	[ 0.766	0.759	0-752	320
45	0-850	0.840	0.832	0.825	0.818	315
50 !	0.907	0.897	0.889	0.882	0.875	310
55	0.954	0.945	0.937	0.930	0 . 924	305
60	0-990	0.982	0.974	0.968	0 . 962	300
65	1.016	1.008	1.002	0.997	1 0.992	! 295
70	1.032	1.026	1.020	1.015	1.011	290
75	1.037	1 .032	1.028	1.025	1.022	285
80	1.034	1 .031	1.028	1.025	1.023	280
85	1 . 021	1 .019	1.018	1.017	1.016	275
90	1.000	1.000	1.000	1.000	1 . 000	270
95	0.971	0.973	0.975	0.976	0.977	265
100	0.936	0.939	0.942	0.945	0 . 947	260
105	0.894	0.899	0.903	0.907	0.910	1 255
110	0.848	0.854	0.859	0.864	0 . 868	250
115	0.797	0.804	0.811	i 0.816	0.821	245
120	0.742	0 . 750	0.758	0.764	0.770	240
125	0.685	0 . 694	0.702	1 0 . 709	0.715	235
130	0.625	0 - 635	0.643	0.650	0.657	230
135	0.564	0.5.4	0.582	0.589	0.596	225
140	0.502	0.512	0.520	0.527	0.533	220
145	0.439	0.448	0.456	0.463	0.469	215
150	0.376	0.384	0.392	0.398	0.404	210
155	0.313	0.321	0.327	0 . 333	0.338	205
160	0.250	0.256	0 . 262	0 . 267	0.271	200
165	0.187	0. 192	0.196 1	0 . 200	0.203	195
170	0.125	0.128	0.131	0.134 1	0.136	190
175	0.062	0.064	0.066	0 . 067	0.068	185
180	0.000	0.000	0.000	0 . 000	0.000	180

40

AIRCRAFT ENGINE DESIGN

Table 4-2. — Piston- acceleration and Inertia Factors Values for (cos & -A Z cos 2,9)

6			l/Z
3.5	3.75	4.0	4.25	4.5
0	1.286	1.267	1.250	1 .235	1.222	360
5	1 . 277	1.259	1.242	1 .228	1.215	355
10	1 . 253	1.235	1 . 220	1 .206	1. 194	350
15	1,.213	1.197	1.182	1.170	1.159	345
20	1.159	1.144	1.131	1.120	1.110	340
25	1.090	1.078	1.067	1.058	1.049	335
30	1.009	0.999	0.991	0.984	0.977	330
35	0.917	0.911	0.905	0.900	0.895	325
40	0.816	0.813	0.810	0.807	0.805	320
45	0.707	0.707	0.707	0.707	0.707	315
50	0.593	0.596	0.599	0.602	0 . 604 ,	310
55	0.476 !	0.482	0.488	0.493	0.498	305
60	0.357	0.367	^ 0.375	0.382	0.389	300
65	0.239	0.251	0.262	0.271	0 . 280	295
70	0.123	0.138	0.151	0.162	0.172	290
75	0.011	0 . 028	0.042	0.055	0.066	285
.80	-0.095	-0.077	-0-061	— 0.048	- 0 . 035	280
85	-0.194	-0.175	-0.159	— 0.145	-0.132	275
90	— 0.286	— 0.267	-0.250	—.0 . 235	-0.222	270
95	-0.368	-0.350	-0.333	-0.319	-0.306	265
100	-0.442	-0.424	-0.409	-0.395	-0.383	260
105	-0.506	-0.490	-0.475	- 0 . 463	-0.451	255
110	-0.561	-0.547	-0.534	-0.522	-0.512	250
115	- 0 . 606	-0.594	-0.583	- 0 . 574	-0.566	245
120	-0.643	-0.633	-0.625	-0.618	-0.611	240
125	-0.671	-0.665	-0.659	- 0 . 654	-0.650	235
130	-0.692	-0.689	-0.686	-0.683	^0.681	230
135	-0.707	- 0 . 707	-0.707	- 0 . 707	-0.707	|225
140	-0.716	-0.720	-0.723	-0.725	-0.727	220
145	-0.722	-0.728	-0.734	-0.739	-0.743	215
150	-0.723	-0.733	— 0.741	-0.748	-0.755	210
155	-0.723	-0.735	— 0.746	— 0.755	- 0 . 763	205
160	-0.721	-0.735	— 0.748	-0.760	-0.769	200
165	-0.718	-0.735	-0.749	-0.762	-0.773	195
170	-0.717	— 0.734	-0.750	-0.764	-0.776	190
175	-0.715	-0.734	-0.750	-0.764	- 0 . 777	185
180	-0.714	-0.733	- 0 . 750	-0.765	-0.778	180

AN'AI.YSIS OF THE CRANK CHAIN

41

Table 4-3. — Piston-travel Factors Values for (1 — cos d -f- sin- 6)

	3.5	3	.75	1 4.0	4	.25	j 4.5
0	0.000	0.	.000 !	0	.000	0	.000	0	.000	360
5	0.005	0.	.005	0	.005	0	.005	0	.005	355
10	0.020	o;	.019	0	.019	0	.019	0	.018	350
15	0.044	0,	.043	0	.043	0	.042 ;	0	.042	345
20	0.077	0,	.076	0	.075	0	.074	0	.073	340
25	0.119	0,	.118	0	.116	0	. 115	0	.114	335
30	0.170	0.	.167	0.	.165	0.	.163	0	.162	330
35	0.228	0,	.225	0.	.222	0.	.220	0	.217	325
40	0.293	0.	.289	0.	.286 1	0.	283	0.	.280	320
45	0.364	0.	.360	0	.355	0.	.352	1 0	.348	315
50	0.441	0.	.435	0.	.430	0.	,426	1 0,	.422	310
55	0.522	0,	.516	0,	.510	0.	505	0.	.500	305
60	0.607	0.	.600	0,	.594	0.	,588	0,	.583	300
65	0.695	0,	.687	0,	.680	0.	674	0.	.669	295
70	0.784	0.	.776	0.	.768	0.	762	0.	756	290
75	0.874	0.	.866	0.	.858	0.	851	0.	845	285
SO	0.965	0.	.956	0.	.948	0.	941	0.	934	280
85	1.055	1.	,045	I 1.	.037	1 .	030	1.	023	275
90	1.143	1.	133	i	.125	1 .	,118	1.	111	270
95	1.229	1.	220	j 1.	.211	1.	204	1,	197	265
100	1.312	1.	303	; 1. I	295	1 ,	288	1.	282	260
105	1.392	1-	383	1 i 1-	375	1 .	369	1.	363	255
no	1 .468	! i<	460	1.	.452	1 .	446	1,	440	250
115	1.540	1.	532	1 1.	525	1 .	519	1.	514	245
120	1.607		600 *	1.	594	1 .	588	1.	583	240
125	1.669	1.	663	1.	657	1 .	652	1.	648	235
130	1.727	1 .	,721	1.	.716	1 .	712	1,	70S	230
135	1.779	1.	774	r.	770	1 .	766	1 .	763	225
140	1.825	1 .	,821	! 1.	818	1 .	815	1.	812	220
145	1.866	1.	863	1 1.	860	1 .	858	1.	856	215
150	1.902	1.	899	1	.897	1 .	895	1.	894	210
155	1.932	1 ,	930	1 1.	928	1 .	927	1	926	205
160	1 . 956	1 .	955	1.	954	1 .	943	1	953	200
165	1 . 976	i ■	975	1.	.974	! i •	973	1	973	195
170	1.989	1 .	.989	1.	989	1 .	, 988		988	, 190
175	1 . 997	1 .	997	1 .	997	1 .	997	1,	997	185
180	2.000	2.	000	' 2.	000	^ 2.	000	1 2,	000	180

42

AIRCRAFT ENGINE DESIGN

With reference to Eq. (4-1), by expanding the radical

(1/2 -

by means of the binomial theorem and neglecting the unim- portant terms, the piston travel may be written as

S ~ R{1 — cos d -h sin2 6) (4-6)

The term (1 — cos 6 -h sin^ 0) is called the 'p'^ston-travel

factor. Values of this factor for different crank angles may be calculated, but it is more convenient to use Table 4-3.

4-3. Example- — Determine the velocity and acceleration for the master- rod piston in Example 1, Table 2-1.

Procedure. — For this example, N = 2,000 r.p.m., R — 5.375/2 = 2.6875 in.- andI//jR = 4. Hence, from Eq. (4-4),

Tf.p.a. = 0.00873 X 2,000 X 2.6875 (sin d -f- sin 26)

By using values of the piston-velocity factor as found in Table 4-1, the values of V for increment crank angles are found (Table 4-4).

Table 4-4

e	Tf.p.s.	6	Ef.p...	B		6	Tf.p.H.
0	0	100	44.3	190	6.15	280	48.3
10	10.17	110	40.4	200	12.3	290	48
20	19.85	120	35.6	210	18.4	300	45.75
30	28.6	130	30.2	220	24.4	310	41.7
40	36	140	24.4	230	30.2	320	36
50	41.7	150	18.4	240	35.6	330	28.6
60 I	45.75	160	12.3	250	40.4	340	19.85
70	48	170	6.15	260	44.3	350	10.17
80	48.3	180	0	270	47	360	0
90	47

The acceleration from Eq. (4-5) is

A = 0.000914 X 2,0002 X 2.6875 (cos 6 + Z cos 26)

By using values of the piston-acceleration factor, the values of A for imn-e- ment crank angles are found (Table 4-5).

It is also of interest to determine the ])iston traved. By using Eq, (4-6) and proceeding as al>ovc, the values vs. crank angle are found (Table 4-6).

ANALYSIS OF THE CRANK CHAIN

43

Table 4-5

6	.4, ft. per sec. 2	e	4, ft. per sec.-	e	A, ft. per sec.-	9	4, ft. per sec.-
0	12,280	100	-4,005	190	-7,350	280	-599
10	12,000	110	-5,240	200	-7,340	290	1,482
20	11,110	120	-6,140	210	-7,280	300	3,680
30	9,730	130	-6,740	220	-7,100	310	5,875
40	7,950	140	-7,100	230	-6,740	320	7,950
50	5,875	150	-7,280	240	-6,140	330	9,730
60	3,680	160	-7,340	250	-5,240	340	11,110
70	1,482	170	-7,350	260	-4,005	350	12,000
80 90	-599 -2,455	180	-7,350	270	-2,455	360	12,280

Table 4-6

9	S, in.	9	S, in.	9	S, in.	9	S, in.
0	0	100	3.48	190	5.35	280	2.55
10	0.0511	110	3.91	200	5.25	290	2.062
20	0.202	120	4.29	210	5.1	300	1.596
30	0.444	130	4.61	220	4.89	310	1.158
40	0.77	140	4.89	230	4.61	320	0.77
50	1.158	150	5.1	240	4.29	330	0.444
60	1.596	160	5.25	250	3.91	340	0.202
70	2.062	170	5.35	260	3.48	350	0.0511
80 90	2.55 3.02	180	5.375	270	3.025	360	0

Graphical representations of Tables 4-4, 4-5, and 4-6 are shown in Fig. 4-2.

4-4. Piston Displacement, Velocity, and Acceleration for Articulated Rods. — When articulated rods are used as in the case of radial engines and in many V-engines, the path of the link-pin center is not a true circle, and the preceding formulas for displacement, velocity, and acceleration of the piston are somewhat in error. Formulas for the articulated system can be derived, but they are too complex for practical use, and a graph- ical analysis is preferable.

Since V = dS/dt, the velocity may be found by drawing tangents to the piston-travel curve at increment positions and measuring the slope. For instance, in Fig. 4-2 at 50 deg. the

44 AIRCRAFT ENGINE DESIGN

piston travel is at the rate of 3.2 in. in 78 deg. of crank travel. At a speed of 2,000 r.p.m., the time in seconds corresponding to 78 deg. is 60/2,000 X 78/360 = 0.0065 sec., and the velocity is 3.2/(0.0065 X 12) == 41 ft. per sec., which closely checks the value determined by calculation. Similarly, the acceleration at 50 deg. is 38/0.0065 = 5,850 ft. per sec.^ By taking a sufficient number of points, velocity and acceleration curves may be plotted.

Fia. 4-2. — Piston travel, velocity, and acceleration, curves for Example 1.

Figure 4-3 illustrates a method of finding the path of the link- pin center. In this figure, which is based on the dimensions of a Curtiss Conqueror engine. Pm is the master-rod piston-pin center. Cm is the crankpin center. Cl is the link-pin center located at 2.406 in. from Cm, and Pl is the link-rod piston-pin center.

