Estimating Battery Capacity and Range 
Using a  24v 10ahr Lithium Polymer Non-Oxide Type with  24volt Tongxin Motor

Below Maurice Wells a student at NSW University came and spent a few days with me to do some research work for his thesis. He did some data logging of amps/voltage during riding for different battery types. Below are some of his results for the Lithium Polymer battery .  One thing to note is these results demonstrate quite well how difficult it can be to estimate range for particular batteries, as during a ride amps (current) is constantly changing. 
Maurice shown below having a go on my small trike with P3 motor in front and 4 lots of 20ahr sla agm batteries.

You can see the track along which Maurice did this part of his testing on this page: http://www.bikely.com/maps/bike-path/Adamstown-to-Brett-s-house
This bike track is an old railway line, so the gradient is quite gentle. Going from my house to adamstown is generally a gentle downhill slope, going from adamstown back to my place is generally an uphill ride.

Below parts of the Fernleigh bicycle track. Left shows the old railway line, right shows the Fernleigh Tunnel ( along the bike track) which goes under the Pacific Highway at Kotara.
 


The Bike used for Testing:

Test done on September 30th, 2006 on the Fernleigh track with a 26’’ mountain bike with a 24V tongxin rear motor and a new 10Ah 24V lithium battery pack, freshly charged at the beginning.  Rider weight 69kg. Distance: 5.37 km one way. Wind conditions calm. 
Throttle was kept on full throttle for all the tests below.

Elevation Data

Overall slope is vertical change is 100-10m = 90m, horizontal distance is 5km.
Slope is rise/run = 90/5000=0.018 = 1.8% degrees average slope
Basically the bike  testing was done on is a gentle downhill slope if going from my house to adamstown, the other direction is a constant uphill slope with a few flat sections, thats how it appears when riding along it.

Test 1: Adamstown to Whitebridge, no pedaling ( uphill ride no pedal assist )
No pedaling, batteries freshly charged.
Initial voltage 28.4V
Ride duration: 14 minutes 43 seconds
Average speed =  21.9km/h (not bad up hills without pedaling!)

 From the graph above you can see the amps remains relatively constant initially thats a constant uphill gradient. He had a couple of stops where the amps drops to zero. There are a few flat sections where the amps drops down then another relatively constant uphill on the last section where the amps remains fairly constant. He didn't pedal at all in this test.
Other data for this part of the ride:
Average amps used was 10.1amp
Total amphours used was 2.48Ahr

Test 2: Whitebridge to Adamstown, no pedaling ( downhill ride)

  No pedaling again, battery has done Test 1 so it is not full anymore. Obviously the elevation profile is the same just the other way. Final battery voltage: 26.45V
Ride time: 12 min 42 seconds
Avg speed = 25.3 km/h

The above graph shows much lower amp draw as it was almost all downhill. You can see even though to the rider the slope appears very constant (an old railway line with bitumen put over it) the amps continues to fluctuate according to the riding conditions. So getting a very accurate prediction of range for a given set of batteries is quite difficult even on the best of test surfaces.This ride was downhill on the same track as test one, so the average speed is higher and time taken shorter.Once again in this test no pedalling was used.
Other data for this part of the ride:
Average amps used was 5.5amp
Total amphours used was 1.09Ahr

Test 3 Adamstown to Whitebridge, with medium pedal assist (approx 200watts): uphill ride

Initial battery voltage: 26.45V
Final voltage: 25.75V
Ride time: 13 minutes 10 seconds
Avg Speed: 24.5km/h

Current profile:

With pedaling the average speed only increased by 2.5km/h on this uphill run. But the current draw has changed quite dramatically. The current is much more variable and much lower than the same ride with no pedalling (test 1).
Other data for this part of the ride:
Average amps used was 8.2amp
Total amphours used was 1.81Ahr

Test 4 Whitebridge to Adamstown, with medium pedal assist (200watts approx.): downhill ride

Now Maurice went  back the other way, the uphill way, pedaling with the motor on. By now the batteries have done 16km, 11km without pedaling.
Initial voltage: 25.75 V
Ride time: 11 minutes 26 seconds
Avg Speed: 27.7 km/h

  Current profile:

  The amount of energy taken from the battery in this case is much lower. Not only did the ride take less time, but the motor was not required to add much to the speed. The current does still continually vary over time but is much lower amount of amps drawn than any of the other tests (makes sense: a downhill ride with pedal assist).
Other data for this part of the ride:
Average amps used was 3.27amp
Total amphours used was 0.62Ahr

DATA SUMMARY:

Below: No Pedalling Uphill                                                              No Pedalling Downhill

Pedalling Uphill                                                                             Pedalling Downhill


Some data on average current (amps) and battery capacity ( amphours ) used for each section of the ride.

Total distance travelled was 21.5km, batteries had not reached low voltage cut off (which is internally controlled in battery pack and is 24.5volts), total range using this motor and battery combination maybe around 35 to 45km. But as you can see from the above graphs the range could actually vary alot depending on riding conditions and amount of pedal assist thats given. There are also other factors that will effect range such as tyre pressure, type of tyre, wind conditions, type of motor used etc etc etc.

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