A bicycle is a machine. More correctly it is merely a power transmission device. The bike itself only translates power from the pedals to the rear wheel. The mechanism if properly maintained is highly efficient, meaning that there is little power loss through the assorted bearings, sprockets, or chain. Let us take away the human aspect of the bike and perform some simple calculations. Then as we understand what’s going on we can add varying levels of complexity. These levels of complexity will become evident as the assumptions are clarified.
So let’s begin. In fact let’s not play smoke and mirrors. Here is how you can lay this out in Excel to keep me honest. So just place this information in the cells indicated;
Descriptions/Field Labels;
A1 = Wheel Size
A2 = Chain Ring
A3 = Rear Cog
A4 = Crank Length
A6 = Total Drag
A8 = Constant Downward Pressure
B7 = Power Variance
A10 = Crank Angle
B10 = Force Required
C10 = Vertical Input
D10 = Output - Horz
E10 = Variance
Now for the values;
B1 = 700
B2 = 53
B3 = 16
B4 = 172.5
B6 = 7
B8 = 73.9
In cells A11 – A190 count from 1 to 180
B7 = D192 – B192
B11 = $B$6
C11 = $B$8
D11 = ((C11*((SIN(A11PI()/180))$B$4))*($B$3/$B$2))/($B$1/2)
E11 = D11-B11
Copy B11, C11, D11, E11 and paste down through B190, C190, D190, E190
B192 = SUM(B11:B190)
D192 = SUM(D11:D190)
Alrighty then what did you just do (or after you read this, what are you getting ready to do)….assuming that you actually followed the instructions……
That ugly formula in cell D11 calculates the force that is applied to the ground by the rear wheel as determined by the crank angle (A11), the gear ridden ($B$3/$B$2), the crank length ($B$4), the wheel size or diameter ($B$1) and the vertical force applied to the pedal (C11).
This tells us that it takes a constant (purely) vertical force of 73.9 #’s for this bike to equal 7 #’s of drag during half a crank rotation (180 degrees). Also that during 80 degrees of crank angle, the bike is producing insufficient power to fully overcome the drag (the bike is slowing).
For those of you who like Excel, create a graph to see the results.
Now go ahead have some fun. You can change the wheel size, gears, crank length, and total drag. Then change the force value in B8 such that the Power Variance in C8 remains close to zero.
Clearly this model is simplistic. It was meant to be. The intent here is to educate those who do not fully understand the concepts or math involved. As this model is more completely developed, hopefully more readers will grasp the concepts involved. With the data and calculations in Excel, anyone will be able to test the theories for themselves.
