**When video motorcycles are used to measure the speed of vehicles, the tilted-position effect occurs. This tilted-position effect is a reduction in the rolling circumference which is dependent on the tilted position. To rule out disadvantages for motorcyclists, limitations in the application are required. PTB has now carried out detailed experiments in relation with the tilted-position effect and has developed – on the basis of the results obtained – a procedure to compensate for the effect without using additional sensors.**

In road traffic, motorcyclists are endangered far above average, in particular when the admissible maximum speed is exceeded on country roads. In addition to technical improvements of the motorcycles and of the road infrastructure, official speed measurements for traffic control are an important possibility of improving the safety of motorcyclists. For different reasons, speed measurements with video traffic enforcement systems which are installed on police motorcycles, are regarded as particularly effective. In the case of these devices, conclusions are drawn from the velocity of the police motorcycle which is driving behind, to the velocity of the motorcycle which is driving ahead of it. In the case of this measurement principle, it must be considered for a tilted position – which inevitably ensues on winding roads, see Figure 1 – that the actual rolling circumference of the police motorcycle is systematically reduced. As a result, the speed measurement value is – to the disadvantage of the motorcyclist driving ahead – greater than the actual speed of the motorcycle. For larger tilted positions, it cannot even be ruled out that the maximum permissible errors in service of 5 km/h or 5 % (for measurement values up to or exceeding 100 km/h) specified in the Verification Ordinance are exceeded. As this effect considerably reduces the application possibilities, in particular on winding roads in the mountains, PTB has been asked by the police to elaborate solutions with technical and/or organizational measures.

Figure 1: Police motorcycle, type BMW R 1200 RT, with video traffic enforcement system during circular driving with a corresponding tilted position in the course of experiments in Aldenhoven (Photo: Courtesy of the Office for Central Police Services of the German federal state of North Rhine-Westphalia).

#### Theoretical description of the tilted-position effect

The tilted-position effect can also be analysed theoretically – at least approximately. Assuming a circular or semi-circular cross-section of the motorcycle tyre, and neglecting all elastic deformations and dynamic effects, the following results are obtained:

- The distortion of the section measurement and/or of the speed measurement is independent of the speed; it only depends on the rolling angle
*α*. - The tilted-position effect is strongly non-linear, the distortion of the measurement values increases in accordance with a factor (1 - cos
*α*) in first approximation for relatively small angles, quadratically with the rolling angle. For small tilted positions, the distortions are, therefore, negligible. - The tilted-position effect is proportional to a tyre-dependent pre-factor
*r*/*R*_{o}(*r*radius of curvature of the tyre contour,*R*_{o}radius of the complete wheel); it is, therefore, larger by a factor of approx. 1.4 for the rear wheel (*r*approx. 90 mm,*R*_{o}approx. 314.9 mm) than for the front wheel (*r*approx. 60 mm,*R*_{o}approx. 299.9 mm). - The angular dependence results from the factor (1 - cos
*α*), It is, thus, identical for front wheel and rear wheel. - For pronounced tilted positions from approx. 30 degrees upwards, distortions of more than 5 % are to be expected.

#### Road tests for the experimental investigation of the tilted-position effect

From PTB's point of view, the most reliable way of obtaining reliable statements on the actual amount of the tilted-position effect consisted in performing targeted road tests with a police motorcycle that was equipped with a video traffic enforcement system. In these road tests, the section determined by the video traffic enforcement system was compared with the section actually travelled, with the curves driven and the tilted position defined as accurately as possible. As it is not possible to have a motorcycle drive a defined section in a tilted position with the required accuracy, the actually travelled section was measured with a GPS-based inertial navigation system (in the following referred to as "GPS/INS device") used as a reference. The comparison was then performed on the basis of the average speed determined completely independently by the two devices. The comparison measurements were carried out in two measurement campaigns, in close cooperation with the police and with the verification authorities of North Rhine-Westphalia, to which we would like to express our gratitude for their contributions.

