Mysteries of early GSX-R750 suspension unraveled.

This time I'll be taking you inside the mysteries behind the GSX-R750F/G/H suspension system that uses the excenter. I always thought the excenter had two functions...
1.) to compensate for the different arc that the swingarm and the lower shock pivot travel.
2.) to create a progressive suspension system

I started plotting travel of the shock against travel of the rear wheel and came up with the graph on the right. As you can see the line is almost straight (I inserted the dotted line for comparison) and doesn't follow a progressive curve. So the early GSX-R's just use a very expensive alternative for the tie-bars Suzuki use now, that also isn't progressive.

The standard shock is 290mm long and has 55mm travel. A shock as long as 300mm is possible, but the spring will probably touch the link pivot that attaches to the frame lightly.

The second reason for wanting to know this because now we can calculate various important figures from these data, like what kind of spring we need.

Here is how to calculate the spring rate...

First we figure out the linkage ration, which means how much the shock moves in relation to the rear wheel.

Linkage ratio = damper travel / wheel travel = 60 / 133 = 0,45

Spring rate = axle load * 2 / wheel travel / linkage ratio

I assume weight distribution front/rear = 50/50
My bike weighs 200kg ready to rock and I weigh 100kg, so the axle load is (200+100) / 2 = 150kg
In this formula the wheel travel means rear wheel travel minus sag. Most shocks have 55mm stroke which according to my table means we have 124mm minus 25mm sag = 99mm wheel travel.
The 2 comes from 2G, the point at which the suspension will bottom out. That means when the suspension has to cope with a force twice the weight of the bike it will hit the bumpstop. Somebody who jumps over buses for a living chooses a higher value than 2, but for a track- or streetbike this is a good starting point.

This brings us at 150 * 2 / 99 / 0,45 = 6,73kg/mm
1,36 * 9,8 = 66N/mm
13,33 * 5,71 = 376lb/in
...which in turn means that every mm that the coil is compressed it gains 6,73kg resistance.

The standard spring is a calculated 6,94kg/mm or 400lb/in, which is about right.

You can calculate spring rate with the followin formula: 80000*d^4 divided by 8*n*D^3
Where d = wire diameter, n = number of active coils and D is the coil center diameter.

You may remember the formula F1*L1=F2*L2 which in turn implies that if we want to keep the rear wheel up we need a force of 150 * 133 / 60 = 332kg to keep the bike up. 332 / 6,73 = 49,3mm... this is the amount of preload we'd have to put onto the spring.