Velocities and forces for a blade element

dT = Thrust dL = Lift dF = Force dN = Torque / radius dD = Drag U = Induced speed UA = Axial induced speed	UT = Tangential induced speed VA = Translation speed nP = Pitch speed ωr = Blade tip speed α = Angle of attack β = Inflow angle

Blade element theory (BET) is a mathematical process originally designed by William Froude

William Froude

William Froude was an English engineer, hydrodynamicist and naval architect. He was the first to formulate reliable laws for the resistance that water offers to ships and for predicting their stability....

 (1878), David W. Taylor

David W. Taylor

Rear Admiral David Watson Taylor, USN was a naval architect and engineer of the United States Navy. He served during World War I as Chief Constructor of the Navy, and Chief of the Bureau of Construction and Repair...

 (1893) and Stefan Drzewiecki

Stefan Drzewiecki

Stefan Drzewiecki was a Polish scientist, journalist, engineer, constructor and inventor, working in Russia and France....

 to determine the behavior of propeller

Propeller

A propeller is a type of fan that transmits power by converting rotational motion into thrust. A pressure difference is produced between the forward and rear surfaces of the airfoil-shaped blade, and a fluid is accelerated behind the blade. Propeller dynamics can be modeled by both Bernoulli's...

s. It involves breaking a blade down into several small parts then determining the forces on each of these small blade elements. These forces are then integrated along the entire blade and over one rotor revolution in order to obtain the forces and moments produced by the entire propeller or rotor. One of the key difficulties lies in modelling the induced velocity on the rotor disk. Because of this the blade element theory is often combined with the momentum theory to provide additional relationships necessary to describe the induced velocity on the rotor disk. At the most basic level of approximation a uniform induced velocity on the disk is assumed:

Alternatively the variation of the induced velocity along the radius can modeled by breaking the blade down into small annuli and applying the conservation of mass, momentum and energy to every annulus. This approach is sometimes called the Froude-Finsterwalder equation.

If the blade element method is applied to helicopter rotors in forward flight it is necessary to consider the flapping motion of the blades as well as the longitudinal and lateral distribution of the induced velocity on the rotor disk. The most simple forward flight inflow models are first harmonic models.

See also

• Computational fluid dynamics
  Computational fluid dynamics
  Computational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with...
  
  
• 4th 5th of empi lights theory
• Circulation (fluid dynamics)
• Strip theory for fixed wing aerodynamics
• Conway non linear momentum theory

External links

• Blade Element Analysis for Propellers
• Helicopter Theory - Blade Element Theory in Forward Flight from Aerospaceweb.org
• Blade element theory
• Stefan Drzewiecki 1903
• QBlade: Open Source Blade Element Method Software from H.F.I. TU Berlin
• Review paper on forward flight inflow models by Robert Chen, NASA