#### Performance of road tests and experimental results

In order to realize reproducible and defined tilted positions, the driver drove circles with the video motorcycle shown in Figure 1 for different radii (50 m and 100 m) and with velocities of up to 90 km/h. For this purpose, the dynamic road surface of Test Center Aldenhoven, which is very well suited for our investigations due to its total diameter of 220 m and the planeness of the road surface, was available for two measurement campaigns. On the road surface, the respective circles for the driver were marked with traffic cones, the radii were checked with a verified measuring tape. To ensure that the measured rolling angles actually represented tilted position angles with respect to the road, the inclination of the test surface was determined. The values measured with a digital clinometer lay in the range from 0.0° to 0.6° (always with an inclination towards the centre), the specified measurement uncertainty of the clinometer amounts to only ±0.05°. Additional corrections could, therefore, be dispensed with. To obtain as reproducible results as possible, a marking with chalk was applied to one point for each circumference, at which the driver started and stopped the ProVida measurement with a flying start. By means of the corresponding electronics, developed by PTB, care was taken that the GPS/INS devices were released synchronously. In the case of the smaller radius, two circumferences were used for each drive, so that a total section of slightly more than 600 m was obtained for all drives. To rule out influences by possible asymmetries of the motorcyle and of the GPS/INS device, corresponding drives were performed in both driving directions, i.e. with tilted position to the left and to the right. During each circular test, the driver, who had been trained for monitoring tasks, tried, above all, to keep the pre-defined speed as constant as possible so that a mostly uniform tilted position was obtained during the whole circular test. For both radii, the pre-defined speed was increased in steps until a tilted position of approx. 42 degrees was achieved in which – due to the geometry of the video motorcycles of the police – the footrest already touched the ground. This value can, thus, be used as an upper estimation for the situation relevant in practice. This angle was achieved for the two different curve radii at clearly different velocities (70 km/h and 90 km/h). In order to analyse the differences between front wheel and rear wheel tapping, all other tests mentioned were first of all performed with rear wheel tapping and repeated immediately afterwards – after modification of the video traffic enforcement system – with front wheel tapping.

The most important results of the experiments for the tilted-position effect were:

- The distortion of the section and/or speed measurement does not depend on the speed or the curve radius, but on the rolling angle
*α*. - The tilted-position effect is strongly non-linear, the distortion of the measurement values increases rather quadratically with the rolling angle. For small tilted positions, the distortions are, therefore, negligible.
- The angular dependence of the effect is similar for the front wheel and for the rear wheel; as expected, the effect is clearly greater for the rear wheel than for the front wheel.
- For pronounced tilted positions (approx. 40 degrees), distortions of more than 8 % occur for the rear wheel. For the front wheel, the maximum distortions are smaller than 4 %.
- The effect did not change with an exchange of the wheels, significant differences between two different rear wheels were not found.

The measurement results are, thus – at least qualitatively – a confirmation of the strongly simplified theory explained above.

In addition, the test site in Aldenhoven was used for some straight-ahead drives at high speeds (up to 160 km/h) to determine the influence of the speed on the rolling circumference with the prepared motorcycle. These tests also showed only a relatively small speed dependence. In the individual case, the deviations amounted to approx. 1 %; in most cases, they lie, however, in the order of parts per thousand.

#### Approximate solutions and outlook

The measurement results obtained by us suggest that the absolute amount of the effect can be reduced when the front wheel is tapped for measurement instead of the rear wheel. For drives with tilted position, the maximum permissible errors are, however, not complied with either when this measure is taken, so that additional analyses were indispensable. Hereby, it was less the complete quantitative understanding of the tilted-position effect which was in the foreground but the search for practicable solutions for the police to ensure compliance with the maximum permissible errors in spite of the tilted-position effect.

