## Rules of Thumb: Estimating Range

JennyB   1 kW

Posts: 448
Joined: Jan 25 2008 12:51pm
Location: Northern Ireland

### Rules of Thumb: Estimating Range

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?

Samba   100 W

Posts: 139
Joined: Sep 26 2010 8:11pm
Location: Pennsylvania

### Re: Rules of Thumb: Estimating Range

JennyB wrote: The time taken would be ED / C hours.
Estimated time taken = 156/C = about 5 hours 50 minutes.
You lost me there.
C is cruising speed on flat 27kph. Its not the same speed used for climbing? I'd expect time to be 100KM/C irregardless of heights. Theres nothing in there about differing speed for uphills just additional power.

Its for calculating energy use -- 156*W -- same WH used for 156KM on flat is needed for this 100KM route with climbs.

JennyB   1 kW

Posts: 448
Joined: Jan 25 2008 12:51pm
Location: Northern Ireland

### Re: Rules of Thumb: Estimating Range

Samba wrote:
JennyB wrote: The time taken would be ED / C hours.
Estimated time taken = 156/C = about 5 hours 50 minutes.
You lost me there.
C is cruising speed on flat 27kph. Its not the same speed used for climbing? I'd expect time to be 100KM/C irregardless of heights. Theres nothing in there about differing speed for uphills just additional power.

Its for calculating energy use -- 156*W -- same WH used for 156KM on flat is needed for this 100KM route with climbs.
I wondered about that too. It does work out surprisingly well for touring cyclists, which is the original application, because that is a constant power scenario. a tourist cannot produce much more than their mean power for very long, so they gear down and go slower on the hills. Whether it would still work for a 1000W hub ridden at a constant 27kph is another question.

John in CR   100 GW

Posts: 13690
Joined: May 20 2008 12:58am

### Re: Rules of Thumb: Estimating Range

That's the most complicated "rule of thumb" I've ever seen. I'd do something more like rolling hills on your route are likely to double your consumption over flat terrain consumption, so it's typically better to look for a flatter way around. You can't apply a cyclist rule of thumb with a hub motor, because current will increase significantly, so the power used up hills is likely to max out your controller limits. If you know the hills on your route, then there are some bike calculators that will give you a pretty accurate picture of the energy requirements to climb them.

John

dogman dan   100 GW

Posts: 34889
Joined: May 17 2008 12:53pm
Location: Las Cruces New Mexico USA

### Re: Rules of Thumb: Estimating Range

My rule of thumb for the typical hubmotor kit has been 1 ah for 1 mile on 36v bikes. This is NOT how far you go, but rather how big a battery you should get for a commute. There is up to 30% reserve there in this rule of thumb to allow for that day when the wind blows in your face 20 mph. It's good for battery lifespan anyway.

JennyB   1 kW

Posts: 448
Joined: Jan 25 2008 12:51pm
Location: Northern Ireland

### Re: Rules of Thumb: Estimating Range

John in CR wrote:That's the most complicated "rule of thumb" I've ever seen. I'd do something more like rolling hills on your route are likely to double your consumption over flat terrain consumption, so it's typically better to look for a flatter way around. You can't apply a cyclist rule of thumb with a hub motor, because current will increase significantly, so the power used up hills is likely to max out your controller limits. If you know the hills on your route, then there are some bike calculators that will give you a pretty accurate picture of the energy requirements to climb them.

John
If you think that's complicated, you should read the original article !

That's how we did things pre-Web, and that's the maths the calculators use. Web mapping apps don't work too well for elevation here, so I just count the number of 10-metre contour lines crossed on an OS map. Compare two trips, one hilly and one flat. If you know the watt-hours expended on each then simple algebra give you your Climbing Index. Since I use power mainly on the ascents, it turns out to be a lot lower than it would be if I was only pedalling or using the motor continuously - about 10 metres. It's probably much the same for most Euro-legal bikes ridden in this fashion.

So the rule for me simplifies even further: to estimate the difficulty of a new route, add a kilometre for every 20 metres climbed, and add or subtract another kilometre for each 20 metres the finish is above or below the start.

That's not so difficult, is it?

busted_bike   100 mW

Posts: 42
Joined: Jun 24 2010 11:18am

### Re: Rules of Thumb: Estimating Range

JennyB wrote: So the rule for me simplifies even further: to estimate the difficulty of a new route, add a kilometre for every 20 metres climbed, and add or subtract another kilometre for each 20 metres the finish is above or below the start.

That's not so difficult, is it?
Now that's a rule of thumb!