Momentum theory approximations can be used to predict the thrust and power requirements for forward flight of the helicopter. It will be assumed that the vehicle is in straight and level flight with the rotor disk tilted at angle (αT) so that the thrust forward component balances drag components and the vertical component balances weight of the vehicle.
T cos (αT) = W αT is small so T=W
The thrust will need to be produced by the rotor is a similar fashion to hovering or vertical climbing flight with the exception that the momentum change will have additional velocity components due to forward motion of the vehicle. The velocity at the disk will no longer be uniform but will be a function of location around the disk.
Local velocity Vdisk on blade at any point around the disk will be made up of two components, an in-plane component U cos (αT) and a normal component U sin(αT) + vi , where the induced velocity vi is assumed to be produced only at right angles to the disk plane.
The mass flow through the disk plane will be,
Thus the total thrust produced will be equal to the change in momentum flow perpendicular to the rotor disk.
T = momentum flow out - momentum flow in
= mass flow x velocity in slipstream - mass flow x incoming velocity.
where vs is slipstream velocity normal to disk
By applying an energy balance as was done for hovering flight it can again be shown that the slipstream velocity is,
vs = 2 x vi