Talk of Torque

With the advent of electric motors into the bicycle world we thought it would be worthwhile taking a look at the torque claims of manufacturers to better understand how motors compare.

Let’s start by exploring Torque vs Power
Power = the rate at which work is done.
A given motor or engine will have a certain output which is fixed or limited by the design. If we take a standard car engine without a gearbox and start it up we can measure the power by adding a brake to the crankshaft and seeing how much force is needed to stall the engine. This force, or brake force, is known as Brake Horse Power BHP. We could add a larger carburetor to the engine so it can process more fuel (energy) and this will increase its output and hence the force needed to stop the engine, but we can still state that for a given engine design the power output is fixed.

Torque is measured in Nm. A Newton is 1kg being pushed down by gravity and a meter is a short distance. So we can picture 1Nm of torque as a 1k weight hanging from a 1m spanner. The force the spanner would apply to a nut would be 1Nm.

1Nm of torque

But the thing about torque is that it can be adjusted.
Looking again at the car engine – the torque that we get from a given motor can be adjusted using gears. Add a reduction gear to a motor and you will gain torque but top speed will be limited. The reciprocal is also true too.

Consequently a motor car has to have gears to work efficiently. The lowest gear has to be set so that there is enough torque to get the car started, fully loaded and up the steepest of hills. However just having this gear would severely restrict top speed so we have a range of gears to get the most from the engine. The graph below shows typical torque curves for a car as it accelerates through the gears. Notice how having just the 5th gear would give a nice top speed but without the ability for the car to get rolling. Notice also that the lower gear gives higher starting torque when comparing points “A” and “B”. The gear ratios are selected so that as torque starts to tail off one gear the next gear is reaching its peak.

Not all motors have torque curves like this. The steam engine interestingly has a flat torque curve; it has the same torque at starting speeds as at full speed.
But since the steam bicycle is inconvenient and electric motors are the future, let’s look at electric motor torque.

Electric motors
The torque of an electric motor is inversely proportional to the speed.
If you wire an electric motor under no load to a battery, it will start, initially, with maximum torque and no speed and once it is running at a steady state, it will have maximum speed and no torque. Torque only occurs during acceleration or against a mechanical resistance, such as a load on the motor. Manufacturers rarely specify at what speed they are quoting the motor torque from, but it is likely they would quote the starting torque since this is the highest number.

However – if we take this to the extreme then we can see from the graph that if we apply a mechanical load to the motor until it stalls and measure the torque at this point, we will get the maximum value that the motor can exert. This is not a very kind thing to do to a motor since the motor will pull whatever current the battery can deliver, to try and get moving. If the battery is small then the system will hold up until the battery is flat; but if the battery is mighty, there is nothing stopping the motor damaging itself by pulling more current from the battery than it can handle; this is why we have fuses.

So let’s look at some motor specifications and decode what some of the values mean.

Nominal Voltage:

This is the voltage that corresponds to the highest motor efficiency. Usually a battery would be chosen to closely match the nominal voltage of a given motor. If a motor is operated outside of its nominal voltage, the efficiency of the motor goes down, often making the motor pull more current and heat may be generated decreasing the life of the motor.
Higher voltage motors can run faster but more significantly they can produce the same power with a lower current draw. To understand this we must briefly visit Watts’ law which states that a motor’s power (in watts) is equal to the current it pulls multiplied by the voltage.

In notation…………… i x V = W

So for example if we say we need 100w from a motor to get a bike up a hill; then on a 24volt system the current draw would be

i = W/V

i = 100/24 = ~4 amps

If we replace the battery with a 48v one then the current needed to get 100 watts out of the motor is……

i = 100 / 48 =~2 amps.

We should also mention that battery capacity is measured in ampere hours (AH). A battery with 1AH will be able to produce 1 amp for one hour before being exhausted.
Therefore a battery with a capacity of 50AH can provide 50 amps of power for 1 hour, or 5 amps of power for 10 hours.

So what happens if we take the current results from the 24v and 48v battery sums above and in both cases use a battery with a capacity of 12AH?

The the 24v system generating 100w of power is pulling 4 amps. So a 12AH battery will last 3 hours.
However the 48V system is only pulling 2 amps for the same power. So a battery with the same 12AH capacity will last 6 hours.
This explains why higher voltage systems are always favoured. Not so much for the higher speeds they might generate but for their lower current draw.

No Load RPM:

This is how fast the final output shaft will rotate assuming nothing is connected to it. If the motor has a built-in gearbox then the motor speed will not be indicated separately, in other words the no load rpm value is the speed of the output shaft of the motor system (geared or not). The motor’s RPM is proportional to the voltage input. “No Load” means the motor encounters no resistance whatsoever so speed will be limited by the voltage input and the motor friction plus any back EMF**.

Power rating:

Power for electric motors is normally given in watts. Horse power can be used for larger motors and 1HP = 750w.
If a motor’s power is not given then as we saw earlier it can be approximated using Watts’ law (i x V = W)
So by multiplying the no load current (i) and supply voltage (V) we get the power (W).
The motor’s maximum power (which should only be used for a short time) can be approximated using the stall current and nominal supply voltage.

Stall Torque:

This is the maximum torque a motor can provide with the shaft no longer rotating. As mentioned previously this is not good for any motor but it is a useful number to know just so you can steer clear of it! In practical terms you really want to specify a motor that operates no higher than 1/3 the stall torque for the majority of the time.

Stall Current:

Under the stall condition mentioned above the motor will pull the most current it can from the supply. With a capable battery this value can be high and damage can occur to the motor or drive circuits if the duration allows it.
If neither the stall nor the nominal current are provided, then once again you can use Watts’ law to estimate the current from the motor’s power rating (in Watts) and the nominal voltage.

Conclusion

  • So when comparing manufacturers torque claims it is worth remembering that torque only occurs when a motor is accelerating or is under a load.
  • Manufacturers may be quoting the stall torque because it is a nice high number, but if they are you should consider dividing this by 3 to get a useable number.
  • Gears can be used to increase motor torque and some hub and most mid drive motors include some reduction gearing to get more torque.

**EMF stands for electromotive force. It is a magnetic force that motors generate as they turn and the faster they turn the greater the EMF. It is one of the factors that limit a motor’s top speed.

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