# B Power needed to climb a hill

1. Mar 12, 2016

### stilbiker

Good Morning to evryboby.
What is the power needed to climb a 20° slope with a 100Kg electric bike + 100Kg for the driver?
Regards to all. Rudy

2. Mar 12, 2016

### Staff: Mentor

Hi stilbiker.

The power needed depends on how quickly you'd like the bike to travel up that slope. Do you have a desired speed in mind?

3. Mar 12, 2016

### Curiosity 1

m_total= 100kg + 100kg= 200kg
Assumption: The bike already has a steady speed (say 80km/h) before going up the slope ( before going up hill, the engine has been producing constant power for the bike to go steadily, constant power does not mean the bike will accelerate, as some of the energy produced is lost through vibration, noise etc until the total energy in the system is constant and so it is in steady state and does not accelerate ). The speed of bike is to remain the same during climbing. Assume the ADDITIONAL power needed is constant.

The additional power needed, P_needed is the work needed to be done per unit time to rise the elevation of the bike.

P_needed
= m_total*g*Δz/Δt

sinθ= z/s ,s is the displacement on the slope
z=s*sinθ
Δz= (Δs)(sinθ)

P_needed
= m_total*g*(sinθ)*(Δs)/Δt ,we want it to maintain speed (Δs/Δt) of 80km/h during the climb
= 200kg*9.81(m/s^2)(sin20)(80km/h)*[(1m/s)/(3.6km/h)]*[(1kW)/(1000kgm^2/s^3)] ,since 1kW=1kJ/s=1000kgm^2/s^3
= 14.91207825 kW

Don't worry about the unit conversion at first. You may "match up" the units to the SI base unit of Watt later.

4. Mar 13, 2016

### stilbiker

Hello NascentOxygen. Many thanks for you answer. the speed may be very low, just to access my house, let's say 5 Km/h.
best regards

5. Mar 13, 2016

### stilbiker

Hello Curiosity 1.
Many thanks for your answer. Wow 14 KW ! The bike will already have a steady speed (say 20km/h) before going up the slope ( before going up hill, the engine has been producing constant power for the bike to go steadily). The speed of the bike can fall to 5Km/h during climbing, only to reach my house.(about 500 m)
I already bought a 2 KW electric bike who's supposed be able to climb 20 deg. according to the specifications. IT FAIL!!! I intend to replace the motor with a stronger one.
But 14 KW hub motor is not available.
Best regards.

6. Mar 15, 2016

### Staff: Mentor

My figures show that at 5km/hr it will take about an extra 1kw to travel up a 20° slope than for the same speed on the level. (Then I'd throw in a 33% margin on the motor rating.) So do you have a way to measure the amps your bike draws at 5km/hr on a level road?

As far as bike motors go, I'd be a bit chary of the figures sellers may quote, especially if the motors come from China. Also, your batteries & controller may not be as ideal as you'd wish. What are the ratings for the batteries you are using?