# connecting wheels to dc motor directly or with gears

In which case speed of car will be faster: if wheels are connected to dc motor directly or with gears? We are making battery powered car in which case our car will be faster?

• The short answer is typically lack torque and packaging. Also, with a gearbox/transmission, you can still drive multiple wheels with one motor. Commented Jun 27, 2016 at 16:24

This depends on the total gear ratio between motor and wheels. You can obtain faster speeds at the wheels but then the torque will be lower.

If you have two gears ($i=1, 2$) with $N_i$ teeth, following holds for the speeds $\omega_i$ and torques $T_i$:

${\omega_2\over\omega_1}={N_1\over N_2}={T_1\over T_2}$

Your first consideration is whether the motor provides enough torque to both allow the vehicle to start from a standstill ( a practical vehicle will also need to be able to do this on a moderately steep slope) and to provide acceptable acceleration across a range of speeds.

Often top speed is the icing on the cake in terms of performance as torque at moderate speeds is generally much more important for overall performance. Similarly there is no point in having a high top speed if you can only achieve it on a 10 mile long drag strip.

On the other hand there is no point in having a lot more torque than traction (although a bit more is usually better than a bit less).

Electric motors have fairly flat torque curves so for a light vehicle direct drive is not grossly unreasonable and the final drive ratio can be fine tuned a bit by the tyre diameter.

It also depends a bit on what you mean by 'fast' as the performance requirements for something like land speed record attempt are very different from a karting circuit or rallycross.

The question can't be answered with the information given.

Gears convert one combination of (speed x torque) to a different combination of (speed x torque). For ideal gears, the (speed x torque) product is the same from input to output. Real gears have some loss due to friction, so the (speed x torque) product of the output will be a little lower than that of the input. Speed times torque is power, which must be conserved. The difference between the output power and the input power is the power lost in the gears, which ends up as heat.

From this it should be clear that just throwing "gears" in a linkage doesn't mean the result will be higher speed. First, the gears can be arranged to provide higher or lower speed depending on the gear ratio. However, even if the gears increase speed from their input to output, the resulting decrease in torque may ultimately result in lower speed.

For the highest speed, the motor must be optimally matched to the load. For any particular (speed x torque) product, optimal matching is the point where changing the speed/torque balance results in less speed. If gears provided more torque at lower speed, then the result would be slower because the lower torque isn't needed and the limit becomes the speed capability. If gears provided more speed at lower torque, then the result would be slower because the smaller torque can't move the load as fast.

Gears between the motor and a drive shaft can result in higher top speed if that matches the load better.

Generally bare electric motors have high speed and low torque compared to what the drive shaft of your car probably wants. The right gearing that reduces speed but increases torque will probably help. To know what the gear ratio should be, you have to know some parameters, or experiment.