Prerotator power required vs RRPM

[Jazzenjohn]

Since you're doing the math Xxavier, can you compare Arcos actual with the actual data i did earlier in the thread. The difference should show the effect of the 23' lightweight DW's i used compared to the longer, heavier ELA 2 place (I believe) rotors. 23' vs 28' and 41 lb vs 81 pounds. using a log log graph should produce nearly straight lines.

 

[Jazzenjohn]

 

[rcflier]

Ralph Taggart's website can be found with the "Wayback Machine". I did.

 

[Jean Claude]

Using fundamental aerodynamic laws, the power absorbed by a fixed-pitch rotor is proportional to the cube (i,e exponent 3) of the rotational speed, all other things being equal.
Of course, this is no longer true when the Reynolds number is below 500,000 but these values are already exceeded at 100 rpm.
However, between 136 rpm and 210 rpm, I find an exponent of around 2.1 for Arco's measurements, and 2.5 for Jazzenjohn's measurements. I assume that the power measurements taken with digital multimeters are distorted by the pulsed currents.

(Jazzenjohn's measurements): 3000W = 750W * (220 rpm/126 rpm)^2.5
( Arco's mesurements): 4000 W =1500 W * (210 rpm/132 rpm)^2.1

 

[Jazzenjohn]

I can't speak for Arco's measurements, but my 3000 watt number was the manufacturers rating. The actual values i gave for the different RRPM's were taken from a Phoenix systems data logging electronic speed control. The difference in Arco and my blades is pretty significant in weight, diameter, and pitch. The system i used for those numbers was a reasonably optimized 2 stage chain reduction. Arco used a dual motor system i believe.

 

[Jean Claude]

Accurate rpm measurements are easy to make, but reliable power measurements are more difficult, especially with pwm electrical sources.
IIt's easier to measure the torque applied, for example, by mounting the frame on a ball-bearing swivel base.

 

[Jazzenjohn]

I'm quite sure it is more accurate to build a giant ball bearing rotating table big enough to accomodate a full size gyroplane, I encourage you to do it. On the other hand, it seems a tiny bit easier to make some adjustments to the formula to reflect real world measurements.

 

[Smack]

Maybe strain gauges / torque tranducers.

 

[Jean Claude]

Another way of measuring the power absorbed by a rotating rotor is to observe its natural deceleration rate in calm weather.
We know that :
Γ = I* dΩ/dt where Γ = braking torque (N.m), I = Rotor inertia (kg.m²), Ω = Rotation speed (rd/s),
And since P = Γ* Ω, then P = I *Ω²/ T
So all we need to do is draw a tangent to the deceleration curve, for any regime (Ω), read time T, and apply the formula above.

Below is an old recording made by Mike Goodrich, which he remembers making with an 8.8 m Averso rotor whose inertia is supposed to be 235 kg.m2.


The tangent to the curve at 200 rpm (i.e. 20.94 rd/s) shows T = 225 -187 = 38 s, giving us P = 2710 W at 200 rpm
The tangent to the curve at 100 rpm (i.e. 10.5 rd/s) shows T = 296 -222 = 74 s, giving us P = 350 W at 100 rpm

Power proportional to (Rpm)³ clearly appears here.
This would correspond to the formula Paerod. = 0.0034 * ρ* Chord * R⁴ * Ω³ for standard pitch setting (in international units)

 

[Jazzenjohn]

Good stuff JC ! the decay numbers aren't going to take into account mechanical and electrical losses, but they are easy to add on. They certainly serve to make a great cross check and probably will be the best way to expand the useable numbers across different lengths, weights, and pitch of different rotors. Does Mike have numbers for a range of different rotors and lengths?

 

[XXavier]

Good stuff JC ! the decay numbers aren't going to take into account mechanical and electrical losses, but they are easy to add on. They certainly serve to make a great cross check and probably will be the best way to expand the useable numbers across different lengths, weights, and pitch of different rotors. Does Mike have numbers for a range of different rotors and lengths?

Just to say thanks to JC for his method. so simple and nice...
And to Jazzenjohn: You can find the curve for any rotor by experiment. You launch it to 200 RPMs (or so) and then note down the RPMs at different times, as the revs decay. You need only a chronometer and the tachometer (it's very accurate when digital...). With four points and using free curve-fitting software (like mycurvefit.com) you can obtain a reasonably good approximation. Once you have the curve, you can easily determine the tangents at the points that you wish, either by analysis or by drawing the curve on paper... There are no electrical losses, and the frictional losses of the roller bearing are probably very, very low...

 

[Jean Claude]

Jazzenjohn,
Mike made a lot of recordings to design his GWS. But it's just a coincidence that this free slowdown was recorded.