# HORIZONTAL FLIGHT: BLADE ELEMENT THEORY

Although momentum theory can be used with some success to determine the power required by a helicopter in horizontal flight it does not gives us a complete analysis of the situation. As with axial flight we have to adopt a blade element approach if we are to understand the power requirements more fully. The elemental thrust, torque and power can be written as:

ST = SL cos — SD sin ^

82 = (SL sin ^ + SD cos ^)r

SP = (SL sin ^ + SD cos ^) )r

On integrating the torque equation, it was found to contain elements that matched those obtained using momentum theory. These elements can be traced to the presence of SL sin ^ in the elemental torque equation. It is therefore possible to simplify the mathematics associated with using blade element theory by only considering the drag component. The estimate of power required using this method is then added to that

the hub. By integrating the drag force acting normal to the blade element a relationship for the profile power is obtained. Unfortunately, this is not the complete picture. Although the power required to drive the rotor around the hub has been found, in the face of a horizontal airstream (V), it has not accounted for the power required to drive the rotor system forward: the rotor parasite power. This additional power arises because there will be a hub force acting rearwards which must be matched by a component of the rotor thrust. The hub force appears because there is an asymmetry of drag acting on opposing blades. When a blade reaches the advancing side, it will see increased drag, a component of which will act rearwards. An opposing blade will see reduced drag as it enters the retreating side. Although a component of the drag on the retreating side acts forwards, it will be less than on the advancing side and a net rearward hub force will result.