This first of all raises the question as to whether, or to what extent, the results can also be explained quantitatively on the basis of the theoretical considerations. Figure 2 shows the measurement values for the rear wheel and for the front wheel for the deviations and fitted curves with the characteristic (1 - cos *α*) shape. For the rear wheel, surprisingly good agreement with the curve is obtained when the pre-factor *r*/*R*_{o}, which suggests itself, is selected. The remaining deviations between the simple theory and the measurement results amount for a maximum titled position to only approx. 1.5 % or 0.5 %. Also for the front wheel, rather good agreement is obtained. Here, the differences amount to approx. 1 % for the maximum tilted position.

Figure 2: Measurement results for the tilted-position effect with fitted polynomials for the front wheel and for the rear wheel and correction of the effect based on the difference of the fitted polynomials

On the basis of the theoretical and experimental results, we would like to put up for discussion an approach for a consideration of the tilted-position effect which is much more attractive for users or manufacturers. This approach is based on the theoretically expected, and experimentally confirmed, findings that the results for front and rear wheel tapping are identical with respect to the angular dependence (factor (1 - cos *α*)), and only differ by the pre-factor *r*/*R*_{o} which results from the different tyre dimensions. On the basis of the tyre data it is expected that the tilted-position effect is greater by a factor of 1.43 for the rear wheel than for the front wheel. The measurement results directly show that for the rear wheel, the effect is roughly twice as great as the effect for the front wheel over the whole area of the rolling angle. A more detailed analysis of the measurement data shows that the effect for the rear wheel corresponds very well to 2.2 times the effect for the front wheel. Due to the fundamental relationship between theory and experiment, we assume that this is a largely general statement. This resulted in the idea to determine the front wheel and the rear wheel for the video traffic enforcement system, i.e. to use two path sensors and to evaluate the difference of the information in a targeted way. If *λ*-times the difference of the two curves is subtracted from the curve of the rear wheel, one again obtains a curve with the factor (1 - cos *α*). If *λ* is suitably selected, a measurement value of the speed is obtained, in which case the tilted-position effect is completely compensated for. For this, the above-mentioned theory suggests – on the basis of the factor 1.43 – a *λ* of approx. 3.3.

In our experiments, the video traffic enforcement system allowed only the front wheel or the rear wheel to be determined each time during one test run. These experiments, therefore, furnished no measurement results with data of both wheels for the same drive or for an identical rolling angle so that the measurement results do now allow a real difference to be formed directly. In spite of this, the potential of this idea can be illustrated on the basis of Figure 2. For this purpose, we have calculated for each, one fitting parabola (without absolute link) from the measurement data of both wheels. If one now subtracts *λ*-times the difference of the two curves from the curve for the rear wheel, one again obtains a parabola. If λis suitably selected, the tilted-position effect can also be completely compensated for here. To optimize the compensation for large tilted positions or rolling angles, a *λ* of approx. 1.9 is obtained on the basis of the experimental data for larger tilted positions. In the figure, the parabola derived from the experimental data is plotted in red as a correction of the tilted-position effect. It can be seen that the curve corrected in this way lies clearly below 0.2 % for all rolling angles. This is a promising result for the manufacturers and users of these devices. For a correct measurement with a video traffic enforcement system which determines both wheels, this measurement could be performed correspondingly. First of all, the device would have to calculate a speed measurement value for both wheels. After that, 1.9 times the difference of the two measurement values would have to be subtracted from the measurement value derived from the rear wheel. The difference calculated in this way would then have to correspond to the value corrected for by the tilted-position effect. A measurement of the rolling angle – and this is the decisive advantage of this method – is not required for this purpose.

### References:

[1] Grohne, H.; Jäger, F.; Märtens, F.: "Einfluss einer Motorrad-Schräglage auf polizeiliche Geschwindigkeitsmessungen mit Videonachfahrsystemen", Polizei Verkehr Technik, 03 (May/June) 2012, pp. 131-134 (part 1) and 04 (July/ August) 2012, pp. 154-157 (part 2) (in German)

### Contact person:

Frank Märtens, Dept. 1.3, WG 1.31, e-mail: frank.maertens@ptb.de