THE EFFECT OF AIR TEMPERATURE UPON THE RATE OF CLIMB OF AN AIRPLANE EQUIPPED WITH A CONSTANT SPEED PROPELLER

C I R C U L A R 1

M A Y 1 9 4 8

THE EFFECT OF AIR TEMPERATURE UPON THE RATE OF CLIMB OF A N AIRPLANE EQUIPPED

WITH A CONSTANT SPEED PROPELLER

C I V I L A V I A T I O N O R G A N I Z A T I O N MONTREAL CANADA

This Publication i s isLmed i n I h z l i s h , fiellch and Spanish.

Published in lbntreal, Canada, by the I n t e r n a t i o n a l C i v i l Aviation Organization.

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I Z k O Circular 1

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³

TABLE OF COhTTEMTS

Page

Derivation

...

⁹

...

General

9 ...

Brake Horsepower 10

...

Propulsive Efficiency 11

...

Thrust ITorsepowcr Required 14 Discussion

... ¹⁶

General

...

¹⁶

OperaLion at a Fixed Throttle SettinP

... ¹⁶

Liquid Cooled Engine Installation

...

¹⁸

Propeller Characteristics

...

²⁰

Carburetor, Cooling, and Outside Air Temperature

.

²¹ Possible Simplifications

...

²¹

Example

...

22

Concluding Rernarks

...

²⁸

...

Table I 30

...

Figure 2 32

...

Figure 4 34

...

Figure

5 35

~ e g e 4 I C A O C i r c u l a r 1

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^,43/1

REFERERCES

a. Wright A e r o n a u t i c a l Corporation "Engineering Notesu

-

(Second E d i t i o n )

b. Pratt and Whitney S p e c i f i c a t i o n No. 5854, Curve No.

T-461

c. NACA Technical Report No. 642 d . Plight Engineering Report No. 10

ICAO C i r c u l a r 1

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F O R E W O R D

T h i s i s t h e f i r s t of a new s e r i e s of ICAO p u b l i c a t i o n s . The I C A O C i r c u l a r s w i l l t r e a t of many d i f f e r e n t s u b j e c t s , b u t t h e y w i l l have t h e cormon purpose of d i s t r i b u t i o n g i n f o r m a t i o n S e a r i n g upon t h e p r o g r e s s of I C k O 1 s work more widely than would be p o s s i b l e f o r t h e o r d i n a r y s e r i e s of documents.

The p r e s e n t C i r c u l a r i s a r e p u b l i c a t i o n of a n a t i o n a l s t u d y on a m a t t e r t h a t h a s a l r e a d y been t h e s u b j e c t of one

s p e c i a l I C A O meeting and t h a t w i l l have t o be f u r t h e r d i s c u s s e d i n f u t u r e meetings

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t h e e f f e c t of temperature upon t h e perform- ance of a i r c r a f t and upon t h e i r a l l o w a b l e o p e r a t i n g weights.

F u t u r e c i r c u l a r s w i l l compare and a n a l y z e n a t i o n a l p r a c t i c e s i n t h e a d m i n i s t r a t i o n of t h e v a r i o u s phases of s e r v i c e t o a i r navi- g a t i o n and i t s r e g u l a t i o n . Others w i l l r e p o r t t h e d e g r e e of implementation by t h e n a t i o n s of t h e world of I C A O ' s S t a n d a r d s and o t h e r recomraendations r e s u l t i n g from I C A O m e e t i n ~ s ,

A g r e a t work h a s been i n i t i a t e d i n t h e p a s t t h r e e y e a r s through t h i s O r g a n i z a t i o n . The n r o g r e s s t h a t h a s been made,

and t h a t w i l l be made i n coming months, i s o f i n t e r e s t f a r beyond t h e l i m i t s of t h e Governmentst a e r o n a u t i c a l s e r v i c e s . The

r e c o r d s of p r o g r e s s concern t h e whole a i r c r a f t - o p e r a t i n g world;

t h e y d e s e r v e a wider d i s t r i b u t i o n t h a n t h e y have had; and t h e s e r i e s of I C A O C i r c u l a r s , o f which t h i s i s 1?0, 1, a r e designed t o make i t p o s s i b l e f o r them t o r e c e i v e i t ,

