What about Watts?

Some comments from our last post regarding torque has raised questions about watts; in particular what is a Watt and how does it relate to torque? Also if torque is so important why does everyone talk about power (watts or horse power) when talking of performance?

Well let’s see…………..

Power and torque are related and this can be seen when looking at their formulae.

Torque as we know is equal to a force multiplied by a radius T = F x R.
Power is the Torque multiplied by rotational speed. P = T x revs
(It should be noted that the revolutions in the power formula need to be “radians per second” not RPM. We can talk about radians another time if there is interest)

The best way to visualise torque and power is to think of  simple internal combustion motor like that shown below.

The force pushing on the piston multiplied by the sweep of the crank (d) will tell us the torque at the crank

This torque is fixed because the force on the piston is a factor of compression and fuel, and the crank sweep is fixed mechanically.
However – power is “the rate at which work is done” and we can increase this by speeding up the engine. Clearly the torque is not going to change much, but by increasing the speed the overall power can be increased because Power = Torque x revs.
So a more powerful car will get from one place to the next more quickly than a low power car because it is doing work at a faster rate. This is true even if the low power car has more torque because of its lower gears.

But torque is what gives us acceleration, so why is a more powerful car faster?
Well this brings us back to the gears.

Let’s compare a 100hp car with 200Nm of torque, with a 200hp car with 100Nm of torque.
Which will win the drag race?
Well the answer is the 200hp car because although it has less torque, it is doing work at a faster rate and we can use gears to convert some of this power into as much torque as we like.
This is why people take power as a measure of absolute performance.

Another analogy might be to compare a 150hp tractor vs a 150hp car. The tractor has more torque yes, but because the car has taller gearing it will arrive first. This is because the tractor has traded more of its power for torque.

Anyway – apologies for this talk of cars, but they are a useful example because most people can relate to them.

Let’s talk bikes.

Electric motors have a fixed power output in watts. This is governed by the type of motor, the number of windings, the number of poles and the amps from the battery.

However Mid-drive Ebikes benefit from driving through the bicycle’s gear train and can therefore vary their torque output.
For example the Shimano E6000 motor is quoted to have a power output of 250 Watts. If we fit this to a 26″ wheeled bicycle with a 42 tooth front sprocket and a durailleur ranging from 11t to 36t what torque do we get?

Well in the high gear we get 65Nm at the rear hub.
In the lowest gear we get 214Nm at the rear hub.
Motor power would be a constant 250W but we can increase torque significanly with the gears. This is one of the major benefits of the mid drive system. Most people cycle with a cadence of about 75rpm and they will select a gear to maintain this in different conditions. Consequently the mid drive motor will stay within similar boundaries and they are typically geared to produce useful torque at these rpm’s.

Hub motor bikes work with a fixed ratio so their torque is fixed;  it is also true that their speed will vary more than mid-drive systems because they don’t benefit from the bike gears. However they are mechanically simple and shouldn’t be dismissed because if a motor is adding 250W to your pedalling effort you’ll certainly be glad when the hills get steep and the wind is in your face.

Conclusion.

Motor output in watts is a useful starting point for comparing Ebike systems; but looking at the torque number will give you a feel for how the motor is set up (ie: how much reduction gearing it has).

If the system is a mid drive then the torque number is what you will get at the crank and you can make the most of this by using any gears the bike has.
If you have a hub gear motor then pay attention to the motor torque because this will be fixed and only varied by what size wheel the motor is built into. Some hub motors have a reduction gear in them to increase torque output but this is at the expense of simplicity.
If you cycle sedately with a large wheeled bike then a hub motor with a reduction gear may be more suited to your usage. A fast rider can make do with a non-geared hub motor and this has the added benefit of no mechanical parts to wear out; or you can take the best of both by using a mid-drive and capitalising on the bike’s gears.

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