Helicopter Hover Analysis

The helicopter rotor can be idealised as a “momentum disk”. It imparts a uniform velocity (vi) to the airflow creating a change in momentum which will result in an upward thrust (T).

HOVER

The variation of pressure will drop below atmospheric above the disk, increas due to the energy input of the disk and then drop bad to atmospheric in the slipstream. Applying and Energy balance will again lead to v s = 2 v i so that, T = 2  A  v i  V c  v

Power required from engine to produce this thrust from the induced velocity  will be

P(hover induced velocity)  = Phi = T.vi

CLIMB

For the case where the helicopter is climbing, the rotor will capture flow from a fixed area above and accelerate this to a final slipstream velocity. The

Solving this as a quadratic equation for vi gives,

or

If climb rate is small then it can be assumed that T = W  so that required induced velocity can be predicted for varying climb rate.

Less induced velocity is required for climb as the momentum change applied to a higher initial velocity is more effective.

Power requirement is not reduced in a similar fashion. While engine power is still needed for thrust creation, there is additional power required to move the vehicle at a climb speed.

P(ideal climb total)  = P(induced velocity for climb) + P(climb)

P(ideal climb total) = T . vi   +    T . Vc

The power required for climbing will thus be,

Assuming climb rates are small, so that thrust approximately equals weight, the variation of power required for different climb rates is shown in the following figure (weight of typical helicopter assumed).

Note : The above power estimates only cover the requirements for the rotor acting as a ideal momentum disk.  This covers induced velocity and climb requirements only.  In reality to produce the momentum change rotor blades must be pushed around within the disk, hence there will be an additional requirement of power to overcome the profile drag of the rotor blades. This will be covered analytically in a following section or may be predicted numerically using blade element theory.

DESCENT

For descent rates that are small and do not approach the magnitude of vi, the analysis can be carried out using a negative value of Vc in the above equations. However there are physical limits on this approach due to the changing flow pattern. As the capture area is now below, problems will arise as the rotor is now capturing its own wake an recirculating it to create momentum change. Eventually at a higher rate of descent the system will become closed and the rotor will simply recycle its own wake ('ring state'). In this condition there is no momentum change and hence no thrust. If decent is fast enough then flow pattern will fully reverse and rotor will 'windmill' or auto-rotate. The momentum change is now negative with the rotor be powered by the airflow. upward thrust will again be produced in this auto-rotation state.