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# Electric motors & "No-load speed min -1".

## Electric motors & "No-load speed min -1".

(OP)
Hello

The lift equation for airplane's wing is:
L=(1/2)*ro*S*CL*V^2
In the case of a rotating wing the mean lift of an untwisted rotor is in actual fact 1/3 the maximum lift at the tip because the lift profile is a parabolic curve.

Thus the lift of a fixed wing becomes modified to lift of a rotating single wing.
L=(1/3)*(1/2)*ro*S*CL*V^2
L=(1/6)*ro*S*CL*V^2

This was quoted from a book on helicopter design by John A. Drake. I have three questions:

1-When I look at helicopter rotor it look almost exactly like the airplane wing. My question is Is this formula applicable to airplane propeller? If not what is the right fomula?

2- I hear that propellers are optimised for hovering and for propulsion. Can the usual airplane propeller be used to lift a payload vertically? What is a "shrouded prop"?

3- Electric motors have "No-load speed min -1". I assume that if I use a smal propeller I would get less rpm than the "No-load speed", and if I use still larger propeller the rpm will reduce even futher. Is this a correct assumption. Is there a formula for taking into account the weight and drag forces of the propeller itself.

Thanks

Tom

### RE: Electric motors & "No-load speed min -1".

1 crudely, yes

2 yes, but it is not ideal. A shrouded prop has a duct around it to reduce tip losses, again, crudely.

3.1 yes

3.2 get the torque vs speed characteristic of the motor. use the helicopter hovering equation to work out the torque vs speed characteristic of the prop. Where they meet is the operating point of that prop and motor combination. If the thrust is less than the weight of the helicopter you have a problem. Google for the equation using the obvious terms

http://aero.sharif.edu/~moayyedi/HeliAero.html

Cheers

Greg Locock

### RE: Electric motors & "No-load speed min -1".

The equation you need at a system level is this one

P=1/(2^.5)*T/M*(T/(rho*pi*R^2))^.5

T is the thrust, M is the figure of merit for the design, take between 0.5 and 0.8, rho is the air density, R is the radius of the rotor and P is the power required.

Cheers

Greg Locock

### RE: Electric motors & "No-load speed min -1".

(OP)
Hi Greg,

Here is an example of the spec I get from the producer.

Specification
Nominal voltage 30 V
Operating voltage range 14.4 ... 36 V
RPM / Volt 210
No. of winds 7
Current drain atmaximum efficiency* 25  50 A
Max. efficiency without gearbox 91%
Permissible motor direction R and L
No. of poles 14
Overall length 120 mm
Case length excl. shaft approx. 85 mm
Diameter 65 mm
Free shaft length approx. 24 mm
Shaft diameter 8 mm
Weight approx. 950 g
* referred to stated operating voltage range
These values reflect the current state of technology, and may vary with continued development.
Variations will occur depending on the speed controller used.

There are no mension of "torque vs speed characteristic of the motor".

Tom

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