(- l.-.

PTD-MT-2'4-3i48-68

00

J2 FOREIGN TECHNOLOGY DIVISION

00

«3

ON THE EQUATION OP RELATIVE WEIGHTS OF AN AIRCRAFT

by

N. A. Fomln

ii

D D C

APR 8 1969

iHSEITÜTSlÜ

4 Rdproducod by l^o CLEARINGHOUSE

(of fadoral Scientific & Tochmcitl Inform.ilion Spflngliold V.i 22lbl }

Distribution of this document is unlimited. It may be reieaned to the Clearinghouse, Department of Commerce, (or sale to the general public.

IS

FTD-MT-24-3Ü8-68

EDITED MACHINE TRANSLATION ON Tiih EQUATION OV RELATIVE WEIGHTS OF AN AIHCHAFT

By : N . A. Komi n

THIS TRANSLATION IS A Rf NDITION Of THI OHICI- NAL FOR!ION TIXT WITHOUT ANY ANALYTICAL OR IDITORIAL COMMINT. STATIMINTS OR THIORIIS AOVOCATIOOR IMf LIIO ARI THOSI OP THI SOURCE AND DO NOT NICISSARILY RIRLICT THI POSITION OR OPINION OP THI PORIION TICHNOLOOY DL VISION.

PRCPARCD RYi

TRANSLATION OlVISION PORIICN TICHNOLOCY DIVISION WP-AP». OHIO.

FID-MT- :^I---^B-6M Date .'(•D W 68

i

i

—w»^ m^

I tm tKTIN D

'utii; Xitioi

u OUR stniM/miuinini cudu

OUT. AVAIL uitr ViCIU.

/

This document Is a machine translation of Russian

text which has been processed by the AN/GSQ-16(XW~2)

Machine Translator, owned and operated by the United

States Mr Force. The machine output haa been post-

edited to correct for major ambiguities of meaning,

words missing from the machine's dictionary, and words

out of the context of meaning. The sentence word

ordtr has been partially rearranged for readability.

The content of this translation does not Indicate

editorial accuracy, nor does It Indicate USAF approval

or disapproval of the material translated.

DATA NANDUN6 PACI

OWACCIMION NO.

TP8f)017O2

t^OOCUMtNT COC

•TITLl ON THE EQUATION OF RELATIVE WEIGHTS OF AN AIRCRAFT

4>tU«JICT AHCA

01

4» AUT ►-o'iTTco./nrmoRs

• TOPIC TAGS

aircraft Industry, alrcrnft performance, civil aviation, flight mechanics, flight simulation, thrust to weight ratio

FOMIN, N. A. IfeOATC Of INFO

67 ••.fouaci i^vESTlYA VYSSUIKH UCHEBNYKH ZAVEDENIY A^IATSIONNAYA TEKHNIKA (RUSSIAN)

•»•DOCUMKNT MO.

■TD-MT-^-3^8-68

• kSCCUNITV AND OOWNGHAOING INFORMATION

.(V. CL, 0

YXUPKASEOCS wfggTsgn

t^PWOJCCT NO.

72302-78 ♦»•COMTMOt. MANKINCfl t>>MKAOCH CcASN

NO:;E

>C>COCnAPHICAL AHCA

UR

UNCL

T^niCL/rAAMC NO.

18B6 1326 T «F iff. W.

MO. o' »»ort

CONTRACT NO.

•ArBoo?o?9

PUtLllHINO DATE

94-00

Tv^e PNOOUCT

Translation

NCVISION PRCO

None iWPW.

02-UH/0l47/t.7/000/004/0149/013^ ACCCtSION NO.

ABSTRACT

Some applicationG of the relative weights of an aircraft and the relative weight coefficients are investigated. The entire weight (or mass) G o; an aircraft is composed of the terms

all The four G terns on the right-hand side of this equation denote, respectively, the structural weight of the aircraft, the weight of power equipment, the weight of fuel, and the weight of the crew, equipment, and payload. Dividing both sides of the total weight equation by Gc yields four relative weight coefficient terms whose sum Is unity. These coefficients are useful In determining, among other factors, certain performance and economy characteristics of cruising speeds. The author concludes that the equation of relative weights is the ba^lc equation which establishes the relationships between the flyiiJt characteristics of an aircraft and its parameters. Orig.art. has: 18 formulas and 2 figures.

