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┃ ┃ 'I ┃ ┃ ┃ ┃
┃ ┣━━━━━━━━━━━━━━━━━━━━━━┫ ┃ ┃ ┃
┃ ┃ 3Lt/4 ┃ ┃- 2 5m ┃ ┃
┗━━━━━┻━━━━━━━━━━━━━━━━━━━━━━┻━┻━━━━┻━━━━━┛
Fig.P3.20 Sketchofturplane.
317
-Om
5-Om
3.21 Using stnip theory, determine the yawing moment developed by a flying
wing having a rectangular planform and moving at a forward speed'of 75 m/s and
a sideslip of 5 m/s at sea level. The wing loading is 2000 N/m2, aspect ratio is 8,
taper ratio is 0.7, sectional lift-curve slope is O.lO/deg, sectional drag coefficient
CD.L = 0.015 + 0.0008a deg, dihedralis 5 deg, and wing span is 16 m. [Answer:
-1289 Nm.]
3.22 Plot the variation of (Cnp)A.W with angle of attack using the strip theory for
a swept-back wing with the following data: ALE = 30deg, aspect ratio- 8.0,
span-Y16.0 m, taper ratio-l.0, sectional drag coefficient CDO.L - 0.013 +
0.0007ce deg, sectional lift-curve slope ao = O.l/deg, sectional stall angle arstaii -
14 deg, and F' = 0.
3.23 An aircraft has a wing loading of 2850 N/m2, a wing span of 27 m, a
maximum lift coefficient of 1.75, and vertical tail lift-cuwe slope of 0.082/deg.
(CnB)fix = 0.015]deg, vertical tail -volume ratio is 0.2, and the coefficient k - 0.90.
Assuming that 1 deg of rudder deflection changes the vertical tail sideslip by 0.3
deg and that the maximum rudder deflectionis restricted to :1: 25 deg, determine the
maximum crosswind speed that can be permitted for takeoff at sea level. Assume
that the unstick velocity is 1.2 times the stall velocity. [Answer 7.3598 m/s.]
318 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
3.24 A twinjet engine aircraft has a thrust of 20,000 N per engine, and the engines
are separated by a spanwise distance of 10 m. The wing area is 60 rn2 and the wing
span is 15 m. Assuming that the rudder effectiveness vanishes beyond +25 deg
deflection, determine the minimum rudder effectiveness to hold zero sideslip with
one engine losing all the thrust at a forward speed of 75 m/s at sea level. [Answer:
0.0013/deg.]
3.25 For a high-aspect ratio swept-back wing with leading-edge sweep angle A
and dihedral r, show that
(CLp)w =: -
aoc(yh)yh dyh
3.26 For the airplane in Exercise 3.20, determine Cip at M - 0.3 and an altitude
of 3000 m and atvM = 2.0 and 15,000 m altitude. Also, assuming'that Ca(Y) =
0.3c(y) ancl ailerons extend from y - 0.6s to 0.9s, where s is the semispan,
determine the aileron effectiveness at low subsonic speeds.
3-27 For the flying wing in Exercise 3.21,using strip theory, determine the rolling
moment.
3.28 For the swept-back wing of Exercise 3.22, using strip theory, plot the vari-
ation of Cip with angle of attack.
4
Equations of Motion and
Estimation of Stability Derivatives
4.1 Introduction
In the preceding chapter, we studied static stability and control of airplanes. We
assumed that the motion following either an external disturbance such as a wind
gust or an intenial disturbance like a control input was so slow that the inertia
and damping forces/moments could be ignored. Thus, we essentially assumed the
airplane to be a static system and studied the stability and control based on the
static forces and moments acting on the airplane following a disturbance.
In this chapter, we will study the auTlane as a dynamic system and derrve
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