# Technical Details

1.1. Calculation of Lean Angle

The calculation is based on the simple physical fact that any two-wheeled vehicle will have the same lean angle when going through a turn with the same speed and the same radius of the turn  (independent of size or weight!)

The so called “neutral” lean angle meant here is not necessarily the lean angle of the bike itself however. Rather, it is equal to the tilt of an imaginary line drawn from the center point between the centers of tire footprints (theoretical tire width of zero) to the total center of gravity of the motorcycle and the driver. The driver in an asymmetrical position (e.g. “hanging off”) will lead to marked deviations of real leaning for example.

The actual lean angle also depends on the width of tire and on the height of the center of gravity, it becomes larger when the COG is lower and the tires are wider. The crucial advantage of the neutral lean angle is therefore, that bends data become independently comparable (=> how fast a certain turn was gone through).

1.2. Reliability of Results

The neutral lean angle can be calculated from the relative change of GPS position. The reliability of the results obtained depends on the accuracy of motion detection and thus on the quality of sequential GPS positioning. The iPhone refreshes its position once per second. To reliably obtain the lean angle, a constant leaning has to be maintained for 2-3 seconds.

The accuracy of the determined leaning will increase with speed and the more constant speed and bend radius are. When speed is low (< 20 mph) and rapidly changing, measurements will be rather inexact. However, if you go through longer turns at higher speed you can expect sufficiently exact results.

1.3. Why is there no direct measurement of lean angle?

The technical measurement of leaning is not simple for different physical reasons. In the professional sector too, so called GPS loggers are often used.

A lean angle sensor of the company BOSCH first placed on the market in 2009 (!) uses two independent acceleration and angular rate sensors. For reliable results, this sensor has to be mounted exactly into the center of gravity of the motorbike.

The iPhone is equipped with an accelerometer and an in-built gyroscope, which allow good measurement of inclination while in rest. On a moving motorcycle however, occuring vibration shocks make the use of the accelerometer nearly impossible. The data of the gyroscope show a drift of the zero point, which could not be corrected sufficiently in the vertical position of the moving bike up to now.

2. Bend Detection

What actually is a turn ? At first glance the answer seems to be simple. But: is a quick swerve with leaning for 1 second to be considered a bend already? I think it might not.

Relevant turns for bikers therefore should require a certain minimum leaning for an appropriate minimum duration. A minimum speed is also necessary, as when lower than 5-10 mph no leaning at all is required to travel through a turn.

Experiments performed have resulted in the development of a suitable algorithm to detect bends. However, as it remains highly subjective what is considered a bend, the sensitivity of detection can be adjusted (within certain limits)  in the settings of BikeTrip.