Center-to-center length of master rod = 10 in. Center-to- center length of the link rod is 7.594 in. Obviously, angle C lCmPm is fixed by the design of the master rod.

Plotting the path of the Jink-pin center consists in locating Cm at increment angles and finding the corresponding position of Cz,. The link-rod piston positions are then found by setting

ANALYSIS OF THE CRANK CHAIN

45

the compass to the link-rod length and striking arcs intercepting the link-rod cylinder axis. The corresponding piston-travel

Fig. 4-3. — Graphical constructioa for finding the path of the link-pin center for a Curtiss V-1570 Conqueror engine.

60 100 140 180 220 260 300 340 20 60

’ Croink oingle, deg.

Fig. 4-4. — Piston travel vs. crank angle for a Curtiss V-1570 Conqueror engine.

positions may be found by measuring the distances from the extreme position of the piston pin to these intercepts.

Figure 4-4 shows the piston travel of the master-i‘od and articulated-rod cylinders for the Curtiss V-1570 engine. As the

46

AIRCRAFT ENGINE DESIGN

slope of the articulated-rod curve is nowhere very different from the slope of the master-rod curve, the velocity and acceleration curves will also be closely similar (Fig. 4-5). This fact justifies the usual simplifying procedure of assuming that the accelera- tion of the articulated-rod pistons may be taken as equal to that of the master-rod pistons. It should be noted, however, that the farther the link-pin center is from the master-rod center, the greater will be the discrepancy. It is also of importance to note that increasing this distance increases the stroke of the

Fig. 4-5. — Piston displacement, velocity, and acceleration for the Curtiss V--1570 Conqueror engine at 2,400 r.p.rn. {From S.A.E, Journal, Vol. 29, No. 4, April, 1931.)

articulated-rod piston with consequent results on compression ratio, tendency to detonate, etc.

4-5. Inertia Forces Due to Reciprocating Parts. — The forces necessary to accelerate the piston, rings, wrist pin, and the upper end of the connecting rod are directly proportional to the weight of these parts, and in consequence, it is desirable to keep their weights to a minimum consistent with the other functions that they perform. When the accelerations are known, the inertia forces may be calculated from

ANALYSIS OF THE CRANK CHAIN

47

where F = inertia force, lb.

M = mass of reciprocating parts.

W = weight of reciprocating parts, Ib.

A = acceleration, ft. per sec.- g = 32.2.

It is convenieiitj in calculating inertia forces, to combine Eqs. (4-5) and (4-7), thus

== 0.0000284iV2TEi2(cos 6 + Z cos 26) (4-8)

where Fr = inertia force of the reciprocating parts, lb,

N = r.p.m.

W = weight of reciprocating parts, lb.

It = crank radius, in.

The term (cos 6 Z cos 26) Is called the inertia factor. It is most conveniently found from Table 4-2.

4-r>. — Gas pressure, inertia, and resultant forces (in respect to direction).

^Method from Angle, '"'Engine Dy/iarnics and Crankshaft DesignA)

In the analysis of an engine, the weight of the reciprocating parts must be known to tletcrmine the inertia forces. For a new unit, this involves practically a complete design of the reciprocat- ing parts. But this is difficult without a knowledge of the stresses involved. Obviously, a preliminary weight estimate is neces- sary to determine the forces, and an intelligent estimate neeevSsi- tates a reference to previous attainments. Figures A 1-3 and A 1-4 are of assistance in this respect.

48

AIRCRAFT ENGINE DESIGN

4-6. Example. — Estimate the inertia force due ’to reciprocating parts at increment angles through 360 deg. for 1 cylinder of Example 1, Table 2-1.

Procedure. — By using the data of Example 1, and referring to Figs. Al-3 and Al-4, the probable weight of the reciprocating parts will be 0.25 lb. per sq. in. of piston area, or a total of 0.25 X 4.5^ X 0.785 == 4 lb. per cylinder, approximately. This weight may be substituted in Eq. (4-8), but inas- much as the accelerations have already been found (Table 4-5), the forces

4

may be found from F — A for the various crank angles. Results of

these calculations are shown in Table 4-7.

Fig. 4-7. — Resultant forces of gas pressure and inertia (in respect to work). (^Method from Angle, ‘’'Engine Dynamics and Crankshaft Design^')

For combining with the gas-pressure forces, inertia forces may- be plotted in either of two ways (Figs. 4-6 and 4-7). •

4-7. Torque or Turning Effort per Cylinder. — The part of the force along the cylinder axis which does useful work is the com-

Table 4-7

a	F, lb.	a	F, lb.	a	F, lb.	a	F, lb.
0	1,525	100	-498	190	-912	280	-74.5
10	1,491	110	-650	200	-911	290	184
20	1,381	120	-761	210	-905	300	457
30	1,210	130	-836	220	-881	310	730
40	988	140	-881	230	-836	320	988
50	730	150	-905	240	— 761	330	1,210
60	457	160	-911	250	— 650	340	1 1,381
70	184	170	-912	260	-498	350	1,491
80 90	-74.5 -325	180	-912	270	-325	360	1,525

ANALYSIS OF THE CRANK CHAIN

49

poaent tending to rotate the crankshaft. This turning force may be expressed in terms of the force parallel to the cylinder axis. Referring to Fig. 4-8, P is the piston-pin center, C is the crankpin center, and M is the axis of the crankshaft. ’

D

£

Fig. 4-8. — Crank-ohaia diagram Ulustrating the method of determiaine the

torque. ^

In the figure, the force parallel to the cylinder axis isFc.i and the force in the connecting rod is PB (= Fcr). From the diagram,

(1) DE = CE cos {6 + (f>) — H, the component tending to bend the crankshaft.

(2) CD = CE sin {6 + <t>) = T, the component tending to rotate the crankshaft.

(3) CE = PB =

COS

Siibsituting (3) in (1),

H = X cos (6 + d>)

cos ^

and substituting (3) in (2),

T = X sin (d +

cos ^

If F CA is in pounds and R is in inches, the torque Q is

Q ^ TR = R X Fca ■ in pound-inches

However, it is best to have the equation for T in terms of 9 only as <i> is difficult to determine; hence

(^ + sin 6 cos 4> -f- cos 6 sin d>

— r CA L —

cos cos 0

50

AIRCRAFT ENGINE DESIGN

but

cos ^ = A / 1 ^ ^ ^

and

sin <p

substituting

sin^

7?

Y sin 6 = Z sin 6

T ^ Fc

sin 6 a/ 1 — Z^ sin^ d + cos 6 Z sin 6

T = sin ^ ( 1 +

(■

1 — Z^ sin‘^ 0 Z cos $

\/ 1 — Z‘^ sin^ 6

)

The expression (Z'^ sin'-^ d) is small and may be neglected with- out appreciable error. Then

T ~ Fca sin 6{1 + Z cos 0)

= Fc7^(sin 6 + Z sin 6 cos 6)

but 2 sin 9 cos B — sin 26 Therefore,

T = Fc^ ( sin

Z . 2.sin

(4-9)

The term [(sin 6 {Z/ 2 sin 26)] is called the tangential- force

factor, and it is most conveniently found from Table 4-1.

The torque,

Q (in Ib.-ft.) = T (in lb.) X R (in ft.)

(4-10)

AIVALYSIS OF THE CRANK CHAIN

51

4-8. Example. — For the engine selected in Example 1, plot a curve of torque per cylinder against crank angle through one complete cycle.

Procedure. — Values of Fca ( = the net or resultant force parallel to cylinder axis) are read from Fig, 4-6, The resultant turning effort and torque at increment crank angles obtained from Eqs. (4-9) and (4-10) are given in Table 4-8, The torque per cylinder is shown graphically in Fig. 4-9.

Table 4-S

e	F (lb.)	T (lb.)	Q (Ib.-ft.)	6	F (lb.)	r (lb.)	Q (Ib.-ft.)
0	620	0	0	370	— 1,4SS	-321	-71.9
10	4,309	930	208	380	— 1,354	-571	-128.0
20	5,220	2,200	493	390	-1,183	— 720	-161
30	5,230	3,180	712	400 1	— 961	-736	— 165
40	4,172	3,200	716	410	— 703	-625	-140
50	3,360	2,980	667	420	-430	— 419	-93.8
60	2,768	2,690	603	430 i	— 157	— 160	— 35.8
70	2,436	2,480	555	440	48	49-4	11
SO j	2,255	2,320	520	450	352	352	78.9
90	2,155	2,155	482	460	471	444	99.5
100 !	2,038	1,920	430	470	677	582	130
110	2,000	1,720	385	480	734	556	124.5
120	1,980	1,500	336	490	809	520	116.5
130 1	1,956	1,258	284	500	834	434	97.1
140	1,880	978	219	510	878	344	77.0
150	1,747	684	153	520	884	232	52.0
160	1,610	422	94.5	530	885	116	26.0
170	1,468	192	43.0	540	SSS	0	0
180	1,230	0	0	550	-893	-117	-26.2
190	-1,119	— 146	— 32.7	560	-897	-235	-52.6
200	— 990	— 259	— 58.0	570	-894	— 350	— 78. 4
210	— 953	— 374	-88.7	580	-SS4	-460	-103.0
220	— 902	-469	-105	590	-841	-541	-121.0
230	— 857	— 558	— 125	600	-80S	-613	-137
240	-782	-593	-133	610	-730	- 627	-140
250	-677	-582	-130	620	-620	-584	— 131
260	— 519	-489	-109.5	630	-468	-468	-105
270	— 352	-352	-78.8	640	-297	— 305	-68.3
280	-95	-97.6	— 21.9	650	-118	-120.4	-27.0
290	163	166	37.2	660	75	73	16.3
300	436	424	95.0	670	205	182	40.8
310	709	630	141.0	680	207	159	35.6
320	967	740	166.0	690	178	10S.4	24.3
330	1 , 1 89	722	162.0	700	— 50	-21 .1	-4.72
3 10	1 ,3(i0	574	128. 5	710	-430	-93	-20.8
350	1 ,470	318	71 .2	720	— 620	0	0
3()0	1 , 504	1 0	0

52

AIRCRAFT ENGINE DESIGN

4-9. Torque Reaction. — The reaction to the torque force is the piston side thrust. Referring to Fig. 4-8, the side thrust is represented by the force vector Fqt and from the diagram = Fca tan but

tan <j> =

sin <j> cos <j>

hence

R/L sin^ sin 6

'v/l — (RyL^) sin^ 0 ->/ (L/Ry ~ sin^ d

Fca sin 6

■V{L/Ry — sin2 ^

(4-11)

It should be noted that the shorter the connecting-rod length

L in proportion to the crank radius Ry the less the over- all dimensions of the engine but the greater the side-thrust component and hence the rela- tive friction and wear in the cylinder.

An example of variation of piston side thrust with crank angle is shown in Fig. 4-10.

4-10. Total Engine Torque. For the purposes of design, it may be assumed that the torque curves for all cylinders will be the same. Hence, to determine the total turning effort

Fig. 4rl0. — Variation of piston side thrust for a typical aircraft engine. (From Angle, '"Engine Dynamics aTid Crankshaf t D esign . ” )

Cylinder Numbers

12 3 4

CL3

180

360

6

540

720

p	c	E	I
E	p	I	c
I	E	C	p
C	I	P	E

Fig. 4-11. — Usual crank-arm. ar- rangement for four cylinder in-line engines.

Fig. 4-12. — Diagram for determining firing orders in conventional four-cylinder in- line engines.

of the engine, it is merely necessary to space the individual cylinder curves properly with respect to crank angle and add the

ANALYSIS OF THE CRANK CHAIN

53

ordinates. To determine the angular spacing, it is necessar\^ to know the arrangement of the crankshaft crank arms and the firing order in the C3"linders.

/ 2 3 4 S 6

Fig. 4-13. — Usual eraiik-arin arrangement for six-cylinder in-line engines.

Cylinder Numbers

in-line engines.

For foiir-cyliniler in-line engines, the usual method of arrang- ing the crank arms is shown in Fig. 4-11. The firing order may

54

AIRCRAFT ENGINE DESIGN

be found from a diagram such as Fig. 4-12. In this figure, the firing order is 1 -2-4-3. The other possible firing order for four-cylinder in-line engines having the conventional crank arrangement shown in Fig. 4-11 is 1-3-4-2.

The usual crank arrangement for six-cylinder in-line engines is illustrated in Fig. 4-13.

A method of determining the firing order for six-cylinder engines is illustrated in Fig. 4-14. In this figure, the firing order is 1-5-4-6-2-3. Other firing orders are 1-2-3-6-5-4, 1-2-4-6-5-3, and 1-5-3-6-2-4. The firing order 1-5-3-6-2-4 is usually con- sidered best as no two adjacent cylinders fire in succession.

