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Assume that the elevator extends from 20 to 80% semispan ofthe horizontal tail.
3.8 Show that
&~. )-= Cm~(8e,R -cSe./)
CL
3.9 The aerodynamic center (a.c.) of wing-fuselage is located at 0.2 mac and the
center ofgravity is at 0.25 mac. Using the following data, determine the horizontal
tail area to give a minimum static margin of 0.08 mac. Cm.f = O.ICL,aw =
O.l/degr: 5.5=m9.08/deg, e - 0.45a, lr/c -. 2.5, r7r - 0.95, and S = 25 fl12.
[Answer: c12,]
3.10 A flying wing employs elevons for pitch/roll control. imetrically de-
fiected. elevons give pitch control and. when asymme .,~I" d, /m2~,ed. give ro,
control. Assumin Cm.ac = -0.02 - 0.018e, W/S - 289C 12, and a static
margin of 79to, determine the symmetric elevon defiection for trim in level flight
at 154 m/s. [Answer: -3.3860;eg.]
3.11 An airplane with an all-movable horizontal tail has the following data:
W/S = 1500 N/m2, S = 30 m2, CL.muL = 1.5, c = 3 m, xac = 0.25, Cmw : - 0.05,
STATIC STABILITY AND CONTROL
315
aoL.w - -2.5 deg, /u, - -2.Odeg, aw = O.I/deg, Cm.f - 0-05 + 0.12CL, ar -
0.08/deg, e -.0.4 rx,tt -2.5 c, and r7t =0.8. Assuming that the most forward
and aft permissible center of gravity (c.g.) locations are 0.20 c and 0.35 c, de-
termine (a) the tail area and (b) tail setting angle. [Answer: (a) 6.87 IT12 and
(b) -5.6475 deg.J
3.12 A canard aircraft has the following data: aw - O.lO/deg, ac = 0.08/deg,
(: -. -0.02, Xa = -0.5 (c.g. ahead of wing a.c.), Cm. f - O.lC/, Cc - 0.3 c,
(.mac,zn -
C -. -0.015, and Sc - 0.3 S. Determine the distance between the canard
( mac.c -
aerodynamic center and the center of gravity in terms of c for a static margin of
O.lO.Ignore upwash/downwash effects for canard and wing. [Answer: 1.6667.]
3.13 An aircraft with a swept-back wing has the following data: wing loading =
2000 N/m2, wing area= 30 m2, xa = -0.15 (c,g..ahead of wing a.c.), Cm. f =
0.05 +0.08 CL, Cmac.w - -0.05, Cmac., - 0, 7r - 0.9, S,/S - 0.3, and /r/c = 2.5.
(a) Determine the tail-lift coefficient for steady level flight at a speed of 250 m/s
and at sea level. (b) If CD = 0.025 + 0.05CZ:ywhat is the approximate trim drag
penalty? [Answer: -0.0903, 7350 N.]
3.14 A light aircraft has the following data: CL = 0.085(a + 1.5), iw = -1 deg,
/r = - 2 deg, Cmac.w = - 0.012, Cm. f = 0.05 +O.lOCL, ar = 0.075ldeg, r7r - 0.9,
-c - 0.4, Vi : 0.7, maximum upward elevator deflection equals 15 deg, and
CL.max - 1.2. For stick-fixed neutral point at 0.35 mac, plot the elevator deflection
vs lift coefficient for various center of gravity locations on either side of the neutral
point.
3.15 For the aircraft in Exercise 3.7, whaL is the permissible most forward center
of gravity location in terms of mac? [Answer: -0.0164.]
3.16 An aircraft with a static margin of 0.15 has the following data: wing
loading = 1800 N/m2,aw = 0.08/deg, at - 0.06]deg, Cmac.w - - 0.04, CmaCJ
= 0, Vl - 0.55, CtoL.w - O,dCL.,/d;Se - 0.025ldeg,6 = 0.36, 77t = 0.95, St = 4 m2,
Ce -0.5 m, iw - O, /r = 3deg, Gi - 1.6 rad/m, Cm. f =0.05 + O.lC/, Cha =
-0.002/deg, Ch8e = ~0.005/deg, and Ch8, = -0.006ldeg. Assuming level flight
at sea level conditions, determine (a) speed for stick force U:im at zero tab deflec-
tion and (b) tab deflection for stick force trim at a speed of 100 m/s. [Answer:
(a) 65.1322 m/s and (b) -4.0209 deg.]
3.17 For the aircraft of Exercise 3.16, determine the stick force gradients for
cases 1 and 2. [Answer: 30.09 Ns/m and 19.6 Ns/m.]
3.18 A trainer aircraft has a wing loading of 1850 N/m2 and a static margin of
0.15 while fiying at 8 deg angle of attack at an altitude of 8000 m (cr - 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 -. 0.35ct, aw - O.lldeg, ar = 0.092ldeg,
c-2.5 m, St/S=0.3, lr=2.5 c, r7t-0.9, r - 0.35, Cha- - 0.003/deg,
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PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL2(91)
