Derivation of the Aerodynamic Forces for the Mesicopter Simulation

The derivation of the aerodynamic forces is resolved using a combination of momentum and blade element theory. Momentum theory is used to derive the inflow or induced velocity. The rotor is modeled as an actuator disk across which there is no discontinuity in velocity, but there is a discontinuity in pressure. The inflow velocity of the air when it crosses the disk, and is assumed to be uniform at all points on the disk. Using conservation of mass through the disk and conservation of energy in the wake leads to an equation for thrust of the form T = 2ρAν 1 . In hover, the thrust is equal to the weight so T is replaced by W . Solving for the inflow velocity in hover results in the following expression: