>>14331118As velocity increases, beta tends to zero.
F_air = alpha v^2 + beta / v^2
Air forces have perpendicular components F_ax and F_ay. Forward velocity of the plane is along x.
F_ax = Induced drag
F_ay = Lift
F_air = F_ax + F_ay = alpha v^2 + beta / v^2
Does this allow me to say
F_ax = alpha v^2 (Drag)
F_ay = beta / v^2 (Lift)
? ( i can't say if i identified drag and lift backwards)
F_ax = -F_ay + alpha v^2 + beta / v^2
I don't know what conditions would change the range or endurance. For (b) I guess maximum endurance comes from having minimum drag. Velocity must be as low as possible while providing enough lift.
F_ay = F_ax + alpha v^2 + beta / v^2
Let the x component tend to zero
F_ay = 0 + alpha v^2 + beta / v^2
Velocity, v, is the forward velocity of the plane and this will be along x. As drag tends to zero, so does forward velocity. There must be some minimum value for lift required for flight, or else everything tends to zero and the flight is zero. This must be contained in the constants alpha and beta.
Take the derivative of the
with respect to
Set F_ax to zero, apply constants, enjoy solution
