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# Electric Bicycles Are at Their Peak. How Are They Designed?

July 21, 2020 by Dr. Steve Arar

## What must e-bike designers consider in building these "green" modes of transportation? Motor power, range, motor type, and more.

Lime is an American transportation company that runs electric scooters, electric bikes, normal pedal bikes, and car-sharing systems in various cities around the world. The company has recently announced that it has reached 150 million rides powered with 100% renewable energy just three years after launching the company.

But how are these new-age transportation vehicles built from an electrical standpoint? In this article, we’ll try to introduce some basic technical concepts for designing e-bikes.

### Estimating the Motor Power

The first step to designing an e-bike is to estimate the required motor power. The motor should provide the power to overcome several different opposing forces in order to push the bicycle forward. For example, as we move uphill, the force of gravity pulls us down the hill. As shown below, the downhill force from gravity is given by:

$$F_d = mgsin(\phi)$$

where m is the total mass, g is the gravitational field strength, and φ is the angle of inclination.

##### Riding up hill, a cyclist must exert more force than the force of gravity pushing against the bike and its rider. Image used courtesy of Be Self Propelled

Wind resistance and bearing and tire friction are other major opposing forces that should be considered. Some of the important factors that determine the force of the wind drag are the rider and bicycle frontal area and the bicycle speed relative to the headwind.

The propulsion force (Fp) provided by the motor should be at least equal to the sum of the three opposing forces mentioned above (force of gravity, wind and rolling resistance). Multiplying Fp by the bicycle speed vb gives us the minimum power that the motor should provide:

Pmotor, min = F• vb

In practice, we need to scale this value upward to take the losses into account. Besides, the acceleration requirement of the e-bike will mandate the use of motors with even higher power values.

### Estimating the Range of an E-Bike

With e-bikes, the maximum speed across level ground is usually limited to about 30 km/h. Hence, utilizing a battery with higher power capacity will increase the range of the e-bike rather than its maximum speed. Battery power capacity, expressed in Watt-hours (Wh), specifies the amount of energy that is stored in the battery. This energy is used to create a force that pushes the bicycle forward.

Assume that the e-bike travels at its maximum speed vbmax and the propulsion force across level ground is Fp, level. In this case, we can use the following equations to estimate the range for a given power capacity:

Power Provided by the Battery = $${F_{p, level}} \cdot {v_{b, max}} = {F_{p, level}} \cdot \frac {Range}{time}$$

$$Range = \frac{Battery Power Capacity}{F_{p, level}}$$

For example, with Fp, level = 30 N and a 480-Wh battery, we can have a range of about 57.6 km.

### Battery Type: Lead Acid vs. Li-Ion

Two common battery types for e-bike applications are lead-acid and Lithium-Ion batteries. The lead-acid battery is cheaper but it has a lower energy density.

The energy density of a battery specifies the amount of energy that the battery can provide in a unit of mass (Wh per kg) or volume (Wh per liter). The mass-based definition is referred to as the specific energy of the battery and the volume-based measure is called the battery volumetric energy density.

As shown below, the specific energy density of a Li-Ion battery is about three times better than that of a lead-acid battery.

##### Energy density comparison of size and weight. Image used courtesy of Epec

Besides, Li-Ion batteries offer a higher depth-of-discharge and efficiency, which means that the effective energy density of a Li-Ion battery can be even better than the above diagram suggests. Moreover, Li-Ion batteries have a longer lifespan.

The major disadvantage of the Li-Ion batteries is that they are sensitive to overheating and need a battery management system (BMS) to maintain the temperature in a specified range. Li-Ion batteries should be protected from being over charged/discharged. As shown in the e-bike block diagram below, the BMS is required to keep different parameters of the battery in check.

##### Electric propulsion system of e-bikes. Image courtesy of Waraporn Puviwatnangkurn et. al

Another common functionality of the BMS is protecting the batteries from overcurrent that could happen in the event of an overload or short-circuit condition.

### Motor Type and Drive: BLDC Motors

Brushless direct current (BLDC) motor is the motor type that is commonly used in the e-bike application area.

A BLDC motor offers several advantages over a brushed DC motor such as higher efficiency, longer lifespan, and lower maintenance requirements. Besides, the size of a BLDC motor is smaller and, hence, is suited for electric vehicle applications that require motors with a high torque-to-weight ratio.

However, a BLDC motor needs complex control algorithms to achieve desired features such as tighter control of the obtained torque/speed, less ripple, and better drive dynamics. For an e-bike application, reducing torque ripples can be the most important aspect since it directly relates to driving comfort.

It’s the BLDC structure that mandates complex control algorithms. With a BLDC, the coils are on the stator and the permanent magnet is on the rotor. An electronic circuit (controller) is required to energize the stator coils in an appropriate sequence so that the magnetic fields generated by the stator make the rotor rotate.

The following figure shows a simplified structure of the BLDC motor along with the block diagram of the controller.

##### Block diagram of BLDC motor control implementing hall-sensors. Image used courtesy of Texas Instruments

The controller needs to know the current position of the rotor with respect to the stator so that it can energize the coils with the correct sequence. The rotor position is usually determined by means of hall sensors that are integrated into the motor.

### Conclusion

Lime estimates that clean energy-based rides, like e-bikes, have saved 1,300,000 gallons of gas. Widespread uptake of e-bikes can reduce dependence on personal automobiles for short-distance transportation and leave future generations with a greener planet.

What are your thoughts on the basic electrical structure of an e-bike? Share your insights in the comments below.

• MrChips July 28, 2020

I have been an ebike owner and rider for over 10 years. I own four ebikes and one e-trike. There is nothing in the article of use for the designer, engineer or potential user. You started off nicely with the physics of riding an incline. Great. Now try some real life numbers. How about pushing a 250-lb rider up 15-degree grade? How much power would you need? So you need a bigger motor and a bigger battery. Great. Now you need a bigger motor and a bigger battery, again. Every situation is an engineering compromise. Where are the limitations? Where is the sweet spot?

The same argument goes for distance. Wind resistance is the least important parameter. What power motor and battery energy would it take to cover 50km? If I want to double the distance how much bigger does the battery need to be? How about pedal assist? 5%, 25%, 50% pedal assists. This plays a huge contributing factor on range. What about charge time? In a typical commuter ride, you travel one way and stay there for 5-8 hours. Then you make the return trip. This is what determines your travel range. This will be great for the first 3 years of battery service. After that your range diminishes.

SLAB vs Li-Ion is cost. SLAB are a fraction of the price of Li-Ion. SLAB will last for 3-5 years if well cared for. SLAB are readily available and easy to replace. What are the best practices for care and maintenance of SLAB?

Li-Ion has higher energy density. We all know that. How long will they last? What do you do when they are dead? What is the cost to replace? I have yet to find the original ebike manufacturer who sell replacement batteries. Price? How about \$1000 for batteries alone.

All in all, the article adds nothing new to what we already know and offers no advice to anyone seeking out to get an ebike.

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• E
ekutik July 28, 2020