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### Standard formula for Calculating Ebike Range

Posted: Apr 16 2018 9:13am
There is absolutely NOTHING more confusing to the inexperienced ebike purchaser that understanding potential range with respect to the ebikes they are considering. So many ebike manufacturers and retailers embellish range claims using tricks that we experienced ebikers know are deceptive at best and down right ludicrous at worst.

Factoring Human power into the calculation is something I personally feel needs to be eliminated, because you just can't make a realistic and honest assessment between two individual humans and their power output.

Range should be based on motor power only, at a specific speed, and under the most simple conditions. And the values used should be towards the conservative side of the spectrum, that one can reasonably expect to achieve, if followed.

I propose the value of 20 Watt-hours per mile at 20 MPH, since the current US ebike guidelines limit legal ebike speeds to 20 MPH, and this is a speed that can be achieved relatively easily with a legal 750W motor. Conditions would also include: a flat, smooth road, no stopping & starting or hills, on an upright mountain bike (high drag coefficient).

The intent is NOT to argue about the minor efficiency differences between system A (DD Hub Motor) vs. system B (Mid Drive) vs. system C (Geared Hub) etc. Yes, there will be minor differences in the efficiencies of these systems.

The POINT is to make a simple method for less experienced ebike customers to assess range between the different bicycles they are looking at, and the most critical component of range is the energy capacity of the battery, in Watt-hours. I argue that WATT-HOURS should be THE ONLY value that can be reasonably compared between any number of ebike power systems.

And the Formula for Calculating range should be as follows:

Battery Nominal Voltage x Battery Capacity (Amp-Hours) / 20 Watt-Hours/Mile.

Example:
48V-12Ah Battery - would have 48x12 = 576 Watt-Hours of Energy / 20 WH/Mile = 28.8 Miles of range (at 20 MPH, motor only).

Apologies to the rest of the world that uses the metric system. The equivalent of the above formula would be 32 KPH speed, and 12.3 Watt-Hours/Km, which is much less easily remembered.

Perhaps Endless-Sphere could create a "Certification" for Ebike manufacturers and retailers who agree to use our formula for range calculation in their advertising...

Call it draconian if you want, but I think the ebike buying community would greatly appreciate some straight talk with respect to range, even if it is very generalized.

Here's my Youtube Rant. (NSFW warning)

### Re: Standard formula for Calculating Ebike Range

Posted: Apr 16 2018 11:20am
I propose the value of 20 Watt-hours per mile at 20 MPH, since the current US ebike guidelines limit legal ebike speeds to 20 MPH, and this is a speed that can be achieved relatively easily with a legal 750W motor. Conditions would also include: a flat, smooth road, no stopping & starting or hills, on an upright mountain bike (high drag coefficient)
I agree, there is never going to be a "perfect" algorithm for all systems and all ebike riders, but...this proposal is very reasonable. It's a good start.

### Re: Standard formula for Calculating Ebike Range

Posted: Apr 16 2018 12:22pm
With respect to lower wattage limits and slower top speeds for other Countries (i.e. 250W limit, and 25 KPH Top Speeds in many countries) it might make sense to add the following range calculation, which due to the slower top speed, would naturally be MORE efficient, and correlate to longer range for these speed & power limited countries (And in Metric):

10 Watt-hours/Kilometer at 25 KPH.

i.e.: 36V-8.8Ah battery = 316.8 Watt-Hours / 10 = 31.68 Kilometers of Range @ 25 KPH.

### Re: Standard formula for Calculating Ebike Range

Posted: Apr 16 2018 4:17pm
Good idea. Maybe call it Max Range on Battery or Max Battery Range.

### Re: Standard formula for Calculating Ebike Range

Posted: Apr 16 2018 5:54pm
I commend the idea, but as long as they can get away with it, sellers (and manufacturers) are going to claim the highest possible range they can to make them sound better than the next guy, like they do now.

Even if that range is supposedly on a forever-length downhill with a hurricane-force tailwind while pedalling like a madman. :/

Just cuz too many people are greedy and deceptive.

Other than that, the formula seems reasonable for average city riding conditions.

