I have attempted to get some indication of the power rating of my Kalkhof Agattu C3 by testing according to EN19154 appendix D (download: pdf file).
In this test, starting from a standstill one accelerates the bike, and times how long it takes to cover 20 metres. According to EN19154 the power is to be calculated from the formula,
P=2*D*D*M/(T*T*T)
where P= power watts, D= 20 metres, M= mass of rider plus bike Kg, T = time secs to cover distance D.
The difficulty in testing a bike with a Panasonic drive where the power is controlled by a pedal torque sensor rather than a hand throttle is that the motor torque is proportional to the torque the rider supplies to the pedals. So, if one attempts to measure the power according to the EN19154 Appendix D test, one can't avoid measuring rider power plus motor power. In order to overcome this, I decided to compare rides with no assist to those on maximum assist where my Panasonic motor system supplies twice the torque provided by the pedalling rider.
The other issue was which of my 3 gears to use, since to change gear during the short ride I would have to remove power for about a second. After some experiments I decided that the middle gear gave the shortest time over 20 metres. So I used that and obtained the following results:
The time was measured by an assistant using a stop watch. She was located opposite the 20 metre point, and started the watch on my count down, "Ready steady, go."
The variation in times could be due both to small timing errors and also variations in my force on the pedals. I was pedalling hard, slightly pulling up on the handlebars when stamping on the pedals for the first rotation, and then maintaining hard pedalling while remaining on the saddle, rather than standing.
So what power does my motor provide? Well looking at my no assist rides they average around 500 watts according to EN19154, whereas the rides on maximum assist are around 1000 watts. So my bike's motor is providing about 500 watts and therefore fails the EN19154 appendix D test. However, I am not really worried because I think the formula in EN19154 appendix D is obviously inappropriate for the reasons I give below. What is perhaps worrying is that if Mr Plod's expert witnesses tried to test my bike and used the appendix D formula they might argue my bike was illegal since that method of calculation gives powers of order of 500w.
I also measured the final speed using my GPS which takes a reading every second. I stopped pedalling exactly on crossing the 20 metre line and then looked closely at the next two readings to appear on the GPS. I took the maximum reading as a measure of my speed at 20 metres. From this speed I calculated my final kinetic energy (0.5*M*V*V) where V in the speed at 20m point in m/s. From this kinetic energy one can calculate the average power by dividing by the time for 20 metres.
Finally I compared the power calculated by the EN19154 method divided by this average power derived from the bike's maximum speed. You can see in my table above that the EN19154 calculation gives about 1.9 times the power calculated from the bike's speed and kinetic energy. Why is this? Well, the formula used in EN19154 assumes that the acceleration is constant throughout the 20 metres. This is obviously not what happens in practice. In fact even the example diagrams given in EN19154 appendix B of torque against speed for a typical bike motor, show the motor torque starting at a maximum at zero speed and falling linearly to zero as the speed increases. Acceleration is directly proportional to torque, and the assumption of constant acceleration used in the EN19154 formula to calculate power results in an over estimation.
In fact using my final speed method of calculation my results average around 250 watts from me and 250 watts from the bike - perhaps I can rest easy since the EN19154 calculation method is clearly nonsense.
There is another method of measuring the "maximum continuous rated power" described in section 4.2.7.1 which involves measurement of the power at the engine shaft. This has to be done according in EN 60034-1. Investigation of EN 60034-1 leads me to believe that all this requires is that the manufacturer decides on a power at which the the motor can safely operate for long periods without damage. The manufacturer chooses how much above the ambient temperature it is safe for the motor to operate for long life, and from this specifies the motor's maximum continuous rated power. Clearly a motor power specified in this way could be exceeded without damage for short periods and even continuously if the manufacturer had set his temperature limit very conservatively. Section 4.2.7.1 appears to say that it should be the maximum continuous rated power which should be verified - not the maximum power. So maybe bikes are legal which deliver much more than 250 watts provided the manufacturer says the continuous rated power is only 250 watts because he wants to limit the temperature rise to ensure longevity of the motor.
The English language version of EN19154 is extremely poorly written and is often unclear in exact meaning. Perhaps it is the product of some Euro Committee all speaking different languages without a firm English speaking engineer ensuring sound theoretical engineering basis, especially for these power measurement specifications. As with many documents which are the product of such Euro meetings - they contain a lot of rubbish. It is a worry that most of the legislators and politicians don't really understand the numbers so we get unsound, even stupid, regulations.
