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Choosing a Gear Ratio

After designing and building the car one of the most difficult things to get right is the gear ratio to use in a particular race. This page describes the methods we have used to determine the best gear ratio to use for a race. This applies to fixed and variable gear cars although variable gear cars may change during the race or lap which complicates things a bit more. The average base line gear ratio would be the same in both cases however.

The nature of a Greenpower race is that you have a certain fixed amount on energy in the set of 4 batteries to last you for the 4 hour race. In order to last the race you must make sure that the average energy usage is low enough so the car lasts the race without stopping (and probably wrecking the batteries) but still uses as much as possible so you can go as fast and hence as far as possible in the 4 hours. If the gear ratios are way out there is also the likelyhood of an overheated and burnt out motor.

The gear ratio to use is heavily dependent on the RollingResitance and Aerodynamics of the particular car. It is a tricky balence, and always difficult to get right. This is especially true due to weather condition changes, battery temperature and the condition of your batteries which is particulary variable with Yuassa batteries in the way we use them.

This info is drawn from the experience of the Chipping Sodbury Rotary Racer team, both past and present members.

This is a rough graph showing distance travelled versis gear ratio choice for a particular car. It is pretty basic and ignores some factors. Due to the motor heating up the distance would drop off more exponentially when the gear ratio was lowered for example. The gear ratio is the ratio of wheel gear to motor gear or overall gear ratio if there are any intervining gears. The  wheel diameter is a part of the gear ratio selection but has been taken into account for the car in question here. Notice that the peak distance travelled, with this particular car, in 4 hours will be obtained with a gear ratio of about 4.7 when the car would be averaging about 17 Amps. If the gear ratio is increased then the car will go slower but use less current and will have a good safety margin for finishing the race. If you gear below 4.6 the car will stop on the track near the end of the race and thus although the car is travelling faster when it is going, it will actually travel less far and its average speed over the whole of the race time will be less. It is also likely that your batteries will be quite damaged after this. Note also how quickly the maximum distance falls off with decreasing gear ratio (it would be more if motor heating was taken into account and/or driver experience).

If you lower the gear ratio a bit to far (~28%) then the average current you are using will be heating the motor so much that it is likely the motor will burn out unless you have a snow storm based cooling system. The graph assumes the motor will last an hour with this abuse, your millage may vary as they say :)

A good choice would be to initially gear higher, giving say a 15% safety margin. As you get more competative, you can reduce this safety margin. (Note that a teams heart rates in the later stages of a race are linked to the degree of safety margin :) )

An interactive calculator for this is at:

http://portal.beam.ltd.uk/greensim/CarGearRatio.py

Initial Ratio

You can calculate a first pass ratio relatively easily. When doing this be pessimistic. It is always better to finish the race rather than stop and it is certainly better to avoid a burnt out motor. Depending on your cars design you can probably aim for a race speed of say 35KmH (22Mph). A calculation for a suitable gear ratio is:

gearRatio = (1800 (rpm) * wheelDiameter (m) ) / (19.1 * avgSpeed (m/s) )

This is based on the Fracmo graphs which show the motor should use about 17 Amps when running at about 1800 RPM. So with 20inch 406 based wheels which are about 0.461m in diameter, depending on tyre size, we get an intial gear ratio of:

4.4 = (1800 * 0.461) / (19.1 * 9.7)

How to Determine the Correct Ratio

Although the above gives a first pass ratio, you really need to tailor this for your particular car on the race circuit in question, with the batteries you have and the wind on the day. This is difficult to do as it depends on the cars weight, the rolling resistance, the frontal area, the aerodynamic drag factor, the drive efficiency etc. Most of these bar the aerodynamic drag factor can actually be measured or calculated but the aerodynamic drag factor is difficult to measure or calculate.

Once you have some experience with a car on different circuits and condtitions it is much easier as you know the base line figure that works and you can simply increase or decrease it a bit based on a finger in the air and looking at the hills. However for new teams and a new car it is much harder.

The basic method is to find out the average current or average RPM of the motor over a lap of the circuit in question.

As test tracks are difficult to find, what we have found best is to test the car on the circuit in question during the practice session on a race day. We get the most expierienced driver to first drive the the car on a 3 lap stint and take measurements during the middle lap. Once the experienced driver has done this, and checked the car out, the less experienced drivers can do their practice while feverish maths activity is performed in the pits.

