Gearing and Power Band

Author Bob Carter

What do you mean by mean by “power band”?

Power is defined as the rate of transfer of energy. In our car, energy from the battery is transferred into movement of the car. The more power we have, the faster the car will accelerate and go. There is more nonsense talked in automotive circles about torque and power than any other subject (and believe me that is saying something!) I will concentrate on power in this discussion, simply because it makes the sums easier!

The Greenpower website includes quite good technical data about the 240W motor we use, in the form of a performance graph. This graph includes data for current, power and efficiency when the motor is operated from a 24Volt supply (like our batteries). Because the graph is actually a collection of 5 or 6 graphs it can be quite confusing, so I have condensed that data into a “motor model” and will display only the parts of interest.

If the motor is just spinning by itself with no load, it is producing no actual power.

If the motor shaft is held stationary, it is also producing NO POWER. This seems wrong because you can see that the motor is trying very hard to twist the shaft; but because the shaft is not moving NO ENERGY IS BEING TRANSFERRED. Perhaps it will help to think of a clock spring, twisting against its gear. If the clock pendulum is stopped – the spring will twist against the gear continuously for a hundred years. It can only do that because no energy is being transferred. When the pendulum is allowed to swing, the spring is doing work, moving hands etc. and the spring loses all its energy in just a few days.

So at no load, with the motor spinning like mad, it is producing no power. And with the motor held stopped, it is producing no power (though it’s using plenty…) In between these extremes is the “power band” of the motor.

If the motor is driven directly by the battery, the motor must be geared to a narrow range of speed or else either: -

1) Too little mechanical power is output so the car goes too slow or

2) Too much electrical power is used so the batteries go flat too quickly and the motor gets too hot.

The Greenpower motor produces maximum output power at about 1000rpm. Note that at this speed it would flatten the batteries in less than 40 minutes and be producing about a kilowatt of heat!

The C.A.U.C. cars use a current controlled speed controller to give a range of advantages: -

1) direct control of heat loss in the motor

2) the controller allows a wider speed range without a catastrophic drop in efficiency

3) controlled current level at startup – not the massive ~150A pulse taken by other teams (strains wiring and transmission parts)

However, the speed controller is itself intrinsically inefficient, losing about 4% of the electrical power input.

How must you determine the gearing for the car?

First of all you must decide what speed you wish to race at. For now, I will pick a figure out of the air – 25mph.

We know that the motor must be run with 25Amps of current.

The graph below shows that we get 25A when the motor is running at 1700rpm. So our gearing should be calculated so that the motor is running at 1700rpm at 25mph.

The calculations are tedious but simple…..

Note rpm stands for revolutions per minute.

1) Measure how far the car travels in 1 revolution of the drive wheel. Do this by marking the floor directly under the tyre valve, then pushing the car forward (preferably fully laden) for 1 revolution of the wheel and marking under the tyre valve again. Measure between the marks with a tape measure – it’s easy to get this very accurate. For our example let’s say this is 1556mm.

2) How many millimetres is 25 miles? Well, in imperial units, 1 inch is 25.4mm. 36 inches is a yard, and a mile is 1760 yards. So 25 miles is 40233600mm!

3) How many rpm must the drive wheel do? Well, in an hour the wheel must do

40233600/1556 turns = 25875 revolutions

So in a minute it must do 1/60^th as many: 25875/60 = 430.95 rpm.

Thus the gear ratio between the motor and the wheel must be 1700:431 or 3.94:1

Unfortunately life is never so straightforward. Nobody can race at exactly 25mph all the time. There are up-hills and down-hills and corners on the tracks, and the wind can blow strongly with or against the car.

What about when the gearing is NOT right for the situation…..?

If the overall gearing is too low, the motor is spinning faster than 1700rpm. This means the car COULD GO FASTER and will not get such a good mileage.

If the overall gearing is too high, there are 2 big problems. The car may go a little faster, but the batteries will go flat before the 4 hrs are up and the car will not get such a good overall mileage (which is the product of speed and running time). Running time will reduce faster than speed increases!

The other big problem is heat build-up in the motor.

The above graph shows that at 1700rpm we have to deal with 200W of heat in the motor. If the gearing is wrong and we are running at 1550rpm, we now have to deal with 300W of heat!

How do we solve this dilemma?

A car without gearing or a speed controller must be geared to too low a gear with a safety margin for the heaviest driver, with the steepest incline and the strongest headwind. Such a car can do well but better solutions are described below.

A car with gears can continuously change gear to keep as near to the magic 25A & 1700rpm as possible at all times. Normal bicycle hub gears are not ideal for this. For example, a nexus 8 speed hub typically shifts ratio by about 20%. In the scenario above with1750rpm on the motor (slightly too high) the next up-shift would go to 1435 rpm (way too low). However a continuously variable transmission (CVT), like the Nuvinci, could keep the rpm and amps perfect, if the car were driven well. However the mechanical efficiency of this product is still unknown.

Our current controlled speed controller allows us to remain efficient and keep the motor cool when away from 1700rpm – so we still get good results even though we use the Nexus hub.