Why is motion ratio squared?

[scorp997]

Can anyone smarter than me explain why motion ratio is squared instead of just based on the ratio itself?

Isn’t this just a simple lever which would multiply the spring rate to provide wheel rate? I’m sure m missing something, please enlighten me..

[2BWise]

It is because the calculation drives from the natural frequency of the suspension. The link below covers the discussion around how you choose spring rates from the desired natural frequency.

https://optimumg.com/springsdampers1/

[DaveW]

Can anyone smarter than me explain why motion ratio is squared instead of just based on the ratio itself?

Isn’t this just a simple lever which would multiply the spring rate to provide wheel rate? I’m sure m missing something, please enlighten me..

The deflection at the spring AND the lever ratio are affected equally by the motion ratio. So, since they are multiplied by each other to give the change in force at the wheel relative to that at the spring, it's MR^2.

[alangbaker]

Can anyone smarter than me explain why motion ratio is squared instead of just based on the ratio itself?

Isn’t this just a simple lever which would multiply the spring rate to provide wheel rate? I’m sure m missing something, please enlighten me..

Because you're changing both the force that results AND the distance over which it changes.

Take a simple 2:1 motion ratio and a 1000 lb/in spring.

The wheel moves 2 inches for an inch of shock movement.

So if the wheel moves up by an inch, the shock moves 1/2 inch and the force rises by 500 lb.

But because of the lever, the force on the wheel only rises by 500/(2/1).

So relatively, the wheels moves twice as far and gets half the force.

Ergo: wheel rate is spring rate divided by (or mulitplied by depending on how you define your term) motion ratio squared.