Edward Warner

Page 6 I C A O Circular 1

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^{A N / 1}

The

r e p o r t y e p ~ o q u c s d ;In this

CSrcylar wss

f P r q O

issued

by t h e

Civil

A @ ' r o n a ~ t i c @

AdmiaiatratS~p

of

ths PnStsd

S t a k e s o r Arnel?$ca,. as

Flight I$n#$naarlrxg

Report ^{N O *} $2, sn't;$tled

'!The sffact o f a i r temperqtqra upon t h e r a t e o f c2imQ

QP

an aeroplane equipped

with

a c o n s t a n t speed p r o p e l l e r f l . Conse-

quent upon recommendatians made by t h e A$~woyth$,ness pivision,

t h e report was subnittad

to

I C A Q

f ~ r

publication, has

been

translated by the B e d r e t a r t a t i n t o French and Spanish and is being published as an I C A O C l p c u l a r in English, French and Spanish.

ICAO Cjrcular 1

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This report covers the derivation of equations by means of which to calculate the effect of air temperature upon the rate of climb, applies the equations to a typical airplane, and discusses the significance of the results of this application.

The derivation is based upon the fundamental equation for rate of climb; the generally accepted relationship between the brake horsepower output of an engine and the temperatures of the air involved in the carbureting, cooling and supercharging pro- cesses; and upon a rational treatment of the effect of outside air tempersture upon propeller aerodynamic characteristics, No new experimental data are contained in this report,

The equatirns are believed useful for the purpose of cal- culating the effect of temperature upon a rate of climb de-

termined by testing at a given temperature and require for their application the establishment of certain engine char-cteristics normally available in the standard engine power output and certain propeller characteristics.

THIS PAGE INTENTIONALLY LEFT BLANK

ICAO C i r c u l a r 1

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9

DERIVATION

The r a t e of climb of an a i r p l a n e i n f e e t per minute may be expressed by means of t h e f o l l o w i n g e q u a t i o n s :

where:

W = A i r p l a n e weight i n pounds THPa = t h r u s t horsepower a v a i l a b l e THPr = t h r u s t horsepower r e q u i r e d

NOW: THPa = BHPS

- - -

_{( 2 )}

where :

BHP = brake horsepower o u t p u t of e n g i n e ( s )

r~

= p r o p u l s i v e e f f i c i e n c y and :

where :

p =

Mess d e n s i t y of a i r i n s l u g s / c u . f t . f ^I A i r p l a n e p a r a s i t e a r e a i n sq. f t . V A i r p l a n e a i r s p e e d ( t r u e ) i n f t . / s e c .

e = A i r p l a n e e f f i c i e n c y f a c t o r ,

-

^CL*

~ ~ C D J

b

=

A i r p l a n e wing span i n f e e t

Page 10 ICAO Pircular 1 r AN/1 The above equations indicate that, in order to establish

t h e effect of air temperatu+e upon the rate of climb, it is ne- c e s s a r y to consider the effect upon the terds involved in

equations (2) and

(3);

v i s i , B H P , q ,

*'

~ 5 0 n p _2w2 a b F

; separa- ' 1 00

t e l y . This is done immediately heri)~nder, Brake Horsepower

=

BHP

~ h k e%perimentaZ 4aka a v a i l p b l e indicate there ' a r e at least two separate , e f f e c t s crf

air

t e m p s r a t u r a 5 u p P h the power output of an engine bpsrating at a g i v e h r n a n i f ~ l d pressure, r p ; ~ ,

and

mixture strength. Qne of' these ,maqifast,s i t s e l f

in a

reduction oP power with i n c r e a s e in

the

tappcratqre ~f

tbe

a4r

mtsrtsg the

carburetor The magnitude o f

the

e f f i e ~ C $8 ~ ~ d l n a r l L y

e x g ~ e B a e d by

w a r = of the following ra$wtitln?

r the absolute temperatme of &he ca~byretor air,Kncler t h e c o n d l t i o n g prpdqc$n$ $ 6 ~ ~ (ie:

st?

i s the tegpp~s$ure Q degreas

pahrspheit

~ l u a 459.43

T

='

t h e , absaluls temperature

of

t h e garbwetor

, air w d e r the conditions producing BHP.

