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o 



CASE FILE^ 



I tt 54078 



ifJ^m^*i*a 



NATIONAL ADVISORY COMMITTEE 
FOR AERONAUTICS 



TECHNICAL NOTE 2078 



HORIZONTAL TAIL LOADS IN 
MANEUVERING FLIGHT 

By Henry A. Pearson, William A. McGowan, 
and James j. Donegan 

Langley Aeronautical Laboratory 
Langley Air Force Base, Va. 




Washington 
April 1950 



BATIOML ADYlSmi GCmaTHm FOR AERomncics 



TECBHICAl NOTE 2078 



EORlZOmiAL TAIL LOADS IS 

mimwmiSQ fligbi 

By Heiirj A- Pearson^ William. A. McGowan^ 
and James J. Donegaxt 

SI3MMAHY 



A method is glTen for determining the horizontal tail loads in 
maneuTerlng flight- The method is "based upon the assignment of a load- 
factor Yariation with time and the determination of a minimitQi time to 
reach peak load factor- The tail load is separated into Tarious comr- 
ponents. Examination of these coiDponents indicated that one of the 
components was so small that it could he neglected for most conYentional 
airplanes^ therehy reducing to a minimum the numher of aerodynamic 
parameters needed in this computation of tail loads . 

In order to illustrate the method,, as well as to show the effect 
of the main yariahles^ a number of examples are giren. 

Some discussion is given regarding the determination of maximum 
tall loads ^ maximum pitching accelerations^ and maxiincum pitching toIoc— 
ities ohtainable* 



im^OOTCTION 



The subject of maneuTerlng tail loads has receiyed considerable 
attention both experimentally and theoretically. Theoretically^ methods 
and solutions have been derived for determining the horizontal tall load 
following either a prescribed elevator motion (references 1 to 3) or an 
assigned load— factor variation (reference k-). 

The first approach has been adopted into some of the load require- 
ments where the type of elevator movement specified consists of linear 
segments whose magnitudes and rates of movement are governed 'bj the 
assigpuent of a maximum initial elevator movement consistent with the 
pilot Vs strength. The rates of movement and the time the elevator is 
held before reversing are so adjusted that the design load factor will 
not be exceeded. 



2 HACA TN 2078 

The results of reference 5 sho^y as is to "be expected^ that only 
vh^::i the aerod^iaaiiilc force eoef f iciants are accxErately loio^wn from wind— 
txmnel tests can good agreeuaant he ohtajned hetwean measxired and 
caloulated tail loads. At the design stage^ however^ only general 
aerodynamio and geoisetrio g^xiantities are arailahle and some of the more 
iBoportant stahility parameters are not toowx acourately, Thxis ^ the work 
inTolTed in the solution for the tail load following a giT^n elevator 
motion is not oonsidered to he in keeping with the accuracy of the results 
ohtained. Conseq,uentlyj there appears to he a need for an ahhreTiated 
desiga method of coiii)utiEg tail loads which, although incorporating 
approxl nations , will neyertheless he hased on the theoretical considera- 
tions of the prohlem. 

If the load— factor Yariation with time is specified and the 
corresponding tail load, eleyator angles, and load dlstrihutions are 
suhseguently determined, a simpler and equally rational approach to the 
tail— load prohlem can he loade. Although this approach has heen used to 
a limited degree (referenoe ^), several shortcomings hare limited its 
use* 

The pxirpose of this paper is to develop further the load— factor or 
inverse approach and to present a method of computing horizontal tail 
loads which is coi!i)rehensive and generally sinrple- To this end, (1) 
the shape of the load— factor curve and the mLnlmum time req.uired to 
reach the peak load factor have heen determined from an analysis of 
pull— up maneuvers that were a-vailahle, (2) the minimum time required to 
reach the peak load factor has heen determined from a theoretical analysis 
which is supported in some measure hy statistical data ohtained from a 
number of flight tests with airplanes of widely varying sizes, and (3) 
the equations relating the various quantities are presented. 



SIMBOLS 

h wing span, feet; also shape factor in equation (13) 

ht tail span, feet 

c chord, feet 

c mean aerodynamic wing chord, feet 

Gl lift coefficient (L/qS) 

C^ pitchingHiioment coefficient of airplane without 
horizontal tail (Mb/qS^) 



NAGA TH 2078 

Guj. pitchingHmoment Goefflcieirt; of Isoiatad Jaorlzoaa^ 

tail surface 

g acceleiration of grayity^ feet par secoad per sacoBfl. 

2 

1 pitohing iQomeixt of inartla^ sl-ug-f eat 

ky radlias of gyration g-bout pitcJxLog axis^ feat 

K ©i!5)lrical constant danotlrig ratio of daii5)JLng xaoiaent 

of coii5)lata airplane to daTTipiixg moioant of tail alone 

L llf t^ pounds 

2 local lift at aoj spanwlsa station 
m airplane mass, sliags (W/g) 

M moment , footr-pounds 

n airplane load factor at any instant 

N loaziiiinni increment in load factor 

q dynamic press^ore, potuads per sq.'uare foot (rP'S^j 

S wing area^ sgioara feet 

S^ horizontal—tail area, square feat 

t time, seconds 

t^L time to reach peak of eleirator daflection, seconds 

Y airplane true Telocity, feet per second 

W airplane weight, pouads 

x^ l6ngi3h l^om center of graTlty of airplane to aerodynamic 
center of tail (positiTa for conrentionyal airplanes), 
feet 

y* noxidiznensloml spaavise dimensioa (^) 



h ' HACA TH 2078 

a^b^c 1 cozistaats occurring in equatioxxB (13)., (23)^ (26)., and 

A,B,C,D,e/ (30) 

