MAE175__Discussion_5

Problem 2.7 (Nelson): Solution Solution : We first need to compute the new value for dC mCG dC L . In order to do so, we first find the position for the neutral point by using the data from the previous scenario: dC m cg dC L | {z } − 0 . 1 = x cg ¯ c |{z} 0 . 3 − x np ¯ c → x np ¯ c = 0 . 4 Now we can find the new slope dC m cg dC L = x cg ¯ c |{z} 0 . 1 − x np ¯ c |{z} 0 . 4 = − 0 . 3 Jordi Ventura Siches University of California, Irvine - Henry Samueli School of Engineering MAE 175: Discussion 5 3 of 17

Problem 2.7 (Nelson): Solution (a) Solution: To find the slope, select 2 points from any of the curves (they have the same slope). For δ e = 0 ◦ : C L = 0 . 4 , → C m , cg = 0; C L = 1 . 2 , → C m , cg = − 0 . 2 and the slope is dC m , cg dC L = − 0 . 2 − 0 1 . 2 − 0 . 4 = − 0 . 25 Therefore x np ¯ c = x cg ¯ c − dC m , cg dC L = 0 . 5 Jordi Ventura Siches University of California, Irvine - Henry Samueli School of Engineering MAE 175: Discussion 5 5 of 17

Problem 2.7 (Nelson): Solution (b) cont’d We get C m 0 = 0 . 1 from the figure (see green). For C m , δ e , we take δ e = 0 ◦ , → C m = 0 , δ e = − 8 ◦ , → C m = 0 . 3 for C L = 0 . 4 (see blue). Therefore: C m δ e = − 0 . 0375 / ◦ . Finally, trim implies C m = 0: 0 = C m , 0 | {z } 0 . 1 + dC m dC L | {z } − 0 . 25, from (a) C L |{z} 0 . 623 + dC m d δ e | {z } − 0 . 0375 δ e → δ e = − 1 . 5 ◦ Jordi Ventura Siches University of California, Irvine - Henry Samueli School of Engineering MAE 175: Discussion 5 8 of 17

Hints for Problem 1 (HW2), cont’d 1 2 Obtain position of the neutral point from static margin h n : h n = − C M , α C L , α = x np ¯ c − x cg ¯ c Impose C M = 0 (trim), α = 15 ◦ , δ e = − 25 ◦ , find C M , α | mostforward . Find corresponding static margin → find CG position. Jordi Ventura Siches University of California, Irvine - Henry Samueli School of Engineering MAE 175: Discussion 5 10 of 17

Hints for Problem 3 (HW2) Problem 3 : An airplane has the following pitching moment characteristics at the center of gravity position x CG c = 0 . 3 : C M 0 L = 0 . 05 , dC M dC L = − 0 . 1 , and C M δ e = − 0 . 01 / deg If the landing gear deployment causes an increase in the drag coefficient at the landing flight condition by ∆ C D = 0 . 05 1 Estimate the induced pitching moment due to landing gear deployment ( ∆ C M 0 L ), assuming that the line of action of the additional drag force is 50% c below the fuselage reference line. 2 If the airplane is loaded so that the center of gravity position moves to x CG c = 0 . 15 , can the airplane be trimmed during landing where C L = 1 . 0 ? Assume that δ e max = ± 20 ◦ . Jordi Ventura Siches University of California, Irvine - Henry Samueli School of Engineering MAE 175: Discussion 5 13 of 17

Hints for Problem 4 (HW2), cont’d First compute h n without the propeller, as h n = − C M , α C L , α considering wing and tail effects for both coefficients: C M , α = C L , α , w x cg − x ac , w ¯ c − η t V H C L α , t ( 1 − d ε d α ) C L , α = C L , α , w + η t S t S C L α , t ( 1 − d ε d α ) Add the effect of the propeller: ∆ prop C L , α = 0 . 27 / rad is given, while ∆ prop C M α = ℓ prop − CG ¯ c ∆ prop C L , α Jordi Ventura Siches University of California, Irvine - Henry Samueli School of Engineering MAE 175: Discussion 5 16 of 17