The second such e f f e c t is an observed reductiop in power with increase in the temperatwe of $he air-entering

the

cooling process f o r an a i r coolQd esgine. $ l t h o u g h , n o t ss w e l l supported by the e x p e r i m e n t a 1 , e v f d ~ e e as in the case of carbuyetor air, the magnitude of this effect is oYdinarily expressed:

where :

Fc

and ?

= the a b s o h t e t e m p e r a t u r e of ^the eooling air

b u t a r e o t h e r w i s e as d e f i q e d above.

~1 \

The primary eCfect sf temperature upon the brake horsepower is theg:

BHP =BHP,@II(~) ,

- ^{- - - - -} - - - - - ^-

⁽⁴⁾

c

T r

I C A O C i r c u l a r 1

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^{A N / 1} Page 11 P r o p u l s i v e E f f i c i e n c y

=q

If p r o p u l s i v e e f f i c i e n c y , T

,

^be p l o t t e d a s c o n t o u r s upon t h e s t a n d a r d power c o e f f i c i e n t v e r s u s advance r a t i o c h a r t

(Cg V S . V

-

^@

^p

^{) ,} t h e r e s u l t i n g diagram ( s e e Fig. 1 f o r example, ND

which h a s been prepared from t h e d a t a of Ref. ( C ) w i l l i n d i c a t e , i n t h e r e g i o n r e p r e s e n t a t i v e of c l i n b i n g c o n d i t i o n s ( i e : compa- r a t i v e l y h i g h v a l u e s of C p and low v a l u e s of V ) , t h a t , a t a

PD

c o n s t a n t v a l u e of

L,

an i n c r e a s e of C p i s accompanied by a ND

d e c r e a s e i n e f f i c i e n c y and a l s o t h a t a t a c o n s t a n t v a l u e of C p , an i n c r e a s e i n i s accompanied by an i n c r e a s e i n e f f i c i e n c y .

ND

T h i s s i t u a t i o n may be summarized by t h e f o l l o w i n g e q u a t i o n s :

\

I t i t can be shown t h a t t h e v a l u e s of A and B , s o d e f i n e d , remain r e a s o n a b l y c o n s t a n t over t h e r a n g e s of C p and -V r e s p e c t - i v e l y r e s u l t i n g from any temperature change which must ND be d e a l t w i t h and a l s o t h e v a l u e of A i s s u b s t a n t i a l l y independent of any v a l u e of jT- and t h a t of B s u s b t a n t i a l l y independent of any v a l u e of C p e i t h e r of which must be c o n s i d e r e d , t h e n t h e r a t e a t which MD e f f i c i e n c y changes with both C p and i s s u b s t a n t i a l l y :

!ID

I n o r d e r t o i n d i c a t e t h e n a t u r e , magnitude and v a r i a t i o n of t h e v a l u e s of A and B w i t h C p and

E,

' ~ i g u r e s 2 and 3 have been prepared from t h e d a t a of F i g u r e 1. MD These d a t a i n d i c a t e t h e assurnption of a p p r o p r i a t e c o n s t a n t v a l u e s ' o f A and B t o be a r e a s o n a b l y c l o s e approximation t o t h e a c t u a l v a r i a t i o n o f ? . ( T h i s i s f u r t h e r d i s c u s s e d below.)

Page 12 ICAO Circular 1

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and t

Also:

wkier a t

ie:

P

=

atmospheric pressure

T +: absolute air teraperature

At a constant indicated airspeed:

N o w D is a constant for a given airplane and with a constant speed propeller, N is also constant. T h e effect of temperature upon p has been separately considered above. S i n c e P

=

^{BHP, the effect}

of temperature upon C p and

E

is therefore as follows:

ND BHP

and;

ICAO Circular 1

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^{AN/l Page 13}

or;

-

^{To which appears} likely always

-

^{- 9}

T to be nearly true:

and r

also t

and :