Kj^yT^yKo po3astants occurring in basic differentla.1 eq.*uation 

(see eqiiation (3) and table I) 

A. time to reach peak load factor., seconds 

p ' loass density of air^ slxags per cubic foot 

T)^ tail effioiency factor (q^t/o.) 

a- ^ing angle of attack., radians 

a average angle of attack of horizontal stabilizer^ 

radians 

o^ tail angle of attack., radians 

3 angle of sideslip, degrees 

7 flight-path angle, radians 

attitude angle, radians (a + 7) 

5 eleyator angle, radians 

e downwash angle, radians ( —O') 

i-j^ tail setting, radians 

Q?he notations a and a, a and 0*, and so forth, denote single 
and double differentiations with respect to t* 



buDScrlpt 


s: 





Initial or selected value 


t 


tail 


■max 


Biaxiifflini value 


h 


zero lift 


geo 


geometric 


c 


ca.Tnber 



NACA TH 2078 



MKEHODB 
Method of Deteirininlng the Dyna-mio Tall Load 



Basic equatlags of motion .— The siii5)le differential eq.'uatlons for 
the longitudinal lootioa of aja alrplaiie for any eleyator deflection (see 
method glTen. in reference 2) maj he written as 



^rv -^^ q-s - (^ n^t ^ = , (1) 



IT "^ r - ^"t + -^ V ^M - rn^ 9^0- (2) 



Egiiatlons (l) aztd (2) represent sunTmations of forces perpendicular 
to the relative wind and of 3iioments about the center of graTlty. (See 
fig. 1 for direction of posltiTe qiuantities. ) Inopliclt in these equa- 
tions are the f ollowljag assuir5)tion^ : 

(1) In the interYal between the start of the maneuver and the 
attainment of maximum loads ^ the flight— path angle does not change 
materially^ therefore, the change in load factor due to flight—path 
chaoge is small. 

(2) At the Mach nuoiber for which computations are madej the aero- 
dyoajnic derlvatlYes are linear with angle of attack and elevator angle - 

(3) The yarlatlon of speed during the maaeuTer may he neglected. 

(4) ITiisteady lift effects may he neglected. 

By use of the relations Q = 7 + a, = 7+ d, and = 7+ a, 
equations (l) axtd (2) are reducihle to the eguiyalent second-order 
differential equation 

a + K^d + K2 Aa - K3 m (3) 

where K-l^ ^^ ^^^ ^^ ^^® constants for a given set of conditions (see 
table !)• 



mcA m 2078 



IQ equations (l) aad (2), Aa^ y, Bj Zs6, aad AL^ vlll^ In a 

glTSD: i]3aa0UT0r^ Tary with time. Using the relations "between 0> 7, a^ 
and their deriYatiyes permits equation (2) to t)e rewritten as follows to 
gire the increment in tail load: 

^t-loT^^lx^ xt X,, ^ d5 %^ -b^x^ ^ ^"^^ 



In a still shorter fona^ egxmtion (k) inaj be written as 

AL4. = i5L. + AL. + AL. + AL. (5) 

^ % % ^7 ^c 

Equations {k) and (5) show that the tail— load increment (the increment 
above the steady-"f light datum -value) at any time is coii5)Osed of four 
parts: AL. ♦ associated with the angle--of-attaclc change; AL^,,^ asso— 

ciated with angular acceleration about the flight path; ALj. ,, associated 

with angular acceleration of the flight path; and Mj^ 3 reijuired to 

c 

coicpensate for the moment introduced by change in camber of the horizontal- 
tail surface. The load /iL^ is generally ^mall but In some extreme 

configurations may amount to 10 percent of the total increm^at and thus 
for the present it is retained in the development. 

If the load— factor—increment variation with time An is Imownj 
then by the usual definition 

so that 

dCr 

g = ft W/S 

da 
and .. / 

dCr 



WACA TH 2078 

Tlie follo'wl.ns relation also exists between. An and. 7: 

Aa g = jfW (7) 



so that 



7 = ^ (8) 



When equations (6) to (8) are substituted into equations (If) and (5), 
the four tail— load components then become 

^t, = a:^i-Aa (9a) 

^% = - ^ ° ■ (9b) 






^t,=^^^ta^^ (9d) 



.Tiiiis^ If the Yarlation of the load factor with tliiie Aa aad the 
geoinetrlc and aerodyaamic ciiaracteristlcs of the airplane were fcaown^ 
the first three coirqponents of the tail load could he found .iTnmediately. 
The magnitude of the fourth ooir5)onentj that due to horizontal-tail caniber, 
would follow from equation (3) in which the eleTator angle is seen to be 



1L3 £3 K3 

Substitution into equation (lO) of the values of Ax^ a^ and a 
ftrom equation (6) yields the Talue of the elevator angle at any instant 



8 „ mCA TN 2078 



A5 = ^ (a + K^^n + K2 Ar^ (11) 

•^ da ^ 



so that, fjjmllj, the fotirth casaponent Is glTexx as 



AL. = r^ T]. ^i— . .y^ fn + Enfi + Kp An) (12) 



to ^3 



The procediire outlined shows that the tail— load magnitude oaxi "be 
determined if the load— factorr variation is kno'wn. 

Types of load--Caotor Yariation *— The relation between the tall load, 
the geometric and aerodynamic characteristics, and the load factor haTing 
heen established, it is desirable to establish a load— factor yariatlon 
which is reasonable as well as critical insofar as loads are concerned. 
The maximum value of load factor is usually specified; however, there 
are many possible variations for the shape- Eegardless of the details 
of shape, the load factor may be considered to rise smoothly aad con- 
tinuously to a maximum, the rate of rise dependiaag upon several variables • 
Beyond the maximum value of the load factor the return to initial condl— 
tioixs caa, at the will of the pilot, be either gradual or rapid. 

Experiments as well as theoretical studies have already Indicated 
that the maneuver that comblxies maximumL angular and linear accelerations 
causes critical loads in both the wing and tail. One such maneuver occurs 
when the maximum, load factor is reached as rapidlj as possible by using 
an initial elevator movement which is greater than that required to reach 
a given steady— trim value of the load factor. This initial elevator move- 
ment is followed by a rapid checking of the maneuver either by returning 
the elevator quickly to neutral or l:)j reversing the controls. 

The shape of the load— factor curve for such a maneuver may be 
expressed approximately by several analytic functions, one of which is 



An = at^e"^* (13) 



By way of illustration, figure 2 sliows details of the shape of the load- 
factor curve obtained with the use of equation (13) for which the constants 
have been adjusted so that an 8g peak is reached in 1 second. By further 



NACA m 20T8 9 

adjiistmjsat of the coaa^tants the loa^L factor caa, withlii certatet liiriits> 
"be made to rise to amy specified peak aoad to diminish. ±xi any presorihed 
manner; 

Becaiise the positiye slopes obtained from, equation (I3) are always 
greater than the negative slopes , the positiTe angular acGelerations are 
greater than the negative ones. In. general ^ this condition is true for 
most high g critical maneuvers performed "by loost classes of airplanes, 
hut 3iianeuyers may occasionally he performed for vhich the reverse may he 
true, particularly for small airplanes. 

Determination of constants. — 'From equations (9)^ (il)j QJ^d (12) 
the required quantities relating to load factor are seen to he ^n, n, 
and n. Since the increm.ent Mi is to he given hy 

An = at^e^"^ (I3) 

then at maximum load factor 



4-) 



n = 0=Ari^-c (ll^) 



is 
Thus t = — at maximum load factor. Let N = An^^y. Tlaen 



N 



= 4) 



^'-b 



so that 



^ ^ / t \ 



e 



(15) 



(16) 



Let - = X. Then 
c 



m.h^J'(}-j) (IT) 



Equation (17) is in nondimensional form vhere X is the time to reach 
the peak load factor and b is a constant. 



10 lACA TN 2078 

When eqiiatioii (17) Is dlff ereaatiated, the first and second derxva— 
tlYes became 






f^i^-') .(18) 



and 






£h - iV - 22. + 1 



^-^ 



^2\ W t 



(19) 



In epilations (IT) to (19) the qtiantitles N^ X^ and "b are now 
regialred in order to determine the variation of Aa^ n^ and ii. The 
value of H is iDamediatelj availahle from the required loaneuTer load 
factor^ "Whereas the time to reach the peak load factor X can he oh- 
tained from examination of availahle records or by specification. The 
constaat h^ as may he seen from equation (l?)^ can best be described 
as a "shape" factor and has no particular physical sig^alficance. 

The values of A. and b should be associated with a maneuver which 
produces maximum tall loads. Therefore the time X to reach peak load 
factor should be the minimum possible consistent with possible pilot 
action and airplane response. The shape factor b should also be con- 
sistent with both of these. 

In connection with the determination of the minimum time to reach 
peak load factor^ the results shown in figure 3 for a typical airplane 
are informative. Figure 3(a) shows the load— factor variation following 
several abrupt Jud?) elevator movements. The load factor varies with the 
elevator position, but the time to reach peak load factor does not. 
Figiore 3(b) shows the load— factor variation for several abrupt hat- 
shape elevator Impulses. Again the load factor is seen to vary with 
the amount of elevator deflection but the time to reach the peak value 
reioalris constant. Although the time to reach the peak load factor 
shown In figure 3(b) remains constant, it is seen to be less than that 
shown in the previous .case; therefore, an lir5)ulse elevator motion pro^ 
duces a smaller value of X than the J-uir^? type. 

Because of Inertia and elasticity in the control system, the pilot 
cannot move the elevator instantaneously but requires some finite time 
tj_ to do so. A possible critical type of elevator iir5)ulse thus appears 

to be one which Increases llaearly to maxiJmiDi and decreases at the same 
rate to zero. In order to determine the minimum time, to reach peak load 
factor associated with such a variation, the equation of motion (equa- 
tion (3)) has been solved for the triangular elevator impulse for 
airplanes of various static stabilities and damping. 



mCA TN 2078 11 

The results of the computations axe glTen in figure k in which the 
Hilnlmum tiine X to reach peak load factor is plotted against the time t] 
regulred to deflect the elevator. 