AWC HS * (Test form under revision) »»•e <A*M»

—•——__i

r ^^m^^m**.

*zr

BLANK PAGE

m ^ ■ t* ■ft/n

U. S. BOARD ON GEOGRAPHIC NAMES TRANSLITERATION SYSTFM

BJock Italic Transliteration Block Italic Transliteration A a A a A, a P p F> P R, r B 6 B 6 B, b C c C c G, c B ■ 3 $ V. v T T T m T, t r r r $ G, g y y y y U, u D, A ü 9 D, d o 4> 0 * F, f E e E t Ye, ye; E, e» X X X X Kh, kh M m M OK Zh, zh u u u H Ts, ts 3 « 3 1 Z, z H M V V Ch, ch H K H u I, i m 111 Ul m Sh, sh n A a a Y, y m 111 Ui H Shch, ßhch K K K K K, k •b \ ■b % n

n n n A L, 1 bi U bl u Y, y M M M M M, -n b b b h i

H H H M N, n 3 > 3 9 E, e 0 o 0 0 0, o 10 » K> » Ya, yu n n n n Pi P fl X X M Ya, ya

* ye initially, after vowels, and after >, L; je elsewhere. wKen written as Ö in Russian, transliterate as yö or e. The use of diacritical marks is preferred, but such marks may be omitted when expediency dictates.

FTD-MT-2iJ-3i48-68

—

r

T\

Mf''<*••••«..■«

POLLWIiQ ARE THE CORRESPONDIMG RUSSIAN AND ENGLISH

DESIQMATKMS Of THE TRIGONOKETRIC FUNCTIONS

Rusilan

•in 001 tg otg MO OOMC

■h oh th oth ■eh otoh

arc •in •ro 00« arc tg arc otg arc •00 arc OOMO

arc •h arc oh arc th are oth are •oh are oaoh

ret If

Englleh

•in cos tan cot sec CiC

alnh cosh tanh coth Mch oseb

•in CO«

Un" cot ••e CBC

•inh-J co^h"J ttnh"1

coth"1

••oh"1

c^eh"1

curl log

PTD-MT-2M-3i*8-68 ii

L

L^ ^d

1

ON THE EQUATION OF RELATIVE WEIGHTS OF AN AIRCRAFT

N. A. Fomln

The total weight (mass) of an aircraft is composed of several

parts with distinguishing features:

(?,-(7B-f Oey+Or+O.,,. (1)

where GK, GCy, GT, and GCgr are, respectively, the structural weight

of the aircraft, the weight of all power equipment, the weight of

fuel, and the weight of systems, equipment, crew, and payload.

The GK depends on a number of parameters of the aircraft and

its parts, mainly on wing loading p, wing aspect ratio A, coefficient

of rated overload n^, the weight of the aircraft, etc.

The GCy depends on the weight of the engine, the value of thrust

of the aircraft, the weight of tanks, etc.

The GT depends on specific fuel consumption, range of the aircraft,

its cruising speed, weight of the aircraft, etc.

'The G in general is not directly connected with the parameters

and characteristics of the aircraft or its weight and is determined in

accordance with technical requirements, depending upon the type of

aircraft and its function.

FTD-MT-2^-3^8-68 1

mm

MUWMIMtw«

If we divide both sides of (1) by Q„ we wli: obtain the equality

- I—!■+J«rl-5f + ieKi (2)

to which attention was turned for the first time by V. F. Bolkhovltdinov [1]; it is called the equation of relative weights of an aircraft, where

«■""jr-i ••»""■Jj • *f"""^~'» ^ctr — ■ ■ are the relative weights of the

structure, propulsion system, fuel, equipment, crew, and loads. The relative weight of the propulsion system can be presented as

*.y-/'."t, (3)

where t0 is the starting trust-to-weight ratio of an aircraft with a

turbojet engine and r0 is the specific weight of propulsion system.

