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314 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
(^5) Civil Airworthiness Specifications, Parts 23 and 25, Federal Aviation Regulations, U.S. Government Printing Office, Washington, DC, 1991. (^6) British Civil Airworthiness Requirements, Section D, Air Registration Board, England. (^7) Roskam, J., Airplane Flight Dynamics and Automatic Flight Control, Part /, Roskam Aviation and Engineering, Lawrence, KS, 1979. (^8) Sova, G., and Divan, P., "Aerodynamic Preliminary Analysis System II," Part 2, User's Manual, NASA CR-182077, 1990. (^9) Seckel, E., Stability and Control of Airplanes and Helicopters, Academic, New York,
(^10) Pamadi, B. N., and Pai, T. G., "A Note on the Yawing Moment Due to Sideslip for Swept-Back Wings," Journal of Aircraft, Vol. 17, No. 5, 1980, pp. 378-380.
Problems
3.1 For an airplane configuration of the type shown in Fig. 3.57, determine the low-speed slope of pitching-moment-coefficient curve using Multhopp's method and the following data: c (^) re = 3.6 m, ct = 2.0 m, c = 3.0 m, S — 43.5 m 2 , b = 15 m,
A = 5.17, A c/4 = 3.5 deg, lh = 5.0 m, hH = O.Q5b h, and CLa, WB = 0.06/deg. The
geometrical data are given in Table P3.1.
Table P3.1 Geometrical parameters of the airplane in Problem 3.
Section Ax, m bf>m^ x,m
3.2 Estimate the lift-curve slope of a wing having a NACA 64009 airfoil section,
leading-edge sweep of 45 deg, root chord 3.5 m, tip chord 2.0 m, span 15m, and
Reynolds number 6 x 106 at Mach numbers 0.5 and 2.0.
3.3 Estimate the slope of normal force coefficient and pitching-moment-
coefficient curve at M — 2 for a cone-cylinder having a semivertex angle of 10 deg,
diameter 2.0 m, and length 15m. Assume that the moment reference point is located at 10 m from the leading edge.
STATIC STABILITY AND CONTROL 315
Hemi-spherical Nose
Fig. P3.4 Generic wing-body configuration.
3.4 For a generic wing-body configuration shown in Fig. P3 .4, determine Cia, WB and Cma ,wB at M = 0.3 and 2.0. Assume a 0 = 0.085/deg (for low subsonic speeds) and Ay — 2.2. (Hint: you may ignore the hemispherical nose cap in lift and pitching moment calculations.)
3.5 Estimate the subsonic downwash gradient with respect to angle of attack at the aerodynamic center of a horizontal tail located 2.5 root chords downstream of the wing aerodynamic center and 5% span above the wing root chordline. For the wing, use the data of Exercise 3.2.
3.6 Estimate the dynamic pressure ratio at the horizontal tail of Exercise 3.5 for M = 0.3.
3.7 Estimate the low-speed elevator effectiveness r and hinge-moment coeffi- cients Cha and Chs using the following data. Horizontal tail: root chord 1 .2 m, tip chord 0.8 m, span 5 m, leading-edge sweep 30deg, and NACA 65A009 airfoil section. Elevator: ratio of chord length ahead of the hingeline to that aft of hingeline 0.085, ratio of chord length aft of the hingeline to the horizontal tail chord 0.165, hingeline sweep 15 deg, and t (^) c/2cf = 0.06. Assume that the elevator extends from 20 to 80% semispan of the horizontal tail and the Reynolds number is 106.
3.8 Assuming (^8) 6t0 = i (^) w = i (^) t = 0 and C^ 0 — 0, show that
dC (^) L free
STATIC STABILITY AND CONTROL 317
tab deflection and (b) tab deflection for stick force trim at a speed of 100 m/s. [Answer: (a) 60.0139 m/s and (b) -3.6044 deg.]
3.17 For the aircraft of Problem 3.16, determine the stick force gradients for cases 1 and 2. [Answer: 7.5540 Ns/m and 4.5334 Ns/m.]
3.18 A trainer aircraft has a wing loading of 1850 N/m 2 and a static margin of 0.15 while flying at 8 deg angle of attack at an altitude of 8000 m (a = 0.4292). (a) To what altitude should the pilot climb the aircraft so that, at the bottom of a 1.5 g pull-out, he is once again at 8000 m altitude? For this aircraft, determine (b) the elevator required per g and (c) stick force per g based on the following data: e = 0.35o?, a (^) w =0.1/deg, at = 0.092/deg, c = 2.5 m, S,/S = 0.3, lt =2.5 c, 77, =0.9, r = 0.35, Cha = - 0.003/deg, C (^) h8 = - 0.006/deg, S (^) e = 1.85 m 2 , c (^) e = 0.61 m, and G\ = 1.2 rad/m. [Answer: (a) 9793.4 m, (b) -6.6605 deg/g, and (c) -65.2776 N/g.j
3.19 An aircraft weighs 66,825 N and has a wing area of 46 m 2 and a tail length of 10.64 m. The center of gravity and wing aerodynamic centers in terms of mean aerodynamic chord are, respectively, at 0.35 and 0.26 from the leading edge of mac. The lift-curve slope of wing and that of horizontal tail are 0.09/deg and 0.07/deg, respectively. The tail volume ratio is 0.6. Assuming C (^) m/ = Q.lC (^) L,e = 0.3a, J] (^) t = 0.9, i = 0.5, C (^) ha = -0.003/deg, Chs = -0.006/deg, Se = 1.9 m 2 , ce = 0.55 m, and GI = 1.2 rad/m, determine (a) the stick-fixed maneuver margin and (b) the incremental elevator setting for a coordinated turn with 30 deg bank at an altitude of 2200 m (a = 0.8) and a lift coefficient of 0.2. (c) What is the stick force per gl [Answer: (a) 0.2374, (b) -0.3886 deg, and (c) -67.9757 N/g.]
3.20 For the airplane configuration shown in Fig. P3.20, the fuselage side area is 40.5 m 2 , the maximum fuselage width is 2.5 m, and the ratio of rudder chord to vertical tail chord is 0.30. The rudder extends from 1.56 to 3.78 m from the fuselage centerline as shown. Assume that the wing, horizontal tail, and vertical tail have NACA 65A006 airfoil section. Determine the following: (a) The static directional stability parameter (Cn ^x at M = 0.3 and an altitude of 3000m. (b) The rudder effectiveness Cn sr at low subsonic speeds. (c) The rudder hinge-moment coefficients C/^ and ChSr at^ low subsonic speeds, assuming that the hingeline coincides with the leading edge of the rudder and Affi - 0. (d) The rudder-free directional stability parameter (C«^)f (^) ree at M = 0.3.
3.21 Using strip 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/m 2 , aspect ratio is 8, taper ratio is 0.7, sectional lift-curve slope is 0.10/deg, sectional drag coefficient CD i = 0.015 -f- O.OOOSa deg, dihedral is 5 deg, and wing span is 16 m. [Answer: -1289Nm.]
3.22 Plot the variation of (C (^) n p)A,w with angle^ °f attack using the strip theory for a swept-back wing with the following data: A/,£ = 30 deg, aspect ratio = 8.0,
318 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
- NACA 65A006 Airfoil for Wing, Horizontal & Vertical Tails
- SB s = 40.5 m^2
Fig. P3.20 Sketch of an airplane.