For coir5)leteness the curves of figure k are labeled for the actual 
values of E^ eiirplojed in the con5)utation as well as for relatiYe values 
of stahility. By a series of coii5)utatiQns the daiDping term K^ was 
founds as was to he expect ed^ to have onlj a secondarj effect on X- 
The curves apply to an average value of the dair5)lng constant. The upper 
curve, laheled "low stability j>" should he associated with rearward 
center-of-^avity positions (that is, low static margin) in coinbination 
with one or both of the following: low dynamic pressure or heavy air- 
planes. The lower curve, labeled "high stability," would be associated 
with forward center-^of --gravity positions in coirflDination with one or both 
of the following: high dynamic pressure or light airplanes. It is seen 
that X increases almost linearly with tj_ and also increases when the 
restoring forces are reduced, that is, when the stability is reduced. 

A preliiainary value of the shape factor b (required in eq.ua— 
tions (17) to (19)) was initially determined from flight records of 
typical in5)iilse maneuvers by fitting curves of the type given by equa- 
tion (13) through several points of the actual time histories and 
determining the constants- The results of this first step were then 
modified by the results of the same computations which had been made to 
determine X, QJ^d. the variation of b with tj_ given in figure 5 was 
obtained. Since the b factor is not found to be critical, an average 
value of 5.0 is suggested, although as a refinement the values from 
figure 5 ^J^y ^® used. 

The question of the value of t-^ to use is one which mast be 
solved either from experience or from a knowledge of the characteristics 
of the controls and the control system. For conv^ational airplanes 
having the usual amounts of boost and no rate restrictors, the following 
values of tj^ are suggested as representative: 

H 

Fighters or small civil aiirplanes with weight limit from 

about 500 to 12^000 poimds^ seconds ...••..••...« 0.20 

Two^ngine airplanes with weight limit from 25,000 

to ^5^000 poxxnds, seconds .•.••,.•.••••.«••. 0,25 

Four— engine airplanes with weight limit from 50,000 

to 80,000 pounds, seconds •..•«•.•.•«.••.••• O.3O 

Airplanes with weight limit above 100,000 pounds, seconds . • ; O.to 



12 IWCA TN 20T8 



The mlidjmm time X sXren In figure 4 was actimllj ©stal)lls]aad. 
*separat©lj from tlie adopted load— factor Tariatloni therefore^ to applying 
tlx© irnrerse matliod^ tlie deriTed elevator iicp-ulse wotild not "be expected 
to agree in detail with the "taat" type iirrpiilse iised in the derivation- 

The first three tail— load c6iii)aaents can now *be coirputed by insert- 
ing the Talues of 4n, n^ and ii from equations (17) to (19) toto 
e(iiiation (9) 3^d xising appropriate Talues of X from figure 4- In , 
order to facilitate this confutation, curTes of Aa/l, ixX/By and nX /H 
plotted against t/x are giyea in figure 6 for the suggested Talue of 
h = 5. Actually to apply the results of figure 6 it is conTeniaat to 
find first the coiii)onents AL , and so f orth_, in te3:ins of the nondi— 

<X 

meiisional time t/x and then to convert to time t in seconds. In 
order either to compute the fourth Gomponexit or to obtain the elevator 
angles for use in chord loading, the constants K^^ "^2, and Ko of 
equation {3) loust also he known. 

Thxis, in terms of t/x and the ordinates of figure 6, the various 
tail—load components are 

^^ = ^ S/ordinate of fig. 6(a)) (20a) 

AL^. = ^^ S-fcrdinate of fig. 6(c)) (20I0) 

gScixt-^/- 



^t; 



-Wk2 



^^ 



X, SfQrdiixate of fig. 6(b)) (20c) 

1. A. \ / 



AL. 



- "^^ ^ ^t" ¥ M 



^ 2 



Orrdlpate of fig. 6(c) ^ 



X^ 



Kn (Ordinate of fig. 6(b)) , \1 v 

-ii — *~1- + K2(0rdinate of fig. 6(a)j|(20d) 

The constants K^^ Kg^ and Eo defined in tahle I are the same as those 
given in reference 2^ except for changed signs caused hy specifying x^ 
as positive. 



MCA fN 2078 13 



The conversion to time t is made by m-ultlplyi33g values of the 
base scale t/X by X^ 

Saiople 'calculatlohs^ f^ incretaental tail loads >^ The results of 
several examples are given to illustrate nOt only the method btit also 
the effect of each of a number of variables on the incremental tail load 
of a typical fighter airplane^ the geometric and aerodynamic character- 
istics of which are gi'V'en in the following tables. In order to illustrate 
the effect of static stability^ results have been computed for three 
center— Gf--gravity poBitions with the assumption that ati 8g recovery is 
made at 19>100 feet from a vertical dive at an equivalent airspeed of 
400 miles per hour* In order to illustrate the effect of the time of 
the elevator iMpulse on the tail load^ computations were carried out at 
one of the center— of -gravity positions for several values of t^. The 

cases considered and the airplane characteristics follow: 



