A method to calculate the optimal shift-point

Disclaimer

When talking to people in the racing business, I discovered that a lot of people have a different view on how to calculate the optimal shift point. What you will read here is my point of view. In my humble opinion this is the correct way to calculate the optimum shift point. If you have additions, corrections of other ideas on this matter, please mail us.

Rule of thump

In the now following explanation is kind of lengthy and theoretical. I can imagine that you do not have the time or interest to read it all and perform the necessary calculations. As a rule of thump you can use the following:
Find in your dyno chart the RPM point with the maximum power (HP). Multiply this value by 1.1 (add 10%) and use this value elect as optimal shift point.
Be warned: this is a rule of thump; there is no guaranty of any kind that this really represents the optimal shift point.

The basic idea

If you want to accelerate as fast as possible and you want to have the highest (top) speed as possible, you need to maximize the pulling force on your final drive, being chain or shaft. With maximizing, I mean maximizing this always, at any moment. If you have an overall look on the drive forces, you will find the absolute maximum in the first gear at peak torque. The problem is that this point represents only one constant speed. The idea is to maximize this force globally, at any given speed. To maximize this as a driver, the only thing you can do is control the shift points. This way you can select the RPM range in which the engine operates and thus selecting a range which will give you the maximum drive force.

The torque curve of your engine

To calculate the optimum shift point, it is necessary to know the torque at a specified RPM of your engine. You will need to put your vehicle onto a dyno. The resulting torque/power map will look like this:

Figure 1 - Engine power/torque map

(If you would like to make it a precision job, you need the measuring points and the measured value at these points. With this information, you can interpolate points between the measured points. For example, use the Matlab spline function to do the interpolation)

The list of measuring points looks like this:

Table 1 - Dyno measument results

If it is only possible to get a power curve, instead of the necessary torque curve, you can use formula in the footnote to convert power to torque.

The results of shifting

When you shift up one gear, the gear ration changes: the gear ratio will be smaller than the gear ratio before the shift. Since the speed of the wheels will be approximately the same at the moment before and after the gear shift, the engine speed needs to drop and is accounted for the total difference. With this in mind, you can make a table with engine revisions and torque of the moment before and after the shift. For a 6 gear engine, you will need 5 tables.
At the moment you find a greater torque in the next gear at a certain RPM, at that point you find your optimum shift point. An example is listed below.

In the manual of your vehicle you find a list of gear ratios. You will also find the primary reduction and the final reduction. These last two you will need if you want to calculate the vehicle speed. They are not necessary for calculation the shift point (introduction of a linear factor).

With the gear ratio table, you can calculate the RPM drop after an up shift (assuming that the wheel speed is constant during the shift):

The RPM before shift of 10.000 is fictitious value, just selected for easy calculation.

Calculation of the shift points

With the information in the previous sections, you can start filling the comparison tables for each gear shift. See the example tables 4 to 8.

First column:	List a set op rpm points in the range you would shift.
Second column:	Get the brake torque at the specified rpm in the first column. Read the torque from your dyno chart.
Third column:	Calculate the shaft torque before shift. Use:
Fourth column:	Calculate the rpm after shift. Use :
Fifth column:	Get the brake torque at the specified rpm in the fourth column. Read the torque from your dyno chart.
Sixth column	Calculate the shaft torque after shift. Use:
Seventh column:	Calculate the percentage gain/loss. Use:

Selecting the shift-point

Formula to calculate the torque from given power at specified RPM:

General:

Specific (given power P in 'horse power' and resulting torque in [Nm]):

Formula to compute the RPM after shift:

Formula to compute the RPM drop: