The blade element momentum theory is actually a combination of two theories: the momentum theory and the blade element theory. This combination allows for a calculation of local forces that may be applied to a turbine blade, propeller, or similar object. Together, the two theories make it easier to calculate the induced velocities of the rotor powering the blade than if it were calculated separately.

The first blade element momentum theory was introduced in 1878, then refined in 1921 and 1926 to modernize the idea as technologies evolved in the aircraft and windmill/turbine industries.

### Two Methods Examine How a Turbine Operates

Within the blade element momentum theory, there are two methods used to examine the operation of a wind turbine.

- A momentum balance is used on an annular stream tube that rotates as it passes through a turbine.
- The forces generated by the lift and drag coefficients are examined in various sections along the blade or propeller.

These methods are then given a series of equations which are solved iteratively. Although the equations are rather simple from a conceptual standpoint, they can sometimes be a challenge when trying to solve them consistently with high levels of precisions. To counter the inconsistency that is often observed within the theory, several solution approached have been developed to obtain the required information that is available.

A complete overview of those equations, along with how and why they apply, has been produced by Andrew Ning with Brigham Young University-Provo.

### Possible Issues with the Blade Element Momentum Theory

For the equations of the blade element momentum theory to be applicable, there are 5 key assumptions and drawbacks that must be taken into account.

**#1. The theory assumes that each annular ring is always independent of every other ring.**

Annual rings are the contact point where different layers connect to each other through a pad and via, allowing traces to connect with one another. Within this theory, the assumption is that the rings are independent of one another to generalize the equations. Otherwise, every application of the theory would need to be independently measured and analyzed before calculations could begin.

**#2. There is no accounting for wake expansion.**

Wake expansion occurs as air movement moves away from the propeller. Think about the wave pattern you would see from a boat traveling at a high speed in water. The wake from the boat is small when it is close to the boat, but can be quite large as it travels away. This occurs with air movement and propellers or blades as well.

**#3. There is no accounting for tip losses.**

Tip losses are vortices that form behind a wing as it begins to generate lift. The air rotates like a vortex from the tip of the blade, propeller, or ring. Because the theory does not account for this type of air movement, equation corrections must be included during the calculation phase to ensure that the results achieved are as accurate as possible.

**#4. It does not account for yaw.**

The equations must be modified within the blade element momentum theory to account for yaw. Yaw is the motion of a rigid body as it changes the direction it is pointing. The velocity of the yaw can affect the movement being calculated, so these adjustments must be individualized to account for various speeds of yaw that are anticipated.

**#5. It is based on steady air movements.**

If you’ve ever flown in an aircraft, then there is a good chance that you’ve encountered turbulence. The blade element momentum theory must make the assumption that the air movement is non-turbulent for the equations to be calculated. Air movement, however, is rarely non-turbulent, which means the outcomes are always the best-case scenario instead of a realistic picture of performance.

### Why Use the Blade Element Momentum Theory?

The blade element theory was initially designed to determine the behavior of a propeller. It breaks down the components of the propeller into its various parts to determine what the forces on each element will be. These forces are integrated along the entire blade, creating a picture of what will be encountered with every rotation.

The momentum theory describes the mathematics behind the movement of an actuator disk, which is why it is applied to rotors and propellers.

When combined, the blade element momentum theory provides a picture of ideal performance that can be used for additional information-gathering purposes. Because of the assumptions that must be made, however, the equations may not provide real-time information that may be needed.