In my article in the current issue of Inside Motorcycles ("Computing Speed II," April/May 2012), I briefly discuss measuring wheel speed and calculating slip as part of a data acquisition system. "Slip" is a broad-meaning term and a difficult parameter to quantify accurately, and I thought it deserved some more attention here. When we talk about slip, we are generally referring to wheelspin and a loss of traction, and there are a couple of ways to consider it. One is the difference in speed between the front and rear wheels; if the rear wheel is turning faster than the front, that is positive slip. Under braking, the rear wheel can turn slower than the front, resulting in negative slip. Slip can also be considered as the difference in speed between either the front or rear wheel and actual ground speed as measured by GPS. Knowing an accurate value for slip in a data acquisition system helps point out areas where the rider is spinning the rear tire or wheelying on corner exits, or skidding either tire on corner entries. Additionally, an accurate slip measurement is the cornerstone of a good traction control system.
A very rough value for slip can be calculated by simply comparing front and rear wheel speeds, or comparing wheel speed with GPS speed. Since most motorcycles are already equipped with rear wheel speed sensors for their speedometers, it's simple enough to record rear wheel speed and calculate slip as a percentage compared with GPS speed. The first and largest error introduced is due to the tire's changing circumference as the motorcycle leans, which affects the speed calculated - just as your speedometer reads higher as you arc into a turn. This can result in a slip calculation of more than 10 percent (the difference in circumference between the center and the edge of the tire) even when there is in reality no wheelspin at all. This error can be reduced by using a math channel to take into account the actual circumference of the tire based on lean angle as measured by a sensor or estimated from GPS data. Some tire manufacturers release this information, as Dunlop does for its spec AMA tires, but a fairly accurate estimate can be made using an arc or parabola formula based on a couple of measurements. BMW's DTC (Dynamic Traction Control) system uses this approach, with a lean angle sensor and maps inside the ECU to take changing tire circumference into account. The ECU can be reprogrammed using the company's HP Race Calibration Tool to account for different tires.
A second error is introduced when the tire deforms under load. As the motorcycle accelerates and decelerates, weight transfer loads and unloads the tire and changes its circumference accordingly. The load on the tire can be calculated based on static weight and longitudinal acceleration, either from an accelerometer or from GPS data. Knowing some values for tire stiffness, or again having actual specifications from the tire manufacturer, an estimate can be made for the change in circumference from tire deformation. Several Kawasaki patents for traction control describe a system that uses compensation maps inside the ECU to adjust measured slip, based on rpm and the gear selected, to account for tire deformation.
If you are generating a slip channel for data acquisition, the more accurate you can make the data by accounting for these errors, the better you will be able to find and analyze areas of actual wheelspin that need attention.