Propeller efficiency with more than 2 blades.

[OwenN]

I recently did a drive efficiency analysis on the table for the 2805.6 1800 KV motor with 9x5 x 3 blade prop,
and it worked out that rpm was about 8,000, thrust was 78 % of expected, motor was 77% efficient, extra thrust due to blade friction was about 75 % effective,
and total drive efficiency over ideal was 55 %
I calculated friction at 0.01 Ca, 2 blades, but actual test prop was a 3 blade.

The motor used less amps and made more thrust on an 8 inch prop of unknown specs.

Computed flow velocity was 21 m/s (about 40 mph).

There doesn't seem to be much room to improve thrust efficiency by adding blades.

was 0.01 Ca a good measure of drag? - a propeller has relatively low profile drag, and higher surface drag.

Is my proportioning of loads and rpm estimate any good? how would errors affect the calculation results?

 

[TheFlyingBrit]

I am interested in this as I fitted a 3 blade prop on my Sportster as opposed to the 2 blade I would normally fly. Not having had chance to fly the 2 blade version I dont know which is the best option ?
I would guess the 3 blades will obviously produce more thrust, but then the current/voltage required to turn the 3 blades would increase so is it less efficient and if so by how much ?
It sounds like your already calculating this, so I would like to see what the comparison is between the 2 blades side by side ?

 

[OwenN]

I also have a problem finding good source info for simple thrust and drag equations.
I get T = 2x den x Vsq x A, - static thrust.

but drag = 1/2 den x Vsq x A x Cd (or Ca for aircraft.)
Cd is appropriate for dominant profile drag, Ca for surface drag.

Why 2 for one equation, and 1/2 for the other??

Is the thrust formula incorrect or over simplified?
It seems to be in line with actual results.

Also, if I have been switching these two , then my drag calcs have been off by a factor of 4 too high!

 

[JasonK]

go here, read the comments:
https://www.electricrcaircraftguy.com/2013/09/propeller-static-dynamic-thrust-equation.html

basically, the most efficient prop is a single blade, each additional prop adds thrust, but less then the prior one.

 

[OwenN]

I am interested in this as I fitted a 3 blade prop on my Sportster as opposed to the 2 blade I would normally fly. Not having had chance to fly the 2 blade version I don't know which is the best option ?
I would guess the 3 blades will obviously produce more thrust, but then the current/voltage required to turn the 3 blades would increase so is it less efficient and if so by how much ?
It sounds like your already calculating this, so I would like to see what the comparison is between the 2 blades side by side ?

I don't know- As far as I can see, extra thrust is not much, extra drag goes up by about a third.

Any thrust gain come if the motor is capable of spinning the two blade prop and the three blade prop at maximum motor
RPMs, as per a WW2 fighter plane. You may also be able to thrust more efficiently with less prop pitch.

Most model airplane motors are not under-propped to this extent.

I assume a bigger pitch than you need is less efficient and uses more power.

However, the 3 blade may have narrower blades and nice pointy tips, so not proportionately less efficient overall.
Also, what is the actual Cd/Ca applicable here?

 

[JasonK]

I also have a problem finding good source info for simple thrust and drag equations.
Why 2 for one equation, and 1/2 for the other??

https://wright.nasa.gov/airplane/drageq.html
https://www.grc.nasa.gov/www/Wright/airplane/propth.html

basically, that is the 'simple' forms for both, in reality they are both much more complicated. The big take away is that drag generally goes up proportionally to velocity squared, and thrust is proportional to the (velocity out squared - velocity in squared), so as the craft goes faster, drag goes up quickly and thrust starts dropping off... which sets a fairly clear max speed given the shape of the 2 curves. actual tests are needed for either to get exact numbers.

 

[TheFlyingBrit]

https://wright.nasa.gov/airplane/drageq.html
https://www.grc.nasa.gov/www/Wright/airplane/propth.html

basically, that is the 'simple' forms for both, in reality they are both much more complicated. The big take away is that drag generally goes up proportionally to velocity squared, and thrust is proportional to the (velocity out squared - velocity in squared), so as the craft goes faster, drag goes up quickly and thrust starts dropping off... which sets a fairly clear max speed given the shape of the 2 curves. actual tests are needed for either to get exact numbers.

Same principle with cars you need a lage increase in power for a small gain in speed due to drag. Air has a lot to answer for, it causes a lot of drag !
At least the discussion has confirmed my thoughts that although my Sportster looks the part with a 3 blade prop, the 2 blade will be more sensible in the future for efficiency and reduced load on the motor.

 

[Merv]

Here is some prop performance data for APC props.

https://www.apcprop.com/technical-information/performance-data/

 

[OwenN]

https://www.masterairscrew.com/pages/mr-drone-propellers
Ditto master airscrew 2-bladed props.
Their tips don't really look high performance-I thought narrow elliptical forms were best?

 

[OwenN]

Here is some prop performance data for APC props.

https://www.apcprop.com/technical-information/performance-data/

What do they mean by advance ratio? Is it related to pitch?
How do I interpret their spec in relation to diameter, number of blades, and pitch?

 

[OwenN]

these 2 look good for static-type thrust?

