Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

13.2 Symmetric Maneuver Loads 387

Theloadsareinstaticequilibriumsincetheaircraftisinasteady,unaccelerated,levelflightcondition.
Thus,forverticalequilibrium

L+P−W= 0 (13.7)

forhorizontalequilibrium

T−D= 0 (13.8)

andtakingmomentsabouttheaircraft’sCGintheplaneofsymmetry

La−Db−Tc−M 0 −Pl= 0 (13.9)

For a given aircraft weight, speed, and altitude, Eqs. (13.7, 13.8, and 13.9) may be solved for the
unknownlift,drag,andtailloads.However,otherparametersintheseequations,suchasM 0 ,depend
uponthewingincidenceα,whichinturnisafunctionoftherequiredwingliftsothat,inpractice,a
methodofsuccessiveapproximationisfoundtobethemostconvenientmeansofsolution.
Asafirstapproximation,weassumethatthetailloadPissmallcomparedwiththewingliftLso
that,fromEq.(13.7),L≈W.Fromaerodynamictheorywiththeusualnotation,

L=

1

2

ρV^2 SCL

Hence,

1

2

ρV^2 SCL≈W (13.10)

Equation(13.10)givestheapproximateliftcoefficientCLandthus(fromCL−αcurvesestablishedby
wind tunnel tests) the wing incidenceα. The drag loadDfollows (knowingVandα) and hence we
obtaintherequiredenginethrustTfromEq.(13.8).Also,M 0 ,a,b,c,andlmaybecalculated(again,
sinceVandαareknown)andEq.(13.9)solvedforP.Asasecondapproximation,thisvalueofPis
substitutedinEq.(13.7)toobtainamoreaccuratevalueforL,andtheprocedureisrepeated.Usually
threeapproximationsaresufficienttoproducereasonablyaccuratevalues.
In most cases,P,D,andTare small compared with the lift and aircraft weight. Therefore, from
Eq.(13.7)L≈W,andsubstitutioninEq.(13.9)gives,neglectingDandT

P≈W

a

l

−

M 0

l

(13.11)

WeseefromEq.(13.11)thatifaislarge,thenPwillmostlikelybepositive.Inotherwords,thetail
loadactsupwardwhentheCGoftheaircraftisfaraft.Whenaissmallornegative—inotherwords,a
forwardCG—thenPwillprobablybenegativeandactdownward.

13.2.2 General Case of a Symmetric Maneuver

Inarapidpull-outfromadiveadownwardloadisappliedtothetailplane,causingtheaircrafttopitch
noseupward.Thedownwardloadisachievedbyabackwardmovementofthecontrolcolumn,thereby
applyingnegativeincidencetotheelevators,orhorizontaltailifthelatterisall-moving.Ifthemaneuver
is carried out rapidly, the forward speed of the aircraft remains practically constant so that increases
inliftanddragresultfromtheincreaseinwingincidenceonly.Sincetheliftisnowgreaterthanthat