# Power output of an anchored propeller

1. Apr 17, 2014

### Leon (AW)

I have a motore with a propeller anchored to a load cell to measure the lift produced at varying power inputs. This is for a student activity I am running and I wanted to show that though more power in gives more lift there is a point after which efficiencey starts to go down again so I tried to also calculate the power output of the propellers to get the efficiency of the blades.

***Edit***:Thought of a better way of explaining this. if it was a fixed wing I would move it D distance in T time generating F force and my power would be F*D/T. but for a rotating blade the distance D it moves in T time depends how close to the end you are and I can't figure out how to calculate ecounting for that.

Any help would be great thanks.

***old thoughts***
I thought at first the propelor would effectively have potential energy as it applies a constant force like gravity does but the energey in goes up by time where the potential goes up by time squared.
I tried to calculate the speed it would have if not anchored by picking an arbitrary time and deviding by the mass however as you can see from the attachment that's wrong as it would accelerate for ever so the power out increases with time while the power in stays the same.

Any idea how I can work this?
Should my speed be the rotational speed of the propeller maybe? (or would that just give me the power output of the motor).
maybe I need to calculate the volumetric air flow from pressure (getting pressure from force and propeller area) and take speed from that.

#### Attached Files:

• ###### prop power.bmp
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Last edited: Apr 17, 2014
2. Apr 17, 2014

### Staff: Mentor

Hi Leon (AW). So you have turned your propeller to point vertically upwards, like a simple helicopter or powered gyrocopter, and wish to calculate the lift it produces? I reckon a google search should turn up a lot of useful information, you surely wouldn't be the first to ponder this!

Good luck, and Happy Easter!

3. Apr 22, 2014

### Leon (AW)

I have googled it for hours but everything I have found either requires it moves or only measures forces. I likely have all the equations I need to figure this out I'm just not making the link somewhere between two of them. That's why I came here to see if anyone can point out the bit I am missing that will be obvious once I know it.

I'm usually pretty good with figuring this stuff out but I'm just drawing a blank this time and can't find an example online. I think it is because I am so used to figuring out power by measuring velocity and calculating out the force to put into a power equasion whereas this time I am measuring the force and trying to calculate the velocity. Every time I try I get the power increasing with time.

Last edited: Apr 22, 2014
4. Apr 24, 2014

### satchurated

So you are trying to build a efficiency curve, right?

5. Apr 24, 2014

### Leon (AW)

Yes, I know the power in but I can't figure out how to calculate power out.

6. Apr 24, 2014

### satchurated

You mean thrust..

7. Apr 24, 2014

### Leon (AW)

It is chained to a load cell I can read thrusting force of the screen. what I want is, knowing the mass of the object, how much power will that thrust be worth if i were to cut the chain.

if I cut the chain I could measure it's speed and calculate the thrust from it's mass. with the chain I can measure it's thrust so how do I calculate it's potential speed from it's mass.

8. Apr 24, 2014

### satchurated

If you're studying the dynamics of a multirotors, speed is not so important as you think

9. Apr 24, 2014

### Leon (AW)

More power in will continually give more thrust (up to a limit) however the peak efficiency, where the law of diminishing returns starts to kick in, is not obvious on a power to thrust graph. It is obvious on a power in to power out graph though.

10. Apr 24, 2014

### satchurated

One thing is power to thrust, which is different to speed as you talk. The force is not calculated as above, but in a way more complex because thrust needs to take into account the weight

11. Apr 24, 2014

### cjl

If it's stationary, power out is zero :)

Alternatively, you could calculate the power in the fluid jet, which would be 0.5 times the mass flow rate of the fluid times the square of the jet velocity (and you'd have to somehow measure or estimate the jet velocity and mass flow rate). There is no simple conversion purely based on thrust though.