The firing order for conventional single-bank radial engines is 1-3-5-7-9-2-4-6-8 for nine-cylinder engines, and the sarpe pro- cedure applies for a lesser number of cylinders. The reason for using an odd number of cylinders is obvious.

American airplane engines are usually designed to rotate clockwise when viewed from the end opposite the propeller. Customary methods of numbering the cylinders are:

1. For in-line engines:

•© © © © © O

2. For V-engines: ^

However, numbering of cylinders is largely arbitrary, and many engines differ from the preceding method of numbering.

3. For single-bank radial engines, the cylinders are numbered in the direction of rotation.

4-11. Example. — Determine the firing order, and plot a curve of total engine torque for Example 1, Table 2-1.

Procedure. — In a five-cylinder single-bank radial, the firing order will necessarily be 1-3-5-2-4. The angular spacing of the cylinder center lines is =72 deg. In spacing the individual torcpie^ curves with No. 1

cylinder starting expansion at 0 deg., No. 3 will start at 144 deg., No. 5 will

ANALYSIS OF THE CRANK CHAIN

55

start at 2S8 deg.^ No. 2 will start at 432 deg., and No. 4 will start at 576 deg.

Individual torque curves for the five cylinders and the curve of resultant torque for the engine are shown in Fig. 4-15.

The mean torque is found by taking the area under the resultant engine torque curve and dividing by the length. The mean-torque line is located at a height above the zero line equal to the quotient.

40 80 120 160 200 240 280 320 360 400 440 480 520 560 600 640 680 720 Crank angle, deg.

Fig. 4-15. — Torque variation i>er cycle for Example 1. Ratio of max Q / mean

<? = 2.14.

‘A check on the work is possible at this stage, for the mean value of torque as found is the indicated torque of the engine; hence

• u.. _ SttAQ _ 27r X 2,000 X 410 _ ,

33,000 33,000

For the assumed niechaiiical efficiency of S5 per cent (Par. 3-3) the brake horsepower is

b.hp.nia-x = 156 X 0.85 = 133

The originally assumed brake horsepower was based on a cylinder dis- placement of 82-5 cu. in. (Par. 2-4), but the torque was based on a cylinder displacement of 4.5- X 0.785 X 5.375 85.5 eu. in. Hence the horsepower

based t)n the original displacement will be about (82.5 85.5) X 133 = 128. I^his is within Ic'ss than 2.5 pta cent of the t)riginany assumed value of 125 b.hp., and therefore indicates that no serious errors have been made in the calculations.

56

AIRCRAFT ENGINE DESIGN

4-12. Torque Variation with Number of Cylinders and Cylinder Arrangement. — In a one-cylinder engine, the torque is negative, against rotation, for a large portion of the cycle.

Hence to keep the engine turning, it is necessary to use a rela- tively heavy flywheel. This is obviously not practical for air- plane engines, and, although the propeller acts to a considerable extent as a flywheel, because of its mass, it is desirable to use several cylinders to reduce the torque variation as well as increase the total power output. Figure 4-16 shows the effect of number of cylinders and arrangement on torque variation and ratio of maximum to mean torque.

r	f\	vcA	n O		\ff\
0		3

0 Fourcyh'nder in !me. Max/mean Q=2.94 720

'5 ^

w	%	m

0 Eightcyllnder60deg.vee.Max/mcanQ= 1.7 720

0 Seven cylmder rofdioil Max/meotn Q=l.45 720

Fig. 4-16. — Effect of number of cylinders and arrangement on torque variation. (From Angle, ‘‘'Engine Dynamics and Crankshaft Design.'’^ )

Suggested I>esign Procedure

Important. Make all constructions and curves to a large cnouj^h scale to permit accurate readings of values. Size B or larger drawing paper is recommended. Keep a record of the man-hours required on cacdi item.

1. For the engine selected for your design, construct curves of piston travel, velocity, and acceleration through 360 deg. of crankshaft travel (for one cylinder) .

2. Estimate the weight of reciprocating parts, and (^')^\strlutt a curves of reciprocating inertia force vs. crank angle (through 720 deg. of crankshaft travel).

ANAJLYSIS OF THE CRANK CHAIN

57

3. Superimpose the gas-force curve (see Suggested Design Procedure, page 35 ; item 4) on the reciprocating inert ia-foree-curve (see item 2 above) coordinates, and plot a curve of resultant force parallel to the cylinder axis.

4. Construct a single-cylinder torque curve (through 720 deg. of crank- shaft travel), and draw a line on the diagram representing the mean torque. Determine the ratio of maximum to mean torque, and place the value found on the diagram.

5. Construct a curve of piston side thrust vs. crank angle (through 720 deg. of crankshaft travel).

6. Determine the firing order to be used, plot a curve of total engine torque vs. crank angle (through 720 deg. of crankshaft travel), and draw a line on the diagram representing the mean engine torque. Determine the ratio of maximum to mean torque, and place the value found on the diagram.

7. By using the mean engine torque value found in item 6, determine the indicated horsepower and brake horsepower for your engine.. If the brake horsepower thus determined does not agree within 5 per cent of the originally assumed value of brake horsepower (Suggested Design Procedure, page 24, item 2), recheck the work for errors.

8. When items 1 to 7 have been completed and put in proper form, submit for checking and approval.

References

1. Angle: Engine Dynamics and Crankshaft Design.^'

2. Huebotter: ‘'^Mechanics of the Gasoline Engine."

3. Cousins: “Analytical Design of High Speed Internal Combustion Engines."

CHAPTER 5

ANALYSIS OF BEARING LOADS

6-1. Crankshaft-bearing Loads. — Before the necessary sizes of the various crankshaft bearings can be determined, it is essential to know the loads to which they will be subjected, and before all these, loads can be determined, it is necessary to know approximately the dimensions, i.e., the mass of the moving parts. Obviously, this knowledge necessitates* the making of assump- tions based on the past experience of the designer or, in the

iPia. fi-1. — Method of determining the resultant force on the crankpin for an engine having one cylinder per crankpin.

case of student^^ of other designers. Only by utilizing the results of previous successful experience can an exhorbitant amount of triaband-error effort be avoided.

5“2. Resultant Force on the Crankpin. — The resultant force on the crankpin may be found most readily by combining graphically the resultant forces along the connecting-rod axes with the centrifugal forces due to the weight of the lower end of the connecting rod.

Referring to Fig. 5-1, Fca is the resultant force along the cylinder axis and Fc is the centrifugal force due to the rotating weight of the connecting rod.

The acceleration toward the axis of a rotating body necessary to keep the body moving in a circle is v^/r; hence the centrifugal force on the body is

58

ANALYSIS OF BEARING LOADS

59

Fc = MA =.!/-=

where Fc == centrifugal force, lb.

= mass.

A = acceleration.

V — linear velocity, ft. per sec.

7' — radius (crank arm), ft.

Wc = centrifugal weight, lb. ( == the rotating weight on the crankpin for the case under consideration). g = acceleration of gravity (== 32.2 ft. per sec.-).

But

2wRN

12 X 60

where n = r.p.s.

N = r.p.m.

R = crank arm, in.

Hence, by combining and reducing

= 0.0000284TFciV2^ (5-1)

The centrifugal force is laid off to scale along the crank arm from the crankshaft axis M, Fcb is the component of F ca along the connecting rod axis. From the diagram,

cos 4>

but from Par. 4-2,

cos (p = — f 5 V sin- 6

Therefore

^ [1 - {R/LY sin‘-= (9]»

Vector Fcr is laid off from the end of vector F c and parallel to the axis of the connecting rod. The resultant Fr closes the force triangle.

Angle a: ' represents the direction of the resultant force with respect to the cylinder axis, d with respect to the crank arm, and y with respect to the connecting rod. Resultant forces on the crankpin are usually plotted as polar diagrams. Figure 5-2a

60

AIRCRAFT ENGINE DESIGN

shows polar diagrams for {A) an automotive engine and (jB) an aircraft engine each plotted with respect to the cylinder axis. Figure 5-25 shows the data of Fig. 5-2a (diagram B') plotted with respect to the crank-arnr axis. The effect of engine speed and

Fig. 5~2(a). — Polar diagrams of resultant forces on in-line engine crankpins with respect to the cylinder center lines. (A) Small-bore high-speed automotive engine with relatively heavy piston. {B) Larger-bore aircraft engine with relatively lightweight piston.

of relative magnitude of gas pressure and reciprocating inertia forces is readily apparent.

When more than one connecting rod is attached to a given crankpin, the vector F cr must be included for each. Figure 5-3 shows the method of finding the resultant force on the crankpin for a V-type engine. Figure 5-4 shows polar diagrams with

ANALYSIS OF BEARING LOADS

respect to (a) the engine axis, {b) the crank arm, and {c) the left connecting rod for the engine in Fig. 5-3.

When many connecting rods are attached to one crankpin through link pins, the determination of crankpin bearing loads

Fig. 5“2(&). — Polar diagram of resultant forces on an in-line engine crankpin with respect to the crank arm. This diagram corresponds to {B) in Fig. 5-2 (a). The diagram is most easily constructed by assuming that the crank arm remains fixed and the cylinders rotate backward at increment angles.

may be simplified somewhat assuming that the forces in the articulated rods pass through the center of the crankpin. This assumption is not strictly correct, but it gives results sufficiently accurate for preliminary design purposes.

62

AlHCHAFT ENGINE DESIGN

Fig. 5-3. — Method of finding the result- ant force on the crankpin of a V-type engine. (^From Angle, Engine Dynamics and Crankshaft DesignC^")

60 A I \

\

I \

IjOf

I I

■^jj20

I ’dfSO, /soy £40

Fig. 5-4. (a) — Polar diagram of resultant force on V-type engine crankpin with respect to the engine axis.^ (^From Angle, Engine Dy~ narmcs and Crankshaft Design

Fig. 5-4 (6). — Polar diagram of resultant force on V-type engine crankpin with respect to crank arm. {From Angle, Engine Dynamics and Crankshaft Design^')

PiQ. 5-4(c) . Polar diagram of resultant •torce on V-type engine erankpin with re- speet to loft connecting rod. (From A nale, ^no%nc dynamics and Crankishnfl

ANALYSIS OF BEARING LOADS

63

6-3. Example. — Construct a polar diagram of crankpin bearing loads for the engine selected in Example 1, Table 2-1.

Procedure, — From Fig. Al-o, the probable rotating weight per crankpin for a 125-hp. engine of five cylinders will be about 10 lb. For a speed of 2,000 r.p.m. and a crank radius of 2.6875 in., the centrifugal force will be [from Eq. (5-1)]

Fc == 0.00002S4 X 10 X 2.6S75 == 3,050 lb.

The component of force along the connecting-rod axis Fcr, varies with the value of Fca and 0, Table 5-1 shows, for the example, values of Fcr at increment angles. It is to be seen from this table that values of Fen do not differ greatly from values of Fca- For many purposes, these differences are small enough to be neglected, and values of Fca may be used directly in plotting the polar diagram.

Tabus 5-1 '

1	2	3	4	5	6	7	S	9	10	11 (« 7)	12
0	Fca	sin d	sin^ B	«Ss	(Si g		1	Fa,:	0	Fca		0 *3 1	Fch
							1					1
					1		>					>
0	800	0	0 .	0	1.0	1.	0	SOO
20	5,300	0.342	0.117	0.0072	0.992S	0.	990	5,320	3S0	- 1 , 400	0.	996	— 1 , 405
40	4,000	0.642S	0.413	0.0254	0.9746	0.	987	4,050	400	- 1 , 000	0.	987	— 1,013
00	2,650	0 . 866	0.751	0 . 0462	0.953S	0.	977	2,710	420	-450	0.	977	— 461
SO	2,200	0.9848	0.9G9	0.0591	0 . 9409	0.	971	2,265	440	50	0	971	51.5
100	2,050	0 . 9848	0.969	0.0591	0.9409	0.	971	2,110	460	450	0	971	464
120	2 , 000	0.866	0.751	0.0462	0.9538	0.	977	2,045	480	750	0	977	768
140	1 , 800	0 . 6428	0.413	0.0254	0.9746	0.	987	1,825	500	SOOj	0.	987	Sll
160	1,600	0.342	0.117	0.0072	0 . 9928	0.	996	1,607	520	8251	0.	996	S2S
180	1,200	0	0	0	1.0	1.	0	1,200	540	850	1.	0	850,
200	1 ,050	0 . 342	0.117	0.0072	0.9928	p.	996	1,054	5C)0	850	0.	996	854
220	900	0 . 6428	0.413	0.0254	0.9746	0.	987	912	5S0	850	0.	987	86 1
240	800	0 , 866	0.751	lo.0462	0.9538	0.	977	819	600	825*	0.	977	845 '
200	600	0.9S4S	0 .969	0.0591	0 . 9409	0.	971	617	620	650	0.	971	670
280	200	0.9848	0.969	0.0591	0 . 9409	0.	971	206	640	300	0,	971	309
300	-350	0 . 866	0.751	0.0462	0.9538	0.	977	— 358	660	— 75	0.	977	— 77
320	-850	0 . 6428	0.413	0.0254	0 . 9746	0.	987	— S62	680	-200	0.	,987	-202
340	— 1 , 300	0.342	0.117 '	0 . 0072	0.9928	0.	996	- 1 . 305	700	50	0.	996'	52
300	— 1 , 500 1	0	0	0	1 .0	1 .	0	1 - 1 , 500 i i	720	1 SOO	1 .	.0	800

For oxaiiiplc, five connecting rods aro attachtal to the crankpin, and although the variation of n'sultant force kFca) per (*ycle (.Fig. 4-6) is assunual to be the same in eaich cylinder, for any given angular position of the crank arm, the force along each individual connecting rod will be different owing

64

AIRCRAFT ENGINE DESIGN

to the fact that the various cylinders are operating on different parts of the cycle. Further, some of the connecting rods will be under compression and others will be under tension. An effort to combine graphically these forces is likely to result in some confusion if a system of keeping things straight is not used. Figure 5-5 shows a system that has been prepared for the example, and a similar figure may easily be arranged for any other engine.

In this figure, the force in the connecting rod Fen' is plotted against crank angle- Forces downward along the cylinder axis are taken as positive; upward forces are considered negative. The angular* spacing of the cylinder axes is =72 deg.; hence with No. 1 cylinder just starting expansion,

6400 5600 4800 4000 . 3200 ~ 2400 ^1600 800 0

-800 -1600 Cv1:No.] C

\<~ Fxpe^ns/on 5- — Exhotusf ' ^ Intake > <-Corrjpressipn

Downward along connecting rod axis

Upward ahng

'^connecting rod axis I 1^1

80 1:^0 160 260 240 280 320 360 400 440 480 5?0 560 6 0 0 640 680 720 Cyl N0.2 440 480 520 560 600 640 680 0 40 80 120 160 200 240 280 320 360 440 C;yl.No.3 160 200 240 2^ 320 360 400 440 480 520 560 600 640 680 6 45 85 ilo" C^l N0.4 600 640 680 6 40 80 120 160 260 240 280 320 360 400 440 460 520 560

C^l No. 5 320 360 400 4^ 480 520 560 600 640 680 6 40 80 120 160 200 240 280

Croink oingle^ deof.

Fig. 5~5. — Methods fox* determining Fcr (the force along the connecting-rod center line) for any cylinder of Example 1 at any position of the crank arm with respect to the center line of No. 1 cylinder.

No. 3 (the next to fire) will be on the first part of the compression stroktu Number 3 is 144 deg. ahead of No. 1; hence its angular position for No. 1 at 0 will be 180 — 144 = 36 deg. past the start of compression (Fig. 5-5). Call this 36-deg. point 0 for No. 3 cylirnhu, and lay off the crank-ang](i scale as indicated. Similarly, the 0 point may be found for the other cylin- ders and scales laid off as shown.

To illustrate the use of the scale, suppose No. 1 cylinder is at the 80-deg. point and it is desired to find the forces in each of the connecting rods. The solution consists in reading up to the curve from tlie 80-deg. point for ea(4i cylinder and taking the forces directly froni the ordinate; senile.

In plotting the pedar diagram (Fig. 5-6), the cylinele;r ax(;s are laid off fre)in Af at their proper angular relation. Then, with M (the crankshaft axis) as a center, the crank circle (radius R) and the centrifugal-force Fc circles

ANALYSIS OF BEARING LOADS

65

are constructed to the dimension and force scales, respectively. These circles are divided into the desired angular segments (20 deg. in this instance).

To determine the resultant force on the crankpin at any given angular position of the crank arm, say 100 deg. in the direction of rotation past the beginning of expansion in No. 1 cylinder, the procedure is as follows. (a) Set the compass to the length of the master connecting rod (dimension scale), and with C (the 100-deg. position on the ’crank circle) as a center,

Fia. 5-6. — Polar diagram of resultant force on a five-cylinder radial-engine

crankpin (Kxaniple 1).

strike arcs intercepting all the cylinder center lines (designated Pi, P^, Ps, etc., in Fig. .5-6). Lines connecting these intercepts with C represent the center lines of the various connecting rods. (6) For a crank angle of 100 deg., read the values of Fcr for the various cylinders from Fig. 5-5. (c) With

the 100-deg. intercept on the Pc circle as a starting point, lay off force vector Fcri parallel to No. 1 cylinder connecting rod PiP and in the direction con- sistent with Fig. 5-5. From the end of Fcri, lay off Fcr-2 parallel to P-^C and in the proper direction. Continue this procedure until all connecting-rod forces are laid off. The resultant force on the crankpin is represented by a

66

AIRCRAFT ENGINE DESIGN

vector connecting the cranksliaft center (^AI) and the end of the last con- necting-rod vector. The direction of this resultant with respect to the center line of cylinder No. 1 is a and with respect to the crank arm is jS.

By connecting the ends of resultant force vectors determined at iricrement crank angles through 720 deg., the polar diagram (Fig. 5-6) was obtained. When constructed to a large enough scale to permit close accuracy, polar diagrams for radial-engine crankpins are symmetrical.

It should be noted that the maximum force- from the diagram is consider- ably greater than the maximum value of Fcr (Fig. 5-5).

7200

6400

5600

4800

.4000

-Q

“^.3200 0 2400

i2«600

800

0

-800

-1600

-7.4CC

	P lansio	n >	-r— £.	(hau6	— f >		itofke	■>-		oressi	on —
\
I'"	cfspre ‘force	ssure
\			Dov^	nwotr	d odor	g cy/ir	ider ot	XfS
	\
	\ \										/ . t
											/ /
				\^\	i						-A-
_ _y	/						r			N
	- Jnertiof force j ft
	1	Upward crjong cyJinder aKis

C^I.NIo.l 0 O 80 .20 !60 200 y-‘-0 ?;?G 35C ^00 ^40 >^37 57.0 DcO 5C0 0^0 580 7?.Q

Cvf.No.2 440 480 520 560 600 640 680 0 40 80 \io 160 200 240 280 320 360 400^ ,C^I.No.3 160 200 24o 2to 3^ 400 440 480 520 5& 600 640 660 6 40 80 120

C:/!.No.4 600 640 680 6 40 80 120 160 200 240 2^0 320 360 400 440 480 520 560 •

C^l . No. 5 320 3&r460 440 480 520 560 600 640 680 6 40 ’ 80 120 160 200 240 280

Crank «nojIe, deg.

Fig. 5-7. — Method for determining Pj (the inertia force along the cylinder axis the inertia component in the connecting rod) and Fg (the gas force along the cylinder axis ~ the gas force in the connecting rod) for any cylinder of Example 1 at any position of the crank arm with respect to the center line of No. 1 cylinder.

Alternate Procedure.- — Construction of polar diagrams for crankpins of multicylinder radial engines is at best somewhat tedious, but some simpli- fication of the foregoing procedure may be made by considering the recipro- cating inertia, gas, and centrifugal inertia forces separately.

It has already been observed that the force on the crankpin due to the weight of the rotating part of the connecting rods is constant (for any given engine speed) and that it always acts along the crank-arm center line. By reproducing Fig. 4-6 in Fig. 5-7 and locating the positions of all the cylinders by the same method used for Fig. 5-5, the resultant forces Fqr^ due to gas- pressure forces, and the resultant forces Fjrj due to inertia of the recipro-

ANALYSIS OF BEARING LOADS

t)T

eating parts, may be found separately. Figure 5-S shows the method of determining the Fir forces. The procedure in making this construction is the same as that for Fig. 5~6 except that inertia forces along the cylinder axes are used (obtained from Fig. 5-7) instead of the total force, i.e., gas force + inertia force. It is seen from Fig. 5-S that the resultant force on the crankpin due to the inertia of reciprocating parts (Fir) is a constant*

reciprocating inertia forces is constant in magnitude (for a given engine speed) and that it always acts along the crank-arm center line. (Values apply only to Example 1.)

(for a given engine speed) and that it always acts parallel to the crank arm. Hence the construction need include only one dotermiiiatioii of Fir to obtain the force due to inertia of reciprocating parts for any angular posi- tion of the crank arm. In Fig, 5-8, the forces due to reciprocating inertia are added graphically to Fc, i.e.^ construction is started from the end of the Fc vector. Hence the end of the F jr vector is distant from M an amount equal to the total inertia force Fit-

* Except for three-evUnder radials.

68

AIRCRAFT ENGINE DESIGN

The resultant force on the crankpin due to gas-pressure forces is found by the construction shown in Fig. 5-9. In this figure, the gas forces in the various cylinders at any crank position are obtained from Fig. 5-7 and summed vectorially in the same way as for Figs. 5-6 and 5-8. The gas- force vectors are started from the end of the total inertia-force vector Fjt; hence a line connecting Af and the end of the For (resultant gas force) vector will give the magnitude and direction of the total resultant force Fn on the

Fro. 5-9. — Alternate method of constructing a polar diagram of resultant force on a five-cylindor radial-engine crankijiii (Kxatnple 1).

crankpin. Determination of Fr by the procedures illustrated in Figs. 5-8 and 5-9 is simpler than by that used in Fig. 5-6, because Fit no(‘d be found for only one crank-arm position, and because the gas forces during most of the exhaust, intake, and the first part of the compression strokes arc negligi- ble, This last reduces the number of vectors to be summed in finding For- If carried through 720 deg. of increment-angle construction, Fig. 5-9 would give the same polar diagram as was obtained in Fig. 5-6. However, for obtaining the usual information desired, f.e., the maximum and nu^^an forces on the crankpin, this procedure is unnecessary as thci eycde is repc^atc'd n/2 times during each revolution, n being the number of cylinders. For the

ANALYmS OF BEARING LOADS

69

five-cylinder engine in Example 1, construction at increment angles through 360/2.5 — 144 deg. is all that is necessary to determine the maximum and mean resultant forces on the crankpin. However, for beginners in polar- diagram construction, it is advisable to carry the construction through at least twice this number of degrees of crank travel [z'.e., 360/ (a/4)] to provide more of a check on the work and to understand more completely the details of construction. Polar diagrams of forces on crankpins are frequently constructed with respect to the crank-arm axis (Fig. 5-45). For radial engines, the construction is illustrated in Fig. 5-10, In this construction, the total inertia-force vector Fit is laid off to scale as indicated in Fig. 5-10, the starting point being considered as the crankpin center C (corresponding to M in Fig. 5-9). From the end of the Fit vector, resultant gas force vec- tors Fgr (determined by the construction illustrated in Fig. 5-9) are laid off at angles 8 to the Fit vector (5 also equals the angle of the gas-force resultant

Force scale : 4000 /b.

Fio- 5-10. — Polar diagram of the resulting force on a five-cylinder radial- engine crankpin with respect to the crank-arm axis (Example Ij.

to the crank-arm center line) for increment crank angles through at least 360/(ri/2) deg. By connecting the ends of the Fgr vector at the various crank angles, a polar diagram of gas forces with respect to the crank-arm center line is obtained. A line connecting the crankpin center C and the end of the Fan vector at any of the given crank angles designated on the polar diagram gives the magnitude and direction ((d) whth respect to the crank-arm axis of the resultant force F r on the crankpin at that crank angle. As the Fgr vector will retrace the polar diagram loop ?i/'2 times per revolu- tion, values and directions of Fr will also repeat n/2 times per revolution. Hence, one loop is sufficient for determining the maximum and mean forces on the crankpin.

The forces dxie to reciprocating and rotating weights, F ir and Fc, vary as the square of the engine speed [Kqs. (4-8) and (5-1)]. Hence, the effect of engine speed on crankpin loadings may readily be found from Fig. 5-10. For instance, tlie inaxinuim force Fr on tiie crankpin is (>,500 lb. for an engine speed of 2,000 r.p.ni., and it is desired tt) know tlie niaxiinum force at 2,400 r.p.in. Assuming that the gas forces remain the same,

70

AIRCRAFT ENGINE DESIGN

o 400^

Fe(2j4Q0 r.p.m.) = 6,500 ==1^ 9,300 lb. (approximately)*

2,000

From this, it is apparent that very high crankpin loadings are likely to occur in power dives, and even in closed-throttle dives when the gas-force vector is negligible, the inertia load Fit will rise to high values. Location of engine r.p.m. points along the crank-arrn axis (Fig. 5-10) adds materially to the information conveyed by the diagram.

