Consider the element at radius r, shown in Fig. 1, which has the infinitesimal length dr and the width b. The motion of the element in an aircraft propeller in flight is along a helical path determined by the forward velocity V of the aircraft and the tangential velocity 2πrn of the element in the plane of the propeller disc, where n represents the revolutions per unit time. The velocity of the element with respect to the air Vr is then the resultant of the forward and tangential velocities, as shown in Fig. 2. Call the angle between the direction of motion of the element and the plane of rotation Φ, and the blade angle β. The angle of attack α of the element relative to the air is then .  
Applying ordinary airfoil coefficients, the lift force on the element is: 
Let γ be the angle between the lift component and the resultant force, or . Then the total resultant air force on the element is: 
The thrust of the element is the component of the resultant force in the direction of the propeller axis (Fig. 2), or 
and since 
For convenience let 
and
Then 
and the total thrust for the propeller (of B blades) is: 
Referring again to Fig. 2, the tangential or torque force is  
and the torque on the element is 
which, if , can be written 
The expression for the torque of the whole propeller is therefore 
The horsepower absorbed by the propeller, or the torque horse-power, is 
and the efficiency is