### Re: Standard formula for Calculating Ebike Range

Posted: Apr 16 2018 6:49pm
I fully agree with this idea, and I have one suggestion which may make it more intuitive and marketable outside of EV enthusiasts. I'm not trying to start an argument here, but I'll include some additional info to back up my suggestion.

Instead of making range the only factor, include the efficiency. The two combined would give a more wholistic view of the bike. Range by itself doesn't say much. For instance, looking at a diesel semi tractor-trailer truck, 240 gallons of fuel is the normal capacity, so, depending on load, speed traveled, vehicles specs, terrain, etc. one can expect 960 to 1920 miles on a full fuel load, roughly. But depending on a number of factors, you can expect just 4-8 miles per gallon. Compare that to a compact car that carries 14 gallons of fuel you can expect it to get 448-532 miles on a full tank. However that compact car is getting 32-38 combined miles per gallon. So you can see that the range alone doesn't really tell us much about the system as a whole.

Here's an example:

Light bike, small battery, lower voltage example: 48V, 7Ah = 336Wh potential.
Heavy bike, big battery, higher voltage example: 52V, 25Ah = 1,144Wh potential.

Using the above formula for the light bike we'd get: 16.8 miles estimated unassisted range (336/20). Likewise, for the heavy bike, we'd get 57 miles estimated unassisted range.

Then we can include two efficiency ratings (like they do for cars with a highway/city efficiency rating): I propose "urban" (for short, interrupted stop and go situations) and "touring" (for non-stop, top speed situations). Just like with cars, these efficiency ratings would be measured by real-world testing and can be determined by the manufacturer during product testing and development.

Lets say the light bike with average riders was seeing consumption levels of 5Wh/m in the "city" situation, and 10Wh/m in the "touring" situation. That would give efficiencies of 0.2 M/Wh "city" and 0.1 M/Wh "touring". Now the heavy bike lets say was seeing more like 20Wh/m "city", and 25Wh/m "touring". That would give the heavy bike efficiencies of 0.05 M/Wh "city" and 0.04 M/Wh "touring".

These additional numbers provide the prospective buyer with a more fully informed image of how the vehicle will perform in their desired typical riding scenario. Do you go with the bike that can go 16.8 miles per charge, but with greater efficiency, or do you get the bike that can go 57 miles but resulting in less efficiency.

You can also use those efficiency numbers to weigh against the price as well since bigger batteries cost more and require a more powerful (and expensive) motor. If light bike costs \$1,200 and heavy bike costs \$4,000, you can say that light bike will get you 240 city miles or 120 touring miles per dollar and heavy bike will get you 200 city miles or 160 touring miles per dollar.

Range alone makes these bikes seem night and day different and very hard to compare. But when you factor in efficiency, you can see that in cost per mile, they are actually very close. It helps make the question of "how far do I want to go and how much to I want to spend" easier.

Just my 2 cents on the topic. Either way, I definitely agree with the OP in that we should have a unified "estimated unassisted range" rating.

### Re: Standard formula for Calculating Ebike Range

Posted: Apr 16 2018 7:25pm
I might be misunderstanding what you mean, but the 20wh/mile in the original equation *is* the efficiency, as a generally worst-case estimation. Inverting the number gives you miles/wh, if you want that number.

Different bikes and different riding styles, terrains, weather conditions, etc., will all affect that, but I think the idea behind the simple formula is to give something that is relatively realisic under most city riding conditions (where most of these bikes would probably be used); 20wh/mile is more than most would use; even my Crazybike2 was 22-30wh/mile most of the time--the higher values during commuting with lots of stops and starts, and the lower values on longer trips with fewer stops and starts. All of my riding is on the flats, with little wind, but either one of those being different could increase or decrease the wh/mile (efficiency) significantly.

So you can use a different number in the wh/mile part of the formula, but its not just the bike that accounts for that--its the usage, and thats where the existing problem lies, in that presently sellers and manufacturers rate the range for the *best* case usage.

It would be possible to characterize each different model of ebike to give efficiencies for all possible conditions, or even just a preselected few that would be standard tests, but I dont imagine most (any) sellers or manufacturers ever doing that (or doing it identically, per a standardized test routine, if they coudl be bothered at all), so they might just estimate what it would really perform like, and at taht point we might as well go with the original single formula.

