Question

10. Consider an aircraft that has the wing shown below: 25° 18 ft H.-.-.-.- 10.8 ft 56 ft a. What is the taper ratio? Ans. b. What is the mean aerodynamic chord? Ans. C. The aircraft's center-of-gravity (c.g.) is located at 30% MAC and the aerodynamic center is located at 61% MAC. What is the static margin? Ans. d. Is the aircraft stable? Explain why or why not. Ans. e. For this aircraft C =0.17 degree. What is C ? Ans.

Answer 1

A. Taper ratio is defined as the length of tip of the wing to length of the root

Length of the tip of the wing = 10.8 ft

Length of root = 18 ft

Taper ratio = 10.8/18

Taper ratio = 0.6

b . Mean aerodynimc chord is given by

MAC =Root chord x 2/3 x (( 1 + t + t2 ) ÷ ( 1 + t ))

where t is taper ratio

$MAC= RC \times \frac{2}{3}[(1+t+t^2)/(1+t)]\\ MAC= 18 \times 2/3[(1+0.6+0.6^2)/(1+0.6)]\\ MAC= 12[1.96/1.6]\\ MAC=14.7$

Mean aerodynamic chord is 14.7 feet

c.static margin is defined as the distance between the center of gravity and the neutral point of the aircraft

Center of gravity is located at 30% of MAC. ie

= 0.3 x 14.7 = 4.41 ft

Aerodynamic center is 61% of MAC. i,e

= 0.61 x 14.7 = 8.967

Static margin = 8.967-4.41 = 4.557 ft

d. Aircraft is not stable, because the centry of gravity is below the nuetral ponit. so aircraft is unstable. The center of gravity must lie ahead of the neutral point for positive stability. If the center of gravity is behind the neutral point, the aircraft is longitudinally unstable (the static margin is negative)