ReStackor Suspension Bottoming Response

There are two ways to bottom a suspension:

  • Hit a bump hard enough to bottom the wheel

  • Hit a landing hard enough to bottom the chassis

Wheel bottoming calculations start from race sag, where all bumps start, and figure out the initial wheel launch velocity that produces enough momentum to blow through the compression stroke and tap the specified “Max Stroke” position at a final velocity of zero. On compression the wheel momentum fights the suspension spring rate, gas force and compression damping of the fork or shock. 

From the "Max Stroke" position ReStackor calculations continue into the rebound stroke computing wheel velocities as the suspension returns to the normal suspension ride height. Rebound velocities are noted by solid lines and compression velocities by dashed lines in the suspension response curves.

Chassis bottoming calculations determine the free fall impact velocity necessary to compress the suspension from full extension to the specified “Max Stroke” position. The calculations also compute the rebound stroke to determine rebound velocities as the chassis returns to the normal ride height. Chassis bottoming response are shown by the green curves.

Symbols on the plot mark the time required for the suspension to return to the normal “race sag” ride height. For the crf250 example above the chassis cycle time is approximately 0.2 seconds. Over that 0.2 seconds the weight of the rider is not considered to be connected to the chassis. Instead the rider is assumed to be hovering over the chassis as the chassis oscillates beneath the rider over the bump. Stiffer springs used for a heavier riders effects chassis response, but rider weight does not.

An important output of the response calculations is determining the bump velocity where the chassis bottoms (aka low speed damping) and the velocities where the wheel bottoms (aka high speed damping). Those velocities define the tuning range of the shock. There is no point in tuning the shock beyond those velocities as the suspension is bottomed out and at that point the bump rubber is controlling suspension motions, not the shock.

Suspension link ratio

Link ratios in ReStackor suspension response calculations are determined from inputs of shock and wheel position measurements. At least four measurements are needed. More measurements (up to 39) improve the fidelity of the link ratio curve.

ReStackor curve fits the wheel position measurement data and any data points that are more than 5% off the “average curve” are flagged with green data point symbols. Those measurements should be double checked to insure accuracy. The final wheel position input is the spec’d suspension max travel and shock stroke length. Those inputs define the max travel limits for ReStackor calculations.

An important point to mark in the position measurement data is the stroke depth where the suspension hits the shock bump rubber. Up to that point suspension motions are controlled by the spring and shock. Beyond that point suspension motions are controlled by the stiffness of the bump rubber. For practical tuning suspension velocities at the bump rubber stroke depth define the tuning range of the shock.

On a fork the cosine of the fork rake angle defines the link ratio. That angle defines how far the wheel moves vertically for a given change in fork stroke position and remains constant over the fork stroke. When computing that value in a spreadsheet it is important to recognize spreadsheets measure angles in radians. To convert degrees to radians multiply by pie/180 (radians= fork degree*3.14159/180). Fork link ratios are input the same way as a shock using a table of wheel position versus shock position measurements.

Shock shaft velocity at suspension bottoming

Suspension bottoming velocities are reported in terms of suspension wheel speed and shock shaft velocity. The shocks low speed damping range is defined by the range that controls chassis bottoming and the high speed range controls wheel bottoming. At bottoming there are two shock shaft velocities of interest: the maximum compression velocity; and the maximum rebound velocity.

ReStackor suspension response calculations mark those velocities on the shocks damping force curve. For the example below the wheels bottom on the compression stroke at a shaft velocity of 110 in/sec and the maximum rebound velocity is 35 in/sec. Marking those limits on the damping force curve are a simple check to insure ReStackor pro damping force calculations have been run over the appropriate range. There is no point in computing damping force values beyond those limits as the suspension is bottomed out.

The chassis bottoming velocity (low speed damping) and wheel bottoming velocity (high speed damping) are important limits to mark on the shocks damping force curve. Understanding shaft velocities where those limits occur allow shim stack ring-shim preload to be tuned to control the appropriate range of low speed damping to get control of the chassis and tuning of crossover gaps to control the appropriate high speed range for wheel damping. Visualizing where those transitions occur are on the shocks damping force curve makes tuning easier and more effective.

Suspension response coefficient

Suspension response is easier to understand when viewed through the simplifications of spring-mass-damper theory. Spring-mass-damper theory defines suspension response in terms of zeta, aka % critical damping. Zeta combines the effect of mass, spring rate, link ratio and damping into a single parameter. The value of that parameter (zeta) instantly tells you how the suspension will behave:

  • Zeta values greater than one are over damped. Over damped suspensions respond slowly making for poor compliance, a harsh ride and a setup prone to packing. The feature of over damped is the suspension will not oscillate or baby-buggy after a bump.

