Engineering Analysis – Why AWD e-bikes underperform in hills.
Rungu Dualie easily outperforms socalled “All-Wheel Drive” – AWD e-bikes – off-road on steep inclines. This article explains the physics that belies the claim that AWD e-bikes perform better than mid-drive e-bikes. It also explains why to choose Rungu if you plan to ride steep inclines off-road.
Sellers of e-bikes with All-Wheel Drive “AWD” (front and rear hub motors) mislead buyers. They allege better off-road performance than e-bikes with mid-drive motors. “After all,” they say, “cars with AWD and Four-wheel-drive (4WD) handle off-road conditions better than rear-wheel-drive (RWD) cars. So, the same is true for e-bikes.” The opposite is true.
Cars get traction in the front; bikes in the back. AWD/4WD cars work great off-road or in snow/mud/etc. Most of the weight of a car is in the front under the engine, and that is where cars get their traction. For most bicycle designs, most of the weight of the rider and bicycle is on the rear wheel. And that’s where the traction needs to be for effective pedaling/power transmission.
With minimal weight on the front wheel, e-bikes have little need of a front-hub motor. There’s a small fraction of overall weight on the front wheel. So, adding power to the front wheel causes the wheel to spin out on soft ground (sand, snow, etc.). Adding power to the front becomes even less effective on inclines (hill climbs). Far from being better, AWD e-bikes in fact perform much worse off-road in hills.
This engineering analysis explains the physics of AWD e-bikes. And it explains how they fail to deliver even half the torque of a Rungu Dualie on steep off-road trails.
Trigger warning – the following contains physics equations and math.
Torque Delivery – a balance of torque and road surface friction
The amount of traction you get from a bicycle wheel depends on three things:
- The weight on the wheel,
- the amount of friction (“grip”) between the wheel and the riding surface,
- and the force exerted by the wheel through torque delivery.
Major automotive tire companies have giant laboratories devoted to finding how to attain the optimal grip for a tire. They analyze slip angle and power transfer – subjects that go beyond the scope of this analysis. In brief, the tire needs enough grip on the road surface to transfer power and move a vehicle forward. Too little grip, or too much power spins the tire in one place (i.e. burning rubber).
The physics diagram below shows the balance of forces from the wheel and the ground that move the vehicle forward. The black arrows show “torque delivery”. Torque delivery is the traction force from the torque acting on the radius of the wheel . The traction force must be equal or less than the force due to friction (grip) to deliver torque from the wheel. The torque comes from the motor and/or pedaling. Torque delivery moves the wheel and bicycle forward.
Minimal torque delivery happens when the traction force exceeds the grip of the tire and the road surface. When torque delivery exceeds grip, the tire spins and may or may not advance the wheel forward. The formulas below show how to calculate maximum grip. Maximum grip equals the weight on the wheel times the coefficient of friction. And the coefficient of friction varies depending on the tire tread, material and the road or off-road surface.
Coefficients of friction generally vary between one and zero. A coefficient of one means that the grip equals the combined weight on the wheel. That’s a lot of grip. A coefficient closer to zero means the opposite. Regardless the weight on the wheel, the tire doesn’t grip (like driving on ice – no grip).
E-bike geometries favor the rear wheel for torque delivery
Most bicycle geometries place 70-80% of the weight on the rear wheel and 20-30% on the front wheel. The diagram below shows the calculated weight distribution of a 170 lb. rider. The calculated weight distribution shows about 21% of the weight on the front wheel and 79% on the rear wheel. The simplified diagram doesn’t consider the weight of the bicycle itself. However, the weight distribution is a fair representation of a rider seated on a bicycle. For most bicycle geometries, the greater of the two forces is on the rear wheel – where the traction is.
Torque delivery and weight distribution go hand-in-hand. Modern bicycles use pedals to move a chain or belt that rotates the rear wheel. E-bikes use hub motors or mid-drive motors to rotate the rear wheel. The force of pedaling or torque from the motor translates to torque in the rear wheel. This torque translates to traction force, or torque delivery. With more weight on the rear wheel, the rider gets more torque delivery to propel the bike forward. Less weight = less grip = less torque delivery.
The formulas below show how to calculate the weight distribution on the two wheels.
Surface friction – where rubber meets the road.