5-4, Crankpin Bearing Loads. — The unit loadings on bearings are based upon the force per square inch of projected bearing area, i.e., the diameter of the crankpin (or journal) times its lengths Numerous factors affect the allowable loadings such as distortion of the journal or connecting rod, condition of the lubricant, relative characteristics of the journal and bearing metal, and rubbing velocity. On the assumption of sufficient rigidity to the shaft and adequate lubrication, usual mean bearing pressures range from 750 to 2,000 lb. per sq. in. or more of projected area, and maximum pressures range up to 5,000 lb. per sq. in. (Tables Al~5 and Al-8).t

Rubbing velocity is the relative speed with which a point on the crankpin or journal moves by a point on the inner surface of the bearing. It may be calculated as follows:

ttD

l2

(5-3)

where V = rubbing velocity, f.p.s.

D = crankpin or journal diameter, in.

N =. engine speed, r.p.m.

Rubbing velocities (Table Al-5) range from 15 to 25 or more feet per second, but in more recent high-powered engines, 30 to 50 or more feet per second is proving quite satisfactory. ^

Rubbing factor, or PV factor as it is sometimes called, is the product of mean bearing load in pounds per square inch of projected bearing area and rubbing velocity in feet per second, PV factors are usually considered to be an indication of bearing capacity. Values range up to 50,000 or more \viih 20,000 to

* The maximum force is slightly less owing to the changed angularity {(3) of vector Fr at 2,400 r.p.m. Fr may be found more accurately by first finding Fit at the desired speed and then scaling Fr from the diagram, t See reference 10 for additional data.

ANALYSIS OF BEARING LOADS

1

35,000 (depending on the size of the engine) being a limit recom- mended some authorities. Actually", man^" details of design contribute in determining allowable values.

The ratio of rubbing velocity to unit bearing load is sometimes used as a still further criterion in determining allowable bearing loads. Lubrication engineers frequentty express the conditions in a bearing by the relation*^ ZN/P where Z is the absolute viscosity"® of the lubricant in centipoises, N is the speed of the journal in revolutions per minute, and P is the bearing load in pounds per square inch of projected area. Since is a function [Eq. (5-3)], some engineers consider V/P as a better expres- sion of bearing conditions than PV. JMe^^er^ recommends using a value of V/P > 0.016.

5-6. ‘Example. — For the engine selected in Example 1, determine the projected crankpin area, diameter, and length if the allowable maximum bearing load is not to exceed 1,200 lb. per sq. in. of projected area, the PV factor (based on mean loads) is not to exceed 20,000, V/P > 0.016, the rubbing velocity is not to exceed 20 f.p.s., and the ratio of length to diameter of the crankpin is to fall within the usual range for radial engines of 1,2 to 1.6 (Table A 1-5).

Solution. — From Par. 5-3, the maximum force on the crankpin was found to be 6,500 lb. and the mean force was 5,245 lb. The smallest permissible projected crankpin area is 6,500/1,200 = 5.4 sq. in., and the corresponding mean pressure is 5245/5.4 = 970 lb. per sq. in. For the allowable rubbing velocity of 20 f.p.s., PV = 970 X 20 = 19,400 < 20,000, the allowable rubbing factor, and V/P = — 0,0206 > 0.016. From Eq. (5-3),

D

720F _ 720 X 20 _ ^ ^ • wN TT X 2,000 A 5.4

and

L 2^ D 2.3

1.02

This L/D ratio would very likely be entirely satisfactory, but it is below the desired range. It is an indication that little ditfieulty will be had in meeting the bearing requirements, however. Assume E/X) == 1.25, and to reduce V below its allowable limit, let D = 2.25 in. U^hen

L =-- 1,25 X 2.25 = 2.82 in., A =■- 2.25 X 2.82 = 6.35 in.,

5,245 „

= 825 lb. per sq. m.

the mean pressure

72

AIRCRAFT ENGINE DESIGN

V

TT X 2.25 X ^,000 12 X 60

19.65

the maximum pressure

6,500

6.35

1,025 lb. per sq. in.

PF = 825 X 19.65 V 19.65 P 825

= 0.0238

16,200

As far as bearing requirements are concerned, for the example, a crankpin diameter of 2.25 in. and an effective bearing length of 2.82 in, ± should be easily satisfactory.

5“6. Crankshaft Dimensions. — To perform its functions prop- erly, an engine crankshaft must (a) be strong enough, to withstand the forces to which it is subjected, (b) he rigid enough to prevent appreciable distortion, (c) have sufficient ma^s properly dis- tributed so that it will not vibrate critically at the usual speeds at which it is operated, (d) have sufficient bearings of adequate size to handle the loads with available lubricants, and (e) for aircraft engines, have the shaft as light as possible. Obviously, some of these requirements are more severe than others, and in meeting the difficult requirements, usually the less difficult will be taken care of automatically. For instance, to meet the rigidity and vibration requirements, it is usually necessary to make the shaft much heavier and stronger than would be neces- sary for (a). Hence, a tedious stress analysis is generally unnecessary and seldom made on modern high-speed-engine shafts.

The present purpose (d) is to investigate main bearing loads and determine the necessary main bearing sizes. To do this, it is necessary to know the crankpin bearing loads, the position of the main bearings with respect to the crankpins, and the inertia loads due to unbalanced parts of the crankshaft. These last two items necessitate resort to past experience, if a great deal of trial-and-error effort is to be avoided. Unfortunately, all too few data have been assembled on crankshaft details, but some assistance may be found in Tables Al-5, A 1-0, A 1-7, A 1-8, and Al-9-

5-7. In-line and V-engine Crankshafts. — Typical exampl(\s of in-line and opposed-engine crankshafts are shown in Figs. 5-1 1, 5-12, and 5-13. For air-cooled engines, crankshafts will usually have to be proportionally longer than for water-cooled engines

ANALYSIS OF BEARING LOADS

73

because of the greater over-all diameter (including cooling fins) of the cylinders. This may necessitate increasing the shaft sections to provide sufficient stiffness and rigidity. To avoid excessive weight, this in turn sometimes necessitates the use of main bearings between all crank arms (Fig. 5-12), To

Fia. 5-11. — Continental A-40 crankshaft — four-cylinder opposed, two main

bearings.

Fig. 5-12- — Four-cylinder in-line crankshaft. Tank-70, five nnain bearings.

„ ,0.&S" 0.74" .0.74” .0,6S"„

Fiu. 5-13-— Continental A-50 crankshaft- ~ four-cylinder opposed, three main

bearings.

permit the necessary axial spacing of crankpin eeiitei's, the L/D ratio of bearings may be increased or the crank arms may be set at an angle. To keep down weight, it is obviously desirable to space the cylinder center lines as closely as cooling fins and other requirements will permit. x\lso for the same reason, for small in-line and V-type aircraft-engine crankshafts, counter-

74

AIRCRAFT ENGINE DESIGN

weights are sometimes omitted. This last increases the main bearing loads due to inertia forces from unbalanced crank arms and crankpins and is a questionable saving.

Fig. 5-14. — Diagram illustrating a method for finding the unbalanced weight to apply in determining main bearing loads in in-line and V-engines.

5-8. Example. — With reference to Pig. 5-14, determine the added load on main bearings A and B due to the unbalanced weight of the crank. Assume 2,000 r.p.m. and a density of shaft material of 0.28 lb. per cu. in.

Solution.

Volume of crankpin = 0.785 (4-1) 3 = 7.06 cu. in.

Weight of crankpin ~ 7.06 X 0.28 = 1.98 lb.

Distance to center of gravity = 3 in.

Volume of unbalanced part of crank arms

= 2X1X3X2.5- 0.785 X 1- X 2 = 13.43 cu. in. Weight of' unbalanced part of crank arms — 13.43 X 0.28 — 3.76 lb. Distance to center of gravity — 3 in.

Total weight of unbalanced parts = 1.98 -f 3.76 = 5.74 lb.

Distance to center of gravity of crankpin and unbalanced parts of crank arms

== 3 in.

The centrifugal force on the unbalanced crank Is Ifroin Eq. (5-1)]

Fc ■■ 0.0000284 X 5.74 X '2,0002 X 3 = 1959.6 lb.

This load may be assumed to be divided equally between the two adjacent main bearings; hence each bearing will be subjected to a load of 979.8 lb. This load is, of course, in addition to that imposed by the forces acting on the crankpin.

The use of chamfered and rounded crank arms (Fig. 5-15) aids materially in reducing main bearing loads by reducing the unbalanced weight and distance to the center of gravity. Idieso refinements are usually possible without sacrifice of cranksliaft strength or stiffness. Chamfering at the main bearing end of the crank arm serves principally to reduce the weight of the shaft.

5-9. Radial-engine Crankshafts.— Although the addcul weight is undesirable, it is always necessary to counterbalance radial-

ANALYSIS OP BEARING LOADS

TO

o

engine crankshafts to attain static balance and to reduce the unbalanced loads on the main bear- ings. These loads are much greater in a radial engine due to the greater number of connecting rods attached to the crankpin. The determina- tion of the size of counterweights will be considered later; their only effect in connection with the pres- ent consideration of main bearing loads is in permitting the assump- tion that the inertia forces are completely balanced by the counter- weights.^ Hence, the sum of the main bearing loads at any crank angle is represented b3^ the gas-load vector Fgr, (Figs. 5-9 and 5-10) at that angle.

The principal dimensions of sev- eral radial-engine crankshafts are

given in Table Al-9. General arx'angement of details is indicated in Fig. 5-16.

Fig. 5-15. — Crank arm details for noncounter weigh ted in-line and V-type aircraft-engine crank- shafts. (A) Methods used in chamfering engine crankshaft arms. {B) Typical crank-arm contours. {From Angle, Fngine I>7/7ianiics and Crankshaft Design.''^)

Fig. 5-16. — General arrangement of typical radial-engine crankshafts. (A) General arrangement of the Pratt and Whitney Wasp two-piece crankshaft. (B) General arrangement of the Wright W'hirlwind two-piece crankshaft, (C) General arrangement of the LeBlond one-piece crankshaft.

76

AIRCRAFT ENGINE DESIGN

5-10. Resultant Forces on Main Bearings. — Load distribution on crankshaft main bearings cannot be determined exactly because of uncertainty as to the effects of crankshaft and crank-- case distortion, misalignment of bearings, bearing clearances, etc., but the following procedure is in common use and has proven satisfactory for conventional designs.

In in-line and V-engines where there is a main bearing on each side of the crankpin, the forces acting on the crankshaft bearings are obtained by considering the force at the crankpin, together with the centrifugal force due to the unbalanced part of the crank arms and crankpin (when counterweights are not used), to be equally divided between the two crankshaft bearings at each side of the crankpin. The load on end maiii bearings may be taken as one-half of the load on the adjacent crankpin bearing plus (vectorially) one-half of the centrifugal load due to the crank (when the shaft is not counterbalanced). The loads on intermediate and center main bearings may be taken as the vector sum of one-half the loads due to each adjacent crank, i.e., one-half of each adjacent crankpin load plus (vectorially) one-half of each of the unbalanced adjacent crank-arm loads.

To illustrate the procedure, assume that Fig. 5-2a (A) repre- sents a crankpin polar diagram for a conventional six-cylinder in-line engine having crank arms arranged as in Fig. 4-13 and a firing order of 1-5-3-6-2-4. Figure 5-17 shows a method of finding the resultant forces on the main bearings. In this figure, 'Fr^ is the resultant force on crankpin 1 at (= 30 deg. of crank angle from the beginning of the power stroke). The magnitude and direction («i) of Fr^ is found in Fig. 5-2a (A). Fcsi (Fig. 5-17) is the centrifugal force due to the unbalanced weight of crank 1. (This force is constant for a given engine speed and always acts along the crank-arm axis.) The resultant force on main bearing 1 is Frm^ = FrcJ2> (Fig. 5-17), and its direction with respect to the engine axis is cri.

The resultant force on main bearing 2 is determined by taking one-half the vector sum of the resultant forces at cranks 1 and 2. Referring again to Figs. 5-17 and 5-2a (A), F is the resultant force on crankpin 2 when crank 1 is at i9i deg. from the beginning of the power stroke in No. 1 cylinder. Fcb^ iw the centrifugal force due to the unbalanced ijart of crank 2, F rc., is the vector resultant of Fr^ and Fas^. Frc^_^ is the vector resultant of F/ec,

ANALYSIS OF BEARING LOADS

and F RCz- The resultant force F on main bearing 2 is equal to one-half of F and its direction with respect to the engine axis is 0-2-

An alternate method, which in some cases simplifies the construction of main-bearing polars, is to divide each vector

- at 0-1 dog. Frm2 at <r*2 deg.

to ^ of engine to ' . of engine.

