# Equation for spring force for a cylinder on compressed air

• CK328
In summary, the conversation discusses the analysis of a Rock Shox Monarch RT3 suspension unit for a mountain bike. The shock uses compressed air as the spring, with adjustable pressure and a separate negative spring to reduce breakaway force. It also features adjustable compression and rebound dampers. The group is trying to model the air spring using F=P*A and Boyle's law, with the addition of the adiabatic gas constant gamma. They are also seeking a more accurate way to model the compression and damping forces.
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.

You just want to make sure that the adiabatic compression is applicable for the situation in hand.
Compressing the shock slowly - say by applying a load - will probably get you a different result to compressing suddenly like if the wheel hits a rock.

## 1. What is the equation for spring force for a cylinder on compressed air?

The equation for spring force for a cylinder on compressed air is F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

## 2. How is the spring constant determined for a cylinder on compressed air?

The spring constant for a cylinder on compressed air can be determined by dividing the force applied to the spring by the displacement it causes. This gives a measure of how stiff the spring is and how much force it exerts per unit of displacement.

## 3. What factors can affect the spring force for a cylinder on compressed air?

The spring force for a cylinder on compressed air can be affected by the spring constant, the displacement of the spring, and the force applied to the spring. Other factors that can impact the spring force include the air pressure inside the cylinder, the temperature of the air, and the material and design of the spring itself.

## 4. How does the equation for spring force for a cylinder on compressed air relate to Hooke's Law?

The equation for spring force for a cylinder on compressed air is a specific case of Hooke's Law, which states that the force exerted by a spring is directly proportional to the amount it is stretched or compressed. The equation F = -kx is a representation of Hooke's Law, where k is the spring constant and x is the displacement of the spring.

## 5. Can the equation for spring force for a cylinder on compressed air be used for other types of springs?

Yes, the equation F = -kx can be used for other types of springs in addition to cylinders on compressed air. This equation represents a general relationship between force and displacement for any type of linear spring, as long as the spring remains within its elastic limit and follows Hooke's Law.

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