What is the equation for the energy needed to operate a bicycle?

I saw in a magazine an equation that detailed the forces for the operation of a bicycle. I can't determine what the equation is because I know nothing about kinetic mathematics or advanced algebra. This is for a tattoo I want to do. There is an equation I know it, I saw it in Tattoo Magazine or somewhere
 
I tried deriving this: A bike is in static equilibrium, that is it will not fall left or right because it is in forward motion. So start with motion:length over time times mass.l/s*m
Umm
I forget the rest, I'll see if I can find something

FOUND SOMETHING!
http://audiophile.tam.cornell.edu/~als93/FYEO/MeijaardPapadopoulosRuinaSchwab2007.pdf

lots of lowercase greek letters, you're in trouble
 
kinetic energy = 1/2 mass * velocity ^2
=1/2 (your mass+bicycle mass) * (your desired velocity not more than 30km/hr)
say your total weight is 80kgs and your velocity * 50m/s^2
=1/2 * 80 * 50^2
=1/2*8000
=4000 joules
additional information an average man can produce about 1/10 of a horse power that is around 75 watt
but total useable is only 60 watt
that means you are useing 60 watt of power to ride your bicycle
 
do you mean how big of a motor?
it depends, how fast, a small child, a big guy, going up hill, down hill?

electric bikes use 200Watt motors.

Guru
 
If you have an Olympic training center or college that studies this , they will have that information. They are able to analyze riders and calculate improvements based on EVERYTHING so they must have methods and equations to run in the computers.
 
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