Aerodynamic Forces Relations: U.A.V

External Forces:

Listed below are the Forces, acting on the body of air vehicle during flight:

1. Drag Force opposite to V_T, D
2. Lift Forces perpendicular to V_T, L
3. Side Force, S

So L, D, S defines one coordinate system.

Transformation:

Rotation about y axis by α, and Z axis by β then inverting the components:

D = -Xcosαcosβ – Ysinβ + Zsinαcosβ

D = cosβ(Zsinα – Xcosα) – Ysinβ ………..Eq (1)

S = X cosαsinβ – Ycosα  + Zsinαsinβ

S =sinβ ( X cosα + Z sinα) – Ycosβ ……….Eq (2)

L = X sinα – Zcosα ……………………………Eq (3)

Inverting all the equations:

X = Lsinα  + (S sinβ  – D cosβ )cosα

Y = -(S cosβ  + D sinβ)

Z = -Lcosα + (S sinβ – D cosβ)sinα