Riding surfaces make a big difference on how much torque delivery you can achieve before a wheel loses grip. The table below shows the coefficients of static friction between a standard car tire and different road (or off-road) surfaces. This article uses these coefficients of friction for calculation purposes. The grip is the total weight on the wheel and the coefficient of friction for the road or off-road surface. To reiterate – the amount of grip defines the maximum amount of torque delivery before the wheel starts spinning.
Example 1 – torque delivery calculation
In the earlier diagram, rear wheel torque delivery has to exceed 115 lbs. to lose grip on dry asphalt or concrete.
0.85 (avg dry concrete/asphalt-tire coefficient of friction) x 134.9 lbs. (force on rear wheel) = 114.7 lbs.
But torque delivery for the front wheel only needs to exceed 13.5 lbs. for the wheel to spin on ice.
0.1 (ice-tire coefficient of friction) x 134.9 lbs. (force on rear wheel) = 13.5 lbs.
No surprise. As the riding surface gets slicker, torque delivery suffers.
Standard e-bike geometry limits access to front wheel torque delivery
Standard bicycle geometry puts more weight on the rear wheel limiting front-wheel torque delivery. A hub-motor-driven front wheel in an AWD e-bike has less grip. Less grip in the front means less torque delivery from the front hub-motor.
Example 2 – Torque delivery limitation for a front wheel with a hub-drive motor even on a flat roadway
In the prior example, the torque delivery on asphalt of more than 115 lbs. could cause wheel spin. For that example, 79% of the weight is on the rear wheel. Only 21% of the weight is on the front wheel. So, any front-wheel torque delivery loses grip once torque delivery exceeds 29.8 lbs.
0.85 (avg dry concrete/asphalt-tire coefficient of friction) x 35.1 lbs. (force on front wheel) = 29.8 lbs.
Assume that the bike in the example is an AWD e-bike. Assume each motor can produce up to 85 Nm (62.7 ft.lb.) of torque. With 29 in. (.37 m radius) tires, each motor can produce up to 230 N (51 lbs.) torque delivery. For the rear wheel, this is OK. 51 lbs. are less than half of the 115 lbs. maximum torque delivery allowed. The rear wheel hub drive of this AWD e-bike can deliver all the torque available without wheel spin. The front wheel hub drive cannot. The 51 lbs. of torque delivery are almost twice the front-wheel maximum grip. The front wheel can only deliver the calculated 29.8 lbs. before losing grip. In other words, EVEN ON ASPHALT, the AWD cannot use all the power it has! While the rear wheel does most of the work, the front wheel spins.
As the trail gets steeper, there’s less and less weight on the front of an e-bike
The front hub-drive lets you down most when riding up an incline. Riding in the saddle, more weight transfers to the rear wheel as the hill gets steeper. The diagram below shows a bicycle on an incline. The black dot represents the center of gravity (COG) of the rider seated on a bike. The COG is a virtual mid-point. The same amount of weight (or mass) is in front as behind as well as above or below. For these physics calculations and representations, all the downward force due to gravity (weight) projects through the COG.
There’s more traction on the rear wheel as the incline increases, but there’s limit. As the incline increases, the COG moves backwards over the rear wheel. The relative location of the COG puts more weight on the rear wheel and less on the front. When the incline is steep enough, the COG is in line with the rear wheel force. That means there is no weight on the front wheel. If the incline gets any steeper, the bike (and rider) tip over backwards. Torque delivery is irrelevant when you’re lying on the ground.
The equations below show how to calculate the weight distribution for a rider on an incline.
Example 3 – Calculating weight distribution on an incline
Let’s find the weight distribution for the original bicycle example on a 20% grade. A 20% grade is a typical steep backcountry road. For a 20% grade, θ = 11.31 degrees. From the first example,
- the Fcog is the same 170 lbs. of force,
- the wheelbase is 46.52 inches,
- the dCOG is 9.6 inches
- and the hCOG is 29 inches.
Ffront calculates to 13.5 lbs. of force, and Frear equals 156.5 lbs. of force. From flat to 20% incline, 21.6 lbs of weight shifts from the front to the rear of the bike making the front tire even less likely to grip the road surface.