In this test, starting from a standstill one accelerates the bike, and times how long it takes to cover 20 metres. According to EN19154 the power is to be calculated from the formula,
P=2*D*D*M/(T*T*T)
where P= power watts, D= 20 metres, M= mass of rider plus bike Kg, T = time secs to cover distance D.
The difficulty in testing a bike with a Panasonic drive where the power is controlled by a pedal torque sensor rather than a hand throttle is that the motor torque is proportional to the torque the rider supplies to the pedals. So, if one attempts to measure the power according to the EN19154 Appendix D test, one can't avoid measuring rider power plus motor power. In order to overcome this, I decided to compare rides with no assist to those on maximum assist where my Panasonic motor system supplies twice the torque provided by the pedalling rider.
The other issue was which of my 3 gears to use, since to change gear during the short ride I would have to remove power for about a second. After some experiments I decided that the middle gear gave the shortest time over 20 metres. So I used that and obtained the following results:
The time was measured by an assistant using a stop watch. She was located opposite the 20 metre point, and started the watch on my count down, "Ready steady, go."
The variation in times could be due both to small timing errors and also variations in my force on the pedals. I was pedalling hard, slightly pulling up on the handlebars when stamping on the pedals for the first rotation, and then maintaining hard pedalling while remaining on the saddle, rather than standing.
So what power does my motor provide? Well looking at my no assist rides they average around 500 watts according to EN19154, whereas the rides on maximum assist are around 1000 watts. So my bike's motor is providing about 500 watts and therefore fails the EN19154 appendix D test. However, I am not really worried because I think the formula in EN19154 appendix D is obviously inappropriate for the reasons I give below. What is perhaps worrying is that if Mr Plod's expert witnesses tried to test my bike and used the appendix D formula they might argue my bike was illegal since that method of calculation gives powers of order of 500w.
I also measured the final speed using my GPS which takes a reading every second. I stopped pedalling exactly on crossing the 20 metre line and then looked closely at the next two readings to appear on the GPS. I took the maximum reading as a measure of my speed at 20 metres. From this speed I calculated my final kinetic energy (0.5*M*V*V) where V in the speed at 20m point in m/s. From this kinetic energy one can calculate the average power by dividing by the time for 20 metres.
Finally I compared the power calculated by the EN19154 method divided by this average power derived from the bike's maximum speed. You can see in my table above that the EN19154 calculation gives about 1.9 times the power calculated from the bike's speed and kinetic energy. Why is this? Well, the formula used in EN19154 assumes that the acceleration is constant throughout the 20 metres. This is obviously not what happens in practice. In fact even the example diagrams given in EN19154 appendix B of torque against speed for a typical bike motor, show the motor torque starting at a maximum at zero speed and falling linearly to zero as the speed increases. Acceleration is directly proportional to torque, and the assumption of constant acceleration used in the EN19154 formula to calculate power results in an over estimation.
In fact using my final speed method of calculation my results average around 250 watts from me and 250 watts from the bike - perhaps I can rest easy since the EN19154 calculation method is clearly nonsense.
There is another method of measuring the "maximum continuous rated power" described in section 4.2.7.1 which involves measurement of the power at the engine shaft. This has to be done according in EN 60034-1. Investigation of EN 60034-1 leads me to believe that all this requires is that the manufacturer decides on a power at which the the motor can safely operate for long periods without damage. The manufacturer chooses how much above the ambient temperature it is safe for the motor to operate for long life, and from this specifies the motor's maximum continuous rated power. Clearly a motor power specified in this way could be exceeded without damage for short periods and even continuously if the manufacturer had set his temperature limit very conservatively. Section 4.2.7.1 appears to say that it should be the maximum continuous rated power which should be verified - not the maximum power. So maybe bikes are legal which deliver much more than 250 watts provided the manufacturer says the continuous rated power is only 250 watts because he wants to limit the temperature rise to ensure longevity of the motor.
The English language version of EN19154 is extremely poorly written and is often unclear in exact meaning. Perhaps it is the product of some Euro Committee all speaking different languages without a firm English speaking engineer ensuring sound theoretical engineering basis, especially for these power measurement specifications. As with many documents which are the product of such Euro meetings - they contain a lot of rubbish. It is a worry that most of the legislators and politicians don't really understand the numbers so we get unsound, even stupid, regulations.
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