How fast and how far will my ebike go?

Simplistically, "It depends".

Allow us to summarize the key components and features that are required for speeds in excess of 40 mph; below that figure – less than 40 MPH, speeds are generally easy to sort out and the solutions for such systems are readily available.

  1. Better Aerodynamics & Lower Drag Coefficient
  2. Understanding Motor Constants
  3. Motor & Wheel Sizing
  4. Higher Voltage
  5. High-Discharge Rated Battery
  6. Large Battery & Phase Wires
  7. The Calculus of How Speed affects Range

Air friction is the single most significant factor in limiting any vehicle's top speed. In fact, VERY aerodynamic velomobiles can achieve speeds of over 80 mph on human power alone, as long as there is sufficient gearing for the rider to continue exerting accelerating force against the ground.

Delft high-tech bike sets new world record

Of course, many ebike builders and riders prefer the more traditional appearance of the upright bicycle. However this does not mean that aerodynamics should be ignored. Even something as simple as a front fairing can improve aerodynamic efficiency and top speed by up to 10%. Kingfish has been experimenting with front fairings for several years.

Endless-Sphere: Bicycle Fairing & windscreens

The bottom line is this: Better aerodynamics will make our bike more efficient in all aspects of riding. Our top speed AND range will improve by the addition of better aerodynamics. Factors that affect aerodynamics:

  • Front and Tail fairing; make the wind go around instead of through us, like a hawk or dolphin.
  • Body paneling: Cover up that loose wiring and open framework!
  • Clothing: Avoid loose-fitting jackets, trousers.
  • Headgear: Goofy cycling helmets foster even more drag. Instead, use lightweight contemporary moped helmets designed to protect both our head and face from raging bugs, inclement weather, and foreign debris kicked up by passing vehicles. Excellent example: AGV Blade
  • Riding position: Reclined, and crouching are best; upright like a billboard is the worst.

One topic that has been argued to no end is whether it is better to have a "High Speed" motor or a "High Torque" motor. For Brushless DC Motors, here are the key terms we need to understand:

  • Kv means "Motor Velocity Constant" or RPM per volt; it is also called "back-EMF".
  • Kτ means "Motor Torque Constant" or Torque per Amp.

These two constants – from a pedestrian perspective – are considered inversely proportional to each other. It is the "Motor Constant" Km that binds the two opposing constants together. Simplistically, the formulas are as follows:

  • Kv = RPM/V = revolutions/minute/volt
  • Kτ = τ/I (Torque/Phase Current as Amps), or as 60/(2π * Kv) = ω/Kv = 1 radians/sec/Kv

Kv and Kτ vary with respect to N (the number of Turns in a Winding) and I (the measure of Phase Current as Amps). For a given motor and stator, Kv scales linearly with N. Therefore is falls upon the Winding Wire Gauge, the number of strands in the wire, and the effective Stator Slot-Fill that affects R, Resistance. HEAT is waste-energy produced by Resistance, therefore we want motors that produce the lowest amount of heat (resistance) and yet provide the best power conversion (albeit Kv speed, or Kτ torque). The "motor constant", Km thus becomes the dominate factor in determining the motor's overall efficiency:

  • Km = τ/(√I²R)

Generally, when we increase the Kv or speed of a motor, there is a proportional decrease the amount of torque per amp that it can produce. This formula holds true for ALL ELECTRIC MOTORS REGARDLESS OF SIZE!

From an engineering perspective, it is better to have higher voltage and less current because it produces less heat. However, the switching electronics of motor controllers work better at lower voltages, but then this means we need more current to create the same amount of power, and in turn creates more heat. There is no panacea, no free lunch; we have to decide on which is more useful: Speed or Power, or some compromise in-between.

Straight-up: Large motors handle heat better than small motors. They are designed to accept more current and can dissipate excess energy more effectively, though often in exchange for cost or efficiency. Small and large motors may offer the same Kv, however their Kτ and Km will not follow likewise. Generally, we want larger motors for heavy loads, rough terrain, and strong starting features like oxen pulling a cart or mountain-climbing, although not exclusively; sometimes we need a strong motor to go faster down the road. It just depends upon the need.

The other factor that affects motor choice and acceleration is tire size: Smaller tires result in faster acceleration – although gated with lower top speed, with larger tires having the opposite effect. Example: Racing tires are small, whereas tractor tires are large. Small spins faster, but large rolls easier and more efficiently. Therefore, sizing the tire to the motor will greatly affect the motor's performance. The key is to pair a high Kv motor with as small of diameter tire as practical to achieve the best combination of speed, acceleration and efficiency.

The speed at which a motor turns (RPM) is directly related to the voltage applied to it. Ideally without a load applied, a motor will spin twice as fast if the voltage is doubled. So why not just use ridiculously high voltages to get high speed? In a word: SAFETY. Higher voltages are inherently more dangerous.

Another reason to reduce voltages is based on the hardware limits of common electrical components within modern controllers. Most ebike controllers based on IRFB4110 MOSFETs; these have a hard voltage limit of 100V, and we prefer to run them lower to prevent failure. Capacitors are also limited in the amount of voltage they can accept. Some "Highway speed" controllers are built with IRFB4115 MOSFETS and higher-rated capacitors that can take up to 150V. New, more efficient MOSFETs are in development and look promising, including the Texas Instruments CSD19536KCS MOSFET which have higher current handling than the traditional IRFB4110 MOSFETs.

