E-Bike Guide: Ideal Motor & Battery
When you are deciding which E-bike will elevate your riding experience, you will face questions about the bike’s range and power. Similar to electric car drivers, E-bike riders can have range anxiety; no one wants to be stuck with a 25+ kg. bike on a mountain when the sun is setting. Many trails have steep hills at 25’+ degrees inclines; you may develop climb anxiety because you’re literally tired of not being able to climb those hills without stopping and pushing your bike. Several thousands euros is a big purchase so you don’t want to make a bad decision, but you may not have any experience with e-bikes and there is limited info about the subjects. After reading this article, you will have a concrete guide for how strong the motor and battery should be, considering your weight, your age, time biking, distance travelled, and motor output. While having the right battery and motor will help your ride significantly, those two factors are only one part of an ideal bike. You must consider the bike geometry (ie: how it fits you and rides) and the bike components (ie: brakes, shocks, shifters, etc). This article does not address those issues, but helps you solve part of the bike search.
Your weight affects how strong the motor needs to be; the heavier you are, the more power is needed to move. Reality sets in as you get older and you realize you are not as strong as you were in your 20’s. Thus, your age must be accounted for when calculating the motor strength, which in turn affects the battery capacity. The duration of the bike ride, excluding time stopped, affects how much battery capacity you will need. Similarly, the length of the bike ride will proportionally increase the required capacity of the battery. However, less battery strength is needed for more efficient motors. The support level, which is the power output for the amount of work put in, determines the motor efficiency that is used in the battery equation. With these factors accounted for, you can determine the necessary battery capacity and motor torque needed for your new E-MTB.
Other minor factors affect the battery capacity, but they are not included in our equation because either they are subjective to the rider or hard to quantify. Too high or too low outdoor temperature (below 45'F or above 90'F) prevents the battery from operating at its optimal efficiency, which reduces your possible range/ climb. Too low tire pressure can increase your rolling resistance, which increases the motor’s energy usage and reduce your range/ climb. E-bike motors have different cadences that give peak efficiency (typically 60–90 rpm); riding your bike at the peak cadence will prolong the battery and increase your range/ climb. Finally, the terrain and riding style will affect the duration of the battery; accelerating often or steeper slopes needs more energy, which reduces your range/ climb. To increase the distance or climb of the ride without increasing the battery capacity, the operating efficiency needs to be increased. You can achieve this by either reducing your weight (self, bike, gear, etc) to reduce the motor’s load or ride in cooler temperature to decrease the energy loss from heat production. You can expect an increase in distance or climb that is proportional to the reduction in total weight or outdoor temperature. For example, a decrease of 25% in total weight from 120 kg to 90 kg or a decrease of temperature from 90’F to 68’F would result in a proportional increase of 25% (tested) in either distance or climb that can be ridden.
For road bikes, the difference in fitness factor is minimal since rolling resistance is much less and riding momentum is easier to maintain. The needed battery capacity for road bikes is determined by climb and age since the distance cancels out in the equation. For the same reasons, the torque needed for road bikes is less. These equations were tested on rides like the road around Lake Tahoe in California (Tour de Tahoe), which is 73 miles and 4000+ feet.
In the examples, we assume typical body and bike weights for a range of ages (older age = higher income = lighter bike & stronger motor, but less endurance & heavier person). We assume the rider uses an assistance level proportional to the grade of the climb. Generally, a 50Nm motor should provide 200% support level and every 10Nm more gives you another 50% support. The recommended battery assumes 10% remaining capacity for emergencies and to prolong the battery life. These equations were formulated based on riding an e-mtb on 50+ trails for over 1000 miles and climbing over 150,000 feet. Regardless of your age or riding distance, there is always a motor and battery that will fit your needs.
MTB Battery, Wh = [meters climb + (hr time * km distance * years over 25)] / (fitness factor * motor efficiency)
MTB Torque, Nm = kg self weight+ kg bike weight — (1.62 * years < 55)
Road Battery = climb % * km dist. * age / hr time * 4 = age * 25 * km climb / hr time
Road Torque, Nm = (kg self weight+ kg bike weight — years < 55) / 1.62
Climb Grade = 100 * km climb / km distance; Efficiency = support level/ 100
Fitness factor: use 2 if athletic, 1.62 if fit, or 1.4 if weak or heavy. Fit means exercise 4 hours per week; use 1 for “years > 25” if 25 or under; use 0 for “years < 55” if 55 or above. 1.62 (rounded up from 1.618) is known as the golden ratio, which occurs often in nature.
MTB Recommendation: 60–120 Nm providing 240–540% support
Road Recommendation: 40–80 Nm providing 160-360% support
For quick estimates while you’re shopping:
MTB Battery, Wh = Age * 15
MTB Torque, Nm = Age * 2
Road Battery, Wh = Age * 8
Road Torque, Nm = Age * 1.5
