Choosing The Best Gear Ratios
“Samir, how would you go about choosing the best gear ratios for your racing car – if you had total freedom?“
A deceptively simple question sent in from a reader. This article helps you work through the challenge, explains the maths and gives you a done-for-you-tool to calculate the numbers for your car.
Having that freedom to choose can be something of a mixed blessing. Yes, on the one hand, you have the chance to gain performance with a better choice. Equally, you have the chance to get it spectacularly wrong with a poor one.
If you have a choice, then what you are after is a certainty to know that you are running the very best gear ratios possible. And not only for your racing car on a drag strip (unless that is your thing) but optimised for your racing car on a specific racetrack.
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Knowing What “Best” Looks Like
This article digs into this. By the end of it, you will have a solid understanding of what goes into defining (and then selecting) the very best possible gear ratios for your racing car.
Knowing you have the best gearing is basically free lap time – or unnecessary lap time loss if you get it wrong. Even if your ratios are all fixed it is worth knowing what “best” looks like and this method and spreadsheet give you that.
The “Does It For You” Spreadsheet
Just before you start, you might be interested to know our newsletter subscribers can get the spreadsheet developed to accompany this article for at 25% discount. After you have read the article, watch the comprehensive VIDEO guide (below) and then sign up below to get your own copy.
Whilst only a spreadsheet, you will see it can actually do some pretty incredible optimisation work (with the “Solver” function) that consequently makes the process very easy for you.
Calculate Your Perfect Ratios
Advanced Racecar Gear Shift AND Gear Ratio Optimisation Calculator
Your Goal:
You want gearbox ratios (inc a final drive) that ensures you hit maximum speed on the straights, whilst ensuring you have the best possible acceleration at launch and coming out of each corner.
Mixed Blessing
You already know how to determine your best gear change RPM for each gear 😎 (no? – seriously have a read because this article builds on that one) And, as you are already shifting gears at the best possible RPM points, you will already be getting the best possible acceleration. But that is only for those specific gear ratios.
With real racing cars (verse simulators) there are always limits on the ratios you can choose. These are either specified by the series you race in or by the gearbox design.
These restrictions, whilst a pain in terms of pure performance, do have the beneficial effect of often making your gear ratios selections one fewer thing to worry about!
When you have freedom in choosing the best gear ratios it can actually become something of a mixed blessing!
If you can change the ratios (and/or the final drive ratio) then there will be an optimum setting for your racing car for each track. One you now need to find!! – as if you are not running the optimum, then you are giving away performance unnecessarily.
Flipping that into a positive. 🙂 If you can change the gear ratios you have the opportunity to run an optimum setup for best performance.
But how do you choose these optimum ratios?
Three Bits of Theory
The good news is that there is some theory and some formulas that you can use. You can take your racing car parameters (and this theory) to then work out the best gear ratios (and final drive) for any track.
The following 3 theories combine to define your racing car’s limits. Once you understand these limits you can select optimum gear ratios to match.
1- Tractive Force From Your Race Engine
The primary theory to consider is the concept of Tractive Force. Have a look at the image below:
On the y axis you have Force (N). On the x axis you have vehicle speed (kph).
The Tractive Force curve shows you the force your racing car can put down at the wheels as your car increases in speed.
Super important point – this curve is totally independent of your gears.
What it is saying is that if your racing car could generate its peak power at all speeds, then this is how much (tractive) force your racing car would be able to put down on the road. It represents the best your racing car could produce.
The tractive force curve, therefore, informs your limit in terms of what your engine can deliver – it becomes your target.
This is because your engine is not delivering peak power at all speeds. The gear ratios, therefore, aim to compensate for this (it is their whole purpose really.)
You, therefore, end up wanting to choose ratio’s that enable you to deliver tractive force as close to that line as possible. More on this in a minute …
2- Traction Limit
At lower vehicle speeds you can see the tractive forces are very high. If you try to apply these high forces at low speeds, you generate wheel spin.
Wheel spin happens when the forces applied at the contact patch exceeds the tyres grip.
The theoretical name for that is the Traction Limit. You can see that as the horizontal line on the image.
It is worth noting that, depending on your racing car (and how you calculate it) the tractive limit line could increase (or decrease) with vehicle speed. This is because of weight transfer and, in an aero car, downforce that effectively gives the rear tyres more grip than when they are stationary. I’m keeping it simple here but for completeness, it’s worth being aware of.
3- Resistive Forces (or Drag mainly)
The third curve on that image is the Resistive Forces. This is a combination of mechanical and aerodynamic forces.
Mechanical losses (in a real car anyway) notionally remain constant throughout the speed range. A good approximation for this is typically estimated at about 2%-3% of your racing cars weight. Assuming you don’t know the mechanical losses precisely.
Aerodynamic drag increases with the square vehicle speed. This is why the line curves up so much.
Aerodynamic drag becomes the primary resistance force, especially at higher speeds.
To calculate the drag forces (Fd) you need your racing cars:
- speed (v)
- its “drag coefficient” (likely to be between 0.3 – 0.7) (Cd)
- its frontal area (A), and
- the air density (p)
Here is the equation for your reference:
With this data you can then calculate the resistive forces and how they increase with speed.
Tip: Working Out Your Racing Cars Frontal Area
A slight challenge you might have is calculating your racing cars frontal area – again assuming you do not know it.
One way to calculate the frontal area is by taking the width and height of your car and then multiplying that by a scaling factor to bring it down to something representative. If you are unsure there are lots of ways people approach this – You might like to try this squares on an imaging approach (comes with image template.)
Armed with these three bits of theory you can now use them to working out interesting things about your racing car. And ultimately choose the best gear ratios for your racing car.