Fig. 5-17. — Method of finding resultant forces on the main bearings of in-line engines. (Six-cylinder crankshaft illustrated.)

component by 2 before applying it in the construction. The resultant vectors are then Frm^, etc., directly.

In finding Fr^ and Fr^^ it is necessary to take account of the firing order as well as the angular relation of the crank arms. To reduce the confusion in doing this, the system illustrated in Fig. 5-18 is useful. For instance, suppose crank 1 is 30 deg. ( = ^i) past the beginning of the power stroke and it is desired to know the value and direction of Fr.^. From Fig. 5-18, crank 2

AJ^ALYSIS OF BEAMING LOADS

will be on the exhaust stroke and at the 27 0-deg. position in terms of crank 1. Hence, from Fig. 5~2a (A), Fr^ is the resultant force at the 270-deg. position, and its direction is ol^, deg. with respect to the center line of the cylinders. Similarly, F may be found for any position of crank 4, etc. Figure 5-18 applies only to the crankshaft and firing order given, but a similar chart may be readily constructed for any other engine.

Fig. 5-19. — (A) End-main-bearing and {3) kitermediate-maiii-bearing polar diagrams for a by 5^^-in. six-cylinder in-line aircraft engine having a

crankshaft and firing order as in Fig. 5-18. Angles in parentheses 0 are relative positions of crank arm on opposite end of main bearing under consideration.

Figures 5-19 and 5-20 show end-, intermediate-, and center- main-bearing polar diagrams for a six-cylinder in-line aircraft engine. The data are based on crankpin loadings as shown in Fig. 5-2a (B) in which the cylinder dimensions, gas-pressure forces, and reciprocating weights are the same as for Example 1. The rotating weight has been taken as 2.5 lb. per crankpin, and the speed is 2,000 r.p.m. The unbalanced weight of each crank arm is assumed to be 6.835 lb. at crank radius distance from the center of the crankshaft.

In single-bank radial engines, it is usually assumed that the inertia forces are completely balanced by the crankshaft counter- weights and that the sum of the main bearing loads at any angular

80

AIRCRAFT ENGINE DESIGN

position of the crankshaft is represented by the gas-load vector Fgr (Figs. 5-9 and 5-10) at that angle. ^ In keeping with the preceding method for in-line and V-engine shafts, it would be logical to assume that each main bearing took one-half of this load. However, experimental evidence indicates that the loads are more nearly distributed as 40 per cent to the rear main

Fig. 5“20. — Center-main-bearing polar diagram for a 43^-in. by 5%-in. six- cylinder in-line aircraft engine having a crankshaft and firing order as in Fig. 5-1 S. Angles in parentheses () are relative positions of crank arm on opposite end of main bearing under consideration.

bearing, 75 per cent to the front main bearing, and 15 per cent radial load in the opposite direction on the thrust bearing in the .nose of the crankcase (Table Al-10).

6-11. Example. — 1. Construct polar diagrams for the -main bearings of the engine in Example 1, using a load distribution of 40 per cent to the rear main bearing and 75 per cent to the front main bearing.

2. By assuming plain bearings, a maximum unit bearing load of 1,000 lb. per sq. in. of projected area, an allowable rubbing velocity of 20 f.p.s., and a maximum allowable rubbing (PV) factor of 15,000, determine the diameter and length of main bearings necessary.

ANALYSIS OF BEARING LOADS

81

3. By assuming ball or roller bearings, determine the sizes necessary .

Procedure 1. — On the assumption that the inertia forces are completely balanced, the gas loads are most conveniently obtained from either Fig. 5-9 or 5-10. In Fig- 5-10, 3 represents the direction of the gas-force resultant P&R with respect to the center line of the crank arm. If 6i represents the crank-arm position with respect to ISTo. 1 cylinder center line, the direction of the Egr vector is -f- (180 — 5) with respect to No. 1 cylinder. Values of Fgr and 3 for various values of 6 have been scaled directly from Fig. 5-10 and arx'anged for convenience in Table 5-2.

Table 5-2

6	3	(180 — 5)	0 + (180 — 5)	Fgr	OAFgr	0.75For
0	16	164	164	1,500	600	1,128
20	28	152	172	6,100	2,440	4,580
40	52.5	127.5	167.5	4,600	1,840	3,450
60	71	109	169	2,900	1,160	2,180
80	92.5	87.5	167.5	1,700	680	1,278
100	104	76 1	176	750	300	562
120	27-	153 '	273	450	180	1 338
140	15	165	305	1,250	500	938
160	25	155	315	5,850	2,340	^ 4,390
ISO	48	132	312	5,200	2,080	3,900

Values of 0.75Fg’a^ (-4) and OAFgr (B) for the various values of 0 are plotted with respect to the center line of No. 1 cylinder as shown in Fig. 5-21.

(B>

Fig. 5-21. (A) Front- and (^JB) rear-main-bearing polar diagrams for a five-

cylinder single-bank radial engine (Example 1).

As F gr (Fig. 5-10) repeats n/2 times per revolution {?i = number of cylinders), the main-bearing polars will also repeat n/2 times per revolution. Hence, one loop is sufficient for maximum and mean force data. However,

82

AIRCRAFT ENGINE DESIGN

the completed diagram may be quickly drawn by shifting the tracing paper angularly the proper amount for each loop. The complete polar is useful in showing the positions and directions of critical loadings on main-bearing supports and for relative wear studies. The relatively high ratio of maxi- mum to mean force in radial-engine main bearings as compared with in-line- engine main bearings and the high rate of change of force (shock loadings) should be noted.

Procedure 2. — For the front main hearing, the projected bearing area will be

4,580 _

From Eq. (5-3),

720 X V 720 X 20

To reduce V below the allowable limit, let D == 2.25 in. Then

L = V ==

4.58 2.25 2.25 X

= 2.04 :

X 2,000

72

The mean force is 1,807 lb., hence

PF = X 19.6 = 7,750

For the rear main bearing, the projected area will be

2,440 ^ .

1,000 ==

and by assuming the same diameter as for the front main

^ = IS =

Procedure 3. — For the front main bearing [Fig. 5-21 (A)], the average force is 1,807 lb., the maximum force is 4,580 lb., and the speed is 2,000 r.p.m. On the assumption that ball bearings are to be used (Table A 1-22), L = 1 ,807 lb., Z = 0.88 for an assumed bearing life of 2,500 hr. and K = 2 0 or 2 5 say 2.25. Then

C = 1,807 X 0.88 X 2.25 = 3,580 lb.

The diameter of the main bearings should not be less than the diameter of the crankpin, and the front main bearing for diroc^t drive will have to he' greater in diameter than the largest diameter of the S.A.E. standard sliaft end that is to be used. The crankpin diameter (Par. 5-5) is 2.25 in., and from Fig. Al-6, the logical propeller-shaft end will be S.A.E. taper ’type

ANALYSIS OF BEARING LOADS

S3

No. 1. From Table Al-20, the maximum diameter of a taper type S.A.E. No. 1 shaft end is 2.05 in. Hence a front main bearing base diameter of 2.25 in. should be about adequate. From Table A1-22D, S.A.E. bearings 212, 312, and '412 are adequate in bore diameter, but from Table A1-22E, it is seen that at 2,000 r.p.m. the ratings are too low. From Tables A1-22F and A1-22G, it is evident that S.A.E. bearing 413 having a bore of 2.5591 in. or bearing 314 having a bore of 2.7559 in. could be used. Use of a shock factor of X" = 2 or of a bearing life of 2,000 hr. would permit the use of S.A.E. bearing 412, but at the expense of a reduction in the factor of safety or life of the engine.

For the rear main bearing L = 962 lb., Z = O.SS, and K = 2.25. Then C = 962 X 0.88 X 2.25 = 1,900 lb.

From Tables A1-22D and A1-22E, S.A.E. bearing 212 having a bore diameter of 2.3622 in. could be used, or if it was desirable to have the same front and rear bearing bore diameters, bearings 213 or 214 could be used.

If roller bearings are desired (Table Al-23) for the front main, L = 1,807 lb., Z = 0.64, and K 1.5. Then

C = 1,807 X 0.64 X 1.5 = 1,735 lb.

From Tables A1-23B and A1-23C, bearings R,LS-16-L or HLS-IO-LL would be adequate. For the rear main, L — 962 lb., Z — 0.64, and K « 1.5. Then

■ C - 962 X 0.64 X 1.5 == 925 lb.

From Table A1-23D, bearing HXLS — 2.25 would be adequate.

5-12. Relative Wear Diagrams. — For the purpose of determin- ing the best location of the oilhole for crankpin bearings having force-feed lubrication, relative wear diagrams are useful. A method of constructing such diagrams follows

The bearing pressure is assumed to be evenly distributed over an arc of ISO deg. on the crankpin. The magnitude and direction of the force with respect to the crank arm is obtained at equal intervals throughout a complete cycle from a polar diagram of resultant forces on the crankpin. These forces are plotted as a series of half rings having their radial thicknesses proportional to the magnitude of the force and their mid-points' falling on a line through the center of the crankpin in the direction of the application of the force considered. The summation of these rings produces an area which is termed the comparative wear on the crankpin. The best location for tlie oilhole is that point on the crankpin where the radial thickness of this resulting area is a minimum.

AIRCRAFT MNOINE DESIGN

ncna/oi/ sccf/e for pfofHncr i r'^25.000/b.

e OO -rv* . ' ^ ^O.UUU /O.

for crankpiis®

ANALYSIS OF BEARING LOADS

85

As an example of the construction, let Fig. 5-2 (a) (B) represent a polar diagram for a crankpin in which the best location for the oilhole is desired. By measuring to scale radiall3" out to the curves [Fig. 5-2 (a) (-B)] at increment crank angles^ values of force in the direction of the crank-arm axis are found (Table 5-3). Plotting these forces as explained above gives Fig. 5-22.

le o~3

e	Forces in direction of crank-arm axis	Total force in direction of crank-arm axis
0	2,250	2,250
20	l,loO	1,150
40	900	900
60	780	780
80 i	790	790
100	870	870
120	1,040	1,040
140	1,320 1	1,320
160	1 ,550, 2,500, 3,700	7,750
ISO	1,600, 1,950.	3,550
200	1,540, 1,680	3,220
220	1,300, 1,370	2,670
240	1,000, 1,010	2,010
260	800, 840	1 ,640
2S0	710, 720	1 ,430
300	730, 730	1,460
320	SOO, 840	1 ,640
340	500, 1,240	1,740
360	2,250	2,250

A relative wear diagram for a V-t\^pe engine is shown in Fig. 5-23.

For radial engines^ the jDolar diagram with respect to the crank- arm axis (Fig. 5-10) should be used to construct the relative wear diagram for the crankpin.

This method of determining the oilhole location has been criticized some sources on the grounds that it does not take into account the effect of centrifugal force on the oil in the crankpin. Thus the^^ maintain that the oilhole should be located on the outer side of the crankpin regardk'ss of what the wear diagram might show. Such a location would undoubtedlv

86

AIRCRAFT ENGINE DESIGN

be satisfactoi^v in most engines and would save considerable tedious construction.

Suggested Design Procedure

Important, Make all constructions and diagrams to a large enough scale to permit accurate work. Size B or larger drawing paper is recommended. Keep a record of the man-hours required on each item.

1. For the engine selected for your design, construct polar diagrams of forces on the crankpin (a) with respect to the engine axis and {h) with respect to the crank-arm center line.

For in-line and V-engines, construct the diagrams through 720 deg. of crank travel. For radials, construct the diagrams through a sufficient number of degrees of crank travel to accurately define the shape and spacing of the lobes. Then, for part a, complete the diagram through 720 deg. by shifting the tracing paper.

For part 6 of radial-engine polars, locate two or more higher r.p.m. points on the crank-arm axis.

2. Determine the maximum and mean forces, and locate values found on the diagrams constructed in item 1.

3- By using bearing loads, rubbing factors, etc., within the ranges given in Appendix 1, determine crankpin dimensions that will be adequate for bearing purposes.

4. Lay out to scale the general arrangement of crankshaft desired. Esti- mate the unbalanced weight per crank arm and the distance to the center of gravity.*

Befer to available sectional blueprints, specimen crankshafts, etc., for assistance in making the layout. Do not try to include details other than those necessary to the determination of unbalanced- weight data. For radials, this item is unnecessary at this point.

5. Construct main-bearing polar diagrams for all differently loaded main

For in-line and V-engines, construct the diagrams through 720 deg, of crankshaft travel.