Substituting these values of dCp and into equation

(6),

the HD

rate of change of propulsive efficiency with absolute temperature ratio is obtained as follows:

and efficiency as a function of the absolute temperature ratio nay be obtained by integration thus:

B- V

To

k

=

a constant

Page 14 ICAO Circular 1

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"then :

Therefore:

ie:

Substituting this value of k into the above expression f o r 3 :

Thrust Horsepower Reauired

It has been shown above that:

and, at constant indicated airspeed, that:

Substituting these values into the expression for thrust horse- power required (equation

(3)):

3

ICkO Circular 1

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^{AN/^} Page 15 ie:

However, when THPro, C

=

Co, BHP

=

BHPo, and 7)

= ?I

^0. S u b s t i t u t i n g these values i n t o e q u a t i o n ( 1 ) a n i s o l v i n g f o r T H e o g i v e s :

and, t h e r e f o r e from equation

( 9 ) :

Rate of C l i m b

=

C

A11 or' t ^tc elements involved i n t h e basic climb equation (I)

have been r e l a t e d t o temperature by e q u a t i o n s (4), (8), and (10).

When t h e s e a r e substituted _{i n t o} e q u a t i o n ⁽¹⁾ t h e following r e s u l t s :

I-

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DISCUSSION General

Equation (11) is strictly applicable to the rate of climb for an airplane equipped with an air-cooled engine and a constant speed propellcr when operated at a constant indicated airspeed and under such powerplant operating conditions as to make possible the maintenance of constant manifold pressure and engine rpm and also when and only when the ratio of initial and final values of outside, carburetor, and cooling air temperatures (absolute) are identical and the rate of change of propulsive efficiency with advance ratio at constant power coefficient is constant over the range of advance ratio produced by any temperature change for which it is de;ired to apply the equation.

It cannot be spplied in the case of an airplane not equipped with a constant speed propeller.

TI-ie remainder of the limitations upon the general applicabilit of equation (11) are discussed below where certain modifications are derived or sugyested in order to obviate these limitations or to simplify the equation to improve its practicability.

Operation at a Fixed Throttle Setting

For an unsupercharged engine operating at a fixed throttle setting the manifold pressure is substantially independent of Carburetor air temperature. The limitation stated above, that the manifold pressure remain constant, is met and equation (11) is applicable.

For a supercharged engine at fixed throttle, however, the effect of carburetor air temperature is such that an increase in temperature is accompanied by a reduction in manifold pres::ure, Page

31

of Reference a) indicates the nature of the relation, of the ratio of suparcharger outlet to inlet pressure to the tempera- ture of the carburetor air. The outlet pressure is substantially the manifold pressure and the inlet pressure, the atmospheric

pressure. The slope of the lines appearing in the referenced dia- gram may therefore be taken to be the rate _{o f} change with respect to carburetor air temperatare of the ratio of manifold to atrnos- pheric FressuItt,s. i~;:

The diagram indicat,es that. this slepe is a I'urlctiori of both the pressure ratio and t,, V a l ~ s s of this slope :;ave keen read at values of tc

=

0 0 , 500, and 1 0 C o ~ and at the corresponding values of the pressure ratio and appear in Figure 4 as:

I C A O C i r c u l a r I

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^{AF/1 P a ~ e 17}

If t h e magfiitade of t h e changes i n t h e t e m p e r a t u r e and the re- s u l t a n t changes i n t h e p r e s s u r e r a t i o which must be d e a l t w i t h be assuined sinall enough t h a t t h e ove r a t e remains s e n s i b l y constant when the t e m p e r a t u r e chan, L , t h e n :

d(s)=

^{a constant = E}

Tc or:

The _above i ; s s c r i o e d { i i a r ~ g e in rAlar~ifo13 pressure is of course accompanied 1 ~ - correspor,dir,ir c2l;nge In t h e b r a k e horsepower out- p u t of t h e (?r6, l n e , The s t a n d a r d sea lt?v91 p o w ~ r chart of BHP vs.

