JennyB
1 kW
Rules of Thumb are not meant to be totally accurate, but they do help to ensure that your ideas are not wildly astray. These are some that I have come up with for estimating range, based on a 1992 article by Bill Bushnell and Chris Hull. Please let me know if they are helpful or misleading. I would also be grateful if others could post similar rules for topics of which I am even more ignorant: motor, batteries, controller, charging etc.
Estimating the Energy Requirement of a route
The climbing index (CI) is the watt-hour equivalent height in metres of climbing to a kilometre on the flat for the riders cruising speed.
For typical ebikes this will lie somewhere between 20 and 50 metres, lower for slower or heavier bikes, higher for lighter bikes or those with a faster cruising speed. An estimate to the nearest 10 metres is close enough.
This index may be estimated by comparing energy drain over various routes, or by using a simulator such as that at http://www.noping.Net/english/ . Note that these show the power required at the wheels, which needs to be checked against actual watt hours consumed, which may be double.
To estimate the energy (and therefore the battery capacity) required for a given trip:
C = cruising speed in kilometres per hour on the flat with no wind
W = the watt hour/kilometre cost of C
D = total distance in kilometres
N = net height gained in metres - the difference between start and finish altitude.
G = total height climbed
ED = the equivalent distance that could be travelled on the flat for the same energy expended.
If the route was uphill all the way ED would be D + ( N / CI ) kilometres and the energy used would be W*ED watt hours. The time taken would be ED / C hours. More normally, there would be G - N metres of downhills. As a general rule, coasting down hills saves 50% of the extra energy needed to to climb them. Maintaining power saves perhaps 30%.
Some examples:
CI = 24 C=27 W=20
Using power lightly on the downhills, so saving 40%
Riding a 100k loop with 2000 metres of climbing.
ED = 100 + ( 2000 / CI * 60% ) = 150
Watt hours needed = 150 * 20 = 300
If the ride ended 360 metres above the start
ED = 100 + ( 360 / CI ) + ( (2000-360)/CI * 60%)
= 100 + 15 + 41 = 156
Estimated time taken = 156/C = about 5 hours 50 minutes.
Limitations
These are, of course, only rough estimates. A strong wind can affect range by as much as 40% either way. Air resistance increases as the cube of speed through the air, so at typical ebike speeds an increase of 10 kph almost halves the range. A route with short climbs and long descents is much easier to ride than the same route in the opposite direction. It follows that the most economical way to ride is to get as close to cruising speed as possible through the slower sections, so that you do not need to go as fast elsewhere. On hilly routes a "good big'n" capable of holding speed on most climbs should have a greater range than a good little'n." Is that borne out by experience?
Estimating the Energy Requirement of a route
The climbing index (CI) is the watt-hour equivalent height in metres of climbing to a kilometre on the flat for the riders cruising speed.
For typical ebikes this will lie somewhere between 20 and 50 metres, lower for slower or heavier bikes, higher for lighter bikes or those with a faster cruising speed. An estimate to the nearest 10 metres is close enough.
This index may be estimated by comparing energy drain over various routes, or by using a simulator such as that at http://www.noping.Net/english/ . Note that these show the power required at the wheels, which needs to be checked against actual watt hours consumed, which may be double.
To estimate the energy (and therefore the battery capacity) required for a given trip:
C = cruising speed in kilometres per hour on the flat with no wind
W = the watt hour/kilometre cost of C
D = total distance in kilometres
N = net height gained in metres - the difference between start and finish altitude.
G = total height climbed
ED = the equivalent distance that could be travelled on the flat for the same energy expended.
If the route was uphill all the way ED would be D + ( N / CI ) kilometres and the energy used would be W*ED watt hours. The time taken would be ED / C hours. More normally, there would be G - N metres of downhills. As a general rule, coasting down hills saves 50% of the extra energy needed to to climb them. Maintaining power saves perhaps 30%.
Some examples:
CI = 24 C=27 W=20
Using power lightly on the downhills, so saving 40%
Riding a 100k loop with 2000 metres of climbing.
ED = 100 + ( 2000 / CI * 60% ) = 150
Watt hours needed = 150 * 20 = 300
If the ride ended 360 metres above the start
ED = 100 + ( 360 / CI ) + ( (2000-360)/CI * 60%)
= 100 + 15 + 41 = 156
Estimated time taken = 156/C = about 5 hours 50 minutes.
Limitations
These are, of course, only rough estimates. A strong wind can affect range by as much as 40% either way. Air resistance increases as the cube of speed through the air, so at typical ebike speeds an increase of 10 kph almost halves the range. A route with short climbs and long descents is much easier to ride than the same route in the opposite direction. It follows that the most economical way to ride is to get as close to cruising speed as possible through the slower sections, so that you do not need to go as fast elsewhere. On hilly routes a "good big'n" capable of holding speed on most climbs should have a greater range than a good little'n." Is that borne out by experience?