GEOMETSIC GHARACTERISTICS 



Gross wing area^ S^ square feet «•.«•;..••..••«• 3OO 

Gross horizontal— tail area^ S-^^ square feet .•.••••••• 60 

Airplane weighty W^ pounds «•..•••.•.••«.•••*, 12^000 

Wing span^ b^ feet « « « • . «••««••> ••«••••••• 41 

Tail span^ b^^ feet •.•#«•....•.««...••..* I6 

Radius of gyration^ ky^ feet .•*...•..••••..•.• G.k 

Distance from aerodynamic center of airplane less tail to 
aerodynamic center of tall^ x^^ feet: 

Center of gravity^ 29 percent M.A.G. *«..•.•.•••# 20,0 

Center of gravity, 24 percent M. A. C* «..«*•.,,..• 20,3 

Center of gravity at aerodynamic center n , • . , , • • , , 21*0 



AEROEOTMIC CEARACTEEISTICS 

Slope of airplane lift curve^ dC|./'da,^ radians • , . . • , . • . 4.87 

Slope of tail lift curves dCj^/dcc^^ radians . , . . , , . . , • 3.15 

Downwash factor^ dc/dcx ..*..*.., , . * •*•..•... 0.5^ 

Tail efficiency factor h /q\j r\ «••••«•#.,.«•«• 1,00 

Empirical airplane daiirping factor^ K .*.*..•••••.• • 1,1 

Elevator effectiveness factor^ dCj_/d8, radians .•.*.••• 1,89 

Rate of change of tail moment with camber due to 

elevator angle > QG^ Idby radian •*..•........•• -^.57 



ik MCA TN 2078 



Rate of change of moment coefficient with angle of attack 
for airplane less tail, dCj^/da, radians: 

Center of grayityj 29 percent M.A.C. • . . . . . • • • • •: 0.625 
Center of gravity, 24 percent M»A.C, . ••••.. , • . • 0.^*03 
Center of gravity at aerodynamic center . . . • • . . • • . 0,000 



The specified conditions for the saiarple computations are given in 
tahle II, The computed results for tail components are given in fig- 
ures 7 and 8, :Figure 7 gives results for varying the center of gravity 
and figure 8 gives similar results for varying t-j- . The tail— load 
components are computed from equations (20) and the derived elevator 
angles, from equation (ll). If the increment in tail load due to camher 
and the incremental elevator angle are not required, the K values need 
not be computed and the computations are considerably shortened, -Fig- 
ures 7 and 8 show that a maximum error of only about h percent is 
introduced by this omission. 



Method of Determining the Total Tail Load 



The initial or steady— flight tail load and elevator angles to which 
the computed incremental values are to be added must also be determined. 
In steady flight, the horizontal tail furnishes the moment required to 
balance the moments from all other parts of the airplane so that the 
initial load may be written as 






. *"o "*-"'m wo / ^^ \ 

^o = "-^^r- + 3n7 T^ =°^ ^o (21) 



Thus the total tail load at any time in a maneuver is composed of the 
four previously mentioned parts plus the components given in equa- 
tion (21), Only the first term of equation (2l) represents a new type 
of load because the second term is a load of the type given by equa- 
tion {9^) or equation (20a) and its effect may be imnediately included 
in the computations by multiplying the ordinates of figure 6 by 
N + cos 7^ instead of by N, 

The initial elevator angle required to balance the airplane in 
steady flight varies with airplane C^ and center-of— gravity position 
so that, in general, 6q must be obtained from wind— tunnel data. With- 
out results of wind— tunnel tests, a rough rule which can be used as a 
guide at the design stage in determining the elevator position is that 



NACA TN 2078 15 

the final elevator setting will te so adjiisted by repositioning of the 
stabilizer setting dtiririg acceptance tests that it "will be near a zero 
position at the cruising speed and at the most preTalent center— of — 
graTit J position. 

Method of Detersdning Maximum Yalues 

Maximum tail loads and ani^ar acceleratiozis .— The method outlined, 
enables a point-by— point eTaluation to be made of the quantities that 
determine the tall load. Such detail may often be xinnecessary and the 
procedure may be shortened by eraluating only those points near the load 
peaks or J altematiYelyj by accepting an approximation to the results. 
One such approximation which may bq made is to balance the airplane at 
the combinations of load factor and angular acceleration which would 
result in maximum up and down tail loads. 

Figure 7 shows that the maximoxm. dowa tail load in a pull—up occurs 

near the start of the maneuver and before appreciable load factor is 

reached. This maximum load is practically coincident with the negative 

maximum in the Lj.., tail— load coiiqponent- Slnce^ for a given configu— 

a 

ration, this coir5)onent increases as the center of gravity is moved forward 

' and since the steady— flight down load increases with speed, the maximum 

doWQ tail load in a pull-up occurs at the highest deslgp. spieed in combin- 

ation with the most forward center-of-igravity position. 

Figures 7 and 8 show that at the time of the maximum down-tall— load 
increment the elevator is near but has not q.uite reached its peak position. 
Also at the time of maximum up— tail— load increment the elevator is near 
its zero position, althotigh it may be on either side of this position 
depending upon the stability and the time t^. These results suggest 
that the maximum down load for the elevator and the hinge brackets would 
occur with the airplane center of gravity well forward and at the start 
of the maneuver. The maximum load for the stabilizer is likely to occur 
at the peak load factor. 

