RCU Forums - Simple method for calculating a prop's thrust

RCU Forums (https://www.rcuniverse.com/forum/)

- The Clubhouse (https://www.rcuniverse.com/forum/clubhouse-190/)

- - Simple method for calculating a prop's thrust (https://www.rcuniverse.com/forum/clubhouse-190/1437061-simple-method-calculating-props-thrust.html)

Simple method for calculating a prop's thrust

Here's a small (I'm not so sure:eek:) article I wrote explaining how to calculate a prop's static and dynamic thrust. Read it and tell me what you think. Error corrections are also welcome;)

As soon as I get the FTP problems I'm facing solved, I will upload it to my website and I will let you all know.

A simple method to determine a propeller's static and dynamic thrust

This is a simple method which I developed for calculating a prop's performance. This method is not perfectly accurate (due to the assumption of a single lift curve for all propellers), but gives a good approximation of the thrust value with around 5-10% of error margin. For accurately determining the static thrust the most recommended method is to actually measure it, same for the dynamic thrust, but it's not that easy to measure the later.

First, let's begin by explaining that a propeller's pitch is the theoretical amount of forward advance in one revolution, as if it was a nut in a screw, with that said we can call it the geometric pitch. The aerodynamic pitch is the angle of attack (AoA or alpha) of the blade with the air-stream coming into it. The common denomination of propellers (at least for model aircraft purposes) includes the geometric pitch in inches, and that's measured at 75% at the length of one of the blades (.75 radius). But this number isn't proportional only to the AoA (aerodynamic pitch) as many people think, due to the nature of the pitch definition, it's also linked with the propeller diameter (or radius). Since any prop has an airfoiled section, we can determine the thrust (and the torque needed to spin it by using the drag, but that's not covered in this article) by calculating the amount of lift it produces based on the prop's airfoil lift coefficient, but since every brand of prop has a different airfoil, and bladewise speaking the airfoil changes it's incidence a lot, to accurately calculate the thrust gets really complicated. But this problem can be solved by using a generic lift curve (modified to account the incidence changes), which greatly simplifies the process.

Now, let's get to the equations. For the equations to work out, the SI units have to be used, so first you have to convert the prop's dimensions from inches to meters by multiplying them by 0.0254, also the speeds will be in meters per second (miles per hour * .447) and the thrust in Newtons (Pounds / 0.221). Since we are using the data at the 75% radius station, let's calculate what the radius is at this position:

R = (Diameter / 2) * 0.75

Now, let's calculate the geometric pitch angle (the blade incidence from the horizontal plane):

GP = Atan(GeoPitchDistance / (6.2832 * R))

We need to know how many revolutions the prop makes in a second, so:

RPS = RPM / 60

Now, we can proceed to calculating the rotating speed at .75 radius:

RV = 6.2832 * RPS * R

And the aerodynamic pitch (AoA) with FV being the forward speed of the aircraft in meters per second (obviously for static thrust it is 0, but in this method using 0 will lead to an error, so the smallest recommended number for FV is 0.5):

AP = GP - Atan(FV / SV)

Calculate the accelerated stream velocity:

ASV = FV / Sin(Atan(FV / SV))

Here we will calculate the lift coefficient by using the generic lift curve. For AoA's smaller or equal to 20 degrees:

Cl = (-0.00868 * AP2) + (0.21131 * AP) - 0.15734

And for AoA's greater than 20 degrees:

Cl = (-0.0000767 * AP2) - (0.000565 * AP) + 0.71244

Calculate the drag coefficient:

Cd = (0.000142 * AP2) + (-0.00671 * AP) + 0.19767

Before we go the thrust equation, we have to calculate the blade chord (which can also be measured at it's widest point, but most propellers have a blade AR of 6, so it's only a matter of dividing the prop radius by 6) and the air density at the altitude (in meters) which the prop is operating:

rho = 1.223 * 0.9 ^ (Altitude / 1000)

Finally, here's the thrust equation:

T = (NumberOfBlades * BladeChord * R * 0.5 * rho * ASV2 * (Cl * Cos(Atan(FV / SV)) - Cd * Sin(Atan(FV / SV)))) * 0.47

In order to make the calculation easier, here's a summary of the data you need to have in hand before solving the equations:

- Prop diameter in meters

- Prop pitch in meters

- The RPM at which the prop is turning

- The prop's number of blades

- Prop forward speed (is also the aircraft's forward speed)

A simple derivation from the Geometric pitch equation

This simple variation allows us to calculate with reasonable accuracy at which speed the prop would stop producing thrust, that also can be called the prop's max speed for a given RPM.

PMS = GeoPitchDistance * (RPM / 60)

Further notes on propeller behavior

By solving the equations presented above, we can see the reason for some important propeller behaviors. For example, why high pitch props have lower static thrust values (thus poor take-off acceleration and 3D flying performance) than low pitched ones (which give higher takeoff acceleration and better 3D performance). Or, by using the derivation from the geometric pitch equation, why low pitch props give slower top-end speeds when compared to high pitched ones.