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ReStackor Sample Applications

Finally computer software to tune a shim stack

Spring Rate Selection 

The general wisdom of the motorcycling community suggest the following guidelines for a motorcycle suspension setup:

  • Fork:

    • 20 to 35% race sag

    • 0.25 to 0.75 inch spring preload

  • Shock:

    • 0.5 to 1.5 inches of free sag

    • 33% race sag

While the guidelines appear to recommend a specific spring rate based on your sag settings, actually applying them to a 180 lb rider turns out to pretty much span the entire range of spring rates available in the Race Tech or Eibach catalog.

Fork Spring Rate Range:

With 12 inches of travel, 25% race sag and a spring rate of 0.40 kg/mm the force produced by the fork spring for an MX suspension setup is:

Spring Rate With Maximum Preload:

If a softer spring is used the suspension is still required to produce 78.4 lbf of force at 25% race sag to hold up the weight of the bike plus rider. Increasing the spring preload to 0.75" at 25% race sag reduces the spring rate to:

Fork spring rate required for 25% fork race sag with 0.75" preload.

Spring Rate At Minimum Race Sag:

At 20% race sag the fork compression is reduced by 0.6". Since race sag is typically measured with the forks bleed there is no difference in the air spring force. The spring rate required at 20% race sag with a preload of 0.25 inches is:

Fork spring rate required for 20% race sag with 0.25" preload.

Setting the fork race sag between 20 and 25% allows a range of spring rates from 0.37 to 0.53 [kg/mm]. The range of spring rates available from the typical vendors are:

  • 0.38, 0.40, 0.42, 0.44, 0.46, 0.49, 0.52 kg/mm [Racetech]

  • 0.37, 0.39, 0.40, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.48, 0.50 kg/mm [Eibach]

Setting the fork race sag between 20 to 25% allows a range of spring rates that pretty much spans the entire range of springs available in the Race Tech or Eibach catalog. Specifying fork race sag between 20 to 25% provides little guidance in the selection of spring rates.

Shock Linkage Ratio

Link systems used in rear suspensions systems have created a lot of confusion in the motorcycling community. Multiple pivot points and complex bend angles along with model year to model year pre-production hype have led many riders to believe link systems produce complex shock compression profiles. The fact is link systems produce a nearly linear spring compression motion, especially in the range where race sag is set, and only kick up near the end of the stroke. At that point the bottom out bump rubber increases the "effective" spring rate more than the non-linear behavior of the shock linkage ratio curve.

Link systems used in MX suspension setups produces a nearly linear motion at the top of the stroke. kx450 data from www.supercross-online.de

Assuming a linear ratio of shock to wheel motion produces little error in estimation of spring rates when setting sag in a motorcycle suspension setup.

Shock Spring Rate Selection

The rear wheel force produced as the suspension moves from free sag to race sag is:

Change in rear wheel force from free sag to race sag.

Where LR is the ratio of shock travel to rear wheel motion. That ratio is nearly constant through the range ware race sag is set and allows the effect of spring rate changes to be easily estimated:

Effect of spring rate change on shock race sag:

To change the suspension free sag from 1.0" to 0.5" the change in spring rate is:

and to change from 1.0" to 1.5" free sag the spring rate is:

Increasing the spring rate one step (0.2 kg/mm) increases the free sag by 0.12 inches:

Any spring from 4.3 to 6.0 [kg/mm] can be used if free sag is allowed to vary over the 0.5 to 1.5 inch range. The range of spring rates available from the typical vendors are:

  • 4.4, 4.6, 4.8, 5.0, 5.2, 5.4, 5.7, 6.0 kg/mm [Race Tech]

  • 4.3, 4.5, 4.7, 4.9, 5.1, 5.3, 5.5, 5.7, 5.9, 6.1 kg/mm [Eibach]

The general wisdom of the motorcycling community suggests selecting the shock spring to keep your free sag in the 0.5 to 1.5 inch range. That range allows a 180 lb rider to use any spring in the entire race tech catalog and get a race sag of four inches and a free sag between 0.5 to 1.5 inches. These generic guidelines are extremely broad and of no help in selection of a spring rate. Determining the spring rate needed for your motorcycle suspension setup requires far more then setting your sag.

Suspension Response, What is the difference between the lightest and stiffest spring rate?

The fundamentals of spring-mass-damper theory provide the mathematical relationships needed to quantify suspension motion as a function of spring rate, damping and bump height. The equation below can easily be programmed into a spreadsheet to give you a tool that relates spring rate and damping to suspension travel.

For the range of fork spring rates estimated above the 0.37 [kg/mm] spring gives 25% race sag and a spring rate of 0.53 [kg/mm] gives 20% race sag. The change in the suspension bump travel for that range of spring rates is shown below. As expected, a softer spring produces a larger suspension motion.

Suspension response to an impulse blow can be directly computed as a function of spring rate and damping coefficient. Softer springs produce a larger suspension motion. 

Compression Damping Tuning

The suspension bump travel can be controlled by tuning the suspension compression damping. Through tuning of the shim stack the softer spring can be made to produce the same suspension bump travel. For this case compensating for the softer spring requires a 44% increase in the stock damping coefficient (c).  

Compression damping can be re-tuned to control suspension bump travel in a motorcycle suspension setup.