Example 4 – Real world weight distribution for a mid-drive, “Enduro-style” e-bike
Using the same equations with a real-world example arrives at a similar conclusion. An Enduro-style, mid-drive e-bike with 29 in. wheels from a very well-known US-based bicycle company weighs 52 lbs. With a six-foot, 200 lb. rider in the saddle, bike and rider have a combined weight of 252 lbs. The combined center of gravity based on this e-bike geometry is located 14 inches ahead of the rear wheel and 32.1 inches above the ground, with a wheelbase of 48.9 inches – this example includes the weight and center of gravity of the e-bike unlike prior examples. On flat (θ = 0), 29% of the weight is on the front wheel (63 lbs.). 71% is on the rear wheel (189 lbs.). On a 20% grade, the weight distribution changes to 10% in front (26 lbs.) and 88% on the rear (226 lbs.).
Weight distribution change due to inclines helps explain why bicyclists stand when pedaling. Mountain bike (and dirt-bike riders) often stand on the pedals (or foot pegs) in a climb. As the front end gets “lighter, steering becomes more difficult. The rider stands up to transfer more weight to the front of the bike. Standing on an incline can more than double the force on the front wheel on a 20% grade.*
Less weight and loss of grip and prevent front-hub motors in AWD e-bikes from delivering torque as inclines get steeper
The grip from each tire is a function of force perpendicular to the tire contact patch. Because of the angle of incline, not all the weight on the wheel is working to generate grip. Only the component of weight that is perpendicular to the road surface contributes to grip. You can observe this effect using a book cover and a flat eraser. Place a flat rubber eraser on a book cover of a book lying flat on a table. If you lift the cover a little, the eraser stays in place. Keep lifting and at a certain point, the eraser slides down the incline and off the cover onto the table. Sliding occurs when grip from the weight of the eraser becomes less than the downslope force on the eraser. For a bicycle wheel, as the incline increases, grip decreases. Less grip = less torque delivery.
Vertical wheel force on an incline decomposes into two forces. There is a perpendicular force where the tire contacts the road and a tangential force or downslope force. In the eraser example, friction force works against the downslope force to keep the eraser from sliding. For a bicycle that’s moving at constant speed (or stopped), the forces balance. The friction force due to the perpendicular force (grip) balances against the downslope force. This is just like the eraser. Too little friction force and the bike will slide backwards. Because the incline loses a component of the weight to downslope force, there’s less perpendicular force and therefore less grip. And less grip further limits torque delivery.
As trails get steeper, AWD e-bike front-hub motors have less and less effect. An AWD e-bike has most of its weight on the back wheel unlike a front engine 4WD car. The front hub-motor on an AWD e-bike generates little to no torque delivery as the trail gets steeper. As the grade of the incline increases, less and less of the total weight rests on the front wheel. And the perpendicular force gets smaller further diminishing grip. With less grip, the front-wheel hub-motor cannot deliver torque.
Example 5 – The impact of different trail surfaces on torque delivery for AWD e-bikes on an incline
As trail surfaces get softer, front hub-motors deliver even less torque on inclines. The table below shows the impact of a 20% incline for an AWD e-bike on a variety of road surfaces. Each row shows the calculations of maximum usable torque for each hub-motor for each surface. These calculations assume the same 200 lb. rider from the prior example riding a 95 lb. AWD e-bike on a 20% grade. This example e-bike uses the same frame geometry as the “Enduro E-bike”. The manufacturer of the example AWD e-bike does not provide frame dimensions to the public. But, it has front and rear suspension very similar to the Enduro E-bike in the prior example. The example AWD e-bike uses 750W hub-motors in the front and rear wheels. Each hub-motor can produce up to 85 Nm (62.7 lb ft ) of torque.
The results are clear – the front hub-motor cannot deliver all its usable torque on ANY surfaces on a 20% grade. At best, the front hub-motor can deliver 75% of its maximum output torque on “Asphalt and concrete (dry)”. Off-road, the front hub-motor can only deliver 60% of its maximum output torque. The rear-wheel, on the other hand, has no such constraint. The maximum usable torque on the same surface is more than four-times what the motor can produce. So what’s the benefit of a front-hub motor climbing off-road trails?