 

[OwenN]

https://wright.nasa.gov/airplane/drageq.html
https://www.grc.nasa.gov/www/Wright/airplane/propth.html

basically, that is the 'simple' forms for both, in reality they are both much more complicated. The big take away is that drag generally goes up proportionally to velocity squared, and thrust is proportional to the (velocity out squared - velocity in squared), so as the craft goes faster, drag goes up quickly and thrust starts dropping off... which sets a fairly clear max speed given the shape of the 2 curves. actual tests are needed for either to get exact numbers.

It still doesn't explain the simple form of the static thrust equation, 2x vs 0.5x ??
I would have thought thrust and drag were similar things?

 

[JasonK]

It still doesn't explain the simple form of the static thrust equation, 2x vs 0.5x ??
I would have thought thrust and drag were similar things?

thrust and drag are very different things.

if you look at the 2 articles, you can see how they came up with them... and given the drag equation has a huge 'measure it to see what the value of this scalar is' value, no idea why it is there. but that is also the drag calculation for something moving through the air at a constant speed, a _prop_ is not moving through the air at a constant speed (the tips are moving faster then the center)... I am sure some sort of integral over the length of the prop could be done to get the effective drag at a specific rate of rotation and airspeed.

 

[telnar1236]

What are the velocities being referenced in your thrust and drag equations? As JasonK said, you need to integrate along the length of the blade to find the thrust and drag if you're using the blade's speed.

 

[telnar1236]

For a simple explanation of why you have the two different values, the thrust values come from conservation of momentum, and so are based on your prop's total area. The NASA website has a very simple derivation using Bernoulli's principle to calculate the change in pressure, and this works out the same as conservation of momentum Propeller Thrust (nasa.gov) . As far as I can tell, your equation is not right. The drag from the prop is more complicated. You can integrate along the blade or use a weighted average. Really, drag is not a very useful measurement for a propeller, unless you're trying to measure the resistance of the blades to being spun and you want to look at the thrust curve as has been mentioned above until you're exceeding the speed at which your prop can generate thrust.

For your drag coefficient, 0.01 seems very low. You need to account for things like induced drag and profile drag, so your surface drag will probably not play too large a role. For airfoils, this is a great source for lift and drag coefficients Airfoil Tools .

 

[OwenN]

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwiQ36eRgvrtAhUlzjgGHfOyBVwQFjAAegQIAhAC&url=https://www.researchgate.net/publication/323198187_Helicopter_Flight_Physics&usg=AOvVaw30EteWbm6-9NoCBm6Foxd4&cshid=1609479498886827
Here is the source I was using.

V1 = sqrt(T/(A x2 x dens)) and P = TV = T ^(3/2) /(sqrt(2 x den x A)) ----- * ^ = exponent,



so F=4.4 x 10^-8 x RPM x (d^(3.5)/sqrt(pitch) ) x (4.23 x 10 ^-4 x RPM x Pitch - V0)

doesn't bear much resemblance. the term in T^3/2 has been converted to d^3/2 somehow???

my calculation of prop drag = (SUM(r x A x V^2 )x 0.5 x dens x Ca), giving torque.

(those thumb substitutions weren't my idea, I was trying to indicate a list of n items)

I had a (stray x 4) in there, so Ca would actually be around 0.04 for the prop blade (114 mm)
There were 9 x 10mm slices neglecting the last 4 mm and the first 20mm per blade.

It actually wasn't very far out from my 2/3 area acting at 80 % of the radius.

The usefulness is demonstrating that there is not much inefficiency in the prop or motor when this is removed.

Thank you for the new reference.

I also was trying to make the point that there is no thrust gain from adding more blades unless rpm
remains the same and blade pitch is reduced.

Even then thrust gain is from not wasting power with too high a pitch speed.

Generally this situation does not occur with model aeroplane motors.

 

[Merv]

What do they mean by advance ratio? Is it related to pitch?
How do I interpret their spec in relation to diameter, number of blades, and pitch?

I don’t know.
For me they provide some good information that is helpful in choosing a prop. The RMP, thrust, and Hp data can get you in the right ball park. I read somewhere that the APC data is model not measured.

 

[telnar1236]

Not sure what's going on in the Researchgate article. There are a couple of mistakes, but as far as I can tell, they try to apply conservation of momentum across the wrong control volume. Vinfinity, should be the velocity at infinity, before the prop, not after. Between Vi and w, the change in momentum should be zero since there are no forces acting in that region. If you apply the conservation laws across the right control volume, using the right techniques, you end up with 1/2 instead of 2.

In terms of using a constant Ca, the angle of attack changes, and often the airfoil changes, along the length of the blade, so the drag coefficient changes. This airfoil is relatively representative of the prop airfoils on larger wooden props, and you can see Cd goes from about 0.02 at 5 degrees to almost 0.2 at between 10 and 15 degrees ONERA HOR07 AIRFOIL (hor07-il) (airfoiltools.com) . Most props have the angle of attack go through that whole range along their lengths. Reynold's number is going to be in the region of 100,000 at the tip for most smallish (9.5") props, so friction will also play a role, but it won't dominate, even at the tip. Here is a thread on RC Universe where professor Mark Drela of MIT weighs in explaining that airfoil and pitch play by far the largest role in prop efficiency Props airfoil - RCU Forums (rcuniverse.com) . Because of how drag works, you can arbitrarily define a reference dimension and find a coefficient of drag that will work for it though, so if your numbers seem to match reality, you probably have a reference dimension and coefficient of drag combo that works. 0.04 would seem to be about right as an average Cd along the prop.