Figure 7 also shows that the up tail load occurs near the peak of 
the L-^;; component as well as near the positive maximum peak in the 

L-t- C03i5)0nent. Since the L-^ component increases as the center of 

gravity is moved rearward and since a decrease in speed generally reduces 
the initial down load, the maxlmzxm up tail load occurs at the upper left- 
hand corner of the T— n diagraju for the most rearward center— of~gravlty 
position. 



l6 NACA Tn 2078 

The inaxiisum tail load In a puLl—up maneu'ver waj be written as 

G^ qSc r\n 



where the smn of the second and third terms is to *be a maximpm in the 
maneuTer. l^om the preTlo"U3 discuss ion the load— factor increment at 
maximum down load is nearly zero and at maximum up load it is^ nearly 
equal to IT so that if the positiye and negatiTe values of 6 can 

he determined^ a relatlTely simple method for dete3rminlng maximum loads 
is aTailahle. 

Since hy definition = bo + 7^ an expression for angular acceler- 
ation can he derived from equations (6) and (7) and written in the form 

W/s •• q • 



The maximum angular acceleration can he approximated hy 



e. 



max '^I^^ ""^YX ^^^^ 

dHT ^ 



For the maximum positiye pitching acceleration, B is the maximum 
positive ordinate in figure 6(c) and C is the ordinate of figure 6(h) 
at a value of t/x for which B was determined. Thus, B is 6.5 and 
C is 0.95 for this exan^le- 

For the maximum negative pitching acceleration^ B is the maximum - 
negative ordinate in figure 6(c) and G is the ordinate of figure 6(h) 
at a value of t/x for which B was determined. Thus, B is —5.8 and 
C is 0.8G. For use in equation (23) the values of X for the maneuver 
are availahle from figure k- and the other quantities are avallahle from 
the conditions of the prohlem. The maximum loads can he given hy the 
following equations: 



NACA TH 2078 17 

For BmxiiDMiii up tail load in tlie pTiLL-up: 

^-fcinax+ ^r^ ^ 1%: tit ^^ "^ ^^ ^ X dC, T^^ ^^^^ 

For inaKimum down tail load in the pull— Tip: 

T - ^^ ° 4. ^^m WS „„„ ~ _ ^ N / 6.5 ¥/S . O.Q^g l /ph-KX 



For jpvBhr-d^omxB to limit load factor^ equations (2k-a) aod. (241)) still 
apply with Ghanged slgas for N axid chajoged directloBS- for L^^ ajad 

inax+ 
L^ . A question arises as to whether the maxinrum down tall load at 

inax— 
the start of a pull—up with forward center— of-gravlty position is greater 
than that which would occur when pulling up from a negatlTe load— factor 
condition^ with the center of gravity in the most rearward position. 
This can be determined only by computing both cases and seeing which is 
the larger. 

Maximum value of angular Telocity .— The maximum value of the pitching 
angular velocity in the pull-up may also be found in a manner similar to 
that used to obtain the maximum angular acceleration. Since = d + 7 
and the relations involving these quantities in terms of load factor are 
given by equations (6) and (7), the following eq.uation may be written: 

The iraximum angular velocity may be approximated by 

a-i,|^..^ (.6) 

da 



18 NACA Tn 2078 

vhere D is the TO.x1.mm posltlYe ordixLate in f igwe 6(*b) «xid 1 is the 
ordixiate of figtire 6(a) at a value of t/X for which D was determiiied. 
Thxis Dy for this ^xmsple, is I.95 and E is 0.48. 

In the steady tixm or puLl—up at oan^tant g^ the ang:ular Telocity 
is Tisttallj given hy the expression Q = 1.0 ^. The difference "between 

the factor 1.0 of this expression and the factor 0.48 of equation (26) 
is more than made up by the angle-of--attack component of the angular 
velocity. 



Approii333ate Method of Determining Load Distrihution 



Symmetrical loading .— The spanwise distrihution of the total load 
can he fo3?mulated with various degrees of exactness. If information 
regarding details of the angle-of-ettack distribution across the span 
were available, then an exact solution could be obtained for the loading 
with the use of existing lifting-surface methods. The following method 
may be used as a first approximation to the solution. 

'From the total tail load^ the total tail lift coefficient 0^ can 

readily be found. The average effective angle of attack a of the 
stabilizer portion is given in the definition 



\'-Jo %"§^^Vo %("°*^'5 t*^ 



(2T) 



where only a is assumed as unknown and cj and c? may be taken 

as the rates of change of section lift coefficient with a and 5, 
respectively. 

Thus, for constant elevator angle across the span. 





(28) 



HACA Tn 2078 19 

In a practical casa "both integrals in eqixatlon (28) need "be eYaluated 
only once for a giren configuration and Mach nmiber. A plot of a 

against Gj_^ with 6 as a parameter woxild "be iis^fall in further ooinpvir^ 

t 
tatlons. with a kaowx as a function of CL- and 6. the local lift 

at any spanwlse station is then ohtained from the expression 

I = c^ge - [^cj^ a + oi^[% + A5j] qc (^9) 



IMsymmetrlcal loading *— Up to this point the total loads have "been 
assumed to he syoimetrical about the airplane center line, whereas^ in 
reality, the load may haTe an unsyimaetrical part. The sources of this 
dissyomietry may "be due to une'ven rigging, differences in elasticity 
hetweaa the tvo sides, or to effects of slipstreairL, rolling, and sideslip. 
The first two sources are usually Inadvertent ones while the last two are 
dlfficuilt to detemnlne without either wind— tunnel tests or a Imowledge of 
how the airplane will he operated. Present design rules regarding dis- 
symmetry of tail load are concerned laore with proYidlng adequate design 
conditions for the Te^T of the fuselage than with recognizing that at 
the maxiHEum critical tall load some dissymmetry may exist. 

