Braking Performance of Motorcyclists Wolfgang Hugemann, Frank Lange Abstract The paper presents measurements of the braking skill for 18 motorcyclists. The test persons were set with the task to decelerate their (own) motor- cycle out of a given initial speed to standstill within the shortest possible distance. The re- cording of the deceleration is described by a Fig. 1 Photograph showing the components of the functional pattern derived from control science. measuring equipment Applicability of the experimental results to real world accidents is discussed. Every reconstructionist knows of motorcycle ac- 1 Introduction cidents where time distance considerations gave evidence that the defense time of the motorcyclist The braking behavior of a passenger car may be was considerably long, but the skid marks left by deduced from skid marks in a narrow range. the motorcycle were rather short. For a motorcy- When choosing the friction coefficient as well as cle, the breaking distance and length of skid the deceleration build-up time, the reconstruc- marks is simply not that rigidly coupled as for a tionist may found on a number of publications. non-ABS passenger car. There is not much room left for discussion on that theme in the courtroom (well, at least in Ger- A longer skid mark always stems from the motor- many). The behavioral pattern of all passenger cycle rear wheel, but it would be remote from re- car drivers is more or less the same: The brake ality assuming that the motorcyclist exclusively pedal is pushed with exaggerated force, at least made use of the rear brake. Front brake usage is until the front wheels lock up. The deceleration sometimes proven by a double skid mark left build-up is mostly determined by mechanical shortly prior to collision, when the motorcyclist at processes, like the rise of the pressure in the last skipped all mental reservations against font braking system. wheel lock-up. For the motorcyclist, emergency braking is a The present paper should help to describe the more difficult task. When assigned with the task braking pattern of motorcyclists in a narrower to reduce speed in the shortest possible distance, range than possible so far. he may not rely on the self-stability of his vehi- cle, as it is based on the gyration of its wheels. 2 Conception of the Experiments The motorcyclist is forced to control his behavior In two earlier papers [1, 2] we developed a as lock-up of the front wheels will result in im- mathematical description of the motorcyclist’s mediate tilt. braking behavior which was based on forty The rise of the deceleration and its maximum braking experiments. Founding on this findings, value is not that much determined by mechanical we conducted new braking experiments with im- processes but by the braking skill of the driver. proved measuring equipment [3]. Thus the individuality of the driver has a strong With a group of 18 drivers using 15 different impact on the braking performance. This gives motorcycles we conducted 74 braking experi- reason to the heading of this paper: We should ments. As these numbers imply, each driver could e not speak of motorcycl deceleration but of mo- use his own motorcycle with the exception of ists torcycl deceleration ability. three persons. This was the only way to make sure that the driver was fully adapted to the – 1 – braking behavior of the motorcycle. The group point of the braking maneuver. used for the experiments represents the complete The fixation points of the accelerometers were spectrum of possible driving experience (less than changed several times at the beginning. At last, 20.000 km up to 130.000 km in total). The ex- the first was mounted on the fork and the other on periments were conducted roughly in the mid of the rear wheel pinion right next to its pivot. The the driving season at dry weather on asphalt road accelerometer mounted on the fork was used as a surface. The drivers were assigned with the task trigger that indicated the start of the braking ma- to brake from an initial speed of some 50 km/h to neuver, as its measurement was very sensitive to standstill within the shortest possible distance. the brake torque applied to the front wheel. The Intentionally, we did not equip the motorcycles second accelerometer measured the deceleration with outriggers or support wheels to prevent tilt of the center of mass. Due to the special fixation when breaking. These would suspend the motor- point, its signal was not much influenced by cyclist’s mental reservation against front wheel brake pitch. lock-up and thus lead to unrealistic braking be- Measuring the dip motion of the