E-bike engineering analysis– why to avoid hub-drive e-bikes for off-road conditions.
Trigger warning – this article contains math and graphs
If you are looking to buy an e-bike for off-road use – off-road use means mud, snow or sand – avoid e-bikes with hub motors. Many e-bike sellers are touting fat-tire, hub-drive e-bikes as suitable for off-road use without qualification. Difficult off-road conditions can include soft sand, deep snow, mud, and rock-crawling. But off-road can also mean a hard or worn dirt trail that is as easy to ride as asphalt. This engineering analysis of hub drives explains why hub-drives are a poor alternative to mid-drive motors off-road. When faced with difficult off-road challenges like soft sand, deep snow, mud and rock crawling, hub motor drives fail to measure up.
You need low-end power off-road
For off-road conditions such as sand, snow, mud and rock crawling you need a lot of low-end power. Usually, riding in off-road conditions needs more than advertised power for a typical e-bike. The physics of bicycling in these off-road conditions are easy to understand. The power required to ride any bike at any speed depends on:
- the weight of the rider and the bike
- the rolling resistance,
- the amount of incline of the road/trail and
- the wind resistance of the rider at that speed.
Calculating power requirements is a known thing
Fortunately, there is a formula for calculating power requirements. Bicycling Science (a book by David Gordon Wilson) includes a formula to calculate the mechanical power required for riding a bicycle at steady speed. It keeps in consideration the factors described above:
- KA = the coefficient of wind resistance, which is between .2 and .3 for a rider sitting upright. (kg/m)
- V = is the velocity in m/s (speed measured in meters per second)
- Vw = is the headwind velocity in m/s (wind speed measured in meters per second)
- m = the mass of the rider and bike in kg (mass is measured in kilograms, converted from weight in “pounds force”)
- g = acceleration due to gravity in m/s2 (9.81 meters per second per second)
- s = the percent grade of the incline (dimensionless)
- Cr = the rolling resistance coefficient, which can be as low as .0017 for a track bicycle tire on asphalt or higher than 0.30 for a fat-tire e-bike in deep snow or mud (also dimensionless)
Example: Consider this case – a 200 lb. (m = 90.7 kg) rider on a fat-tire electric bike (m = 40 kg) in deep snow (Cr = 0.30) on a flat field (s = 0) riding at 10 mph (4.47 m/s) on a windless day (KA = .25 and Vw = 0). Using the formula shows that the rider (or e-bike) needs to produce 1,740 Watts (1,740W – more than 2 Hp) of mechanical power to keep that pace!
Considering most off-road e-bikes advertise less than 1,740 Watts of power, the example asks a lot of the e-bike and the rider. The rider can use leg power to make up the difference or more likely, slow down. In this example, rolling resistance produces most of the power loss.
The example also shows that power is directly proportional to speed. The rider needs less power at slower speeds. The rider and e-bike need to produce a little over 861 W of mechanical power to maintain five miles per hour. And around 689 W to plow ahead at only four miles per hour.
Manufacturers hide mechanical power ratings
E-bike sellers rarely advertise the mechanical power output of their bikes and focus instead on marketing motor power ratings. Power output and ratings are NOT the same. Motor power ratings are often the nominal (or average) input power specification for the motor on the bike. The actual power output varies with the input voltage (which also varies) and the efficiency of conversion from electrical to mechanical power. A fully charged battery delivers more input power to the motor compared than one that is almost fully discharged. Battery voltage changes as you use the battery. And then there is efficiency loss…
All e-bike motors lose some input power to inefficient conversion from electrical power to mechanical power. E-bike motors with rare exception convert the DC voltage from a battery into three-phase AC power to turn the motor. AC motor design is more efficient at high power than DC motor designs. But efficiency varies with the speed that the motor turns. In general, efficiency varies from 30% (only 30% of the input power is translated to mechanical power) up to 90%. As an example, leading e-bike producer Pedego advertises the Trail Tracker – Fat Tire Electric bike. It uses a hub motor that has a power rating of 500W at 48V. The Trail Tracker uses a Bafang G060.500 fat-tire hub motor. It has a peak efficiency of 86%. That means that at peak efficiency, mechanical power is 14% less than input power, or around 430W at 48V.