Tests in the Langley full— scale tunnel (reference 6) and flight 
tests (reference 7) of a fighter-type airplane^ as well as unpublished 
flight tests of another fighter-type airplane, indicate that the tail- 
load dissymmetry varies linearly with angle of sideslip so that the 
difference in lift coefficient between the two sides of the tail can be 
given as 

^L^ -% = AP ' (30) 

^Right ^eft 

The average values of A per degree found for the two fighter— type 
airplanes are approximately 0.01. Ho similar values are available for 
larger airplanes nor for tail surfaces having appreciable dihedral. 

In 333aneuvers of the type considered herein it is doubtful that 
angles of sideslip larger than 3^ would be developed at the time the 
maximum tail load is reached. If the value of the sideslip angle at 
the time of maximum tall load can be established, equations (27) to (29) 
are easily modified to include this effect, provided the approximate 
value of A is loxown. 



20 MCA TN 2078 



Ghortiwls e loadl3ag > — The chordwise MstributicxQ can be detaririlxted 
for axij one spaawise station in either of two ways. One ^aj for design 
work is outlined in reference 8* A knowledge of tke airfoil section 
and the q.xiantities contained in equation (29) suffices for this deter— 
mi nation* 

If pressure-distribution data are available for a similar section 
with flaps ^ ajx altei*nate way would, be to distribute the load chordwise 
according to the two-dimensional pressure diagrams with the use of the 
coinputed values of section lift coefficient and elevator aiagle. 



DISCDSSION 



The loethod presented is another approach to the determination of 
tail loads. 'From the results given in figures 7 s^^ 8^ it can be seen 
that the camber coir5)onent L^^ is so sjmll that for all practical cases 

it may be omitted with cojisiderable simplification in the coii5)utation of 
tail loads. This omission reduces to a minimum the nuiaber of aerodynamic 
parameters needed to compute the tail loads. 

It is possible^ in the application of the present miethod with the 
use of the suggested values of t-i_^ that the derived elevator angles 

may not be within the pilot's capabilities. Since it mxist be assumed 
that all airplanes^ to be satisfactory^ should have sufficient control 
to reach their design load bounda^riesj such an occurrence requires only 
that the time to reach elevator peak deflection t]_ be increased so as 

to reduce the elevator angle* The results of figure 8^ in which the 
time ti is varied^ furnish a useful guide for determining the in- 
crease ti that might be required. 

If sufficient information is available, it is recommended that 
existing lifting-surface methods be used in determining the spanwise 
distribution of the total load; however, if information of the angle- 
of-attack distribution across the span Is not fcaown, the method presented 
may be iised as a first approzl7nation> 

Along some of the boundaries of the V-na diagram, tail buffeting may 
occur. Measurements show that buffeting usually occurs along the line 
of maximum lift coefficient and again along a high— speed buffet line 
which is associated with a conrpressibility or force break on some major 
part of the airplane. All ai3rplanes are subject to buffeting at the 
design conditions associated with the left-hand comer of the V—n 
diagram. 



NACA TN 2078 21 



Only Mgh-epaed aod/or highr-altltude airplanes are capable of reaclilag 
the other hoimdary. Measiireinieaats show that the oscillatory TD-uff etlng 
loads loay he so high that the designer shoxild at least he cognizant nf 
them at the. design stage. 

The maxlmma angular acceleration varies inTersely with airspeed 
and directly with the load factor^ with the contribution due to acceler- 
ation in angle of attack likely to be more iir^ortant than the angular 
acceleration of the flight path- A somewhat similar variation is indi- 
cated for the maximum angular Telocity (equation (26)) where it is seen 
by direct substitution that the part due to angle of attack is likely 
to be larger than the part due to the angular Telocity of the flight 
path. 



COUGLDDIHG EEMAEES 



A siii5)le method has been presented for determiniisg the horizontal 
tail loads in maneuTerlng flight with the use of a prescribed incremental 
load— factor Tariation- 

The incremental tail load was separated into four components repre- 
senting a, a^ yy and c The camber ■ coirqponent L^ is so small that 

c 

for most conTentional airplanes It may be neglected, thereby reducing to 
a minimum the number of aerodynamic parameters needed in this coxi5)utatlon 
of tail loads. 

An approximate method is presented for predicting maximum angular 
accelerations and maximum angular Telocities . 

The method indicates that maximum tail loads in a pull-^p occur at 
forward cante3X)f-graTity positions and early in the maneuTer. The 
maximum down tail loads in a pull-^p occur at the highest design speed 
in combination vith the most forward centei^of— gravity position. The 
maximum up tail load occurs at the upper left— hand comer of the V— n 
diagram for the most rearward cent er-of— gravity positions. 



