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I wanted to design an ebike with good enough specs to satisfy my requirements, my first consideration was the power required to move the bike at my required speed and from there I can choose a motor.

I started by setting the max speed, max total weight (rider + bike), and acceleration:

  • Top speed: 50 km/h, 13.88 m/s
  • Maximum weight: 200 kg, 1,974 N
  • Acceleration: 0-50 km/h in 30 sec, ~ 0.5 m/s^2

Then what forces to consider:

  1. Drag.
  2. Friction.
  3. Force required to reach the required speed.
  4. As the force required to overcome inclination of the ground is regained, I decided to neglect it.

To calculate each one I used rough conditions. Here is how I calculated each one of the forces:

F1:

Equation : ( (air density) (wind resistance coefficient) (Area) (wind velocity)^2 ) / 2

1. air density: 1 kg/m^3
2. coefficient: ~ 1
3. Area: ~ 0.5 m^2
4. (wind velocity)^2 : average 15 km/h + max speed = 65 km/h, ~ (18)^2 = 324 m/s

Total = 81 N

F2:

Equation: (coefficient of rolling resistance) (mg) 
1- coefficient: ~ 0.01
2- mg: 1,974 N

Total = 19.74 N

F3:

Equation: ma
1- ma : 100 N

Total = 100 N

Ftotal = 200.74 N

Ptotal = Ftotal * Velocity = 2,786.27 W, ~ 3.75 HP

Here is where I stalled. I think this power is the power required to move from rest to the required velocity, then the momentum will keep the bike moving and the power it will consume would be the power required to overcome friction and drag, which is around 1.4 kW.

What did I miss and is there a flaw in these calculations?

1400 W to maintain my speed sounds a lot to me. What does the total power of 2,786 W mean in W per hour and what motor power do all these calculations translate to?

Where does work and K.E. fit into these calculations, if relevant?

P.S. I know that there are inefficiencies in the bike, the motor,and in energy getting lost converting from electrical energy to mechanical energy, but it can be considered later.

Edit 1:

What I meant by "what does 2,786 W mean in W/h" is if I was choosing a motor do I need it to be able output 2,786 W of power or I can divide it as it is a quantity of energy.

Edit 2:

I calculated Kinetic Energy ~ 5 W/h or 20kJ and work with 1 km displacement to be ~ 56 W/h or 200kj.

Work might be correct as the numbers seem close to typical ranges, but K.E. Is really small.

I think my calculations are flawed because I use constant values Ie. When I start driving the wind wouldn't be 65 km/h, but thankfully I think it can be solved by integration of wind velocity squared vs time (not sure yet I will do calculations and post it) .

Also if it had 2,786 W - 1,400 W of power as momentum, when I brake I will experience 1,386 W of power divided by time I take to stop which if we set to 3 sec as an arbitrary value I will experience ~ 45 kg if I braked in a distance of 1 meter for 3 seconds continuously and that is if the tire's sliding friction allows for it (I think, but please correct me if I'm wrong)

I know that W/h is energy, which gets consumed from the battery, I'm asking for it because of peak power requirements as @johnBreakhead commented, which is the more appropriate term.

P.S. All the inefficienies will be calculated later and I will divide the total power by it to get the final peak power.

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  • \$\begingroup\$ There are lots of calculators that determine the power to cycle at a particular speed. Look in the cycling stack exchange or Google "bicycle performance prediction calculator" \$\endgroup\$
    – D Duck
    Jul 11, 2022 at 8:08
  • \$\begingroup\$ I searched a couple, they give different answers I want to make a calculator of my own which I can reach a relatively close answer I inputed close values to the above, also I want to be able to calculate it at any condition for different vehicles and I can use the same equations for any type of motor not only electrical, but thanks It will be helpful to compare my values with them. \$\endgroup\$
    – AhmedH2O
    Jul 11, 2022 at 8:13
  • \$\begingroup\$ I can get 50 kph on a derestricted Bosch 250 W system with leg assistance. Bear in mind that a bike's drive train and wheels will not be rated for more than a human can give (300 - 500 W for very fit rider and typically < 150 W for normal rider). Coming off at 50 kph may result in very serious and permanent injury. \$\endgroup\$
    – Transistor
    Jul 11, 2022 at 8:25
  • \$\begingroup\$ No such thing as watt per hour. Do you mean energy as in watt-hour? Also, your 3 is just the result of 1 and 2. \$\endgroup\$
    – winny
    Jul 11, 2022 at 9:34
  • \$\begingroup\$ Keep in mind regulations around max speed for e bikes. e.g things get complicated above 25kph around here. \$\endgroup\$
    – Mat
    Jul 11, 2022 at 9:52

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