Hub motors are inefficient at slow speeds
Hub motors are inefficient at slow speeds. The Torque/Power/Efficiency graph for the Bafang G060.500 motor below (from Grin Technologies ). The graph shows that motor efficiency is quite low at low speeds and only breaks 80% at around 18 mph. Below 18 mph, efficiency drops fast. The reasons for the change in efficiency are beyond the scope of this article. All e-bike motor curves (hub and mid-drive) have a similar shape. Low efficiency at low rotational speeds. A plateau of high efficiency – higher rotational speeds. Then a speed “cliff” where the motor can no longer provide mechanical power.
Example: Let the same rider use a Trail Tracker. The Trail Tracker would need to produce 689W of mechanical power at four miles per hour. Looking at the graph, the motor is only 46% efficient at four miles per hour. In other words, the motor only produces mechanical power equal to 46% of the input power at four miles per hour.
At that efficiency, the Bafang motor only produces 230W (@48V) of mechanical power. That is less than one third of what our rider needs.
The extra power heats up the motor
Hub motors can burn up off-road. Hub motors convert input power not used for mechanical power into heat – not more torque at low speeds. With older controller systems, riding at slow speed in difficult terrain overheated the motor. The extra input power burned through the insulation in the coils destroying the hub motor. More recent motor controllers have more advanced shut-off capability and avoid overheating the motor. The best case for our 200 lb. rider in the example – the motor shuts down. The rider walks the bike out of the snow back on to easier terrain.
Gear reduction makes mid-drive motors the better off-road choice
Mid-drive motors transfer power to the rear wheel more efficiently and are superior for real off-road conditions. Mid-drive motors suffer similar efficiency curve variations as hub motors. But they have one HUGE advantage – the ability of the rider to change gears to optimize power delivery. With a chainring in front and a selection of cassette cogs in back, a rider can match speed using gear selection.
Using gearing with a mid-drive is like driving a car with manual transmission. At slow speeds, a small chainring in front to and a large cassette cog in back lets the motor rotate faster than the wheel. The motor operates nearer to its optimum efficiency while the rear wheel rotates slower. This also allows the rear wheel to deliver power with better efficiency at a speed lower than the motor speed. At high speeds, the rider changes gears so the chainring drives a smaller cassette cog. This change lets the wheel rotate faster than the motor speed to get more efficient power delivery.
Example: Using the graph above, The Pedego Trail Tracker operating at the midpoint voltage of 48V has approximately 46% efficiency at 4 mph. This translates to approximately 230 W of output power for 500W nominal power. If the same motor could be placed in the middle of the e-bike to drive the same first gear as a Trek Rail 7 e-bike (34T chainring – 51T cog: drivetrain ratio of 0.67), the motor could spin 50% faster while the wheel rotates at the same speed. At the equivalent speed wheel of 6 mph, the same motor operates at 55% efficiency, which translates to 275W of output power – a 20% increase in power output!
Rungu is designed for off-road use.
Rungu relies on its double wheel technology and the efficiency of its drive train to tame real-world, difficult, off-road conditions. The 2021 Rungu Dualie Standard uses a Bafang BBSHD mid-drive motor with a nominal power input of 1,120W and 30T chainring with a 11-42T cassette in the rear of the bike; in other words, it has a minimal drive train ratio of 0.71. With the bike in first gear riding at four miles per hour, the motor efficiency is 66%. This efficiency translates to 739W of output power to the rear wheel – more than enough to get through the snow at 4 mph (with 50W to spare).
The team at Rungu has done the math and validated the results. If you have questions about how this math applies to the terrain you want to ride with a Rungu, call us! We’ll get you a custom report on what you can expect in performance using Rungu on your real off-road terrain.
For questions or more information, contact info@riderungu.com
