Wow, that's a tall order Nigel!
In the following, don't let the numbers overwhelm, just look at each section in turn and take your time to understand the general relationship.
First the speeds and hill climbing
Most hub motors run through a hub turns per minute (revs) range from zero to about 300 turns each minute. That's roughly true of the same hub fitted in both the Quando and the Torq which run from 0 to about 280 turns of the hub each minute, equal to 16800 turns each hour.
Now in the Quando the hub is in a 20" wheel, which has a circumference around it of 62.8", so with each turn it travels 62.8" inches forward. Therefore, if we allow it to turn at it's maximum of about 16800 turns in one hour, it will have travelled enough inches (16800 x 62.8") to travel just over 16 miles in distance. So it's doing 16 mph.
In the Torq, the same motor is in a 28" wheel, which has a circumference of 87.9", so it travels that with each turn. That means that if we allow it to turn at it's maximum 16800 times each hour again, it will have travelled more inches (16800 x 87.9"), equal to just over 23 miles. So it's doing 23 mph although it's exactly the same motor.
Since both motors are the same and have the same power, the Torq in travelling further has had to divide the power between more metres travelled. That means that each metre had less power applied to it. That in turn means the Torq is not as good a hill climber. To explain that further, lets say we test the Quando to find the steepest hill it can climb, using all the power per metre that it has. Now if we try to climb that on the Torq, it won't manage it, since it has less power per metre than is necessary, it will have to ask it's rider to do a lot more to make up the difference to bring it to the Quando's power per metre.
So why can't we just ride the Torq at the same speed as the Quando, and therefore have the same power per metre? That brings us to:
Peak motor powers
As a motor starts turning, it starts to use the battery energy, but it turns very little into driving power, most is just draining away, wasted. As it's number of turns per minute rise, it starts to turn more of the energy into power, this showing as a rising line on a power graph. At about half it's possible turns per minute, it reaches a point where most of the energy turns into power, and this is it's point of maximum torque (pulling power). This is the point we need to use to best climb hills.
Since the Torq uses its turns per minute to run to about 23 mph if derestricted for off road use, at half the turns (revs) it will be doing about 12 mph, and that's where its best pulling power will be. On the Quando, half it's possible turns per minutes is equal to half 16 mph, so about 8 mph, so we climb at that.
If we climb at a lower speed on the Torq, say 8 mph, we won't have reached that maximum torque point so will only have about two thirds of the power, so we don't gain anything.
Power curves and Power band
We've seen above how the power curve rose towards maximum torque which we climb at, about half the speed a bike can do, and in doing that wasted less and less power. From then on as the speed increases when riding on the flat for example, the pulling power (torque) starts falling again, but this time without wasting any energy.
Eventually at about it's maximum speed it will be using very little energy and also wasting virtually none, so we call that the point of maximum efficiency. We call the area between the Maximum Torque and the Maximum Efficiency the Power Band, since that's the best area of turns per minute to use.
Gears
As above, it's best to stay within the power band, but we also need to ride at very slow speeds. We also want to climb hills that are steeper than the bikes speed that the maximum torque point can allow. The way to best get round that is to have some way of shifting the maximum torque and efficiency points to speeds that we need to ride at to do those extra things.
That can be achieved by having the motor drive through gears that can be changed, so that a number of turns can result in less road speed or more, and that's the way the old Twist does it. By changing down so that the maximum pulling power appears at a lower speed, so less distance travelled over a minute, that power is spread over less metres travelled, so there's more power for each metre. That makes it possible to climb a steeper hill.
By changing up the gear to put the point of maximum efficiency at a higher speed, the bikes speed can be increased up to the point where wind and rolling resistance overcomes the available power.
Volts and Watts
These are often compared to mains water supply in teaching the subject Nigel. Purists need not correct!!!
Imagine you hold your thumb over the end of a tap and turn the water on. You can feel the pressure but it's not doing anything. Electrically that's what Volts are, a potential for something.
Now have your thumb off the tap and the water flows at a certain rate of gallons per minute. Electrically that's current in Amps, an amount flowing through.
If there's a lot flowing through at very high pressure, that's lots of power. Electrically that's watts, the current flow multiplied in power by the pressure, therefore Amps x Volts = Watts.
If there's less of either the volts (pressure) or the amps (current flow) the power will be reduced. That's how we control our motors.
Hope this has been of some help Nigel, but I think you'll need to print it out to get the best out of it with a couple of re-reads.
