RPM with a prop vs. kv*V unloaded RPM
I had another question about a specific motor/prop combo, but I think I can ask the question in a generic way and get a better response:
Should the maximum RPM with a prop installed be related through some function to the maximum unloaded RPM (kv*V) for maximum power and/or efficiency?
For example: If I have a 2000 kv motor on a 3S LiPo, I would expect approximately 2000*10.5 = 21,000 RPM without a prop on the motor. If I install a prop, and the motor runs within spec for amperage/wattage, but now I look at the RPM and it's say down to 8,000 RPM on a static test, is that bad in any way? Would I stand to get a better efficiency/power if I install a smaller prop that would bring me up closer to the unloaded RPM?
Also, how would this affect things in-flight, rather than just a static test on the ground. I know the motor unloads and can reach higher rpms with air already moving through the prop.
Is it something to worry about, or so long as the wattage is OK I'm fine?
Thanks in advance! I'm stuck inside at work and am doing some armchair flight physics in my head, and can't think how this would work out
Peter Angus suggests somewhere around 74% for "Prop RPM as % of Kv x V"
At less than that the motor is probably over-loaded and will be converting lots of energy into waste heat.
So for your example: 2000Kv x 10.5v = 21000..........~15750rpm would be the number to aim for.
There is a close relationship between the ratio of loaded to unloaded rpm, and motor efficiency. The motor slows down under load due to voltage drop in the resistance of the copper windings. This resistance causes a power loss (called 'copper loss') which is proportional to current draw squared. There are also losses due to magnetic effects (called 'iron losses') but they are proportional to rpm, and (usually) much smaller than copper loss at high power.
At 50% rpm, half of the input power is wasted heating up the windings, and the motor is 50% efficient (actually slightly less to due iron losses). This is also the point of maximum power output, though the losses may be too high to allow continuous operation (and it's a poor use of the available power). At even higher loading the power output decreases, with more power being wasted in the motor than getting to the prop.
However, there are situations where pushing a motor beyond its maximum power output can still work. Smaller motors have larger surface area relative to their weight, so they can dissipate relatively greater power without overheating. Unfortunately they also tend have lower peak efficiency, and so have to be pushed harder to get sufficient output. Very small motors (<20g) may be able to get away with being operated below 50% efficiency.
Another factor is that the prop may 'unload' by up to 80% as airspeed increases, so you could be overloaded static and yet still be OK at flying speed. As the prop unloads the current goes down, so efficiency improves. This is often the situation in small 3D planes, where the static thrust advantage of a larger prop compensates for the inefficiency of the motor, and full power is used sparingly so overheating is not a problem.
If you know the prop you want to use and calculate the recommended maximum RPM for it, and also know the battery you will use, you can start by choosing a motor that will get that prop up to it's maximum RPM.
I've been keeping a text file on RPM limits when I find it, some is published, some is the expert opinions of testers and users. You're on your own as far as liability but these are either published or generally agreed upon limits.
Prop RPM Limits Summary:
Aero-Naut Folding Propellers - 6,000 RPM (16.5") to 16,000 RPM (10" and less) depending on size.
APC Glow/Speed 400 Electric = 190,000 RPM / Diameter (inches)
APC Thin/Folding Electric = 145,000 RPM / Diameter (inches)
APC Slow Fly = 65,000 RPM / Diameter (inches)
APC Racing (8.75 N,W,8.8,Series 40 Pylon) = 225,000 RPM / Diameter (inches)
Great Planes Slow Fly = 65,000 RPM / Diameter (inches)
GWS Reduction Series or RS (EP marked) props = 40,000-50,000 RPM / Diameter (inches)
GWS 6" to 10" Direct Drive Series (marked HD) = 80,000-100,000 RPM / Diameter (inches)
GWS 5" or smaller Direct Drive/HD = much tested/used at 15,000-20,000, max safe RPM 80,000 RPM / Diameter (inches) or more
Master Airscrew (Windsor) = 165,000 RPM / Diameter (inches) (some consider this to be a little too high, but that is what the maker says is OK)
With those limits and the advice from Dr Kiwi and Bruce Abbot, you can really get your motor choices narrowed down to suit your prop choices.
Another fairly recent and very useful resource for choosing props is the Prop Calculator that has been added at FlyBrushless.com. You can get feel for a given prop's the thrust across the RPM range there. And if you know what RPM you will run it at you can see about what you can expect for thrust at that RPM.
The thrust figures are from static testing (by guys like Dr Kiwi for example) and is real, it will be different in the air but it is a good starting point.
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