The relative weight of the fuel load RT can be expressed as

follows: for a given duration t' of flight of an aircraft with turbo-

jet engine:

it^^Cp,^; (M

and for a given range L x of flight of aircraft with a turbojet engine

at MKp ■ const and HKp ■ var,

Ä,-«/?»Cn Jr-a—+». (5)

where s ■ 1.15-1.20 - a coefficient considering aeronautical margin,

R - 0.00145, if IcT < 0.3, R - 0.001, if 0.3 < IcT < 0.5, u - 0.0009 HKp, if lop < 0.3 and M < 2.0, u - 0,0009 HKp + HQirnty"* lf 0.3 < fcr < 0.5 and M > 2.0, u ■ 0.0009 HKp + 0.09, if 0.3 < fcp < 0.5 and M < 2.0,

FTD-MT-24-3i*8-68

MHIMMM

^mm 1 ■ —

^ - coefficient, considering the influence of speed of flight on

specific fuel consumption,

C - coefficient considering the influence of speed of flight on

engine thrust,

ü - relative air density,

t' - time of flight (for Formula 4),

t" - time of acceleration [takeoff run] (for Formulas ^ and 5),

CTQ — specific fuel consumption, 2 c - drag coefficient at c = 0, Dn = c /c xo y ^ *i y

MKÜ - Mach number corresponding to cruising speed,

HKp — raean value of cruising altitude.

Using the equation of relative weights (2) and the given equalities

(3)-(5) it is possible to obtain expressions for "available" thrust-

to-weight ratio t0p (turbojet engine):

(6)

if duration of flight, is given, and

7 idLz5 '•»" T:— rtMm (7)

if range is given; they permit Judging about the character of the influence of one or another parameter on the "available" thrust-to- weight ratio of the aircraft. It is necessary to keep in mind that use of the formula

is meaningful only for designed aircraft; to find t0 for projected aircraft in this way is impossible, since Gc is a quantity dependent of P ocy Analysis of (6) and (7) permits Judging about the qualitative influence of different parameters on t Op*

FTD-MT-24-348-68

mim^mtjm ■■■■MM

I; ■:

wm

Quantitatively this Influence can be determined with help of the

formulas

^-5^

v. J

(8)

*' C' L' r where t,..-^-. (|M^L, ^■■JSSL, «4M-iL; ft is a new value of En, ••i

obtained If Ic Is Increased by Alcn. If we Increase thrust-to-welght

ratio E0, Installing on the aircraft two engines Instead of one, at

L„«v ■ const, Q^ ■ const and Kl • e,I{v: max C3r H i K

7' *-(*'«'i+'*») 0.5 *,

to— + V«

The formulas In (8) can easily be obtained from the equation of

relative weights:

i + ^+^ + ii-l.

If R, Is Increased by Alc1, then Rj» Kg, and R^ will be changed and the

equation will take the form

Then S

- ^^^^MMM«^^^ M^iM^M^

Setting P' = P , we will obtain

-<-<^)

or

'.'-'-•('-A) (9)

For actual realization of an aircraft with a prescribed M number of

horizontal flight to be possible requires first of all equality of

"available" and "required" thrust-to-welght ratio. The latter can be

expressed on the basis of the equalities

Af«..-0.0148

and

Thus,

AfM-0.012 l/-ÄL.

or

"4-^?=^. if M Qv is given, max

(10)

MOM'« t-i, if M is given

Equating tQp and tgn » we have

*« *e»r

—Tr~~ (ID

•■ v

and

'«r (11')

Prom this we will obtain equations with respect to M which enabling us

to determine that value of M„0„ or M,.- which Is possibly and practical: max «p realizable for an aircraft with the selected parameters:

*«. it*, p, C't, Cu, r,, Lmn or /'.

