## Summary of math formulas for calculating things for e-Bikes

DasDouble
100 kW
Posts: 1047
Joined: Jul 12, 2015 1:35 pm
Location: GERMANIA :D

### Summary of math formulas for calculating things for e-Bikes

So here real quick all sorts of math formulars I have written down in the past 2-3 years I figured out by myself for calculating stuff on my e-Bike.
Calculating the highest, possible speed you can get
DasDouble wrote:
Dec 20, 2015 6:19 am
I have tried myself on this to figure out the highest real speed I could get with 4kW motor.

P(Motor)=((A/2 x CW x D x v³)+(Cr x m x g x v)) x 1,11

P(Motor) = 4kW = 4000W = 4000
A = Stirnfläche des Objekts = face of the object = around 0,6m²
CW = Luftwiederstandswert = Air resistance = around 0,7
D = Dichte der Luft = Density of air = at 400 meters over the sea at 25 degree Celcius = 1,196 kg/m³
V = Geschwindigkeit = Speed = That´s what we want to calculate
CR = Rollwiederstandwert = Roll resistance = (downhill wheel with bad conditions) = 41 Watts
m = Masse = Weight of Rider and Bike together = (65kg + 44 kg bike) = around 110 kg.
g = Erdanziehung = gravity = 9,81
Verlustfaktor = Dissipation Factor = 1,11 at efficiency 89%.

RED COLORE = not real, surce on example motorcycle, google search motorcycle.
BlUE COLORE = personal value or just real data.
GREEN COLORE = differnt, not consistently data.

-When calculating it with your datas, you have to change the green marked data, and parts of the blue marked data.

4kW = ((0,6/2 x 0,7 x 1,196 x v³)+(41 x 110 x 9,81 x v)) x 1,11
4kW = (0,25116v³)+(44243,1v)) x 1,11
4kW = (0,25116v x 0,25116v x 0,25116v + 44243,1v) x 1,11
4kW = 4510,015938Vv x 1,11___________I /4510,015938
4000 / 4510,015938 = v x 1.11
0,8869148268 = v x 1,11_______________I / 1,11
0,7990223656 = v

=> 79,9 KM/H

Im just not shure if this means 79,9 km/h.
Tell me if you have something to add.
https://endless-sphere.com/forums/viewt ... =3&t=75005

Calculating the maximum amperage for your cable with a given cross-section in mm²
DasDouble wrote:
Dec 27, 2017 9:57 am
OK guys, so just here relly random the math formula to calculate the maximum amperage for your cable with a given cross-section in mm²:

Cross-Section of given cable (mm²) / 0,812(AWG20) * 11 (optimal °C) or * 16 (acceptable °C) or * 22 (poor/hot °C) => maximum amperage for your given cable.

For example I want to know how many amps I can push trough my AWG 10 cable so it becomes acceptable warm:

AWG 10: mm²: 5,26

-> 5,26 / 0,812 * 16 => 103,64 Amps.

How big is the cross-section of AWG x cable: https://de.wikipedia.org/wiki/American_Wire_Gauge
Source for the "0,812 value of a AWG20 cable": https://endless-sphere.com/forums/viewt ... 14&t=68005