# Mathematical modeling of a mountain bike rear shock

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1. Apr 8, 2016

### CK328

Evening all,
I've recently undertaken a project where my roll is to analyse the suspension of a mountain bike. The suspension unit in question is a Rock Shox Monarch RT3. To give a brief summary:

The shock uses compressed air as the spring, the pressure is adjustable via an air valve.
The shock also has a negative spring- a separate air chamber which opposes the main spring and reduces the breakaway force to get the shock moving.
The shock features adjustable compression and rebound dampers.

The first thing is to try and model the air spring. Currently, to find the force on the piston, I'm using F=P*A.
Then I'm using Boyle's law P1*V1=P2*V2 to model the compression.
Since the compression is not isothermal, I've added the adiabatic gas constant gamma.
P1*V1^gamma=P2*V2^gamma.

I want to get a decent Force/Displacement graph for the air spring so my final formula is:
F=P0*A*(V0/(V0-chang in V)^1.4
where P0 is the initial pressure and V0 is the initial volume.

If anyone can offer a more accurate way to model the compression of a gas please let me know!

I also don't really know where to start with modelling the damping forces other than F=cv so anyhelp would be greatly appreciated.

Cheers.

2. Apr 13, 2016