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FAQ: Electric Bike Range Calculations

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    FAQ: Electric Bike Range Calculations

    One of the most confusing aspects of electric bike is range. If you have done much research on electric bikes you will have noticed that most people start waving their hand around a lot when talking about how far the bike can go. The marketers hold up a finger chanting, “We’re number one.” Engineers look at the math and throw up their arms in despair. While this is an exaggeration, there is a kernel of truth.

    Marketers are under pressure to promote and sell their bike in a market full of bikes with similar specifications. Journalists, while they mean when, often misquote the marketing materials. Which just adds to the confusion.

    From an engineering perspective, calculating vehicle efficiency is extremely hard. Accurate calculations require running fluid dynamic simulations on supercomputers. Even then, the simulations are only accurate for a very specific set of conditions. Much of the time engineers find it cheaper to build a prototype and test it in a wind tunnel. If you are interesting in this subject, try googling aerodynamicist, fluid dynamics, or wind tunnel. Be careful it can be hard to climb back out of that particular rabbit hole.

    The complexity of the math creates a second set of problems. People who work in the in the field throw around terms like co-efficient of drag, joules, watts, and amp-hours. To a casual user, these terms mean about as much as inches, feet, yard, and miles mean to someone raised in a country which uses the metric system of measurement.

    What is a consumer to do? Let’s look at the automobile industry for some lessons. Prior to the 1970’s, fuel was an insignificant cost of vehicles. Few people really cared about fuel economy. The sharp increases in fuel costs resulted in several years of mass confusion and manufactures started to use fuel economy as a selling point. The confusion was similar to that we are experiencing in the electric bike world today.

    Manufactures started to provide information in terms of distance per unit of fuel such (mile per gallon) and (kilometer per liter.) This was an improvement. However, because different manufacturers used different testing processes it was impossible to compare fuel efficiency between manufactures. It took 50 years for national agencies such as the EPA to create a set of standardized test.

    These standardized fuel economy tests consist of having an independent third party drive vehicles around a predetermined course in a consistent manner. While imperfect these tests are the most reliable measure consumers have for predicting fuel economy. The tests are constantly evolving as manufactures and testing agencies play cat and mouse as manufacturers attempt to gain a competitive advantage.


    Now that I have scared everyone off with the complexity of the problem, the good news is that most people have a pretty good intuitive sense of fuel economy. The harder you have to pedal your bike or push on your gas pedal of your car, the worse you fuel economy is at that moment. Accelerating, going quickly or going up a hill tends to reduce your economy at a partial moment. Sitting more upright (increasing frontal area) or towing a load (increasing weight) tends to reduce overall fuel economy.

    With the help of I think I have identified the key factors required for calculating the range of an electric bike. I'll figure out the units and try to create a working range calculator. My last physics class was embarrassingly long ago :(

    I just thought that I would get this out for review in case I am totally off base.

    Sheet1 Force Aerodynamic=( Density of Air)*( Coefficient of Drag)*( Frontal Area)*( Velocity^ 2)/ 2, Force Aerodynamic Density of Air Coefficient of Drag Frontal Area Velocity Force Rolling Resistance=( Coefficient of Rolling Resistance)*( Mass)*( Gravity), Force Rolling Resistance Coeffi...
    Last edited by funwithbikes; 04-03-2017, 12:14 PM.

    that would be awesome i look forward to using your range calculator!


      Good luck with this!
      As a driver of an electric car for the last 3 1/2 years, what you are proposing is nearly an impossible task!
      There are far too many variables to reliably predict the range of an electric vehicle (or really any vehicle regardless of propulsion source). With any fuel source you need to factor in wind speed & direction, topology, rolling resistance, vehicle weight, speed (drag), driver/rider ability (mash the power, or smooth acceleration) among others. With battery powered vehicles, now you need to bring in temperature and battery condition.

      I have a place in the mountains 99 miles from door to door with an elevation change of 9,000 feet at the highest point about 3/4 way through the commute, and then back down to 4,000 feet higher than the starting elevation. Because of all the factors mentioned above, I can complete this drive consuming anywhere from 120 miles of range (driving slow in the warm) to over 200 miles of range (driving fast in cold temps) and the car has the ability to heat the battery, where the bike doesn't.
      Conversely, the drive home (thanks to regen in the car) I can complete the same 99 miles only consuming about 60 miles of range. Some days more, some less depending on all the variables mentioned above.