MP

6'

N NndfcGtos tilst t h e r 2 t 2 ';t _111~ickr t 1 l i : i ch;~n{;e i n power t a k e s p l z c e is, a t cons4,slit, c n g i n c r p n , ⁴ ~ c l r 1 : ; t ~ i . t 11hich ma;r 1,e r e a d c l i r c e t l y from the; & I ; - r t zncl tl,,~

-

^{~ t , l tz:'a c h ~ ri} a r s u n e s t h i s r a t e a c o ~ s t ~ ~ n t ; ie:

o r :

S u b s t i t u t i n g th's ~ a l u e ci' db;F i n t o er;uc:liori (12) g i v e s : dIil-iP

=

pEFdT,

I n t e g r a t i n g :

When Tc

,

^{T c o 7 EHP = BHPo, and,}

S u b s t i t u t i n g t h i s v a l u e of kl i n t o e q u a t i o n (13) g i v e s : BHP pEi.'Tc 4- BHP,

-

^pEFTco

Page

18

ICAO Circular 1

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and combining this with equation

(4)

previously derived, the total e f f ~ c t of temperature upon BHP becomes, for the case under considera tion:

I-- -I

where:

p ^+. atmospheric pressure in inches of mercury.

E

=

d.

My

p which may be read from Figure 4 dTc at the initial values of PIP, p, Tc.

F = dBIJ which may be read from the engine power chart for the initial

values of M,P. and M.

If equation (ha) be substituted for equation ( 4 ) ^{in the deve-} lopment of equation (11), the following results:

4

Liquid Cooled Engine Installation

.

The temperature of the air entering the cooling process in a liquid cooled engine affects the power output of tke engine only in so far as it affects the temperature of the coolant. The temper- ature of the coolant is, however, usually thermostatically con-

trolled and remains substantially constant once the engine is warmed up and operating equilibrium established. Under such con- ditions the power output would be independent of cooling air tenper*

ature and the term in equation

(4)

to account for this temperature must be eliminated, leaving:

ICAO Circular 1

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^{AR/l Page 19}

BIIP

=

^BHP,

- - -

- - - ( b b ) This term must also be eliminated from the derivation of equations

(7) and ( 8 ) , ie: (see page 4)

or, making the same assumptions concerning

T

To T o c

and equation

(7)

becomes:

Then:

and equation (8):

q = ? l a + [ a c ~ o t % ) d ( , / ~

^{T o -I)--}

- - -

^(8b)

Finally, equation (11) becomes:

Page 20 I C A O Circular 1

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Propeller Characteristics

In order to indicate a region on Figures 2 and

3

appropriate to climbing flight a point i l ~ s been located on each of the figures to represent for each of the 35' airplanes of Table I the values of C P ,

TJ

a n d 7 corresponding with climb at sea levet at MET0

ND .

power at best rate of climb speed. Some of these airplanes are equipped with two blade propellers and in such cases the value of C p used in these figures is the actual value divided by CJ.70 to make it correspond with the three blade characteristics of the figures. It may be noted that all these points lie within the following limits,

Appropriate lines bounding the area contained within these limits have been drawn on Figures 1 and 2. The corners of this boundary have then been relocated to correspond with departures of outside air temperature from initial conditions such that

,,/

=

!i^{1.10 and} & These would represent temperatures of

167'~

and

- 3 9 O ~

at sea level or 1 ~ and 5

-68O~

~ at an altitude of ~ 10,000 feet respectively when To is assumed to be the standard

temperature and are probably in excess of any temperature variation likely to be encountered. The variation of the slopes,

A = and B ₌

a

within the original area is reprsscwtntive

dC P

v

d~

of that likely to be due to differences among types of airplanes while the variation between boundaries of the two extreme areas is representative of that due to the extremes of temperature variation likely to be encountered. These variations lie within the following limits:

Slope Airplane to Airplane Temperature to Temperature

ICAO Circular 1

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^{AN/1 Page 21}

These limits indicate that in order to establish values of A and B with very much precision, it is necessary to use Figures 2 and 3 or their equivalent and in any event, this may as well be done since Cpo and

1

must be known in order to apply any of the

RD ⁰

three alternative forms of equatio; (11) and these values locate an appropriate point on the figures ,1 which the corresponding values of A and B may be determined,

The extent to which the characteristics of the 6101 blade three blade propeller is representative of those of any constant speed propeller likely to be encountered is a question upon h i c h it is very difficult to shed much light. It appears desirable, however, to use the characteristics of the actual propeller if these are available particularly if great accuracy is necessary Or

desirable.