ReStackor can be used to figure out the shim stack modifications needed to correct the bump response for the soft spring rate case. The baseline case uses a simple tapered stack and produces a damping coefficient of 0.3 [lbf-s/in].

ReStackor pro calculation of compression damping coefficient for the baseline motorcycle fork suspension setup.

To increase the damping coefficient by 44% five 24.20 shims on the shim stack face were changed to a 24.30 thickness. With that modification the damping coefficient is pretty close to the target +44% compression damping increase needed for the softer spring rate.

ReStackor pro calculations used to estimate stack modifications needed to control suspension travel with softer spring rate.

For the stiffer spring the compression damping needs to be reduced to increase the suspension travel and match the suspension response of the baseline case. By tuning the compression shim stack the suspension bump travel for all three cases can be made to be the same. 

With modified compression damping all three spring rates produce nearly identical suspension bump travel.

With the compression bump travel matched it is easy to see the effect of spring rate on the suspension rebound response. The softer spring produces a slower response and that slower response is going to cause the suspension to pack. To avoid packing with the softer spring rate the rebound damping needs to be reduced.

Rebound Damping Tuning

The stiff spring uses light compression damping and stores the bump energy in the spring. This allows heavy rebound damping to be used to dissipate the bump energy on the suspension extension stroke. The light spring case uses heavy compression damping to keep the suspension from blowing through the stroke. With less spring energy in the light spring case the suspension has difficulty re-accelerating the un-sprung mass of the wheel on the extension stroke. For the case below the rebound damping was zeroed and the suspension was still unable to match the rebound response of the baseline case using the stock spring rate.

Re-tuning the fork rebound damping sets all three spring rates to have nearly identical suspension response.

A suspension setup with a stiff spring and light compression damping gets to the peak of the response curve faster. That faster wheel response allows the wheel to clear the top of the bump without jolting the bars. The baseline setup and softly sprun case user heavier compression damping and take longer go get to the maximum travel position. Since the wheel can't clear the top of the bump the bars feel a jolt. For plushness, selecting the stiffest possible spring that still uses all of the suspension travel and tuning that setup to use light compression damping and heavy rebound damping will produce the best ride.

Beyond these basic concerns of bump response there is forward weight transfer during breaking, rear transfer during acceleration, weave, wobble and response of the motorcycle chassis as well as the tire itself. Tuning of the entire setup and modification to the basic chassis dimensions that control the dynamic response of a motorcycle is an art that goes far beyond selection of spring rates. (Cossalter)  (Foale)

Summary

Through tuning of the compression and rebound damping both the soft and stiff spring setups can be made to produce identical bump travel and nearly identical suspension response times. Soft springs require heavy compression damping and light rebound damping. At the limit, soft spring rates are not able to produce the wheel acceleration rates needed in the rebound stroke to keep the suspension from packing.

Stiff springs with light compression and heavy rebound damping produce the fastest suspension response and the plushest ride. The trick in setting up a motorcycle suspension is to find the stiffest possible spring that still uses all of the suspension travel for the speeds and terrain that you ride. For a trail setup at low speed a light spring will be needed to insure the suspension uses all of the travel. For the higher bike speeds of a desert suspension setup a stiffer spring is needed to keep the suspension from bottoming.

 

Spring Rate Selection

Conventional wisdom suggest the following range for setting your sag:

  • Fork race sag: 20 to 25%, 0.25 to 0.75 inch preload.

  • Shock free sag: 0.5 to 1.5 inch, 4.0 inch race sag.

That range of sag and preload allows a 180 lb rider to pretty much use any spring in the Race Tech catalog and produce a suspension within the above range. Through tuning of compression and rebound damping the suspension can be made to produce nearly identical bump travel and rebound response times for any of the setups. 

Selection of the optimum spring goes far beyond setting your sag. Selection of a spring rate depends on how your bike handles, the speed that you ride and the range of terrain that you ride on:

Fork

  • If your fork spring rate is too stiff there will be little forward weight transfer on a corner entrance and the front wheel will push or skip over bumps.

  • If you fork spring rate is too soft the bike will tuck.

Shock

  • If the shock spring is too soft the suspension will fall onto the rear wheel under acceleration, pull the front wheel off the ground and run wide on a turn exit.

  • If the shock spring is too stiff there will be little weight transfer to the rear wheel under acceleration and the bike won't hook up. 

Spring rate selection is heavily influenced by the speed and terrain that you ride. If you are a trail rider hitting stuff at low speed a very light spring is needed to exaggerate weight transfer and get the front and rear wheels to properly load on a corner entrance or exit. Attempting to use those same spring rates in a 40 mph desert sand wash is going to cause the fork to tuck. Higher speeds require stiffer springs. Discovering the spring rate that works for the range of terrain and speeds that you ride requires tuning, plenty of seat time and acquiring a library of spring rates to experiment with to allow you to find that magic combination that matches your riding style, speed and terrain.

Once you have the combination of front and rear springs that strike the best compromise between the fork pushing or tucking and rear wheel traction the compression damping can be tuned to control bottoming and the rebound damping tuned to dissipate as much bump energy as possible just short of packing the suspension. Optimum response and the plushest ride require the stiffest possible spring that still allows the front to back weight transfer needed to optimizes handling. Discovering the spring rate that produces that balance for your suspension setup and speed and terrain that you ride goes far beyond setting your sag or the suspension sags of a generic recipe.