Tire Rolling Radius and Correcting Wheel Speeds

In the introductory pages of Data for Motorcycles, we briefly discussed tire rolling radius and GPS speed vs. wheel speed, and the potential errors that can arise when using a wheel-speed-based data acquisition system. Here we will address this issue and how to compensate for that error when using tire rolling radius in other channels.

GPS speed vs. wheel speed with no correction

Figure 1: GPS speed is shown in black and wheel speed in red. Whenever the motorcycle is leaned over, wheel speed reads significantly higher than GPS speed due to the change in rolling radius of the tire.

To recap, when a motorcycle leans into a corner, the rolling radius of the tires decrease, and this alters the relationship between measured wheel speed and actual ground speed. The most common evidence of this is in the speedometer, which will show a higher speed the more the motorcycle leans over, even though actual speed does not change. Wheel speed is typically measured by using a sensor that counts pulses from a transmission gear, a sensor ring, or some other set of objects. This count gives a number of wheel revolutions per minute or second, which is then converted to speed by multiplying by the tire’s circumference.

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Data Acquisition Math Channels Reference

This page is a summary of useful data acquisition math channels that are referenced on Data For Motorcycles. Because every data software package deals with operators and channel names differently, you may have to make changes specific to your software. For example, some packages have a built-in derivative function that can be used, while others use a completely separate derivative channel and a second math channel must be built to accommodate the entire formula.

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Suspension Analysis – Squat

suspension squat data

Suspension data for a typical lap showing speed (black), front fork travel (blue), rear wheel travel (red) and squat (green).

One important aspect of motorcycle setup, especially as bikes become more powerful, is how the suspension reacts when the motorcycle accelerates. As we have discussed previously in the section covering front and rear weight, load transfers during acceleration and braking and acts to compress or extend the suspension. This load transfer causes the bike to “squat” to the rear under acceleration, and in an extreme example, all the weight can transfer to the rear wheel in a wheelie.

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Front and Rear Weight

An approximation for front and rear dynamic weight can be determined from longitudinal acceleration and values for the wheelbase and center of gravity position.

An approximation for front and rear dynamic weight can be determined from longitudinal acceleration and values for the wheelbase and center of gravity position.

Now that we have looked at static weight distribution and also found how cornering forces add to the total weight of the motorcycle and rider, in this post we will show how total weight is distributed between the front and rear wheels. As the motorcycle accelerates, weight is transferred from the front wheel to the rear wheel; under braking, weight transfers from the rear wheel to the front wheel. Note that the acceleration and braking forces act on what we have designated the total weight of the bike and rider, which includes cornering forces.

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Total Weight

A typical vector force diagram for a cornering motorcycle

This is a typical vector force diagram for a cornering motorcycle. The horizontal cornering force can be added to the vertical static weight using vector addition and the Pythagorean theorem to find the total force (or weight) along the axis of the motorcycle. (Photo courtesy of Repsol Honda)

In the discussion on mass, weight, and center of gravity, we introduced the idea of weight transfer and how the amount of weight on each wheel of the motorcycle changes as the bike accelerates, brakes and turns. The first step in determining values for that weight transfer is to calculate how the total weight of the bike changes during cornering. Note that “weight” here refers to the weight or force of the motorcycle along an axis parallel to the lean angle of the motorcycle, and not perpendicular to the ground. This will provide an estimate of the total load on the suspension, which can be further refined using other GPS data.

 

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