Carburetor, Cooling, and Outside Air Temperature

The temperature of the air entering the carburetor is ordi- narily above that of the outside air due either to the heat

absorbed from the engine or to a certain amount of compression in the intake process, It may also be higher due to the deliberate application of heat to prevent the formation of ice in the intake system. In most of the caseswith which the Civil Aeronautics Administration has had experience the carburetor air temperature is of the order of QOF to 1 5 O ~ above outside air temperature when the heater control is "Full Coldw. Also when full heat is applied the carburetor air temperature rarely exceeds the outside air

temperature by more than 120°~, and this heat rise tends to de- crease with increasing outside air temperature, Under most oper- ating conditions the heater is not used,

For conventional installation of an air cooled engine, the temperature of the air entering the cooling process is substantially that of the outside air, For engines buried deeply inside the

airplane strccture it appears possible that the temperature of the cooling air might be elevated by compression in the intake duct, Possible Simplifications

The only simplification of the various alternative forms of equatlon (11) which appears warranted under any likely circumstances is that made possible by the assumption already made in the deri- vation of equation

(7)

above; viz:

Page 22 ICAO Circular 1

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Upon this basis, equations (ll), (lla) and (llb) become:

EXAMPLE

(T~-T) BHP,

In order to illustrate the application of the equati0n.a~

well as the effect of outside air temperature upon the rate of climb, the variation of two typical rates of climb for the Douglas DG3-SlC3G airplane at two altitudes will be calculated over the range of outside air temperature likely to be encountered.

- - - -

^-(llat)

For this purpose the airplane will be assumed to operate at a weight of 25,2OO# and YIETO power on the operating engine(s).

The best rates of climb with both engines operating and with one engine inoperative and its propeller featliered with, in each case,

XCAQ'Circular 1

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^{AN11 Page 23}

the a i r p l a n e i n t h e "cleann configuration ( i e : wing f l a p s and -)anding gear fully retracted), each a t sea l e v e l and a t ^10,000

!feet are s e l e c t e d f o r t h e purpose, Under standard atmospheric conditions these r a t e s of climb are a s follows:

C o n f i g u r a t i o n Sea Level 10,000

'

Both Engines c ~ l ~ " ~ 690

One Engine 295 109

The engine a c t u a l l y i n s t a l l e d

In

t h i s a i r p l a n e i s a n a i r cooled engine and a t s e a - l e v e l w i l l b e assumed t o operate a t

constant manifold pressure while a t 10,000 feet a l t i t u d e t h e oper- ation w i l l be assumed t o be a t f i x e d ( f u l l ) t h r o t t l e . The sea l e v e l , v a r i a t i o n of rate of climb will also be c a l c u l a t e d assuming a l i q u i d

"cooled engine e : :onstant manifold pressure t o i l l u s t r a t e t h a t case.

The p r o p e l l ~ r ; ~ + a r r a t i o i s _16:9 and the p r o p e l l e r diameter 11'-6*.

The values o f t h e terms in the various f orrns ^of equation (11') which w i l l b e used _{f o r} the purpose and the calculations are a s

. f o l l o w s : Sea Level

p

=

2 9 - 9 2 "Hg.

BHP,

=

1050 p e r engine

MP

=

^{manifold pressure}

= tt1,5"

^Hg,

U A ' L I

-

E

= ^A

^;rm

=.

^{-.00058 ( s e e} i?ig,4)

F

.,

^dBHP

= +

^{29,O BHP/tlHg, ( s e e Ref ,b )}

dMP

Both Engines One _Engine

110 HPH

Page 24 I C A O Circular 1

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^AN11

For t h e a i r - c o o l e d engine actually installed, t411ntioa 111 a p p l i e s as f o l l o w s :

Page 26 ICAO Circular 1

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^AN/1

10,000 Ft. a l t i t u d e T o

=

4 8 2 . 8 O ~

p

=

20.6" Hg.

BHP,

=

^{960 p e r engine}

MP

=

j6tt IIg.