### Re: Standard formula for Calculating Ebike Range

Posted: Apr 16 2018 7:40pm
zro-1 wrote:
Apr 16 2018 6:49pm

You can also use those efficiency numbers to weigh against the price as well since bigger batteries cost more and require a more powerful (and expensive) motor.
Mmm...I think you have that backwards unless Im misunderstanding what you mean.

The batteries dont weigh that much vs all the other stuff to require significantly more power to move a bigger one around vs a smaller one, but a bigger motor (and higher power controller) does generally require a bigger battery to either support it at all, or at least to get the same range as a smaller motor/lighter bike/etc might need.

### Re: Standard formula for Calculating Ebike Range

Posted: Apr 18 2018 8:02am
FWIW, I did help fact check the ranges claimed by one vendor, E-bikekit. I did real tests of range at level 2-5 power settings. EBK never considered claiming the range you'd get riding in level 1 like most do. We called that limp home mode.

For 20 mph, 20wh/mi is pretty dead on. If its flat or mild rolling hills, the rider is not fat, and the weather is mild.

I'm sticking by my rule of thumb from 2008, 1 ah per mile of 36v, and .75 ah per mile of 48v. This is NOT your range, but what will get you a practical size battery for a commute or other repeated ride. It includes a fairly large reserve, which will still not be enough when the wind is in your face riding home in winter. This number is also based on about 25 wh/mi, at speed slightly over 20 mph. Many will want to ride full speed on 36v. Full speed 48v will be back to 1 ah per mile.

For max range at sub 20 mph, including moderate to mild pedaling, double it.

### Re: Standard formula for Calculating Ebike Range

Posted: Apr 19 2018 12:55am
I always get asked about "How far can you go on that thing"

Then I say things like...

"Well the battery determines that, think of the battery as the fuel tank"

"Depends on how hilly it is, how fast you are going, your total weight including cargo"

"My battery can go 25km"

Then they ask how fast can you go. Which depends on the voltage, but I usually say 55km/h. When asked by The Fuzz, 30kph

### Re: Standard formula for Calculating Ebike Range

Posted: Apr 19 2018 7:45am
20wh/mile is a nice benchmark, but 100wh/mile or more is just too much fun.

### Re: Standard formula for Calculating Ebike Range

Posted: Apr 19 2018 7:59am
Hmmm... tried searching this thread for "ambient"... "Ambient" includes road surfaces, air temps, winds speeds and directions... weights added to vehicle as cargo or passenger... urban or rural aka "traffic"... and "stop-and-goes"... "age" of battery... Hehe... probably goes on and on... so maybe just qualify with Plus/Minus AMBIENTS to any "standard formula"?

### Re: Standard formula for Calculating Ebike Range

Posted: Apr 19 2018 8:45am
John in CR wrote:
Apr 19 2018 7:45am
20wh/mile is a nice benchmark, but 100wh/mile or more is just too much fun.
I like your way of thinkin! Yes fun is probably why most here have Ebikes. I know commuting is one thing, mine too, but many use the bike to have fun while commuting. No they don't see 100wh/mi like you, but, fun is fun!
I see from 18 to 24wh/mi at 20 mph. So I average about 2 miles per AH.
At 35mph I don't even bother to look at the CA.

Dan

### Re: Standard formula for Calculating Ebike Range

Posted: Apr 21 2018 4:34am
teslanv wrote:
Apr 16 2018 9:13am
There is absolutely NOTHING more confusing to the inexperienced ebike purchaser that understanding potential range with respect to the ebikes they are considering. So many ebike manufacturers and retailers embellish range claims using tricks that we experienced ebikers know are deceptive at best and down right ludicrous at worst.

Factoring Human power into the calculation is something I personally feel needs to be eliminated, because you just can't make a realistic and honest assessment between two individual humans and their power output.

Range should be based on motor power only, at a specific speed, and under the most simple conditions. And the values used should be towards the conservative side of the spectrum, that one can reasonably expect to achieve, if followed.

