Power Measurement in Cycling using inductive Coupling of Energy and Data (P80) Reinhardt Tielert, Norbert Wehn 1, Thomas Jaitner 2, Roland Volk 1 Topics: Bicycle; Innovation & Design; Measurement Systems; Performance Sports; Testing, Prototyping, Benchmarking. Abstract: The power exerted on the pedal is the most reliable parameter to determine the training load in cycling biomechanically and hence a crucial factor to optimize performance. Commercial power meters are meanwhile part of the standard equipment of professional cyclists, but also used by an increasing number of non professional cyclists. In this paper we present a system to measure the torque, the cadence and power in cycling using inductive coupling of energy and data. Sensors and signal pre-processing electronics work without any battery on the turning parts. Under dynamic conditions, an overall accuracy of ±10% can be determined. The newly developed power meter can be characterized by low maintenance and energy consumption as well as by an increased number of detected physical values (e.g. 30 degree sectors, individual measurements of left and right pedals). This allows long-term measures as well as more detailed analyses of the pedalling techniques (coordination between left and right leg, e.g.). The first prototype has been successfully integrated into a bicycle and was tested under conditions of training. A second prototype that allows more detailed measures (e.g. section-wise detection of torque and power) runs under laboratory settings. Keywords: power meter; inductively air gap coupling of data and energy; sub-milliwatt range. 1- Introduction The power output exerted on the pedal is the most direct parameter to determine the training load in cycling biomechanically and hence it is a crucial factor to optimize performance (Jeukendrup & van Diemen, 1998, Stapelfeldt et al. 2007). Due to technological innovation during the recent years, power meters are meanwhile part of the standard equipment of professional cyclists, but also an increasing number of non professional utilizes technological support to improve their training. There are three systems that are widely used: The SRM power meter, the Power Tap system (PT) and the 1. Department of Electrical and Computer Engineering, Technical University, Kaiserslautern, Germany E-mail: wehn, volk@eit.uni-kl.de. 2. Department of Social Sciences, Technical University, Kaiserslautern, Germany - E-mail: jaitner@sowi.uni-kl.de
398 The Engineering of Sport 7 - Vol. 1 Ergomo Pro system (EP). The SRM system consists of a crank set that continuously measures the power output from torque and angular velocity. The torque is determined by up to 8 strain gauge sensors that are located between the crank axis and the chainring. Due to its high validity and reliability the SRM system often serves as a reference system for the measurement of power output (Gardener et al. 2004, Bertucci et al. 2005, Duc et al. 2007). The PT system is also based on strain gauge measurement, but the sensors are located in the hub of the rear wheel. Both devices, the SRM and the PT, calculate the overall power output generated at the left and right pedal. The EP uses two optoelectronic sensors located in the bottom bracket. The torque is calculated by the torsion of the bottom bracket against the left crank. Hence, only the power output generated by the left limb can be determined. Assuming that the power output on both pedals is almost identical, the overall power output is displayed by multiplying the measured values by 2. This is considered as a major disadvantage of the EP because some cyclists have shown asymmetries in pedalling technique (Duc et al. 2007). On the other hand, the EP sensors are not sensitive to temperature and only a low additional mass is added compared to the standard equipment (0,074 kg /EP vs. 0,152 kg /PT or 0,280 kg /SRM, respectively). In this paper we present a new power meter system to measure the torque and power output using inductive coupling of energy and data. The main features of this system are the sector-wise detection of the torque, the differentiated measurement of the torques generated at the right and left pedal, its low weight, low power consumption and energy concept for turning parts. 2- Power meter The system for measuring the torques consists of two sensor units. One strain gauge sensor is located in the chain-ring and measures the torsion against the axle. This torsion is proportional to the torque and hence the total torque generated by the cyclist can be calculated. A second strain gauge sensor is integrated in the bottom bracket. By the torsion of the axle, the torque of the left pedal can be determined (fig 1). By subtraction of the torque of the left pedal from the total torque, we can distinguish the torque of the left pedal and the torque of the right pedal. For cadence measurement, 12 reed relays are arranged in a way that one turn of the crank-set is divided in sectors of 30º (fig. 2). Additionally, the torque and the power output can be detected in these 12 sectors for the left and right pedal, respectively. The overall weight of the power meter is 58g. Sensors and signal pre-processing electronics work without any battery on the turning parts. The power input is 6,4 ma. Not only the sensor values, but also the energy is inductively air gap coupled transmitted. The energy consumption of the total electronics is in the sub-milliwatt range.
The Engineering of Sport 7 - Vol. 1 399 Figure 1 - Bottom Brackets with Sensors for measuring torque of the left pedal. Figure 2 - Crank-set with the turning part of the sensor-system. 3- Principle of transport for energy and data The measure system consists of fixed and turning parts. In figure 2, the circuit board that is turned by the chain-ring can be seen in front. Behind, there are the fixed parts of the measure circuits. The transmission of energy and data is realized by over-air magnetic induction via two coils that are fixed on each circuit board. A low power microcontroller is located on the circuit board which belongs to the fixed part of the measure system. The clock signal produced by the microcontroller is used to generate the signal for the energy transmission. In fig. 3, this signal is displayed in a dark blue colour.