Average Speed Method

In the early days, before we had current measurement logging and telemetry we used the Motor RPM method which is based on average speed. Using a stop watch we time the middle lap. With a knowledge of the circuit length we calculate the average speed:

avgSpeed (m/s) = circuitLength (m) / Time (s)

Now knowing your gear ratio and wheel size you can calculate your motors average RPM:

motorRpm = (19.1 * avgSpeed (m/s) * gearRatio) / wheelDiameter (m)

The motor uses roughly 17 Amps at about 1800 RPM. You can calculate the average current using:

motorTorque = 13.5 - (motorRpm * 13.5 / 2020.0)
current = 2.0 + (motorTorque * 128.0 / 13.5)

After the practice session we then change the gearing as appropriate to get the motorRpm above 1800 or the current below 17 Amps depending on which we are calculating. We actually have a table printed from the maths equations that help us make this choice.

Average Current Method

This is better than the average RPM method as it takes into account any issues or differences from specification of the motor. This requires an instrument on the car to measure the average current used. A home built data logger or something like a "Watts Up Meter" can be used typically using a Hall effect current measuring device. It is important to only measure the average current for the middle lap though as the start and slowdown laps will have biased average currents.

You really need to be able to measure the average current. On a lap of a windy and possibly hilly circuit the instantaineous current could easily vary from 2 to 45 Amps.

After the practice session we then change the gearing as appropriate. We actually have a table printed from the maths equations that help us make this choice.

Current to Aim For

This depends on your batteries condition and their temperature on the day. Performing battery discharge tests help you calculate this for your particular batteries. Note however, every deep cycle discharge will perminatly reduce the batteries capacity. The damage becomes much greater the deeper you discharge them. If you take them down below 10.5 volts you will normally see a lot of degredation, so aiming for a minimum voltage of 11 volts gives you a bit of a margin for error.

On a reasonably good set of batteries, a current of about 17 Amps should be able to be sustained at 20 degrees C. A set that has been relatively well cared for but done 8 races can probably put out 16Amps on average.

Changing the Gears

To optimise the gearing you need relatively small steps in adjustment. As Rotary Racer has a fixed gear, using a chain, we have a set of cogs with 1 tooth increments. We use the appropriate cogs to get the gearing we need. Our gearing at the 2012 final was 2.72 (18:49). At Merryfield 2012, a tigher slower circuit and where we used old batteries, we used a ratio of 2.82 (17:49). Changing the front cog by 1 tooth is about a 5.5% change in gear ratio with an 18 tooth cog. Changing the rear cog by one tooth would be aproximimately a 2% change in gear ratio.

Affect of wind

Wind has a large affect on a Greenpower car due to the fact that the aerodynamic drag is a squared law relationship with respect to air speed. A car going at 25MPH into a 20MPH wind is actually going at 45MPH with respect to the wind and thus has a huge amount more drag than in still conditions. Although the car is going into the wind for only a portion of the circuit and going downwind the car has less drag, this does not cancel out due to the square law.

As a rough guide you should increase your ratio by about 10% for a 20MPH wind to achieve the same average current.

Affect of Hills

The slight hills on a Greenpower race circuit don't affect the average current much. Although you use more current going up a hill you use almost proportionaly less coming back down. There is a small increase in current due to secondary affects however, mainly our old enemy aerodynamic drag's squared law (The car is going faster down hill and so the aerodynamic drag will be greater which is not canceled out by our slower speed up-hill) and reduced efficiency under higher torque levels.

Geared and Motor Speed Controlled Cars

Geared and motor speed controlled cars still need to get their overall gearing about right for the circuit in question. However with average current feedback during the race they can tweak their current usage to handle errors, changes in conditions and batteries failing earlier than expected. This allows them to be more likely to get the average current spot on for the day in question. However, an equivalent (same rolling resistance/aerodynamics) fixed gear car with no motor speed controller is more efficient and if on the day has their gear ratio spot on will be the fastest car.

With a hub gearbox you should find out what the most efficient gear ratio is and aim to set the drive gearing such that this would be the main gear used. Most hub gear boxes have a large step in ratios and thus only the one gear above and the one below the normal one used will probably be useful.

Additional Information

Some technical info is at: http://www.greenpower.beamweb.co.uk/files/TechnicalInfo/index.html

Motor Heat calculator: http://portal.beam.ltd.uk/greensim/CarMaths.py

There is a Greenpower car simulator at: http://portal.beam.ltd.uk/greensim