For radials, construct the diagrams through a sufficient number of degrees of crankshaft travel to define accurately the shape and spacing of the lobes . Then complete the diagrams through 720 deg. by shifting the tracing paper.

6. Determine the maximum and mean forces, and locate values found on the diagrams constructed in item 5.

7. By using bearing loads, rubbing factors, etc., within the ranges given in Appendix 1, determine main-bearing dimensions that will be adequate for bearing purposes.

8. Construct a relative wear diagram for the crankpin of your engine, and show the best oilliole location, or locate hole on outside of crankpin in plane of crank arms.

* When this distance is not equal to the crank radius, as is usually the case, it is frequently the custom to use an equivalent unbalanced weight that is considered to act at crank radius from the center of rotation.

ANAI.VSIS OF BBARI.VG LOADS

87

9. When items 1 to 8 have been completed and put in proper form, submit for checking and approval.

References

1. Heldt: “Automotive Engines.”

2. Angle: “Engine Dynamics and Crankshaft Design.”

3. A.SA.C. 421.

4. S.A.E. Jour., Vol. 28, No. 4, April, 1931.

5. S.A.E. Jour.^ Vol. 29, Nos. 4 and 5, October, November, 1931.

6. Mark’s “Handbook,” 2d ed., p. 279.

7. S.A.E. Jour., Vol. 35, No. 6, December, 1934.

8. Unpublished design notes of A. J. Meyer.

9. Design of Engine Bearings, Automotive Ind., Aug. 1, 1939.

10- Willi: Engine Bearings from Design to Maintenance, S.A.E. Jour., Vol. 45, No. 6, December, 1939.

CHAPTER 6

DESIGN OF RECIPROCATING PARTS

6-1. Design Requirements and Limitations. — The design of any machine element can be of reasonably certain effectiveness only when the designer (a) is fully aware of and properly con- siders the functions that the element must perform, and (6) is cognizant of the capabilities and limitations of the materials that can be used for the element. Hence, in proceeding with the design of individual parts of the engine, it is advisable to consider briefly the requirements, possibilities, and limitations of these parts in somewhat the same way that was done with the unit as a whole (Chap. 1).

6-2. Functions of the Piston. — Aircraft-engine pistons are called upon to satisfy a rather formidable list, of requirements. Most, but not necessarily all, of these requirements are listed as follows:

The piston must

1. Take the gas-force load without appreciable distortion.

2. Fit closely enough in the cylinder to prevent iDiston slap, excessive blow by, or oil pumping.

3. Be capable of conducting away a large portion of the heat

generated in the combustion chamber. #

4. Have a coefficient of expansion such that the piston will not be too loose in the cylinder when cold or too tight when hot.

5. Have cross sections and a coefficient of heat flow sufficient to conduct awa3^ the heat absorbed by the head at a rate that will prevent hot spots and a resulting increased tendency of the fuel to detonate.

6. Have skirt dimensions sufficient to conduct a considerable portion of the heat absorbed by the head to the cylinder walls and to provide adequate bearing area to take the side thrust.

7. Be capable of giving up some of the heat absorbed to the lubricating oil without raising part of the- oil to a temperature that might impair its lubricating qualities.

88

DESIGN OF RECIPROCATING PARTS

89

8- Provide adequate support for the piston rings.

9. Have adequate bearing area for the piston pin and support- ing-pin bosses rigid enough to prevent excessive localized pin- bearing pressures.

10. Be as light in weight as possible.

11. Have adequate resistance to wear.

At best, some of these items are directly conflicting, and the designer is faced with the ever-present problem of judging where to strike a proper compromise. If he strives to reduce reciprocat- ing inertia forces by reducing the piston weight to a very low value, he usually will have to sacrifice section thicknesses to a point where heat-flow characteristics will be impaired. Quite often the attainment of close piston fits in the cylinder necessi- tates the use of a denser metal to get the proper coefficient of expansion characteristics, and this is apt to mean a heavier piston. Many other conflicting problems requiring compromise solutions will occur to the student.

6-3. Piston Materials. — In keeping with the preceding require- ments, an aircraft-engine piston should have

1. Adequate mechanical strength at working temperatures.

2. A low coefficient of linear expansion.

3. A high coefficient of thermal conductivity.

4. A low density.

5. A high resistance to abrasion.

By far the most common metals used for pistons are aluminum and cast iron. Important properties of these two metals are given in Table 6-1. ObviousB^ neither of these metals is superior from every standpoint. HoAvever, owing partly to improved characteristics imparted by small quantities of other metals and partly to improved fabrication technique, almost all modern aircraft engines use aluminum-alloy pistons. Usuall3^ they are cast in permanent molds or forged.

The most commonly used aluminum alloys for pistons are S.A.E. 34 (Aluminum Co. designation 122), S.A.E. 321 (Alu- minum Co. designation. A132), and the so-called Y-allo^^ (Alu- minum Co. designation 142). Important i:>i*operties of these alloys as given by the Aluminum Company of America are listed in Tables A2-1 to A2-5. Alloy A 132 is recommended by the Aluminum Co. as being particularly desirable for aircraft-

90

AIRCRAFT ENGINE DESIGN

engine pistons because of its low coefficient of expansion and low specific gravity.

6-4. Piston Dimensions. — Detailed dimensions of pistons are to a very considerable extent a matter of engineering judgment. The functions of the piston are so numerous and the heat flow, stresses, etc., are so involved that a rational approach is too complex to be of practical value. However, useful aids may be had from a study of previous designs (Table A 1-1 4) and from empirical rules.

Table 6-1. — Properties op Piston Metals*

1	Specific gravity ; 1 1	Tensile strength , lb. per sq. in.	Coefficient of linear expansion, per deg. F.	Heat conduc- tivity, B.t.u./ (min.) (sq. ft.) (in.) (deg. F.)	Brinell hardness
Metal	At 32°F.	At 200®F.	At 400°F.
Alumi- num. .	2.7	15,000	0,0000124	24.0	150	138	120
Gray iron. . .	7.1	20,000	0.00000556	5.5	165	165	165
Magne- sium. . '	1.74		0 . 0000145	18.2	66	60	35

* Pure metals, not the alloys.

Huebotter and Young, ^ following extensive tests on automotive pistons, have drawn «the following conclusions relative to piston design :

1. A deep section at the center of the head is very effective in lower- ing the maximum temperature. For this reason a liberal center-hole boss is recommended.

2. If ribs are used to reinforce the piston-pin bosses, they- should extend to the center of the head.

3. The aluminum alloy piston .has a wide margin of safety over the gray iron piston on a temperature basis.

4. The ring belt dissipates about 60 per cent as much heat from a given initial temperature as that . . . from the piston skirt.

Temperature gradients for a typical aluminum-alloy and a gray-iron piston are shown in Figs. 6-1 and 6-2. Although not

DESIGN OF RECIPROCATING PARTS

91

geometrically identical, these two pistons are sufficiently’' similar in section to show the decided thermal advantage of aluminum - The relative weights of the two pistons are also of interest.

Typical aircraft-engine pistons are shown in Fig. 6-3. Current practice indicates the desirability of three or four rings above the pin bosses, frequently one ring near the bottom of the skirt,

( ^600 -

Fiq. 6-1. — Temperature gradients in an aluminum-alloy piston. Weight = 2.635 lb. CT^linder diameter = 4.5 in. {From Huebotter and Young ^ Plow of Heat in Pistons. Purdue University Engr. Exp. Sta. Bull. 25).

Fig. 6-2. — Temperature gradients in a gray-iron piston. Weight = 5.S53 lb. Cylinder diameter = 4.5 in.

{From Huebotter and Young ^ Flow of Heat in Pistons. Purdue University Engr. Exp. Sta. Bull. 25.)

ribs under the head for rigidity and better cooling, and amply supported pin bosses .

Piston clearance must be adequate to prevent /^hot seizure” and small enough to prevent cold slap.” Customary practice for automotive engines has been

For gray iron, clearance = 0.001 X bore in inches. For solid-skirt aluminum, clearance = 0.0006 X (bore) ^ in inches.

These rules should not be applied to special types such as Invar or steel-strut and flexible-skirt cam-ground pistons.

Aircraft pistons may be fitted with greater clearances as they operate nearer rated load most of the time (see Table A2-3 for

92

AIRCRAFT ENGINE DESIGN

coefficients of expansion). Clearance and other data on current automotive pistons will be found in Table Al-3. Swan sug-

(h>

(ci) Axelson Cb) Warner

(d> Lycoming; Low compression

(e) K inner

(f) LeB/ond

(g) Continental

(h) Lycoming : High compression

Fia. 6-3. Typical aircraft-engine pistons.

piston clearances for Y and similar aluminum

Top of head . . . . Bottom of head Top of' skirt . . . . Bottom of skirt,

Inch per Inch of Diameter 0.006 0.004 0 ..0025 0.0015

rz

DESIGN OF RECIPROCATING PARTS

93

skirt. Current practice on relative diameter-length ratios of pistons and other details may be observed from Table Al-14. The piston skirt below the upper ring belt is usually considered to take the side thrust, i,e,, act as the bearing area between the piston and cylinder wall. This area is the equivalent of the crosshead bearing area in engines using that type of construction. Angle suggests using about 1 sq. in. of bearing surface for each 60 lb. of average side pressure. From the piston side thrust (see Par. 4-9 and Fig. 4-10), the average side thrust may be determined. Then the necessary length of piston skirt vdll be

Ts

I> X 50

(6-1)

where Tsa = average side thrust against the cylinder wall, lb.

D = cylinder diameter, in.

Pl = length of the piston skirt.

The total length of the piston will be Pl plus the width of the upper ring belt. However, if the value of Pl as found from Eq. (6-1) is appreciably greater or less than current practice, the length of the skirt should be altered to fall within the range of values for similar engine pistons.

As there is very little side pressure on the piston in the direc- tion of the piston-pin axis, a reduction in piston weight may be made by cutting away the skirt below the ends of the pin. However, it is doubtful if the gain in reduced inertia forces off- sets the added complexity of construction and probable increased lubrication or oil-pumping problems except in very high-speed racing engines.

6-5. Piston Rings. — Piston rings should be (a) sufficiently elastic to exert the necessary side pressure against the cylinder walls and to permit insertion* of the ring in its groove by sliding it over the piston, and (&) soft enough to prevent excessive wear on the cylinder walls. Close-grained cast gray iron is almost universally used for piston rings.

Special shapes and types of piston rings are sometimes used to permit closer control of the lubricant, more rapid seating, and to reduce blow by of the combustion gases (see reference 3). However, as it is quite common practice to purchase piston rings from companies specializing in their manufacture, the engine designer will probably do well to merely specify over-all

94

AIRCRAFT ENGINE DESIGN

S.A.E. standard dimensions (Table Al-16) and follow the specific recommendations of the ring specialists on details.

End clearance on rings should be great enough to* prevent any possible binding from heat expansion but small enough to pre- vent excessive gas leakage. A gap clearance of 0.003 in. per inch of bore is commonly specified® by automotive-engine manu- facturers. Butt, diagonal, and lap-joint ring ends (Fig. 6-4) are most common. Side clearance of rings in piston grooves

should be about 0.001 in. to minimize leakage through the piston groove behind the ring (Table Al-16).

6-6. Piston or Wrist Pins. — Pis- ton pins, the connecting links between the piston and connecting rods, may be either clamped in the piston, clamped in the connecting rod, or full floating. This last method per- of mits the pin to turn gradually so that wear is more evenly distributed, but it requires some form of snap ring or soft metal button to pre- vent the end of the hard pin from coming in contact with and scoring the cylinder wall.

The average distance between the pin bosses for the pistons in Table Al-14 is about 48 per cent of the piston diameter, and by allowing for end clearance on the small end of the connecting rod, the length of the piston-pin bearing in the connecting rod will be about 45 per cent of the piston diameter. For full- floating pins (after allowing for end buttons), this will permit about equal bearing areas in the upper end of the connecting rod and in the piston. Hence the piston-boss length may be made approximately one-fourth of the piston diameter, and the length of the pin bearing in the connecting rod may be made 45 per cent of the diameter.

The diameter of. the piston pin will be determined by the maximum allowable bending moment and the allowable bearing pressure. Maximum stress in the pin will occur at full-throttle- low-speed (low inertia) conditions, and the pin may be assumed to take the full force of the explosion pressure in the combustion chamber. Maximum gas pressures were assumed to be about 75 per cent of the theoretical pressures (Par. 3-3). Hence the

Butt joint

DitTigonoil joint

Loip joint

iFiG. 6^. — Common types piston-ring joints.

DESIGN OF RECIPROCATING PARTS

95

maximum force on the piston pin in pounds is

where D = cylinder diameter, in.

