D D C J2 FOREIGN TECHNOLOGY DIVISION 00. ihseitütslü APR PTD-MT-2'4-3i48-68 ON THE EQUATION OP RELATIVE WEIGHTS OF AN AIRCRAFT. N. A.

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1 (- l.-. PTD-MT-2'4-3i J2 FOREIGN TECHNOLOGY DIVISION 00 «3 ON THE EQUATION OP RELATIVE WEIGHTS OF AN AIRCRAFT by N. A. Fomln ii D D C APR 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

2 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

3 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 postedited 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.

4 DATA NANDUN6 PACI OWACCIMION NO. TP8f)017O2 t^oocumtnt COC TITLl ON THE EQUATION OF RELATIVE WEIGHTS OF AN AIRCRAFT TOPIC TAGS aircraft Industry, alrcrnft performance, civil aviation, flight mechanics, flight simulation, thrust to weight ratio 4>tU«JICT AHCA 01 4» AUT -o'ittco./nrmors FOMIN, N. A..fouaci i^vestlya VYSSUIKH UCHEBNYKH ZAVEDENIY A^IATSIONNAYA TEKHNIKA (RUSSIAN) ksccunitv AND OOWNGHAOING INFORMATION IfeOATC Of INFO 67» DOCUMKNT MO. TD-MT-^-3^8-68 t^pwojcct NO » COMTMOt. MANKINCfl t>>mkaoch CcASN.(V. CL, 0 NO:;E UNCL T^niCL/rAAMC NO. 18B CONTRACT NO. YXUPKASEOCS T «F iff. W. wfggtsgn PUtLllHINO DATE ArBoo?o? iwpw. 02-UH/0l47/t.7/000/004/0149/013^ ABSTRACT >C>COCnAPHICAL AHCA UR Tv^e PNOOUCT Translation ACCCtSION NO. MO. o'»»ort NCVISION PRCO None 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 The four G terns on the right-hand side of this equation denote, respectively, the structural weight of the aircraft, the weight of all power equipment, the weight of fuel, and the weight of the crew, equipment, and payload. Dividing both sides of the total weight equation by G c 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

5 r ^^m^^m**. *zr BLANK PAGE m ^ t* ft / n

6 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-3 i 48-68

7 T\ r 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-3 i *8-68 ii L L^ ^d

8 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: (?,-(7 B -f Oey+Or+O.,,. (1) where G K, G C y, G T, and G C g r 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 G K 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 G C y depends on the weight of the engine, the value of thrust of the aircraft, the weight of tanks, etc. The G T depends on specific fuel consumption, range of the aircraft, its cruising speed, weight of the aircraft, etc. 1 '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

9 mm MHIMMM 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. relative weight of the propulsion system can be presented as The *.y-/'."t, (3) where t 0 is the starting trust-to-weight ratio of an aircraft with a turbojet engine and r 0 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 turbojet engine: it^^cp,^; (M and for a given range L x of flight of aircraft with a turbojet engine at M K p const and H K p var, Ä,-«/?»C n Jr-a +». (5) where s a coefficient considering aeronautical margin, R , if Ic T < 0.3, R , if 0.3 < Ic T < 0.5, u H K p, if lop < 0.3 and M < 2.0, u - 0,0009 H K p + HQirnty"* lf 0.3 < fcr < 0.5 and M > 2.0, u H K p , if 0.3 < fcp < 0.5 and M < 2.0, FTD-MT-24-3 i *8-68

10 ^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, c - drag coefficient at c = 0, D 2 x n = c /c o y ^ *i y M KÜ - Mach number corresponding to cruising speed, H K p 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" thrustto-weight ratio t 0 p (turbojet engine): (6) if duration of flight, is given, and 7 idlz5 '»" T: rtm m (7) if range is given; they permit Judging about the character of the influence of one or another parameter on the "available" thrust-toweight ratio of the aircraft. It is necessary to keep in mind that use of the formula is meaningful only for designed aircraft; to find t 0 for projected aircraft in this way is impossible, since G c 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 mim^mtjm MM

11 wm - ^^^^MMM«^^^ M^iM^M^ I; : 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 i s a new value of E n, i obtained If Ic Is Increased by Alc n. If we Increase thrust-to-welght ratio E 0, 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 Alc 1, then Rj» K g, and R^ will be changed and the equation will take the form Then S

12 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« and Af M l/-äl. Thus, "4-^?=^. if M Q v is given, max or (10) Equating tqp and tgn» we have MOM'«t-i, if M is given *«*e»r Tr~~ (ID

13 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, C u, r,, Lmn or /'. 4660M.,, 1 c J (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 Ar 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,

14 L 1 and \li and by 13) calculate M. Construct a curve In coordinates M 3aÄ and M MCT (FIK. v 6 1); M can be found from Its intersection with '' max a straight line drawn from the origin of the coordinates at an angle of ^5 ; M 3&n and M MCT must be taken In the same scale. M -# Fig. 1. Example of graphic solution of equation (13) The quantity M K p 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 FTD-MT-2'<-3^3-68 M f t B ^ / 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 t 0. Between points A and B the given value of L max and other things being equal cannot be obtained.

15 ^^" 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 (ll 1 ), It can be expressed: ') (15) or ««' * ' r^3 t -M^ t (i6) The "available specific weight of the structure It H p 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,) (17) for aircraft with delta wing of small aspect ratio, I» (o.049fm4 O;* /y + y) 0 + M* «+ W (18) Here Q c - in m total weight (mass) of aircraft, ß, for supersonic aircraft, 0, for heavy subsonic and transonic aircraft, ß, for transonic trans^. :»rt aircraft, PTD-MT ii ii ^^

16 m 1 1, f-yrrlffl- (' *» + v.ä, y ) - for supersonic aircraft, for subsonic and transonic aircraft, for supersonic aircraft, for subsonic and transonic aircraft, coefficient of relief of wing, n - e, z-, - e^ - Zo - 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" Ic K p 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, Fomin N. A. Proyektlrovanlye samoletov (Designing of aircraft). Oboronglz, 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