The other challenge with high voltages is dealing with the more complex battery management systems (BMS) that accompany batteries with more cells in series required to produce the higher voltage. Therefore, as voltage goes up, the complexity of the BMS also increases.

The "Comfort Zone" for battery voltage in recent years is right in the 90V range for high-performance systems. In terms of Lithium cells, that would equate to using "22S" or 22 cells in Series at a maximum of 4.2V per cell which results in a fully charged battery voltage of 92.4V. However 22S is kind of an odd combination, and when building with pre-made blocks of batteries of 4S, 5S, and 6S, an 18S or 20S battery is more common, albeit a bit lower voltage than a 22S battery.

High voltage is worthless if our battery is unable to supply enough current under load, leading to a condition we call "voltage sag". Batteries are rated by their discharge capability or "C-rating". Many consumer batteries are "1C" rated, which means that they can output at one-times the capacity of the battery. Example: If the battery is rated at 1C @ 10 Amp-hours, it will output just 10 Amps of current continuously.

Lithium Polymer batteries, often used in the RC Hobbies, can output upwards of "100C" – in other words, 100 times the capacity, so a 5 Amp-hour battery can output a theoretical maximum of 500 Amps of current (although at the cost of lifespan). While we don't recommend running RC LiPo batteries at their rated discharge currents, they do provide for significant improvements to output as compared to more mainstream battery formats and chemistries. The pragmatic approach towards reasonable discharge rates is to take the rated output of an RC LiPo battery and divide by 4, so that 5 Amp-hour "100C" battery might perform reliably well at 25C or 125 Amps of current continuously.

Similarly high-performance batteries can be created from "high-power" 18650-style units such as the Samsung 25R cells which can reliably output up to 8C discharge rates and are safer than RC LiPo batteries.

If we're are aiming for a specific current output (Say 50 Amps), we simply need to size the battery such that it can output the required current within its continuous C-rating. If the battery is rated at 1C, it will need to build a 50-Amp-hour battery. If instead we choose an RC LiPo battery rated for "20C" (and judiciously de-rated by 1/4 to "5C") then it would need a 50A/5C = 10 Amp-hour battery to produce the 50A of current to the controller.

High current will generate heat in any system, including the battery and phase wires, connectors, controller's power stage and motor windings. To minimize the heat (and energy loss) we want both short and large-diameter wires to carry that current from the battery to the controller, and then on to the motor. We also want to use high quality oversized gold-plated connectors where possible, otherwise those become bottlenecks and will produce large heat losses. Quality insulation grade also plays a role in safety, though not necessarily in efficiency: A silicone insulated wire will get hot, but not melt (and cause a short) until the temperature gets very high, however it is still inefficient if not properly sized.

Realistically, we cannot size the battery and phase wires too large; however there are limits and expense to making connections once they get too big. Generally speaking both 10AWG and 8AWG wires are about as large as practical without needing special crimping/swaging tools and supplies: Wires larger than this become problematic if not impossible to solder. We recommend the practice of crimping and swaging, which is also useful if needing an in-field repair.

Within a given aerodynamic profile (such as an upright bicycle without any fairings) the amount of power required to travel at a specific speed will increase exponentially as velocity increases. Example: An electric vehicle having 330 lb. curb weight (including the rider) on level ground will take:

372 Watts of power to travel at 20 MPH (21.5 Watt-hours per Mile)
1045 Watts of power to travel at 30 MPH (39.5 Watt-hours per Mile)
2314 Watts of power to travel at 40 MPH (67.4 Watt-hours per Mile)
4400 Watts of power to travel at 50 MPH (104.5 Watt-hours per Mile)
7419 Watts of power to travel at 60 MPH (150 Watt-hours per Mile)

If we want a bike than can go fast for long periods of time, it will require a large battery: Exactly how big will depend on how fast and how far. To calculate the size of battery we need to know the desired speed and range. For example, let's figure on a constant-speed of 40 MPH and having a 50-mile range:

  1. At 40 MPH we will consume 67.4 watt-hours per mile. Multiply that by the distance we would like to travel: 67.4 x 50 = 3370 watt-hours, the required battery size.
  2. Take a nominal battery voltage (say 72V) useful to create 40 mph and divide the above watt-hours by the voltage: 3370 / 72 = 46.8 Amp-Hours
  3. Add 20% as a safety margin, and to allow for the gradual decrease in range over the 5-year life of the battery: We will need about 56 Amp-hours of battery at 72V nominal to create a useful range of 50 miles at 40 MPH. In Ebike tech, this is a VERY large battery.

The beauty though is that to increase our range for a given battery, all we have to do is reduce our speed: The same 72V- 56 Amp-hour battery will go 70% farther just by dropping down to 30 MPH. This is a very important option, particularly when facing unexpected stiff headwind; the smart practice is to drop gear and pedal more to extend our battery.

Safe Travels!