Pc = calculated theoretical maximum pressure, lb, per sq. in. abs. [Eq. (3-3)].

The projected bearing area in the upper end of the connecting rod is

S = dL 0A5Dd

where d = diameter of the piston pin, in,

L == effective length of the piston pin, in.

D — cylinder diameter, in.

Because of the low rubbing velocities, much higher bearing pressures may be used for piston pins than for crankpins pro- vided suitable bearing metals such as. phosphor bronze (Table A2-8) are used for connecting-rod bushings and the crankpins are casehardened.

Heldt® suggests an average piston-pin pressure of 3,200 lb. per sq. in. as representative of automotive practice, but values of 10,000 to 15,000 are not uncommon in high-po\vered aircraft engines. Thus

Q.59D^Pc _ p OAbDd ^

where = 3,000 to 15,000, with 5,000 to 10,000 probably being a safe range for small aircraft engines of good design. Hence the piston-pin diameter may be found from

(6-2)

where K = 4,000 to 8,000. Data in Table Al-14 indicate that piston-pin diameters are usually about 25 per cent of the piston diameters.

The piston-pin diameter as determined by Eq. (6-2) is that necessary for adequate bearing area. However, the piston pin must also be strong enough to withstand the stresses involved and as light in weight as possible. Reduction in weight may be made by using a hollow piston pin, the size of the hole in the pin

96

AIRCRAFT ENGINE DESIGN

being determined by the maximum bending moment and the allowable stress.

For determining the diameter of the hole in the piston pin dj (Fig. 6-5), it may be assumed that the gas-force load Pras.^ is

O./yz? H equally divided between the pin

— — bosses and acts as a concentrated

load at the mid-point of their -t f lengths. The reaction load in the ^ connecting-rod bearing may be assumed as equally distributed over the length of the bearing.

^ I Then from Fig. 6-5 {B), the maxi-

mum bending moment (at the mid- point along the piston pin) will be

-0J5D >

^OJ5D\^—OA5D-->\

= 0.1125Z)P„

where M = maximum bending moment, in. -lb.

(B) Prtxi,^ == maximum gas force

Fig. 6-6. — Average location and ' on the piston, lb.

magnitude of forces on aircraft- = diameter of the pis-

engine piston pins. v/x w ^

ton; in.

For equilibrium conditions, this moment [Eq. (6-3)] must equal the internal moment.^

where ;S = maximum allowable stress, lb. per sq. in.

I = moment of inertia of the piston-pin cross section. C = one-half the diameter of the piston pin.

For hollow piston pins, the section modulus is

C Z2d

vhere d ~ diameter of the piston pin, in. . d, = (d^ — 1.146

DESIGN OF RECIPROCATING PARTS

97

Expressing in terms of P„,

d, = (d^ - 0.675 (6-7)

where the symbols are the same as above.

Piston pins may be made of plain carbon steel casehardened (S.A.E. 1020), nickel steel (S.A.E. 2315, 2320, or 2515), or chrome nickel steel (S.A.E. 3120, 3215, or 3220).* An allow- able stress of 25,000 lb. per sq. in. may be used wdth the carbon steel, and 35,000 lb. per sq. in. with the alloy steels. S.A.E. 2315 steel is one of the most commonly used materials for aircraft- engine piston pins.

6-7. Knuckle or Link Pins. — Dimensions of knuckle or link pins for attaching the articulated rods to the master rod may be calculated in much the same way as those of piston pins. Owing to the greater mass of inertia-producing parts between the link pins and the gas force on the piston, link pins may be made somewhat smaller than piston pins. Probably the easiest way to determine the size is to use the same fundamental formulas that were used for the piston pins and assume higher allowable bearing loads and bending stresses. Meyer® suggests as an allowable bending stress 30,000 to 50,000 lb. per sq. in. Unit bearing loads may be somewhat higher than for piston pins because link pins have more positive force-feed lubrication. Link pins may be made of the same materials that are used for piston pins. For severe service, nickel chromium steel (S.A.E. 3125) may be used. For very severe service, such as very highly supercharged racing engines or Diesels, nickel molybdenum steel (S.A.E. 4615) may be advisable.

Link pins should be locked securely in place to prevent any endwise movement and resulting damage from contact with adjacent parts. A rather common method of securing link pins in one-piece master rods is to use small locking plates that are bolted to the outside of the master-rod flange between the link pins [Fig. 6-6 (A)]. The ends of the link pins are flared and either cut away or beveled, and the locking plates extend over their edges to prevent movement of the pins. When two- piece master rods are used, the cap bolts may be so located that

For an explanation of the S.A.E. steel-numbering system, see Table A2-6. For detailed data on the various S.A.E. steels, see reference 8.

98

aircraft engine design

they pass through milled slots* in the sides of the link pins, thus securing- them positively (see Fig. 6-14).

T.ink pins are commonly lubricated by pressure feed through holes in the master-rod flanges and a passageway inside the pin [Fig. 6-6 (B)].

Link pins should be located as close to the crankpin center as clearance and structural dimensions will permit (Par. 4-4). This

Fig. 6-6. — (A) Method of holding link pins in place, and (B) section through the crankpin and a link pin of a Lycoming Type R-CSO nine-cylinder radial engine showing the means provided to lubricate the link-pin bearing.

makes it desirable to keep the diameter of the pins as small as bearing loads and strength requirements will allow. When six or eight articulated rods are attached to one master rod, care must be observed in providing adequate clearance between adjoining rods.

6-8. Connecting-rod Shank Stresses. — Connecting rods are subjected to

1. Compression stresses due to combined gas and inertia forces.

* Angle patent owned by Pratt and Whitney.

DESIGN OF RECIPROCATING PARTS

99

2. Tension stresses due to inertia forces.

3. Tension and compression stresses due to ‘^whipping’’ or lateral acceleration of the rod.

4. Master rods in articulated systems are subjected to an additional bending stress owing to the axes of the articulated rods not passing through the center of the crankpin.

Considering these conditions in order:

1. Compression stresses are most severe at full-throttle low- speed (low-inertia) conditions, and as the connecting rod is of intermediate length in proportion to its cross-sectional area, the slenderness ratio L/k (= center-to-c enter length of the connect- ing rod divided by the least radius of gyration), usually falls

within the range in which Rankine^s column formula is most applicable. Hence critical compressive stresses may be found from

A q{L/ky

(6-8)

where P^ax = maximum gas force on the piston, lb.

A = cross-sectional area of the connecting rod at the mid-point in its length, sq. in.

Sc == allowable stress, lb. per sq. in.

L = center- to-center length of the connecting rod, in. k = least radius of gyration of the mid-section. q = coefficient depending upon the arrangement of the column ends.

Connecting-rod shank sections used in aircraft engines are most often a modified form of I or H section, but tubular sections are frequently used in articulated rods, and sometimes, when oil is supplied under pressure to the piston-pin bearing, a hollow I section [Fig. 6-7 (C)] is used. In any event, the desired end is a rod of adequate strength and stiffness with a minimum weight.

100 AIRCRAFT ENGINE DESIGN

In determining the shank dimensions, account should be taken of the fact that the end supports for the connecting rods are essentially free in the plane of rotation but fixed in the plane containing the crankpin and piston-pin axes. With. free ends,

the deflection of the rod under load will be as in Fig. 6-8 {A), whereas with fixed ends the deflection of the rod will be as in Fig. 6-8 (jB) . As the distance between the two inflection points m and n, Fig. 6-8 (JB), is one-half of L and since the stress in the rod varies as the rod must be four times as strong in the plane of rotation as in the plane of the crankpin and piston-pin axes.

. For carbon-steel rods, Sc should not exceed 25,000 lb. per sq. in.; for alloy- steel rods. Sc should be held to less than 35,000 lb. per sq. in. For aluminum-alloy rods. Sc should be about 12,000 lb. per sq. in.

Values of g = 1/10,000 (for free ends) and q == 1/40,000 (for fixed ends) maybe used. Values for moment of inertia and radius of gyration for several useful geometric shapes will be found in Table A3-1.

For I and H sections, a small draft angle (7 to 10 deg.) must be provided to permit forging, although this will be removed when the rods are machined all over, and usually all corners are rounded with fillets. These details make it difficult to determine the moment of inertia of the section, and to simplify the pro- cedure, an equivalent section without draft or fillets is frequently used for determining over-all dimensions. Helative proportions of equivalent shank sections useful for this purpose are shown in Fig. 6-9.

2. Greatest tension in the connecting rod will occur (for normal operation) at highest speed at the beginning of the suction stroke. Still more severe conditions can exist in high-speed closed- throttle dives. Maximum tension may be found by means of Eq. (4-8). By using conservative values of stress, i,e., values the same as for column effect in the rod (case 1 above) and investi-

Fio-. 6-8. — Connecting- rod deflection (exagger- ated) . {A) In the plane of

rotation, (J5) in the plane of the piston and crankpin axes.

DESIGN OF RECIPROCATING PARTS

101

gating for rated speed, usually the strength will be sufficient for any diving condition encountered. Ordinarily, a rod strong enough as a column is adequately strong in tension.

3. Whipping stresses are obviousl^^ greatest at highest speeds. These stresses are due to centrifugal force on the body of the connecting rod, and, as the forces act parallel to the crank arm, they tend to bend the connecting-rod shank. Magnitude of

the maximum bending mo- ment may be found from methods outlined in refer- ences 4, 9, and 11, but ordinarily, whipping stresses need not be inves- tigated in aircraft engines as they are well below the maximum stresses due to the gas force on the pis- ton.^ Hence, a connect- ing-rod shank section adequate for column con- ditions (case 1 above) will be strong enough to

y

‘-y-r- h ^	I — ' i r<- ^
^ 1 !	"'1-1 I
L r_	1 t
) '7"Se	-b—A / ^.ch'on '■od xT ^o9xT

-- J=h

-b — <

H

Y

"N^SecNon b=6fo 7 xT N-9/0//XT X-X -Neufrcil axis, free 'end column Y- Y -Neutral cfxis^ fixed -end column

Fig. 6-9. — Equivalent mid-length connect- ing-rod shank sections representing usual proportions in aircraft-engine practice.

withstand the maximum whipping stresses. This may not be true for very high-speed automobile racing engines, however.

4. Bending stresses in the master rod of an articulated-rod system due to the forces in the link rods not passing through the center of the crankpin are ordinarily not critical because of the small distance between the line of these forces and the crankpin axis. The conventional practice of tapering the master-rod shank, f.e., increasing the cross section toward the crankpin, usually provides an adequate safeguard against critical stresses in the master rod owing to forces in the articulated rods. In cases where extremely light weight is desired, it may be advisable to investigate these bending stresses, howcA^er. The method suggested in reference 4 may be used for this purpose.

In general, for conventional aircraft engines, a connecting-rod shank section adequate for case 1 above will be amply strong in

tension, whipping, and bending due to articulated rods. In tapering the shank section, care should be taken to avoid reducing the section near the piston pin to a point where it becomes critical.

102

AIRCRAFT ENGINE DESIGN

6~9. Connecting-rod Cap Bolts. — When a one-piece crankshaft is used (Figs. 5-11, 5-12, 5-13, and 5-16c), the big end of the con- .necting rod must be made in two pieces in order to get it onto the crankpin. In place, the two parts are held together by two or four bolts usually called cap holts. subjected

> tensile stresses when the rod is under tension. The maximum tension occurs at maximum speed at the start of the suction stroker This tensile force is due to the inertia of the reciprocating parts plus the centrifugal force due to the rotating parts, since these forces act in the same direction at the start of the suction ~ The reciproi^a ting force may be found by means of Eq. (4-8), and the centrifugal force may be calculated by Eq, (5-1). The reciprocating weight may be taken as the sum of the weights of the piston, piston rings, piston pin, and one- third of the weight of the connecting rod, or the value found in item 2, ’Suggested Design Procedure, p. 56, (from Figs. Al-3 and Al-4) may be used. The centrifugal weight may be taken as two-thirds of the weight of the connecting rod minus the weight of ^the cap, ^or (for radials) the rotating weight may be the value you have used in calculating bearing loads (Fig. Al-5).

The diameter of the cap bolts may be found by using an allow- able tensile stress of about 20,000 lb. per sq. in. Connecting-rod bolts should conform to S.A.E. standard dimensions and materials whenever possible (see Table Al-17). S.A.E. 2330 steel is one of the most commonly used aircraft-engine connecting-rod cap- bolt materials.

6-10. Connecting-rod. Ends. — Connecting-rod ends provide the necessary backing for the bearing metal and transmit the loads to the bearing pins. In addition, they conduct away some of the heat generated in the bear