E Bike Battery Sizing Calculations

Calculating How Far a Battery Will Go on a Single Charge (Metric System)

To calculate how far your ebike will go on a single charge, consider several factors, including battery capacity, efficiency, terrain, and riding style. Here’s a step-by-step guide on what you need to know and how to work it out using the metric system:

Key Factors to Consider

Battery Capacity (Wh)

• Definition: The total energy the battery can store, measured in watt-hours (Wh).
• Calculation: Battery capacity (Wh) = Voltage (V) × Amp-hours (Ah)
• Example: A 36V battery with 10Ah capacity has 36V × 10Ah = 360Wh.

Motor Power (W)

• Definition: The rated power of the motor, typically measured in watts (W). Common ebike motors range from 250W to 1000W and beyond.

Average Power Consumption (Wh/km)

• Definition: The average power your ebike consumes, measured in watt-hours per kilometer (Wh/km).
• Typical Range: Depends on motor power and efficiency. For a 250W motor, it might be around 10 Wh/km, while a 500W motor might consume closer to 15 Wh/km, and a 1000W motor might consume 20 Wh/km or more.

Efficiency

• Definition: Efficiency of the motor and controller, typically around 70-90%. This can be factored into the average power consumption.

Riding Conditions

• Terrain: Flat terrain consumes less power than hilly terrain.
• Speed: Higher speeds consume more power.
• Rider Weight and Cargo: Heavier loads increase power consumption.
• Wind: Headwinds increase power consumption.

Steps to Calculate Range

1. Determine Battery Capacity:

   • Use the formula: Voltage (V) × Amp-hours (Ah) = Watt-hours (Wh).

2. Estimate Average Power Consumption:

   • Use an average value based on the motor power and typical riding conditions (e.g., 15 Wh/km for a 500W motor).

3. Calculate Theoretical Range:

   • Theoretical Range (km) = Battery Capacity (Wh) / Average Power Consumption (Wh/km).

4. Adjust for Efficiency:

   • Adjust the theoretical range based on efficiency. If efficiency is 80%, multiply the theoretical range by 0.8.

Example Calculation

Suppose you have a 52V battery with a 14Ah capacity, and you're using a 500W motor. Let's estimate the range with an average power consumption of 15 Wh/km on moderately hilly terrain.

1. Calculate Battery Capacity:

   • Battery Capacity = 52V × 14Ah = 728Wh.

2. Estimate Average Power Consumption:

   • Average Power Consumption = 15 Wh/km (for a 500W motor).

3. Calculate Theoretical Range:

   • Theoretical Range = 728Wh / 15 Wh/km = 48.53 kilometers.

4. Adjust for Efficiency:

   • If the system is 85% efficient, adjust the range:
   • Adjusted Range = 48.53 kilometers × 0.85 = 41.25 kilometers.

So, with a 52V 14Ah battery and a 500W motor, you can expect to travel approximately 41.25 kilometers on a single charge under these conditions.

Comparative Analysis of Different Battery Systems

Let's compare three identical motors, each rated at 2000W, but powered by different batteries (36V, 52V, and 72V), all with a 20Ah capacity.

Key Factors to Consider

Battery Capacity (Wh)

• 36V Battery: 36V × 20Ah = 720Wh.
• 52V Battery: 52V × 20Ah = 1040Wh.
• 72V Battery: 72V × 20Ah = 1440Wh.

Average Power Consumption (Wh/km)

• 36V System: 35 Wh/km (due to lower voltage requiring higher current).
• 52V System: 30 Wh/km.
• 72V System: 25 Wh/km (higher voltage typically means lower current draw for the same power, leading to increased efficiency).

Calculating Range

1. 36V System:

   • Theoretical Range = 720Wh / 35 Wh/km = 20.57 kilometers.
   • Adjusted Range = 20.57 km × 0.85 = 17.49 kilometers.

2. 52V System:

   • Theoretical Range = 1040Wh / 30 Wh/km = 34.67 kilometers.
   • Adjusted Range = 34.67 km × 0.85 = 29.47 kilometers.

3. 72V System:

   • Theoretical Range = 1440Wh / 25 Wh/km = 57.6 kilometers.
   • Adjusted Range = 57.6 km × 0.85 = 48.96 kilometers.

Summary of Results

• 36V System: Approximately 17.49 kilometers on a single charge.
• 52V System: Approximately 29.47 kilometers on a single charge.
• 72V System: Approximately 48.96 kilometers on a single charge.

Which is the Most Economical and Why?

72V System: The 72V system is the most economical in terms of range per charge. Here’s why:

1. Higher Efficiency: Higher voltage systems typically operate more efficiently because they draw less current for the same power output. This reduces energy losses in the system.
2. Better Energy Utilization: With higher voltage, the same amount of stored energy (watt-hours) is utilized more effectively, leading to longer range.
3. Lower Current Draw: A higher voltage system requires lower current to produce the same power, which means less stress on the components and lower heat generation, contributing to overall efficiency.

Practical Tips

• Use Online Calculators: Several online range calculators allow you to input specific details for a more precise estimate.
• Test Real-World Range: Actual range can vary based on real-world conditions. Test your ebike under typical riding conditions for a more accurate measure.
• Monitor Power Usage: Use a display or app that shows real-time power consumption to adjust your riding habits for better range.

By understanding and applying these principles, you can make informed decisions about which battery voltage and capacity will best meet your ebiking needs