8/11/2019 AER716

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AER716 Aircraft Stability and Control

Problem set #1 (Due date: Sept. 26th

)

1. A subsonic aircraft has a tapered, untwisted sweptback wing with straight leading and

trailing edges. The tail uses a symmetric airfoil with no local moment about its own

aerodynamic center. The narrow fuselage may be neglected in the consideration of total liftand moment and the engine thrust is aligned through the mass center. The followingnumerical data is supplied.

Wing area : S= 253 m2

Wing mean aerodynamic center : c = 5.87 m

Wing mean aerodynamic center :xac= 5.5 m (back from wing apex)

Tail area : St= 70 m2

Tail ac location :t

l = 16.75 m (back from wing ac)

Wing lift-curve slope : aw= 4.2 (CL/rad)

Wing local moment coefficientwac

mC = -0.025

Tail lift curve slope : at= 4.0 (CL/rad)Tail incidence angle : it= 2.0

o(down from wing ZLL)

Downwash angle at zero wing angle-of-attack : !0= 0.5o

Downwash angle change with angle-of-attack : !"= 0.25 (rad/rad)Static margin for typical cruise flight : (hn- h) = 0.06a. Calculate the (elevator-fixed) neutral point location with respect to the wing apex.

b. Calculate the wing angle-of-attack (from the wing ZLL) required to hold the aircraft inpitch balance with zero elevator deflection.

2. An aircraft has the following data: The center of gravity is located 0.45c behind the

leading edge of the wing, the aerodynamic center of the wing-body is at 0.25c, the tail

volume ratio is 0.4, the wing lift curve slope is 0.08/deg, the tail lift curve slope is 0.07/degand #!/#"= 0.3, the tail setting angle is 3o, CMa.c. = -0.05,and the downwash angle at zero

lift is zero. The weight is 2500 lbs, the wing area is 200 ft2and the aircraft is flying at sea

level conditions.

a. Calculate the neutral point.b. Calculate the static margin.

c. Is this aircraft stable?

d. Calculate CM !, CM o , and !ee. What is this aircrafts trimmed lift coefficient?

f. What is this aircrafts trim speed?

3. A conventional aircraft (tail to the rear), is in trimmed, level, unaccelerated flight. Thewing is generating 40,000 lbs of lift and has a moment around the aerodynamic center of -

20,000 ft-lb. The aerodynamic center of the wing is located at 0.25c, the center of gravityis located at 0.45c, the aircraft has a chord of 5 ft, and the symmetric tail aerodynamic

center is located 10 ft behind the center of gravity. What is the lift generated by the tail andwhat is the weight of the aircraft? {Hint: Draw a sketch and assume thrust and all drag

forces act through the center of gravity.