Measuring voltage given prop size, speed and amps?

[davidleitch]

I posted this question in motors but couldn't get an answer.

I have a tachometer and a clampmeter. Using the information namely the propspeed and the amps I would like to estimate the voltage under load.

Can anyone suggest a formula.

I imagine work done = thrust + speed
Thrust + speed = prop revs * diameter* pitch

work done less gearbox loss = power in
volts = watts/amps

Am I on the right track? Units are a problem. Work done would probably be in ft.

Thanks for any suggestions
dave

[steve lewin]

I'd buy a voltmeter (if I didn't already have 4 or 5).

However if you really want a rough estimate then why not use Motocalc and adjust the battery voltage until it gives the revs and current you're reading.

Alternatively if you like forumlae, read Jim Bourke's "Understanding Electric Power Systems" series of articles (available with a search from EZone front page) you'll find enough information to derive your own formula. You still won't get better than an estimate because it depends on knowing various motor characteristics plus the efficiency factor of the particular prop you're using.

Steve

[vintage1]

Its easier than that. Find someone using te same cells as you and see what they drop under load. Or use motocalcs estimated internal resistance. That, times the current rawn is teh loss of volts due to pack resistance.

[BMatthews]

Aside from the fact that it's easier to use a voltmeter as others have suggested it is just not possible to calculate the motor voltage from the amps and rpm. There's NO relationship here that isn't dependent on at least a few other factors.

There is just no avoiding it. It's time to buy a voltmeter. If you're messing with electrics it is a must have in any event. An electric modeler without a voltmeter is like a nurse without a thermometer.

[davidleitch]

Steve

Thank you for your reference to Jim Bourke's articles where I was able to find the formula I was looking for. To quote fromt the 3rd article in the series:

"Power (Watts) = Kp * D^4 * P * RPM^3

In English: The power required to spin a propeller is equal to the propeller constant times the diameter of the propeller to the fourth power, times the pitch of the propeller times the RPM to the third power. Note that Diameter and Pitch are specified in feet (not inches) and the RPM is specified in thousands."

Filling in the relevant data for my system, namely a 17x13 prop spinning at 4300 on 7 cells and using a folding prop constant of 1.18 and a measured 90 amps the implied voltage is around 0.65 per cell, a bit lower than what I was expecting. Maybe 0.75 volts if I allow for gearbox losses and 90% efficiency in the motor.

[davidfee]

Right, that equation only gives an estimation of the power absorbed by the propeller and that's it. The "propeller constant" is an empirically derived number... an approximation.

You would need to add power absorbed by your gearbox, and the power used to heat the motor, controller, connectors, wires... etc. I suspect 90% efficiency for your motor is rather optimistic.

It really is easiest (and ultimately most accurate) to simply measure the voltage drop across the battery under load using a voltmeter. Compare that to open circuit voltage and use Ohm's law to get resistance for the battery.

-David

[davidleitch]

I suppose that's true. However I'm happier now that I know the equation.

[Bruce Abbott]

You don't need to know how much power is absorbed by the propellor or gearbox. All you need are the motor constants Kv and Rm.

V = (rpm*gearratio/Kv) + (I * Rm)

This gives the input voltage to the motor.

If you want voltage at the battery you need to know the resistance of your ESC and wiring. If you use short, thick wires and a high-current ESC, the voltage drop should small enough to ignore. Taking a poor example, the GWS ICS-300 has a FET resistance of about 0.01 Ohms, but it has thin wires with a resistance of about 0.017 Ohms. This would cause a 0.24V loss at 8 Amps (ie. battery voltage would be 0.24V greater than motor voltage).

[Marion]

If you look hard, you can buy a decent digital voltmeter for under $10 (Try Harbor Freight). You gotta admit that is an awful easy way to find the battery voltage.

I fully understand your interest in the equations, but if you want to know the voltage - then measure it !!