400 The Engineering of Sport 7 - Vol. 1 For over-air transmission of the data, a long and a short pulse are modulated on the 8 MHz frequency by the turning part of the circuit. The rising and falling edge of the long signal can be detected quite clearly on the 8 MHz signal (dark blue) at the bottom of figure 3. On top, the demodulated signal (red) with its short and long pulse is shown. A change of the torque exerted at the pedal results in a variation of the electric resistivity. This variation is used to modulate the time shift between the short and the long pulse. Hence, the change of the torque is quantified by the time shift between the rising edges of the modulated signals. The amplitude of the power supply signal should not affect the detection of the position of the rising edge as well as the duration of the pulses to ensure a reliable data acquisition. Therefore, we use an analog comparator. So the rising and falling edge of the data signal (red) can be determined by a comparison with an additional modulated signal with a lower gradient (green). The light blue signal in figure 3 shows the positions of the rising and falling edges resulting from the analog comparator. In the following the calculation of the torque is described more detailed. Figure 4 shows exemplarily two pulses, a short one and a long one. The duration of short pulse is about 11μs, the long pulse lasts for about 45 μs. The length of these pulses is only necessary for the microcontroller to distinguish the two pulses by counting. t1 refers to the time interval between the rising edge of the short pulse and the rising edge of the long pulse, t2 indicates the interval between the long and the short pulse. The Sum of t1and t2 is fixed to about 3.36ms (figure 4). Figure 3 - Signal for over-air energy- and data-transmission.
The Engineering of Sport 7 - Vol. 1 401 Figure 4 - Sequence of the short and the long pulse in the modulated signal. A change of the torque does not affect the sum of t1+t 2, but varies the length of t1 and t2. So the torque can be calculated as follows with calibration factor k and offset factor d. Due to tolerance range induced by the hardware components, t1 and t2 will not have the same length if the torque equal to zero. Therefore, an offset factor d is determined during the first milliseconds at the beginning. This factor is calculated as the mean value of t1-t2 under no-load-condition. The calibration factor k is a constant factor that can be derived by an initial calibration under static conditions. This calibration has to be carried out once for each power meter. Figure 5 shows exemplarily the results of a static calibration procedure with loads from 0 to 8.8 kg. A linear relationship between the difference of the time intervals t1-t2 and the load can be observed (correlation r=.99997). Similar results were obtained if the static calibration was repeated with loads up 45 kg. Figure 5 - Determination of factor k by static calibration.
402 The Engineering of Sport 7 - Vol. 1 4- Accuracy under dynamic conditions Figure 6 shows the test set-up for the accuracy measures under dynamic conditions. A swinging-stator-dynamometer was connected to the axle of a bicycle. The bicycle was fixed on a TACX 1680 FLOW ergometer. Tests were run with a power output between 50 and 250 W. A high correlation (r =.995) was observed between the power exerted by the swinging-stator dynamometer and the power output measured by the power meter. Error values were in the range of 1.38% to 10.86% by a mean percent error of 7.22%. Figure 6 - Bicycle coupled to the swinging-stator-dynamometer. 5- Discussion and Conclusions The newly developed power meter can be characterized by low maintenance overhead and energy consumption (no battery necessary on turning parts) as well as by an increased number of detected physical values (e.g. 30 degree sectors, individual measurement of left and right pedals). Due to the low energy consumption, it can be applied during long lasting training sessions or competitions such as cycling marathons. In addition, the power meter offers a wide range of application for more detailed analysis of the pedalling techniques. As example, the coordination between the right and left leg can be analyzed by a comparison of the power output exerted by the single legs. Further, the power output in the different sectors of the pedalling cycle provides an insight in the muscle force production at different joint angles or might even be used to optimize the cycling position. A first prototype has been successfully integrated into an Assisted Bicycle Trainer, an Ambient Intelligence system that was developed at the University of Kaiserslautern to support team training in cycling (Fliege et al. 2006). Up to now, several test runs were performed under training conditions. A second prototype that allows more detailed
The Engineering of Sport 7 - Vol. 1 403 measures (e.g. section-wise detection of torque and power) runs under laboratory settings. Further work emphasis the improvement of the accuracy of the current system which is not yet satisfactory. 6- Acknowledgement This work was supported by the research centre Ambient Intelligence at the University of Kaiserslautern. 7- References [BD1] Bertucci W, Duc S, Villerius V, Pernin JN, Grappe F. Validity and reliability of the PowerTap mobile cycling power meter when compared with the SRM Device. Int J Sports Med. 10:868-73, 2005. [DV1] Duc, S., Villerius, V., Bertucci, W. and Grappe, F. Validity and Reproducibility of theergomo Pro Power Meter Compared with the SRM and Powertap Power Meters. Int. J. Sports Phys and Perf, 2:270-281, 2007 [FG1] Fliege, I., Geraldy, A., Gotzhein, R., Jaitner, T., Kuhn, T., Webel, C. An ambient intelligence system to assist team training and competition in cycling. In: Moritz, E.F., Haake, S. (Eds.) The Engineering of Sport 6. Volume I: Developments for Sports, 97-102, 2006 [GS1] Gardner AS, Stephens S, Martin DT, Lawton E, Lee H, Jenkins D. Accuracy of SRM and Powertap power monitoring systems for bicycling. Med Sci Sports Exerc. 36:1252-1258, 2004. [JA1] Jeukendrup, A. E., van Diemen, A. Heart rate monitoring during training and competition in cyclists. J. Sports Science, 16: S91-S99, 1998 [SM1] Stapelfeldt, B., Mornieux, G., Oberheim, R., Belli, A. and Gollhofer, A. Development and evaluation of a new bicycle instrument for measurements of pedal forces and power output in cycling. Int J Sports Med, 28: 326-332, 2007