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Electricity concepts for electric bikes: W, Wh, A, Ah, V

Electricity Concepts

Electric current cannot be seen. To try to visualize it more intuitively, let's use a dam as an example. The height of the water in the reservoir determines the pressure. When the water height decreases in the reservoir, the water flow rate at the outlet of the dam decreases. To increase the water flow rate, simply reduce the diameter of the outlet: we all did this as children, playing with the garden hose!

The Basic Formula

Let's summarize: The water pressure at the outlet of the dam depends on the water height in the reservoir and the outlet diameter.

> In electricity, the principle is similar:

Power (water pressure) = Voltage (water height) x Current (outlet diameter).

> Power is expressed in watts (W), voltage in volts (V), and current in amperes (A). This gives:

Watts = Volts x Amperes, or W = V x A

> From this formula, we can also calculate:

Volts = Watts / Amperes, or V = W / A
Amperes = Watts / Volts, or A = W / V

Calculate the power in Watts (W)

The output voltage (V) and current (A) are always indicated on the label of your electric bike's battery charger.

EXAMPLES

With a 36V Li-ion battery charger:
Voltage: 42 V
Current: 2 A
> Power: 42 V x 2 A = 84 W

With a 48V Li-ion battery charger:
Voltage: 54.6 V
Current: 2 A
> Power: 54.6 V x 2 A = 109.2 W (110 W rounded up)

Calculating the Available Energy Amount (Wh)

How do we determine the battery life or the time required to charge a battery? To do this calculation, we need to factor in the time factor into the formulas, and this is where we'll use the capacity expressed in Ampere-hours (Ah) and the amount of stored energy in Watt-hours (Wh).

Here is the formula:

Wh = V x Ah

From which we can deduce:

Ah = Wh / V and V = Wh / Ah and also h = Wh / W

EXAMPLES

What is the energy stored in a 36V, 10Ah battery?
> 36V x 10Ah = 360Wh.

What is the capacity in Ah of a 576Wh, 48V battery? > 576 Wh / 48V = 14 Ah

What is the average consumption per km if you can travel 110 km with a 576 Wh battery?
> 576 Wh / 110 km = 5.23 Wh/km

If a solar panel produces 50W for 5 hours, how much energy is produced?
> 50 W x 5 h = 250 Wh

What is the charging time for a 360 Wh battery with an 84 W charger?
> 360 Wh / 84 W = 4.28 h or 4 h 17 min (0.28 x 60 min = 17 min)

What is the charging time for a 480 Wh battery with a 110 W charger? > 480 Wh / 110 W = 4.36 h or 4 h 22 min (0.36 x 60 min = 22 min)

How long does it take to charge a 96 kWh electric car battery with 4 kW of solar panels producing an average of 20 kWh/day?
> 96 kWh / 20 kWh = 4.8 days or 4 d 19 h (0.8 x 24 h = 19 h)

Losses

The results of all these calculations must be put into perspective. Indeed, any energy transfer in an electrical circuit induces losses (in the form of heat), and battery capacity depends on many factors (temperature, state of charge, aging, etc.). It is quite difficult to accurately estimate these losses, but a safety margin of between 10 and 20% can be taken into account in your calculations.