text: Consider fluid flow around an airfoil. The flow of the fluid around the airfoil gives rise to lift and drag forces. By definition, lift is the force that acts on the airfoil normal to the apparent fluid flow speed seen by the airfoil. Drag is the forces that acts tangential to the apparent fluid flow speed seen by the airfoil. What do we mean by an apparent speed? Consider the diagram below:
  The speed seen by the rotor blade is dependent on three things: the axial velocity of the fluid, ; the tangential velocity of the fluid due to the acceleration round an airfoil, ; and the rotor motion itself, . That is, the apparent fluid velocity is given as below:
  Thus the apparent wind speed is just the magnitude of this vector i.e.:
  We can also work out the angle  from the above figure:
  Supposing we know the angle , we can then work out  simply by using the relation ; we can then work out the lift co-efficient, , and the drag co-efficient , from which we can work out the lift and drag forces acting on the blade.
  Consider the annular ring, which is partially occupied by blade elements. The length of each blade section occupying the annular ring is  (see figure below).
  The lift acting on those parts of the blades/airfoils each with chord  is given by the following expression:
  where  is the lift co-efficient, which is a function of the angle of attack, and  is the number of blades. Additionally, the drag acting on that part of the blades/airfoils with chord  is given by the following expression:
  Remember that these forces calculated are normal and tangential to the apparent speed. We are interested in forces in the  and  axes. Thus we need to consider the diagram below:
  Thus we can see the following:
   is the force that is responsible for the rotation of the rotor blades;  is the force that is responsible for the bending of the blades.
  Recall that for an isolated system the net angular momentum of the system is conserved. If the rotor acquired angular momentum, so must the fluid in the wake. Let us suppose that the fluid in the wake acquires a tangential velocity . Thus the torque in the air is given by
  By the conservation of angular momentum, this balances the torque in the blades of the rotor; thus,
  Furthermore, the rate of change of linear momentum in the air is balanced by the out-of-plane bending force acting on the blades, . From momentum theory, the rate of change of linear momentum in the air is as follows:
  which may be expressed as
  Balancing this with the out-of-plane bending force gives
  Let us now make the following definitions:
  So we have the following equations:
  Let us make reference to the following equation which can be seen from analysis of the above figure:
  Thus, with these three equations, it is possible to get the following result through some algebraic manipulation:
  We can derive an expression for  in a similar manner. This allows us to understand what is going on with the rotor and the fluid. Equations of this sort are then solved by iterative techniques.