4660M.,,1cJ(r# + «t<AC^O -*/»(!- A.-*,.r)-0. (12)

W^O^V^-Af^lpd - J.-Ü« -a) + »WCuLmnpYcZB]-*. (12 •)

Any greater value of M can be found with decrease

Lmn, km, '%, Cf, , CM,, t'.

Any smaller value of M will provide the possibility of Increasing

LmM i A«»r i • •

Solving the first equation (12), we will obtain for M at a given

duration t'

(13)

Note. For determination of the value of M It Is possible to max use graphic procedure. Pursuing several values M, determine f,, c ,

1

and \li and by 13) calculate M . Construct a curve In coordinates

M3aÄ and MMCT (FIK. 1); M can be found from Its intersection with v 6 '' max a straight line drawn from the origin of the coordinates at an angle

of ^5°; M3&n and MMCT must be taken In the same scale.

M-#

Fig. 1. Example of graphic solution of equation (13)•

The quantity MKp can be found also, using a graphic solution (Fig. 2), taking the following functions for plotting of curves:

eWOAfi^r.-l,

and

(1^)

•..«,

I

MO

• •

/ 1 M f ^

B

t

M

Fig. 2. Example of graphical solution of equation (1^) . In points A, B, and C a given value of L^

can be obtained, other things being equal and wltb corresponding values of MKP and t0. Between

points A and B the given value of L and other max things being equal cannot be obtained.

FTD-MT-2'<-3^3-68

L

^^"

The point of Intersection of these curves on the graph In coordinates

M, 6,, and op will determine the unknown value M .

Prom (13) and (14) It Is easy to see that to each M, at constant

values of all parameters, there will con^spjnd Its own tc^, which can

be called the "necessary" specific weight of the structure of the

aircraft. Using (11) and (ll1), It can be expressed:

') (15)

or

««• ' •*•' r^3 t-M^—t—• (i6)

The "available specific weight of the structure It Hp Is the weight

which can be obtained at given strength of the structure and selected parameters of wing, fuselage, etc. It can be expressed by these

formulas:

for aircraft with sweptback wing,

i

^-(o.Otfw^^l/I + .^d -HP^m + p,) + 0.065. (17)

for aircraft with delta wing of small aspect ratio,

I„ » (o.049fM4 O;* |/y + y) 0 + M* « + W + 0.066. (18)

Here Qc - in m total weight (mass) of aircraft,

ß, ■ 0.07-0.09 - for supersonic aircraft, 0, ■ 0.065-0.08 - for heavy subsonic and transonic

aircraft,

ß, ■ 0.08-0.115 - for transonic trans^. :»rt aircraft,

PTD-MT-24-348-68 8

ii ii —^^—

m ■ 1

1,2-1.3

- 0.27

- 0.15

f-yrrlffl- ('•••*» + v.Ä,y) - n -

e, —

z-, -

e^ -

Zo -

for supersonic aircraft,

for subsonic and transonic aircraft,

for supersonic aircraft,

for subsonic and transonic aircraft,

coefficient of relief of wing,

wing taper,

portion of fuel In wing,

relative coordinate in fractions of semlspan of CG of fuel in wing,

portion of weight of propulsion system in wing,

relative coordinate in fractions of semlspan of CG of power plant.

The major problem of designing reducd to ensuring the equality

of "available" IcKp to "necessary" RK-.

On the basis of the material outlined above it can be concluded

that the equation of relative weights of an aircraft is the fundamental

equation with which the relationships between the flight characteristics

of an aircraft and its parameters are established.

Literature

1. Bolkhovltdlnov V. F. Puti razvltlya letatel'nykh apparatov (Paths of development of aircraft). Oboronglz, 1962.

2. Fomin N. A. Proyektlrovanlye samoletov (Designing of aircraft). Oboronglz, 1961.

3. Badyagin A. A., Cvrutskiy Ye. A. Proyektlrovanlye passazhlrskikh samoletov s uchetom ekonomlkl ekspluatatsil (Designing of passenger aircraft, taking into account economics of operation). Mashlnostroyenlye, 19o^.

Received 25 July 1966

PTD-MT-2^-3^8-68