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I need to calculate the velocity of an airplane after it executes quarter loop (starts horizontally, pitches up and ends vertically). Because I also need to know the velocity at several intermittent points I wrote an incremental equation (below).

But this is only correct (if it is correct at all) as long as lift does not change. But as velocity falls so does lift. So how do I include this?

Fdt – drag force [N] (calculated separately)

Ft – thrust force [N] (calculated separately)

t – time step

m – mass of the airplane [kg]

theta – pitch rate [°/s]

g – gravitational acceleration [m/s˄2]

alfa=alfa+(theta*t) % pitch angle relative to ground [°]

v=v-(t*Fdt/m)-(g*cosd(alfa)*t)+(t*Ft/m) % vehicle velocity in its longitudinal direction [m/s]

note: pitch rate can be substituted for anything more usable

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# Calculation of velocity during pitch up

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