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.
Previously we have looked at braking G – a math channel that shows only the braking portion of longitudinal acceleration – and derivative channels, which show the rate of change of a value over time. Here we will look at the rate of change of braking G, which can be used to show further detail on braking performance. This channel is simply the derivative of the braking G channel, and is referred to as delta brake.
Figure 1: A lap of Willow Springs International Raceway, showing speed (black), lean angle (orange) and roll rate (blue). Spikes in the roll rate data indicate transitions from full lean to full lean, while in long corners roll rate should be at a minimum.
While it’s possible to see from the lean angle data how quickly the rider makes transitions and how well maximum lean is held in long corners, it’s much easier to see graphically and put numbers on that data by using a math channel. This channel is the derivative, or rate of change, of lean angle, and shows roll rate in degrees per second. We know that lean angle (Φ) can be approximated from lateral acceleration data as follows:
Figure 1: This data shows just the entry to a turn, with speed in black, braking G in red, corner G in green and total G in blue. The shaded areas represent where the rider is trail braking, with a combination of corner G and brake G.
One important aspect of riding a motorcycle well is trail braking – a combination of braking and cornering on the entrance to a turn. When the rider approaches a corner, the brakes must be released as the bike is leaned into the corner and cornering G increases, until the brakes are completely released just as the motorcycle reaches full lean. Using a math channel, it’s possible to put a number on trail braking that can be used for a quick reference.
Previously, we have split the lateral and longitudinal acceleration channels into their component parts. Here we are concerned with corner G (the all-positive lateral acceleration channel) and braking G (only the braking component of longitudinal acceleration). Figure 1 shows a typical corner entry with these two channels along with speed and total G. The shaded portion represents when the rider is both braking and cornering; as braking G decreases, corner G increases, and this gives the trail braking area its characteristic triangular shape. We can eliminate everything but the trail braking data by using the minimum function in a math channel:
Figure 1: The radius channel, shown here in blue, graphically depicts the rider’s line through a particular turn. The vertical lines indicate radius is approaching infinity – in other words, the motorcycle is going straight and not turning.
When we introduced G-force and lateral acceleration, we used the equation for lateral acceleration as follows:
r=radius of turn
With most GPS-based systems we know lateral acceleration and velocity, and by rearranging the above formula can calculate a value for the turning radius: