# Alternator with torque proportional to angular velocity

Im interested in buying or designing an alternator/electrical generator that increases torque as rpms increase - is there an alternator design that increases resistance as rpm/angular velocity increases? The alternator is for an exercise bike and would simulate real life pedal resistances.

I intend to collect the energy (however insignificant it is) to do something small like charge my cellphone.

• By "increases resistance" do you mean that it increases torque or power as angular speed increases? With constant torque power increases. The difficulty according to a user should increase (with increasing speed) at a faster rate than power, unless there is a non-zero minimum to the biological effort/output ratio. Since this is likely I should quality my last sentence with "at a sufficiently fast speed". This could be a moot point given the alternator physics but it can help in making a technically sound question. – AlanSE Jun 20 '11 at 1:52
• yes I mean torque - I changed the word resistance to torque – Dale Jun 20 '11 at 3:16
• Agreed... I'll send it over and they can decide whether it belongs over there. – David Zaslavsky Jun 20 '11 at 5:41

What you are asking about is a generator that presents "viscous friction" to the rotating shaft. That means the torque is proportional to the rotation rate. Yes, this can be done with a electric generator. Torque is proportional to the current, and open circuit voltage is proportional to rotation rate. A resistor is the right load to get torque proportional to rotation rate, at least it will be as close as the generator is efficient.

For more fancy control and to harvest the energy, you need what is essentially a switching power supply on the output of the generator. The controller of this power supply has a input that tells it the rotation speed. It can then put any load it wants to on the generator output to get the desired torque. Usually the generator output is bucked to a higher voltage. This voltage is not regulated except that it gets whatever power the generator puts out at the current operating point.

Another switcher then keeps this voltage within some range so that the first switcher can continue to dump power onto it as it sees fit. The second switcher usually produces a well regulated lower supply. It can also handle excess power in various ways, including shunting it to a resistor when there is nothing else to do with it. If you want to get really fancy, you could dump any excess power back onto the AC power line. However, that would take considerable electronics, has regulatory and safety issues, and will certainly not be worth it economically.

• For the amount of energy that you can produce pedaling, it would probably not be worth trying to dump it on the grid. To make even 1kW-hr per week would require, for example, 5 hours of 200W effort, every week, for the princely sum of about \$5/year. (If you don't already know if you can do 200W for an hour, you can't; if you can, you probably race bicycles.) Anyway, +1 – JustJeff Jun 20 '11 at 22:24

My inclination, if you weren't worried about harnessing energy, would be to use some big MOSFETs to switch current to some resistors or light bulbs and then use a microcontroller to control the MOSFETs. Light bulbs are cheaper than power resistors, and they're designed to dissipate power (given a suitable enclosure), but their resistance varies substantially with temperature, which could complicate your logic.

The basic idea would be to pulse-width-modulate the MOSFETs to vary the load based upon what the processor determines is appropriate. To avoid having massive flyback pulses kill the MOSFETs, I would suggest having a number of parallel resistor-plus-MOSFET combinations, plus a resistor which is "always in", and a circuit to turn a MOSFET full on with a moderate-value resistor if the voltage gets too high. If you switch from having 10 ohms of effective resistance to having 25, that will cause an instant momentary 2.5x increase in voltage; the MOSFETs should be chosen to allow for that.

I would expect that monitoring and controlling the effective mechanical resistance is going to be easier if one can switch the MOSFETs and resistors in such a way that you never hit a flyback clamping point. If your allowable flyback voltage is 5x the voltage produced by cranking, it may be good to have two MOSFETs and resistors per decade (e.g. values of 1, 3.3, 10, 33, and 100 ohms). To produce effective resistances between 33 and 100 ohms, turn the 100 ohm resistor on and modulate the 33-ohm resistor. This should limit the flyback voltages to 3x the voltage produced by cranking.

Because the voltage a DC machine produces (the back EMF) is proportional to it's speed, if you simply hooked up an electrical resistor to it, it would also translate into mechanical resistance on the input shaft.

If you want varying resistances, you could alternately connect varying resistors across the motor to create additional load.

Bear in mind that if you want to dissipate the energy that a human can put out for a good length of time you will need to absorb several hundred watts of power, which will mean using quite a large motor, and some non-trivial resistors.

• I was hoping to collect the energy (however insignificant it is) to do something small like charge my cellphone. I will add that to my question. – Dale Jun 20 '11 at 3:22
• @Joe, if you're capturing enough power from a pedaling human to provide some variable load, it's nowhere near insignificant (hence my comment about hundreds of watts). Given the proper circuitry, you could skim some of the power off and charge a cell, but I doubt it will accept any more than 5-10 watts. – Nick T Jun 20 '11 at 3:54
• Unless you're a bicycle racer, you don't need to worry about getting too far past 200W for any sustained effort. – JustJeff Jun 20 '11 at 22:31

Come on people does everything here have to be about quantum equations do we forget the fun of the pure mechanical-physics…. A 200 Lb Pearson standing on a 6” pedal will suplay 100 Ft.-Lb. for a 1/4 of a turn hence 2 pedals the force is applied ½ the time. “There’s a formula to calculate the exact torque. Because the force is applied in a circular motion from a single direction like a piston it’s actually little less.” Now assume the main sprocket is ½ the diameter of the pedals that will make the torque 200 Ft-Lb. Ok so connect it to a 3” sprocket in the back this will double it yet again So the force is 400 Ft-Lb to the generator. So “1 watt ≈ 44.25372896 ft-lb/min” now in a very crude calculation a 200 lb person can generate 10 Watts per minute This is way more than whets necessary for my phone charger. It takes .5V DC, 850 mA

Now as far as increasing the load as you pedal faster. It relay does take some electronic tinkering to design a variable load and some feed back to control it.