Horizontal tail loads in maneuvering flight Page: 2 of 12
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REPORT 10 07-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
N maximum increment in load factor
q dynamic pressure, pounds per square foot
Qp V2)
S wing area, square feet
S, horizontal-tafil area, square feet
t time, seconds
t time to reach peak of elevator deflection,
seconds
V airplane true velocity, feet per second
W airplane weight, pounds
xf length from center of gravity of airplane to
aerodynamic center of tail (positive for con-
ventional airplanes), feet
y spanwise dimension, feet
y* nondimensional spanwise dimension (b2)
a, b, C constants occurring in equations (13), (23),
A, B, C, D, E5 (26), and (30)
K,, K2, K constants occurring in basic differential equa-
tion (see equation (3))
X time to reach peak load factor, seconds
p mass density of air, slugs per cubic foot
it tail efficiency factor (q,/q)
a wing angle of attack, radians
a average angle of attack of horizontal stabi-
lizer, radians
ag tail angle of attack, radians
p angle of sideslip, degrees
y flight-path angle, radians
0 attitude angle, radians (a+y)
8 elevator angle, radians
e downwash angle, radians ( a)
it tail setting, radians
The notations a and 0, a and 0", and so forth, denote
single and double differentiations with respect to t.
The symbol A represents an increment from the steady-
flight datum value.
Subscripts:
0 initial or selected value
t tail
max maximum value
lo zero lift
geo geometric
c camber
METHODS
METHOD OF DETERMINING THE DYNAMIC TAIL LOAD
Basic equations of motion.-The simple differential equa-
tions for the longitudinal motion of an airplane for anyelevator deflection (see method given in reference 2) may
be written asm tiV-dO a qS- d) ,qS, AO=O
SAa q-S ALIx+ dOm sZA Mk=0(1)
(2)Equations (1) and (2) represent summations of forces
perpendicular to the relative wind and of moments about the
center of gravity. (See fig. 1 for direction of positive quanti-
ties.) Implicit in these equations are the following assump-
tions:
(1) In the interval 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 change is small.
(2) At the Mach number for which computations are
made, the aerodynamic derivatives are linear with angle of
attack and elevator angle.
(3) The variation of speed during the maneuver may be
neglected.
(4) Unsteady lift effects may be neglected.
By use of the relations 0=-y+-a, =iy+&a, and O=I+&,
equations (1) and (2) are reducible to the equivalent second-
order differential equation&+Ka+K2 Aa ==K. AO
where
(3)
K,=pV dCLi SX d (K df+d d
2m Lda, ky b -I J "7'+;5 da
p jVdCm S d C Sxt de
2m Ida ky'b dcct k'2 Ld)+
dCK pSz11
9 -a 2 m ]
and
Kp V d , 8,,
2m d , -
dCS, St, dCL, dCiKntg p xLS,)
d6 ' bkyd da, do JV 2 mkry
In equations (1) and (2), Aa, j, 3, A, and AL, will, in a
given maneuver, vary with time. Using the relations between
0, , a, and their derivatives permits equation (2) to be re-
written as follows to give the increment in tail load:
ALd=4 Aa S mk r& mk r% dmItq A8 (4)
da b x z, X, da b gxt
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Pearson, Henry A.; McGowan, William A. & Donegan, James J. Horizontal tail loads in maneuvering flight, report, February 9, 1950; (https://digital.library.unt.edu/ark:/67531/metadc60347/m1/2/: accessed April 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.