Equilibrium of the Aggie Micro Flyer (AMF III)
220.127.116.11 Airplane Lift and Moment Curves
The equilibrium code calculated the lift and moment coefficients for the complete configuration at low incidences to be:
CL (a, tt) — 4.47a + 0.37tt + 1.11
См, о(а, tt) — -1.30a – 0.33tt – 0.28
corresponding to AR — 4.9. The main wing aspect ratio is ARm — bm/cm — 8. The difference is due to the wing+tail combination, whereby
amCL m + atCLt
am + at
Therefore, the lift slope and the apparent aspect ratio is a weighted average of the wing and the tail aspect ratios.
As seen in class, the aerodynamic center xac location is given by
The aerodynamic center is located at xac = 0.29lref = 0.6 m.
18.104.22.168 Equilibrium Incidence
The center of gravity is located at xcg/lref = 0.21.
The static margin is SM = (xac – xcg)/lref = 0.08 = 8%.
The equilibrium incidence a(tt) satisfies the equilibrium equation
CM (aeq) + CL (aeq) = 0
Solving for aeq one obtains
22.214.171.124 Take-Off Conditions
Substituting the previous result in the lift equation provides the equation for the tail setting at take-off
CL, to = 2.0 = 4.47(-0.7tt – 0.13) + 0.37tt + 1.11
Solving for tt one finds tt, to = -0.533 rd = -31°.
The incidence at take-off is therefore ato = 0.24 rd = 14°.
The tail lift coefficient at take-off is CLt, to = 2.49ato + 2.61tt, to – 0.36 = -1.15. The lift force (in N) on the tail at take-off is Lt = 2 pU 2atCu = -12 N.
The force on the tail is down.
126.96.36.199 Extra Credit
Free body diagram at take-off, see Fig. 15.19.
15.6 Solution to Problem 6