Brief reference for equations relating to flight dynamics. Taken from the book “The Illustrated Guide to Aerodynamics” by H.C. “Skip” Smith and “The Science of Flight” video course on the Great Courses.
Lift Equation
Relates aircraft velocity, air density, and wing area to the amount of lift generated by the wing. Coefficient of lift is essentially a fudge factor that is dependent on the wing shape, airfoil type, and angle of attack.
Deploying flaps increases the coefficient of lift, which decreases stall speed.
L = C_L * ( \frac{\rho * v^2}{2}) * AC_L: \text{Coefficient of lift} \\
v: \text{Velocity through the air} \\
\rho: \text{Air density} \\
A: \text{Surface area of the wing (top projected)}\text{Note that } \frac{\rho * v^2}{2} \text{ is dynamic pressure}Drag Equation
Similar to the lift equation, this relates drag to velocity, air density, and aircraft surface area. Coefficient of drag is a fudge factor to account for other factors such as aircraft shape and angle of attack.
D = C_D * ( \frac{\rho * v^2}{2}) * AC_D: \text{Coefficient of drag} \\
v: \text{Velocity through the air} \\
\rho: \text{Air density} \\
A: \text{Aircraft surface area (front projected)}Load Factor
Describes the load put on the aircraft structure while maneuvering in flight. In steady state flight the load is equal to 1.
n = \frac{L}{W}n : \text{Load Factor} \\
L : \text{Lift} \\
W : \text{Weight}Stall Speed
Speed below which the aircraft no longer has sufficient lift.
V_{ss} {\propto}\sqrt{\frac{n*W}{S* C_L}}V_{ss} : \text{Stall Speed} \\
n: \text{Load Factor} \\
W : \text{Aircraft Weight} \\
A : \text{Wing area (top projected)} \\
C_L : \text{Lift Coefficient}Turn Radius
R = \frac{V}{g * tan(\phi)}R: \text{Turn radius} \\
V: \text{Flight speed} \\
\phi: \text{Roll angle}