Langley Aeronautical Laboratory 

National Advisory Committee for Aeronautics 

Langley Air Force Base, Ya. , February 9y 1950 



22 NACA TH 2078 



EEFERMCIS 



1. Scimiidt^ W,^ and Clasen^ B.: Lioftla'afte auf Fliigel imd Holieiileitweirk 



GeradeatiBflug* Jahrl). 1937 <ie^ deutsclisa LuftfaJxTtforscifuzigj E» 
Qldeaaboxcrg (Munich), pp* I I69 - I 173* 

2. Pearson^ Saury A.: Derl-VBtlon of Charts for Datermlxdjag the Horizontal 

Tall Load Tarlatloa with Any Elevator Motion. HACA Eep. 759, 19i|"3. 

3. Eelley, Joseph, Jr., an.d Mis sail, John ¥. : Maneuver log Horizontal 

Tall Loads. AAF TR No. 5185, Air Technical Service Conamnd, Anay 
Air Forces, Jan- 25, I945. 

k-^ Dickinson, H. B. : Maneuverahlllty and Control Surface Strength 

Criteria for Large Airplanes. Jour. Aero. Scl. , vol. 7, no. 11, 
Sept. 1940, pp. 1^69--^77- 

5. Matheny, Cloyce E. : ConEparlson "between Calculated and Measured Loads 

on Wing and Horizontal Tall in Pall-4Jp Maneuvers. NACA ARR L5H11, 

19^5- 

6. Sweherg, Harold H. , and Dingeldeln, Eichard G. : Effects of Propeller 

Operation and Angle of Yaw on the Distribution of the Load on the 
Horizontal Tail Stirface of a Typical Pursuit Airplane. NACA ARR 

teio, 19^^. 

7. Garvin, John B,: Flight Measurements of Aerodynamic Loads on the 

Horizontal Tall Surface of a Fighter-Type Airplane. NACA TN 1^83, 
19^7- 

8. Anon.: Chordwise Air-Load Distrlhution. AN0"l(2), Army-Jfavy-Clvil 

Committee on Aircraft Design Criteria, Oct. 28, 1942. 



MCA TW 2078 



23 



TABLE I 



COIBTAITS OGCnRRim UT BASIC DIEFEEEDIEIAL EQaflTIQII 



Gonstaxit 



Defliiitlcm 



K, 



Pi 

2m 



dGx Q ^ 2 



^<H k^ -^1/% 



^l./TTT da dot. 



E2 



D?^ 



2m 



iCm s2 



•i^ k^^ 






fcv 



■(' 



da/ da . /rf- 2 m 



\/\ 



2m 



'iGLt Stxt "^^ St^ ^% ^%,t KTlt^ D ^t^St^^ 



P 

2 ™v 2 



ky- -" - D^ky2 dot dS ^ ^ ^^ 



21* 



mCA Tl 20^8 



TCABLE H 



SPEQIPISa) eOjEDIHIOlS OF SMBM lECEBlIM 



Incremfint In. load factor • • . • 
Altxtude, feet ...,,... . 
Air density, sltig per eiibic foot 



8.0 

19,100 

0. 001306 



Case 


= eg 
(pereeait M. A, C. ) 


: *i 


; % 


% 


1 % i 


: (fig. k) 


1 


a.e. 


0.2 


: 4.93 


\ 30.4 


■ -33 'k- 


0.45 


2 


2k 


.2 


: k.l2 


16.2 


■ -32.2 { 


.50 


3 


29 


.2 


k.6l 


8.45 


: ^1.7 


.56 


\ 


2h 


.4 


: 4.72 


; 16.2 


-32.2 


.77 


5 


24 


.6 


4.72 


; 16.2 


-32.2 ; 


1.02 



NACA TN 2078 



25 



(tag. 




/r'e/af/i'^e j^/nd 



Tanqenf fo- 
ilicjhi paih- 




C/pord hne 




path 



Figure 1.- Sign conventions employed. Positive directions shown. 



26 



NACA TN 2078 



iT JO 

o 

^ 6 



I 



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"^^^Z^nKa^ 



.Z .4 .6 .8 1.0 /^ 



1.4 /.6 



/.8 



Figure 2.- Variation of load-factor increment. Zlsn = N250t5'53e-5.53. 



KACA TS 2078 



27 



AS . ^ 




: 


1 1 




:: 








"~ 


1 1 1 1 




fllg^^l^g^g^ 



i H i f 







t 
(b) Impulse. 



Figure 3*" Incremental-load-factor yariations folloving control movement* 



as 



NACA TU 2078 



a.o 



KB 



16 



14 



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LO 



B 



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1 1 
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Figure 4.- Variation of X with t-^. 



NACA TH 2078 



29 



7 



^ 4 

I J 

/ 

























































(T 






















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t 


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,Z d .6 .& 1.0 /.Z 



Figxire 5»- Variation of shape factor b with t-^^. 



30 



HACA TN 2078 




Z.0 
IB 



IZ 



^ 



a 



14 



-4 

-3 
-IZ 



■JX^ 


tx 


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^ .4 .6 , /£ /6 £.0 ' 4 B , IZ 1.6 dD 
t/X t/A 

ib) (c) 



Figure 6,- Variation of incremerxtal-load-f actor cuTYes with time ratio. 



mcA TN 2078 



31 



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Figure 7*- Effect of center-of -gravity position on incremental-tail-load 

coniponents. 



32 



lAGA TN 2078 



§0 

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Figure 8-- Effect of t-^ on incremental-tail-load components. Center 

of gravity, 0.2^ c. 



NACA-Langley -4-21-50 -1050