Static torque and power
This post has turned to be rather long I am afraid. In summary, I have measured the stalled torque provided by the Panasonic motor when pressing the pedals with the bike held stationary. When I am in first gear the force at the wheel trying to drive the bike forward increases from around 9 lb with just my force on the pedal of 32 lb and the motor off to somewhere around 24 to 30 lb with maximum motor assist. This helps nicely on hill starts, or for very rapid acceleration from traffic lights. The power taken from the battery is 164 watts, and after about a minute stalled in this way the overheating warning starts flashing.
My bike has a first gear of 44 inches (distance moved forward for 2 radians revolution of the pedals, ie for 1 pedal rev divided by pi). So the gearing on my bike is equivalent to a rear wheel of 22 inches radius coupled to the pedal crank with an overall 1:1 gearing ratio. My pedal operates on a radius of 6.9 inches. Ignoring the frictional losses in the chain, gears and bearings, this ratio means that a force of 32 lbs on the pedal will yield a drive force from the rear wheel onto the road of 10 lbs.
I was able to get a rough experimental confirmation of this calculated drive force by setting up the bike with a rope attached to the rear tyre pulling a spring scale:
I could read the spring scale to an accuracy of about +/- 2 lb. this is nicely close to the value of 10lb which I calculated above from the gearing ratio.
With the bag weighing 32 lb on one pedal crank I measured 9 +/- 2 lb at the rear wheel.
46 lb on the pedal gave 10.5 +/- 2 lb at the rear wheel.
It is interesting to note that with the pedal force of 46 lbs I would just be able to hold a bike + rider weight of 210 lb stationary on a hill with gradient 10.5/210 = 5% ( 1 in 20) I would need more pedal pressure to actually start riding up such a hill. By standing on one pedal I would be able to increase the force by about 4 times and so start riding up the hill (alternatively just hold stationary on a 20% hill)
Next, I removed the pedal weight and turned the motor power on so that the torque sensor would calibrate. I then replaced the 32 lb weight on the pedal and obtained the following readings on the spring scale:
Assist level 1 (minimum): 17-19 lb (less 9 lb from the pedal weight = 8-10 lb from the motor) current drawn by motor 1.4 to 1.6 Amp = 38 Watt
Assist level 2: 23-25 lb (less 9 lb from the pedal weight = 14-16 lb from the motor) current drawn by motor 2.8 to 3.4 Amp = 78 Watt
Assist level 3 (maximum): 24-30 lb (less 9 lb from the pedal weight = 15-21 lb from the motor) current drawn by motor 6.5 Amp = 164 Watt
I am not sure the measurement was reliable when in assist level 3, for I noticed that after less than a minute stalled at 164 watts from the battery the mode 3 light started flashing, according to the Kalkhoff manual this indicates motor over heating. I therefore discontinued the measurements. It is be be expected that a motor rated at a continuous OUTPUT of 250 watts might overheat if operated stalled. In this situation all the 164 watts from the battery would be being dissipated in the motor windings and the controller.
During these static measurements I noticed that every 18 seconds the battery current dropped momentarily and the forced was removed for a fraction of a second. The current and force was then resumed at a slightly different value. This brief interruption every 18 seconds is readily observed on my bike when standing stationary with weight on the pedal, eg at lights with the bike held by the brakes ready to release and accelerate when the light changes. It causes a brief slight jerk on the pedal.
I also tried different weights on the pedal:
7 lb or 14 lb were not sufficient to cause the motor's torque sensor to cause the motor to draw current. However, I noticed that with the 14 lb weight hanging from the pedal, if I added a further force by hand, the motor would come on, and remain on at constant current with just the 14 lb weight after my hand pressure was removed.
The accuracy of reading the wheel force with the spring scale was limited in these experiments. One could set up with a better scale to make up more accurate measurements, but I am not sure, that this would be particularly useful. One can already see from the data that in maximum assist the effect of a pedal force of 32 lbs is roughly tripled from about 9 lb to 24 - 30 lb, so one should be able to easily start this bike on hills steeper 10%, as I have observed in practice.
Measurements when moving
I am more interested in making measurements to confirm the assistance provided when moving. This is not so easy. Flecc has described the the use of hills of known slopes, and that is what I want to try with better instrumentation to measure the battery current.
I have managed to smooth the fluctuating current readings one gets during pedalling at modest force by using a 5 MOhm resistor in series with the 10 MOhm input impedance my voltmeter in conjunction with a 0.5 microF capacitor across the meter. Unfortunately this setup causes varying offsets up to 1 mV. I have not yet tracked down the cause - in the resin dipped ceramic capacitor or the carbon series resistor?
I would like to have a data logger. There are nice little USB loggers available but these only take 1 sample per second. I want at least 10 samples per second, so I can start to record and analyse the pedal stroke. I could get a Cycle Analyst with its logger for some £200 which would do the job (and a lot more which I don't absolutely need). The Eagle Tree data logger device sold to RC enthusiasts is quite a bit cheaper but I am not sure whether the 100 Amp current measurement capability will have enough resolution for accurate measurement of my currents of just a few Amps. The Eagle Tree has to be inserted in series between the battery and the motor, and it will not quite as simple as the current shunt which I have already manged to install.
Do any of the people on here, who have electronics experience, have any advice on a suitable (cheap) datalogger to record up to say 25 amps at 10 samples/sec.?