I propose the value of 20 Watt-hours per mile at 20 MPH, since the current US ebike guidelines limit legal ebike speeds to 20 MPH, and this is a speed that can be achieved relatively easily with a legal 750W motor. Conditions would also include: a flat, smooth road, no stopping & starting or hills, on an upright mountain bike (high drag coefficient).

The intent is NOT to argue about the minor efficiency differences between system A (DD Hub Motor) vs. system B (Mid Drive) vs. system C (Geared Hub) etc. Yes, there will be minor differences in the efficiencies of these systems.

The POINT is to make a simple method for less experienced ebike customers to assess range between the different bicycles they are looking at, and the most critical component of range is the energy capacity of the battery, in Watt-hours. I argue that WATT-HOURS should be THE ONLY value that can be reasonably compared between any number of ebike power systems.

And the Formula for Calculating range should be as follows:

Battery Nominal Voltage x Battery Capacity (Amp-Hours) / 20 Watt-Hours/Mile.

Example:
48V-12Ah Battery - would have 48x12 = 576 Watt-Hours of Energy / 20 WH/Mile = 28.8 Miles of range (at 20 MPH, motor only).

Apologies to the rest of the world that uses the metric system. The equivalent of the above formula would be 32 KPH speed, and 12.3 Watt-Hours/Km, which is much less easily remembered.

Perhaps Endless-Sphere could create a "Certification" for Ebike manufacturers and retailers who agree to use our formula for range calculation in their advertising...

Call it draconian if you want, but I think the ebike buying community would greatly appreciate some straight talk with respect to range, even if it is very generalized.

Here's my Youtube Rant. (NSFW warning)

just noticed this, can't you just calc the same way that the industry does for electric cars? for example you didn't even include weight. just look at how electric cars calculate their mileage, adjust for motor efficiency, you should be in the ballpark. the problem isn't that the companies aren't giving good mileage numbers, to be certain they are not, but you seem to be heading at it from the bottom instead of noticing that for years this has been a normal calculation in an established industry, one that include allot of variables that the manufacturer of a bike really cannot know. the creator of a diy bike could figure it out, but only roughly because aero is a pretty big factor. i got an ebike specifically because of wind, i bet that plays a role huh?

### Re: Standard formula for Calculating Ebike Range

Posted: Apr 21 2018 12:26pm
Wind can easily cut your range in half. When I had it 15 uphill miles home on my commute, it took me 12 ah of 48v to get home at 25 mph/15 mph. 15mph on the steepest two miles. Add 30 mph headwind to that, and I'd better slow to 15 mph the whole ride, and even then I often ran out a block from home.

The basic problem with industry range claims is that many want to claim the maximum range as typical, when its not.

Typically you buy an ebike to pedal less, and go faster. So putting a guy that generally rides 200 miles a week on an e bike, then selecting level one, doesn't give you a real range number. Yes, its not a lie, just a bit like saying my car gets 60 mpg, because it did once, going 30 mph with a 30 mph tailwind.

My first kit, they said 20 miles at 20 mph.. for 36v 12 ah lead. The truth was 6 miles at 20 mph, which started me on this journey to find out what real range was. If you go back to my rule of thumb, and figure that at full speed you get 6 ah from 12 ah lead, you start to see where my range rule got its start. Once I got lithium, 20 ah took me a maximum 22 miles @ 25 mph.

Back to the EBK ranges.. we got good data that allowed us to really explain ranges, and then we put it up on the website in the blog. There we were able to explain how different assist levels changed the maximum speed, greatly affecting range, and why. The simpler range claim we put on the product page was a spread. So say the kit was 36v 10 ah battery, we'd say something like 10-30 miles range for it. To get the 30, you indeed had to pedal a lot, as you must if you ride in level 2. in level 2 no pedaling, you'd barely be reaching 8 mph. Pedaling hard, more like 12 mph. At 12 mph, just about any e bike gets fantastic wh/mi, like 12 in this example.

So while many vendors will be saying some crazy ranges, ( technically true btw) those Jason claims are real. Some sound crazy high, like the range from a liberty trike with 10 ah battery. But that trikes max speed is 12 mph. So it does go an unbelievable distance.