fork was in- havior. tended to allow compensation of any gravitational acceleration coupling into the measurements, 3 Measuring Equipment which later turned out to be obsolete. The reflex The demand that every motorcyclist should use taster recording the rotation of the rear wheel al- his own machine called for a mobile measuring lowed to draw conclusions on the driver’s control equipment, fig. 1. In the driving experiments, the strategy regarding the rear wheel. data recorder was located in a back package that the drivers had to carry. The sensors consisted of 4 Evaluation Technique two accelerometers, a thread potentiometer that The low pass characteristic of the mechanical ac- measured the dip motion of the fork and a reflex celerometer used in the previous experiments [1] taster that recorded the rotation of the rear wheel. resulted in a relatively smooth function plot for Data recording was triggered automatically by the acceleration. The higher resolution of the driving through a speed trap. After that point, the electronic accelerometer tends to cause confusion drivers could make a free choice on the start at first glance, fig. 2. When structuring the experimental results, the 10 exponential description derived in [2] proved to 9 be very useful. The recorded acceleration may 8 thus be approximated by 7 −t 6 a(t) = a 1− e T .(1) 0 5 4 The static factor a0 is equivalent to the maximum value of deceleration. The time constant T de- Deceleration [m/s²] 3 scribes the rising behavior of the deceleration. A 2 Measurement large time constant T results in a slow rise of the 1 Approximation acceleration, small values result in steep rising 0 behavior. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Time [s] For each acceleration recording the functional pa- rameters a0 and T of the function pattern eq. 1 were adjusted such that maximum coincidence Fig. 2 Original acceleration recording and approxima- with the recorded signal was achieved. The term tion by exponential function ‘maximum coincidence’ was represented by the minimum of the functional – 2 – 0.5 te = []− D 10 G(a0 ,T) ∫ ameas. (t) a(t) dt D 2 0 (2) 0.4 D 7 t D 15 e −t = − − T ∫ ameas. (t) a0 1 e dt 0.3 0 Eq. 2 is often referred to as the ‘loss function’. Consciously, we used the simple, linear weight- 0.2 ing including the sign of the deviation. This Time Constant [s] mathematical treatment guarantees that the differ- 0.1 ence between the actual speed and the speed cal- culated by the exponential function is minimized 0.0 for time te. As an alternative, we applied the 678910 ‘classic’ square loss functional [4] a0 [m/s²] te = []− 2 G((3)a0 ,T ) ∫ ameas. (t) a(t) dt Fig. 3 Coupling between maximum deceleration and 0 time constant for different drivers Big bullets indicate best combination of a0 and T which is more suitable for analytical treatment if the function is linear in respect to the parameters (which is not the case for our function). The dif- With growing driving experience we may state a rise in the maximum deceleration value achieved. ference between the parameter sets a0, T esti- mated by the use of different functionals was only This is accompanied by a leveling of the braking small. abilities between the drivers, as the span between best and poorest driver also narrows. As each group consisted of four or five drivers, the nar- rowing may not be assigned to just the size of the 5 Experimental Results group. To the contrary, the time constant, fig. 5, is nearly 5.1 Rising Behavior and Maximum Decel- independent from driving experience. From the eration diagram we may draw the conclusion that the The shortest braking distance is achieved by a time constant first decreases with the driving ex- high maximum value combined with a steep rise 10 of the deceleration. But the motorcyclist cannot 8.9 8.8 fulfill both claims at the same time. The individ- 8.2 8.6 7.8 ual abilities will limit braking performance such 8 8.5 ] 7.9 ² 7.5 that a rise of the maximum deceleration is always 7.3 7.2 accompanied by a rise of the deceleration build- 6 6.4 up time, fig. 3. 5.8 For each initial speed, there is one combination of 4 parameters a0 and T which results in the mini- mum braking distance. Depending on driving ex- Max. Deceleration [m/s perience, the drivers may be assigned to four dif- 2 ferent groups. Fig. 4 depicts the maximum decel- eration value a0 depending on driving experience. 0 Each bar group represents the mean values for the < 20 30 - 60 70 - 120 > 130 best and poorest driver in the according group. Driving Experience [1.000 km] In-between, the white bar indicates the mean value for the whole group.