E

=

²

⁼

^{,00135 ( s e e Fig. 4)}

dTc

Both Engines One Engine

145

MPH 124 MPH

773 ^,660

ICAO Circular 1

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^AM/1 P a g e 27 F o r tile air cooled engine actually installed, equation ( l l a t ) applies.

T h e r e s u l t s of these caleulatfor-s appear a s curves o f rate o f climb versus air t e m ~ e r a t u r e in Figure 5*

Page 28 ^ICAO C i r c u l a r 1

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^{A N / l}

The r a t e a t which climb i s a f f e c t e d by a change i n a i r temper- a t u r e ; i e : t h e f e e t per minute r e d u c t i o n i n climb per degree F a h r e n h e i t i n c r e a s e i n temperature, may be o b t a i n e d by d i f f e r e n - t i a t i o n of t h e a p p r o p r i a t e v e r s i o n of e q u a t i o n (11)- The d e r i v a - t i v e of e q u a t i o n (11') i s :

Yhen secondary e f f o c t s a r e e l i m i n a t e d by c a l l i n g T- To

=

5OOoF and s u b s t i t u t i n g t h e f o l l o w i n g t y p i c a l v a l u e :

q O =

0.70

I

t h i s becomes:

These e q u a t i o n s i n d i c a t e t h e f o l l o w i n g :

1, For a given a i r p l a n e t h e magnitude of t h e e f f e c t of a given change of temperature upon t h e r a t e of climb d e c r e a s e s - w i t h i n c r e a s e i n t h e g e n e r a l l e v e l of t h e two t e m p e r a t u r e s between which t h e change o c c u r s ; i e : t h e B f f e c t i s s m a l l e r a t c o m p a r a t i v e l y h i g h t h a n a t comparatively low temperatures. T h i s f a c t i s a l s o i n d i c a t e d by t h e c o n c a v i t y upward of t h e c u r v e s of F i g ,

5,

The e f f e c t of a t e m p e r a t u r e r i s e of 2 0 ° ~ from -20°F t o ^OOF upon t h e r a t e of climb

ICkO C i r c u l a r 1

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^{AK/P Page 2 9}

with b o t h e n g i n e s o p e r a t i n g a t sea l e v e l i s t o reduce t h e climb by 90 f e e t per minute, whereas t h e r e d u c t i o n i n climb due t o t h e same t e m p e r a t u r e r i s e from 1 0 0 ~ ~ t o 120°F i s only 80 f e e t p e r minute,

d

2 , For an a i r p l a n e c l i m b i r ~ a t a given power l o a d i n g , any i n c r e a s e i n r a t e of climb such a s i ~ h t o b t a i n from g r e a t e r aero- dynamic r e f i n e m e n t of t h e a i r p l a n e , th2.z reducing t h e power re- q u i r e d f o r l e v e l f l i g h t a t t h e climbing speed, w i l l a l s o reduce t h e magnitude of t h e e f f e c t of a given change of a i r t e m p e r a t u r e

upon t h e r a t e of climb. T h i s i s c l e a r l y i n d i c a t e d by e q u a t i o n (14).

3. A s a c o r o l l a r y of 2 above, f o r an a i r p l a n e o p e r a t i n g i n climb a t a given power l o a d i n g t h e g r e a t e r t h e r e s u l t i n g r a t e of climb, t h e s m a l l e r t h e e f f e c t of a g i v e n t e m p e r a t u r e change upon t h e r a t e of c l i v t ~ , Consider f o r example t h e curve l a b e l e d "sea l e v e l w w i t h n, e n g i n e i n o p e r a t i v e , The r a t e of climb a t a temper- a t u r e of 60'-'i i s 295 Ft,/Piin, From e q u a t i o n ( 1 4 ) t h e r a t e of

change of climb w i t h temperature i s : .295

-

z 9 3 5 ' j = -2.06 ft. per min. per d e g r e e , F a h r e n h e i t , I f , however, t h e i n i t i a l r a t e of climb were 600 f t . / m i n , r a t h e r than 295 f t . / n i n . , t h e r a t e of change would become +,600

-

^{2.355 =}

^-10755

f t . / m i n . / O ~ .