For riding steep off-road trails, the Rungu Steep is your best option
AWD e-bikes with two hub motors deliver power much less efficiently than mid-drive motor designs in off-road conditions. The engineering analysis of hub-drives off-road shows that the low-end torque is essential in off-road conditions. But hub-motors deliver only a fraction of the advertised peak torque at low speeds. AWD e-bikes try to overcome the weakness of a rear-hub motor by adding a second hub-motor in front. This analysis has already shown that the advantages of the second motor are minimal. Only a small fraction of the torque from a front hub-motor can contribute to power the bike off-road. So, is adding the extra hub-motor worth it?
Example 6 – Comparing mid-drives to AWD e-bikes off-road on inclines of increasing grade
The AWD e-bike in the last example has a lot of torque and power (on paper). This example compares the AWD e-bike to two mid-drive bikes by the amount of usable torque on increasing grades. As the incline changes weight distribution, grip increases on the rear wheel allowing more usable torque. But grip decreases on the front wheel, limiting front-hub usable torque. The usable torque for the AWD e-bike is the sum of the usable torque from the front and rear hub-motors. So how does AWD e-bike usable torque compare to rear-wheel-only output from mid-drive motors?
Reference – AWD e-bike marketed with two batteries and dual 750W hub-motors for a total 1,500 W of input power. According to the manufacturer, the e-bike weighs 95 lbs. Each motor can produce up to 85 Nm (62.7 ft-lbs.) of torque. MSRP of $5,495. For the comparison we use the same frame geometry that generated table in example 5.
Comparison A – Mid-drive “Enduro-style” e-bike from a very well-known US bicycle manufacturer. The mid-drive motor carries a 250W nominal power rating. The e-bike weighs 52 lbs. The mid-drive motor provides a peak torque of 85 Nm. However, the e-bike has a 34T chainring and a 51T cog as the first gear in a 10-gear cassette. The e-bike has a drivetrain ratio of 1.5. This e-bike can use the ratio to convert an 85 Nm into 127.5 Nm (94.1 ft-lbs.) of torque to the rear wheel. MSRP of $5,995.
Comparison B – Rungu Dualie Steep has a mid-drive motor carrying a 1,120W nominal rating. Rungu Dualie Steep weighs the same as the AWD e-bike. Rungu Dualie Steep has a mid-drive motor with a peak torque output of 197 Nm (145.3 ft-lbs.). It has a 30T chainring and 42T cog in first gear to produce a maximum drive train ratio of 1.4. A ratio of 1.4 means that this bike can deliver 275.8 Nm (203 ft-lbs.) of torque to the rear wheel.
All three e-bikes have the same 200 lb. rider.
Results
Rungu Dualie Steep has up to 66% more usable torque than AWD e-bikes in hills
The steeper the trail, the worse the AWD e-bikes perform. At 10% grade, the AWD e-bike starts to lose grip and power from the front wheel. And the losses accelerate as terrain gets steeper. The AWD e-bike loses an average 7% usable torque for every 5% increase in grade. On a 25% grade, the maximum usable torque from the AWD e-bike is less than that of the Enduro-style e-bike. And the Enduro-style e-bike has only one quarter of the advertised power output! The message – if you take an AWD e-bike off-road, be prepared to walk it up steep sections.
Rungu Dualie Steep is the clear off-road hill-climbing winner in this comparison. The AWD e-bike fails to achieve more than 75% of the usable torque of the lower-powered (and lower-priced) Rungu Dualie. The Rungu Dualie Steep, which weighs the same as the AWD and advertises 25% less power than the AWD, has 25% to 66% more usable torque on all inclines. Rungu Dualie Steep has 44% to 58% more than the more expensive Enduro-style e-bike! The table also shows the impact of Rungu Dualie’s “Straight Up” Climb-ability. For the Rungu Dualie, maximum usable torque INCREASES as the trail gets steeper.
Rungu Dualie e-bikes outperform AWD e-bikes off-road. The exceptional off-road performance relies on the efficiency of Rungu Dualie’s drivetrain and the stability of the double front-wheels. These features tame real-world, difficult, off-road conditions better than AWD e-bikes. The math does not lie. Rungu Dualie has a up to 66% more usable torque off-road. The team at Rungu has done the math and validated the results. If you have questions about how this math applies to the off-road terrain you want to ride, call us! We’ll get you a custom report on what you can expect in performance riding Rungu on your real off-road terrain. Why pay more for less?
Rungu Dualie. Far more stable. Far more able.
Questions? Contact info@riderungu.com.
*For calculations with riders out of the saddle contact Rungu for specific analysis.
