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Does the length of a shock not have anything to do with how much travel a bike has? I'm just curious because I've been looking at different bikes and the Trek Fuel EX 7 has a 210 x 55 shock and has 130mm of travel. I looked at a GT Force Elite 29 that has a 185 x 55 shock, but the bike has 150mm of travel. Also, the Slash 8 has a 230 x 62.5 shock and has 160mm of travel.

I'm just wondering how the GT achieves 150mm of travel with a shorter shock. Is it in the design of the frame?
 

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From a simple standpoint, a single pivot design is just a lever.

Think of it like a see-saw --- where you put the fulcrum (your pivot point) controls how high one side can move when you push down on the opposite end.

Linkage designs add a little more complexity if you're doing the math to calculate the path, but the end effect is pretty similar.

Azure Slope Font Line Plot
 

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Most every suspension frame has a shock linkage leverage ratio. Foes used to sell a frame with a 2:1 ratio and many other frames are over 3:1. For example, the Foes rear wheel travel was twice the shock stroke. To calculate rear wheel travel simply multiply the shock stroke length times the frame shock linkage leverage ratio. Foes claimed the lower ratio allowed for more precise shock tuning and a benefit of a higher ratio is a smaller lighter shock.
 
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