# Prop Thrust Questions

## Main Question or Discussion Point

The following are a few questions that i have come across while writing takeoff distance code:

1. Assuming a known static thrust, how will this thrust vary as the airspeed increases?
ex. Is the relationship linear? quadratic? how can i determine the coefficients of the "thrust in terms of velocity equation"?

2. Assuming i know my engine power output at given rpm, and given some known prop parametrs. What program/website contains the equations needed to find the static thrust output?

3. Does anyone know of some good Take Off Distance Calculators that i can use as a sanity check for my code?

Related Aerospace and Astronautics Engineering News on Phys.org
http://selair.selkirk.bc.ca/aerodynamics1/Performance/Page8.html [Broken]
http://www.epi-eng.com/propeller_technology/selecting_a_propeller.htm
http://www.mh-aerotools.de/airfoils/propuls3.htm
This is a more advanced approach
http://www.allstar.fiu.edu/aero/BA-Background.htm

The problem with props is that it is hard to get efficiency numbers for them. The manufacture may provide them if you ask.

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One of the websites you listed had the following graph:

http://www.epi-eng.com/images/Redrives/PropEff-01.gif

which is EXACTLY what i am looking for.

However i need to know how to generate something like this mathematically
using my own horsepower, rpm, and prop paramaters

Any ideas?

I'm going to bump this thread because I think its an interesting question. Have you already figured out the answer? I'd like to see what you did. I'm going to try and read the links provided and help if I can.

Yes i found a good chapter in the following book describing what i wanted:
Propeller Theory and Applications in the book "Airplane Aerodynamics and Performance" (Roskam)

The problem is that the geometry of the propeller and in particular the integrated design lift coefficient ( CLi) and blade activity factor ( AF ) must be known to analytically solve for static thrust and thrust at any given airspeed.

In my case i am working on sizing a roughly 40 lbs UAV and will be using R/C props, which as far as i can tell do not have these required parameters readily provided so what i am doing is assuming a linear thrust profile starting from the static thrust and decreasing at about (1 ft/s every dv = 30 ft/s ) this is based on the output of some "prop calculators" available online. This set-up is numerically iterated for a range of thrust values in MATLAB and a curve has been generated.

Since your using R/C props, check out www.rcgroups.com. Theres a lot of threads there that provide tons of data on props and motors. There is also a UAV forum as well.

I talked to some friends of mine who do blade stuff and they said you're probably going to have to do some form of a blade element analysis.

I might have a trick to try though that will give you roughly (hopefully) a close answer.

2. Assuming i know my engine power output at given rpm, and given some known prop parametrs. What program/website contains the equations needed to find the static thrust output?
To determine the static thrust, I would use the following $$Eq^n$$:

$$T=\frac{c_T}{c_p}\frac{P}{nD}$$

Where:
P = power (ft-lb/s or kWW)
T = Thrust (lb or kN)
D = Prop Diameter (ft or m)
n = rotation speed (rev/s)
$$c_P$$ = Power coefficient
$$c_T$$ = Thrust coefficient

And:

$$c_P=\frac{P}{\rho n^3 D^5}$$

$$c_T = \frac{T}{\rho n^2 D^4}$$

Given the fact that you can mesaure the power and rpm on your static test stand, you can formulate a curve for the static thrust vs. rpm data you are collecting and compare the theoretical value to your measure value if you place a scale on the bottom of your test stand to measure the thrust.

It would be interesting to see how close the two come to eachother.

Source: Aircraft Design: R.P. Raymer p. 393-400

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Ok, so I was talking to a friend of mine and he came up with this equation. He tried to apply his Helicopter Theory equations to forward flight of an airplane. Hopefully these are somewhat appropriate. I like the approach because it simply matches power and disregards propeller efficiency.

The standard $$Eq^n$$ in texts is:

$$TV=\eta P$$

The problem is when you solve for T in terms of V, the 1/V relationship means that the thrust blows up to infinity as V approaches zero. Now, the catch is that $$\eta$$ goes to zero as V goes to zero. So the limit of $$\frac{\eta}{V}$$ as V goes to zero should approach the static thrust value. In order to evaluate this limit you would need to know $$\eta$$ as a function of V: $$\eta=\eta(V)$$. You do not know this, so I dont see this as being a feasible solution.

My friends approach:

Match the power. Because you are measuring the max static thrust, the amount of power being consumed by the engine in this case cannot exceed the maximum power in forward flight. This means:

$$T_sV_s=T_{\inf} (V_{\inf}+V_{d} )$$

Where:
$$T_s$$ = Static Thrust
$$V_s$$ = Velocity of air as it is sucked into the propeller plane while sitting on the test stand
$$V_\inf$$= Forward Velocity of A/C
$$V_d$$ = Differential increase in velocity of the freestream air resulting from the propeller accelerating it.
$$T_\inf$$ = Thrust at freestream velocity

Rewritting this gives:

$$T_\inf= \frac{T_s} { \frac{V_\inf}{V_s} + \frac{V_d}{V_s} }$$

From momentum theory:

$$\frac{V_d}{V_s}=\sqrt{ (\frac{V_\inf}{2V_s})^2 + 1 } -\frac{V_\inf}{2V_s}$$

Where:

$$V_s=\sqrt{\frac{T_s}{2\rho A_{prop}} }$$

Where:
$$A_{prop}$$ = Area of the Propeller -> $$A_{prop} = \frac{\pi}{4} D^2$$

Thank you for your reply, the information has been very helpful, ive also received some additional data from the prop manufacturer that i can use as a sanity check.

Cyrus,

i used the equations in your first reply because the manufacturer provided me with the related data.

attached is an output for Thrust vs Velocity, it seems pretty reasonable to me.

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Cyrus,

i used the equations in your first reply because the manufacturer provided me with the related data.

attached is an output for Thrust vs Velocity, it seems pretty reasonable to me.
Which reply? I don't have any equations in my first reply so I dont know how you are coming up with this curve.

I meant 3rd, sorry.

I meant 3rd, sorry.
But that was for static thrust. You used the wrong equation then. You should have used the one #9.

The following are a few questions that i have come across while writing takeoff distance code:

1. Assuming a known static thrust, how will this thrust vary as the airspeed increases?
ex. Is the relationship linear? quadratic? how can i determine the coefficients of the "thrust in terms of velocity equation"?

2. Assuming i know my engine power output at given rpm, and given some known prop parametrs. What program/website contains the equations needed to find the static thrust output?

3. Does anyone know of some good Take Off Distance Calculators that i can use as a sanity check for my code?
nP=Tu, thats a given
can you please give the values of the prop parameters you have? thatl help figure out the power equation
take off distance is different for each aircraft. which one are you dealing with? what info have you been given about it?

(i just finished a project involving take-off and landing and im thinking urs is similar to that..)