4. For a given a i r p l a n e , t h e e f f e c t o f changes i n power o r weight upon t h e r a t e of change of climb w i t h t e m p e r a t u r e i s l e s s simple. I t may be n o t e d from t h e d e r i v a t i o n above t h a t e q u a t i o n (14) s t a t e s t h e r a t e of change of c l i m b i s e q u a l t o one t h o u s a n d t h of t h e r a t e of climb a c t u a l l y a v a i l a b l e minus approximately twa and one h a l f t h o u s a n d t h s of t h e r a t e of climb which would e x i s t i f no power were r e q u i r e d f o r l e v e l f l i g h t and a l l power t h e r e f o r e a v a i l a b l e f o r climb, T h i s l a t t e r f i c t i t i o u s climb i s d i r e c t l y p r o p o r t i o n a l t o power and i n v e r s e l y t o weight. The e f f e c t of a change i n power o r weight upoh t h e r a t e of change of climb w i t h t e m p e r a t u r e t h e r e f o r e depends upon t h e r e l a t i o n between t h e s e two r a t e s of c l i m b and upon t h e e f f e c t of power and/or weight upon t h e a c t u a l rrnt,e of climb. I f , f o r example, a t e n p e r c e n t i n c r e a s e i n power i n c r e a s e s t h e a c t u a l r a t e of climb by 25$, t h e r a t e of change of ciilrlb w i t h t e n p e r a t t ~ r e i s vnaffectecl, I f t h e 10%

i n c r e a s e i n power i n c r e a s e s Co l e s s t h a n 25%, t h e t e m p e r a t u r e e f f e c t i s i n c r e a s e d ; i f C o i s i n c r e a s e d by more t h a n 25$, t h e t e m p e r a t u r e e f f e c t i s reduced. The r e l a t i o n between weight and

t h e a c t u a l r a t e of climb C o i s e s t a b l i s h e d and d i s c u s s e d i n ~ e f . ( d ) .

Page 30

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I C A O C i r c u l a r 1

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TABLE I,- PhOPELLER OPERATING CONDITIONS AT BEST RATE OF CLIMB AT SEA LFJEL AIRPLANE

1, Beech C-17-B 2. Beech D-17-S

3. Beech 18-5

4. B e l l a n c a 31-50

5.

Boeing 2 4 7 - ~ 6. Boeing S-307

7 * Boeing SA-307-B

8, Boeing A-314

9 . Douglas DC-2 (WF2B) 3. Douglas DC-2 (TWF3A) 21. Douglas DC-3 (WG102) 1 2 , Douglas DC-3 (WG102A)

2-3. Douglas DC-3 (WG202A)

14. Douglas DC-3 (P&W SlC3G)

15.

Douglas DC-5

16. G r w a n G-21-A

17, Lockheed 10-A

18. Lockheed 10-B

19, Lockheed 1 4 - ~ 2 20. Lockheed 18-07 21. Lockheed 18-08 22. Lockheed 18-50

23. M a r t i n 130 24. S i k o r s k y S-40-A 25. S i k o r s k y S-42-B 26. S i k o r s k y ~ - 4 3 - ~

27. S i k o r s k y VS-&-A 28, S t i n s o n SR-5B 29, S t i n s o n SR-8B 30, S t i n s o n SR-8C

31. S t i n s o n SR-8E

32, S t i n s o n SR-9F

- 33. S t i n s o n SR-IOC

34. \dACO EGC-7

35. VRCO EGC-8

~CAO Circular 1

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AN/^ Page 31

~QfNOaQfC\IOa~fcvOa~f~0 S?????N?NNN1111???9?

Figure

3

Page 32 ICAO Circular 1

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kN/Z

.IC;H(J C i r c u l a r 1

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~ : ; / 1 page 33

pace 34 ^:iCA3 C i r c u l a r 1

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^AIJ/L

I C A O Circular 1

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~ l ; / l P a g e

35

Variati'on of R a t z of Climb d i t 5 AS ^r' Temperature

Douglas TIC-3 - 2 I C 3 G Airplane a t 25,200 l b s . Me+a Power