ReStackor pro
Scaling of suspension systems:
Spring-mass-damper theory defines the parameters tau and zeta which control the response, feel and behavior of a suspension. Tau defines the oscillation frequency and is a function of mass and spring rate. Zeta defines the damping characteristics and is a function of mass, spring rate and damping. Changing spring rates in a stock suspension shifts the value of zeta and forces the suspension into an under-damped or over-damped condition. Correcting the suspension setup and restoring the suspension response, feel and performance the factory intended for your bike requires modifying the damping rates to return the value of zeta to the setup the factory intended.
Spring-Mass-Damper theory defines two parameters tau and zeta that control the ride, feel and response of a suspension.
Scaling Stock Suspensions
Weight scaling of a suspension setup determines the change in damping force needed to keep the values of tau and zeta constant and maintain the response of the original suspension setup. Getting the suspension natural frequency right (tau) is pretty straight forward. Tau is defined as the ratio of mass to spring rate (m/k). That ratio makes tau basically equivalent to race sag. If you setup your suspension to match the factory recommended race sag it will have the factory value of tau and the same natural frequency as the stock suspension.
High Speed Damping
At high speed the suspension needs to damp the un-sprung mass of the wheel. Since the wheel weight does not change the damping correction only needs to account for the change in spring rate. Setting the value of zeta to be equal for both suspensions gives:
Low Speed Damping
At low speed the shock needs to damp oscillations of the chassis. Getting the low speed value of zeta right requires adjusting the damping to correct for the change in both spring rate and rider weight. Since tau defines the ratio of mass to spring rate the definition of tau can be substituted into the expression for zeta and the damping correction written in terms of the change in spring rate.
Correcting low speed damping requires a larger modification to the damping rate to correct for both the change in spring rate and rider weight.
ReStackor pro Suspension Weight Scaling
The above relationships specify the change in damping force needed to correct for a change in spring rate. Using those relationships require the damping force of the baseline or stock suspension to be known and some way to estimate the shim stack modifications needed to produce the required damping force change.
This problem is custom made for ReStackor. The ReStackor weight scaling spreadsheet is shown below.
The ReStackor pro weight_scale.xls spreadsheet computes the damping performance of the baseline stock suspension setup, the damping force needed to setup the suspension for a spring rate change and the damping force produced by changes in the shim stack.
Weight scaling a suspension requires these steps:
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Enter the stock shim stack configuration in columns C and D and the details of the suspension valve geometry in cells H4 through K10. Click the "Run" and "Load_Output" buttons to compute the damping performance of the baseline stock configuration
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Enter the spring rate for the stock setup in cell M8 and the spring rate you want in cell N8. Click on the "Weight_Scale" button to compute the damping force needed for the new spring rate and the "Load_Output" button to load the calculation results into the Weight_Scaled tab of the spreadsheet.
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All of the plots in the spreadsheet are updated when you hit the Weight_Scaled "Load_Output" button.
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The damping force curve shows the damping force produced by the stock suspension setup (Uclk.stk) at the clicker settings specified in cell H10. The Uwo.stk and Uclsd.stk curves show the stock damping force with the clickers wide opened and closed.
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The dashed blue curve (F.trg) is the damping force needed for the new spring rate, the weight scaled damping rate.
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The final step is to hack on the shim stack configuration to determine the number of shims to add or subtract to match the target damping force curve. This simply involves modifying the shim stack configuration in columns C and D, clicking on the "Run" and "Load_Output" buttons, and inspecting the plots to see how close the new configuration is to the target curve.
It is that easy. The frames below step through the process.
One Face Shim Added To Baseline Stack
With one face shim added to the baseline stack the damping is slightly stiffer but short of the target damping rates. Matching the target stack is going to require more shims to be added to the stack.
Modifying shim stacks in ReStackor is as simple as adding shims to the stack and clicking on the "Run" and "Load_Output" buttons to see how close the shape and magnitude of the new damping force curve is to the desired damping profile.
Baseline Stack With Two Face Shims Added
With two face shims added the damping curve is close to the target stack stiffness at high speed. The low speed damping is too low. Getting more low speed damping is going to require modifications to the stack taper.
Adding two shims to baseline stack produces a damping force curve close to the target stack at high speed but the low speed damping is too low.
Oil Viscosity Effects On Damping Performance
Increasing the thickness of the clamp shim and the first to shims in the stack stiffens the low speed damping. Getting the high speed right requires removing some face shims to compensate for the stiffer stack taper. Getting the low speed right requires changes in the stack taper and increasing the oil viscosity from 7.5 wt to 10 wt.
A stiffer stack taper and oil viscosity increase from 5wt to 7.5wt is needed to match the weight scaled target stack stiffness.
For tuning a suspension you could just add face shims until the suspension stops bottoming. Weight scaling allows you to go a step further and preserve the low speed, high speed and damping profile the manufacture developed for your bike. While this may not be the optimum profile it usually provides a good starting point to begin the tuning process.
Weight Scaling Damping Rates of the Stock Suspension for a Rider of Different Weight
Spring-mass-damper theory defines two parameters that control suspension response.
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Tau defines the oscillation time constant of the suspension and will be the same for two riders of different weight if the spring rates are setup to produce the same race sag.
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Zeta defines the damping characteristics of the suspension and is a function of mass, spring rate and damping coefficient.
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Changing the rider weight and spring rate in a stock suspension drives the value of zeta into an under-damped or over-damped condition.
If two riders of different weight setup their bikes so that the values of tau and zeta match the suspensions will produce the same travel on any given bump and the same response, feel and behavior.
Manufactures spend millions setting up suspensions on their production bikes. Weight scaling provides a method to preserve that performance while correcting the suspension setup for a change in rider weight and spring rate.
ReStackor gives you the capability to determine the values of tau and zeta the suspension was designed around and scale those values to correct for changes in rider weight and spring rate. Setting up your suspension to restore the factory values of tau and zeta allow you to setup your suspension to deliver the ride performance, feel and behavior the manufacture intended for your bike.
Simple inputs - Thorough analysis - Practical results. ReStackor introduces a new era in suspension tuning.
