# How many ways/methods to calculate propeller/rotor's power output? Which one is the best?

Source: Wikipedia

I want to know how many ways/methods to calculate the output power of a propeller? So far I knew three methods:

My question are:

1. Is any other way/method?
2. If any, what way/method is it?
3. And what is the best way/method to calculate the output power of a propeller (Power = Thrust x Velocity)?
4. Are those ways/methods applicable for Computational Fluid Dynamic (CFD)?
5. If those ways/methods are applicable for CFD, which one is the best?

There are many approaches that have been used to model propellers. Each has their pros/cons and tradeoffs of what they can capture vs. their computational cost.

Momentum theory (also called actuator disk theory) treats the prop as an impulsive pressure jump -- there are no individual blades modeled. It does not capture the detailed shape (chord, twist, lift coefficient) of the prop. It usually does not model a complex load distribution -- but can be extended to load distributions.

Blade element is basically a strip-wise integration along a blade. Each strip is treated as if it is in 2D flow. There are some empirical tip-loss factors that can be applied. This theory does not generally capture the induced inflow to the propeller well. There is no blade-to-blade interaction in this model.

BEMT combines the above to better capture the induced inflow to a propeller. It still does not capture blade-to-blade interaction. It still uses an empirical factor for any 3D effects.

Next you go to potential flow and vortex theories that can start to capture discrete blade effects and blade-to-blade interaction. These can also better capture 3D effects.

Then you move to more traditionally numerical methods. Rotating lifting line and rotating vortex lattice -- these can be done in an unsteady formulation, or in a steady formulation with a rotating reference frame.

Then you move to a rotating panel code, followed by various CFD formulations.

The ability of these methods to predict thrust and power varies on the flow condition.

A heavily loaded prop (high thrust and/or static/hover conditions) is harder to predict than a lightly loaded cruising prop.

Tips that are transonic or supersonic complicate matters.

Heavily loaded props that exhibit significant blade-to-blade interaction and 3D effects may have 3D shapes that can not be modeled by some of the more simple methods.

• Thank you for your explanation. I just didn't know where to go. Normally in Wikipedia will be referred to another link if any, but I didn't see it there. Let me dig deeper to those methods you mentioned. Thanks a lot. Commented Oct 23, 2023 at 19:13
• Btw, how accurate do you think the Momentum Theory aka Actuator Disk Theory if I used to calculate subsonic angular speed propeller? Commented Oct 23, 2023 at 19:17
• Actuator disk theory is extremely limited. It only calculates the ideal induced power for a uniformly loaded disk. It can not calculate viscous and other sources of power. Thrust is an input to actuator disk, so it captures that exactly. Actuator disk theory is only based on conservation of mass and conservation of linear momentum -- it can't be very wrong. It just might not give all the answers you want. Commented Oct 23, 2023 at 22:46
• From those three methods I mentioned above and those another methods you mentioned, which one is the (still) acceptable method to calculate propeller output power for subsonic angular speed (common propeller, turbo fan is not included) used by hobbyist? Means, maybe the result is not fully accurate but still acceptable, yet not to complicated. Commented Oct 23, 2023 at 22:58
• They are all acceptable under certain circumstances. There is no easy answer here. I would suggest you first look at the UIUC propeller database m-selig.ae.illinois.edu/props/propDB.html, the data provided by APC Propellers apcprop.com/technical-information/performance-data or if you really want to do computations, XRotor web.mit.edu/drela/Public/web/xrotor, QProp web.mit.edu/drela/Public/web/qprop, or CCBlade github.com/byuflowlab/CCBlade.jl or VSPAERO openvsp.org Commented Oct 24, 2023 at 1:01