Working Out Your Racing Cars Maximum Speed
One thing you can now work out straight away is your racing cars top speed (Vmax). Have a look at the annotated image below.
The point at which the resistive forces and the tractive forces intersect defines your racing car’s theoretical top speed (Vmax). Again. this is totally independent of your gearing choices.
I found this quite cool when I first worked it out. Really clear.
Rule of Thumb To Check Top Speed Calculations
There is also a super simple, rule of thumb method you can try. Primarily to cross-check your top speed calculations are giving you sensible numbers.
Try the following (fairly crude) equation to make sure you are in the right ball park:
Top Speed (mph) = 20 cube root of horsepower
So for example, say your racing car makes 140bhp (@ 6000 rpm). The top speed would be:
Cube root of 140 bhp = 5.19 --> Top Speed = 20 times 5.19 = 104 mph
This calculation works fairly well for a regular car shaped racing car. I find it can be quite useful, especially if you are struggling to sanity-check your frontal area calculations.
Calculating The Optimum Gear Ratios
To quickly recap, to optimise your gear ratios you want to have them so that they are:
- As close to the tractive force line as possible,
- Sensibly managed around the traction limit and,
- Enable you to achieve Vmax in top gear.
All you need to do therefore is to calculate these tractive force curves for your racing car in each gear (Torque x wheel radius) and then tweak the ratios so that you get the perfect set up.
But what about for a specific track?
Track Specific Gear Ratios
Follow those rules and it will give you a great setup for a drag race but will not necessarily be optimised for your specific race track.
For example, you might have a track where the straights are never going to be long enough for you to reach Vmax. There are 3 things to consider here:
1- Length of Straights
What you can do in that situation is instead of optimising your gear ratios to hit the cars theoretical Vmax, you can shorten them a bit so you are instead aiming at hitting your peak power in top gear at the Vmax for the track instead.
2- Minimum Corner Speeds
Equally, it might be that the track has mainly fast corners with very few slow ones.
Once you are up to speed and doing laps, a more optimum gear ratio stack might be one with slightly longer lower gears that enables you to stay closer to the tractive force limit, at those higher speeds, more often than a more “standard” gear ratio set.
3 – Positional Timing of Gear Changes
Finally another thing to consider is the timing of your gear changes.
You know at what RPM to change between each gear but it is not good if you need to make a mid-corner gear change or an up change just as you are coming into a braking zone.
Therefore, what you can do is plot a velocity profile of the track you are trying to optimise for, on the tractive force chart.
The velocity profile you can get in a real racing car from the data logger or you try get your driver to remember the speed (or RPM) figures coming on too, and at the end of, each straight.
Pulling This All Together
So pulling this all together you end up with something like this:
The chart is a bit busy, but it is just the same as before but now with all the new information added to it to help to choose the best gear ratios.
Trust Applied To The Road In Each Gear
The new curved lines starting from near zero, represent the actual tractive forces generated by your racing engine. One line for each gear.
Notice how close (or not) they end up being to the theoretical maximum.
The little gaps you can see are what you need to minimise to get an optimum gear ratio set. See below:
The reason is that anytime you are NOT on the tractive force curve limit, you are wasting the potential of your racing cars engine.
The size of the little gaps will be different for each gear ratio set you choose.
Therefore, what you need to do is to work out the area of these little gaps for each gear ratio stack that you choose. You then compare the results – the smaller the area of losses the better and more optimum the gear ratio selection is.
To work out the area is tricky. If you are able to do this in a spreadsheet you can use the equations from a trend-line and integrate these to give you the areas under the curve. You then take away the theoretical maximum area from the area your gear ratio will offer.
Do that for each gear, then add them up and it gives you the overall force losses from your given gear ratio set.
Once you have that setup though all you then need to do is keep trying different combinations of gear ratios and final drives until you find the one with the lowest losses.
Track Specific Optimisation
You can also see on that chart I’ve added Track Vmin and Track Vmax. I have also added 8 little horizontal lines (at the bottom) which represent the minimum and maximum speed for each straight.
Hopefully, you can also see where the optimum gear change speeds, intersect the track velocity profile lines? This shows you what gear you will be in at what point of the straight.
The idea is, therefore, to make sure that you are changing gear well along the straights not right at the beginning nor right at the end.
With this setup you can now simply change the ratios and see how it effects both the optimum setup (in terms of losses) but also what is best for the track.
Final Thought on Choosing The Best Gear Ratios
In summary, choosing the best gear ratios is some theory, some maths and also some practical tweaks to make sure you end up with a sensible set of gear ratios and final drive ratio for any given track in any given car.
You have seen that it is possible to use the maths and formulas to optimise your gear ratios but, for such a simple question, it quickly gets fairly involved – as you will no doubt have discovered!
A quick reminder that our newsletter subscribers get my spreadsheet on this at 25% discount. If you are keen to take the next step with choosing the best gear ratios for your own racing car, I strongly suggest you grab a coffee and watch the video walkthrough for the spreadsheet. It plays pretty well in 1.5x speed and I’ve done the subtitles in case sound is an issue where you are watching. You will see how I am using the Solver function, combined with some automated trend-line functions to be able to automate the gear selection process. The aim is to hopefully save you a lot of effort 🙂
If the spreadsheet is not for you then all good. Hopefully, there is enough guidance here to be able to work it all out.
Best of luck!
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Want to take the guesswork out of setting your tyre pressures? Try this article including a free calculator: https://www.yourdatadriven.com/how-to-set-your-racing-car-tyre-pressures-perfectly-every-time/
“I’ve got data but I’m not sure how to interpret it”. Try starting with the one channel that matters: Introduction to Motorsport Data Analysis: Delta-t
