I am trying to calculate the maximum braking force/deceleration for a bicycle. Note: the question assumes only the front brake is used
Free body diagram:
For dry tarmac where I know there is enough grip to get the rear wheel to lift I managed to calculate the max deceleration (result=6.8m/s^2). (this is the deceleration where all weight is transferred onto the front wheel (rear wheel will start lifting up at higher deceleration)).
From the moment equilibrium equation (using the front tire contact patch as the origin) I got the following equation for maximum deceleration before the rear tire starts lifting off (assuming there is enough grip):
I used this to calculate max deceleration in dry conditions
However I am now trying to calculate the max deceleration in wet weather (lower coefficient of friction) where the front wheel slipping should be considered as an option.
I tried expressing Nf (normal force on front wheel contact patch) in terms of a (deceleration) and got the following result:
Assuming that there won't be enough grip (in the wet) to make the rear wheel lift up.. I can then use Nf to determine Fbr (braking force). To determine maximum deceleration (assuming wheel slip occurs before rear lift up) I can use the equilibrium of forces in x-direction:
ΣFx=0=Fa-Fbr =ma-μNf --> a=μ*Nf/m
My questions: - Are my assumptions/calculations correct? If so: is there a better/faster way of doing this? To check if the rear wheel lifts up or if the tire slips first I will compare the max deceleration for slipping tire scenario and max deceleration for lifting rear wheel scenario and see which deceleration has a lower deceleration value to see which scenario will happen first
When braking some weight is transferred from the rear to the front wheel, but if the deceleration is too high the front wheel will slip. Gently increasing brake pressure will lessen the chance of front wheel slipping...
How should I go about determining max deceleration without the front wheel slipping, given a certain friction coefficient μ ? I can calculate the max braking force without slipping for a given Normal force on the front wheel but as soon as you start braking this normal force changes due to weight redistribution and I don't know how to account for this.
Thank you very much for any input! It is greatly appreciated