      In reality, it has been the same with any vehicle that carries and consumes energy since the beginning of time. Most of us have grown up with a fuel gauge, and when it get's close to the "E", we start to look for places to replenish our fuel source. Rarely (at least I never did) did we get into our fossil burning vehicle and try to figure out how many miles we could go on a tank before we ran out (to the exacting level people try to do with electric vehicles).
      It's a little different when you are in an electric powered vehicle because the fuel replenishing stations are not as abundant, and it takes more time. But it is still the same in some respects. Instead of looking at a fuel gauge, we need to look at battery voltage. I ride with a 52v battery, and I know it will shut down somewhere between 41-44 volts depending on where I have it set. So, I then take my starting voltage, subtract my ending voltage (41-44), and figure my ride out from there. If the terrain is flat, I can generally consume about 45-50% of my battery on the way out, and have plenty to make it back. If the first part is mainly uphill, I can consume about 75% on the way out, and use the remaining 25% to get back down the hill.
      Sometime you win, sometimes you loose. Yesterday I went out when it was really windy. Most of the first half was with the wind and I underestimated how strong it was. Long story short, I came up about 5 miles short in my calculation, so I was under manual power for the last part of the ride.
      I know a lot of people have put in a lot of time trying to calculate the range of electric cars (google electric car trip planner), and some come close, but it takes a ton of data elements to get it close; however not many that I've found are accurate enough for me to use reliably. My car has a screen that will predict range based on energy consumption of the last "X" miles (depending on the range I have it calculating from), but it can't ever get close either... again depending on the above factors.

      Not meaning to rain on anybody's parade, and I hope like hell you are able to come up with something that nobody else has thought of. But, for now I'll stick to my battery volts fuel gauge.



      • funwithbikes
        funwithbikes commented
        Editing a comment
        Yes. I agree with you on the futility of the exercise.

        While I am not a aerodynamicist, I have done a substantial amount of fluid dynamics calculations on velomobiles. There is a reason that top racing teams spend 100's of millions of dollars on wind tunnels and supercomputers :) The coefficient of drag is hard to calculate.

        On the flip side there are a couple of rules of thumb that one can use.
        1. Range increases proportional with an increase capacity of the battery as measured in kilowatts-hour.
        2a. Range decreases as the square of speed as the vehicle starts to get above ~ 25 mph where aerodynamic drag is the most important factor.
        2b. the aerodynamic efficiency (coefficient of drag) is significantly affected by the rider's body position.
        3. Below 15 mph weight and rolling resistance are the dominant factors.

      Yeah I've heard of people who will, upon buying any new vehicle, carry a gas can in the car, and then drive it until the engine DIES completely from fuel starvation. Since most newer cars have a Range display on the dashboard, with a safety factor, that tells them about how far they can go once the Range indicator gets down to zero. I know on my wife's Mazda CX-5 I've run it down to less than 10 miles of range, but to fill up the tank still took about 1.5 to 2 gallons less than the tank capacity, which means I could go for at least another 30 miles or so.

      I still have a lot of reading to do on battery voltage readings when at 100%, 80%, and 20% for my 52V 13.5aH battery. I hope to be able to make a 31 mile round trip commute on one charge (rolling hills, both up and down hill sections in both directions), but I suspect it will be quite a lot of trial and error.


        Depending on how interested your are...

        You can get some surprising good results for rolling resistance and coefficient of drag at home doing something called a 'coast down test'. It is fascinating to see how small changes in a cyclist's body position can affect the coefficient of drag.


          It would be interesting to start a table to have users submit several attributes to help get at the more general question...
          "How much bike do I need?"

          I propose as a starting point for variables to provide. It's similar to the mpg challenge going on, though hopefully eliminating math might improve participation...(please chime in on the variables, I'm a total newbie)

          Commute distance
          Vertical feet in commute
          Average speed
          Level of effort (Low [Just cruising], med [Moderate pedaling], high [working hard]

          Motor size
          Bike wheel size (Tire?)
          Battery size
          Average battery consumption

          Given a table, we could start to build an empirical database of distances and specs to help people not only size batteries for range, but also build rigs that would meet their distance, speed and comfort expectations.

          for instance, I'm researching a 40-mile round trip commute, and am Ok using a set of aero bars since I've commuted on bikes in the past and appreciate the efficiency gains. I'd like to move at a brisk pace since I have a long distance to cover and don't want to lose too much of my day to a commute. Also because I'm an active rider. I'm OK pedaling a fair amount to get the job done and see the bike offering mixed levels of subsidy for downhill and uphill stretches.

          This would help users figure out what they need and speed up purchase decision making (e-hem...).

          The more I read, the more questions I have before pulling the trigger.


          • PatrickGSR94
            PatrickGSR94 commented
            Editing a comment
            Yeah I'll bite.

            Commute distance = 31 miles round trip
            Climbing = 244 feet (Strava), 548 feet (RideWithGPS)
            Average speed = 16-17 MPH moving average
            Effort = Moderate Pedaling

            Motor: BBS02 750W motor
            Wheels: 26" disc brake wheels with 26x2.15" Big Apple tires
            Battery: 52V 13.5aH GA bottle battery
            Consumption: around 56 volts (90% charging) down to 48 volts after complete round trip commute

            Probably should also add:
            Bike = custom built Marin Pine Mountain steel MTB frame
            Bike weight = ~60 pounds with motor and battery, more with cargo in trunk bag and panniers for commute.

          Thanks for the data point. I'm also finding general range tables around the web, but it seems like this is something that can be pulled into a table to generate living data. I'll pull it together an will have to figure out the best way to render it.