  • Zeta values less than one are under damped. Under damped suspension respond faster which minimizes packing and gets the wheels back on the ground faster improving bump compliance. The problem is the suspension will baby-buggy after a bump and that reduces rider feel for what the chassis is doing.

  • Zeta values of 0.707 or higher, formally one/sqrt(2), damp resonance motions in the suspension. Zeta values less than 0.707 allow resonance modes to amplify producing suspension motions that are larger than the bump driving the suspension. Zeta values around 0.7 are the magic value producing stiff enough damping to control resonance and the fastest possible response to minimize packing and improve suspension compliance.

Tuning suspensions in terms of zeta combines the effect of spring rate, mass, damping and link ratio into a single parameter (zeta) and the value of that parameter tells you how the suspension will respond. Bikes with different weights, spring rate and damping will produce the same suspension response, feel and behavior if the value of zeta is the same. Zeta provides a simple reference for comparing suspension setups between bikes and scaling suspension setups from one bike to another.

The problem in modern suspension systems is the value of zeta changes over the stroke due to the shape of the shocks damping force curve and the change in link ratio over the stroke. ReStackor analysis of a 9 inch crf250 suspension stroke provides an example. As the suspension rolls into the rebound stroke at a depth of 9 inches, zeta values spike into the over damped regime at values around 1.5. That spike is caused by the high damping coefficient of the shock at low velocity and the increase in link ratio with stroke depth. As the suspension accelerates into the rebound stroke the value of zeta falls to end up near critical damping for the wheels on return to the suspension normal ride height. The race sag normal ride height is marked on ReStackor plots by the symbols on the suspension response plots.

The nonlinear zeta behavior through the crf250 suspension stroke is almost entirely due to the link ratio variation over the stroke. That can be demonstrated by re-running the above case with a constant link ratio. When the link ratio is held constant the value of zeta turns out to be nearly constant over the entire suspension stroke.

For short strokes around the suspension normal ride height link ratios don’t change much and the chassis is lightly damp at zeta values around 0.6 (green curve). When driven deeper into the stroke the increase in link ratio drives zeta values into the 0.8 range. That helps stabilize the chassis on large hits. As the suspension returns to the normal ride height the drop in link ratio reduces zeta to a lightly damped condition and that improves suspension compliance on small bumps.

Modern linked suspension systems create zeta values that change with stroke depth. Zeta values at the normal ride height are an important parameter in quantifying suspension response for  small bumps oscillating around the normal ride height. ReStackor marks those values on the suspension response plots. For larger bottoming strokes suspension link ratios create large changes in the instantaneous value of zeta. For larger strokes ReStackor determines the stroke averaged zeta coefficient (zetaC) that quantifies the effect of variable zeta coefficients over the stroke.

Stroke averaged zeta coefficient

ReStackor determines the stroke averaged zeta value by creating an equivalent suspension setup that runs a constant link ratio and damping coefficient over the stroke and adjusts zeta so that the suspension goes through the same stroke, in the same amount of time and returns to the normal ride height at the same final velocity. That creates a stroke averaged zeta coefficient that dissipates the same bump energy, in the same stroke, in the same amount of time. ReStackor labels the stroke averaged zeta coefficient as zetaC in the suspension response curves.

Stroke averaged zeta values are created through an internally automated series of calculations that run progressively deeper stroke depths to determine the stroke averaged zeta coefficient over the range of suspension motion from race sag to bottoming. Results of those calculations are shown on the stroke averaged zeta plot along with the instantaneous zeta value for each stroke on return to the race sag position.

The difference between the stroke averaged at instantaneous zeta quantifies the bump energy dissipated by the nonlinear link ratio deeper in the suspension stroke. For the example above that works out to a zeta increase of about 10% to 20% with the effect maximized at a stroke depth around 8 inches.

In terms of suspension tuning the bottom line of the above crf250 example is the chassis is damped at zeta values around 0.7 and the wheels are over damped at zeta values near 1.2.

Suspension Tuning Secrets

For suspension tuning there are several “rules of thumb” used to setup a racing suspension system. The first “rule of thumb” is chassis rebound damping should be around zeta values of 0.7. Higher zeta values in the 0.8 range give a tighter suspension feel at the expense of packing, compliance and a harsh ride. Lower zeta values in the 0.6 range improve suspension response (compliance) but the suspension will baby-buggy after a bump loosing "feel" for what the chassis is doing.

The basic problem in suspension tuning is when the shock is stiff enough to produce chassis damping in the 0.7 range the lighter weight of the wheels end up over damped. The usual compromise is set chassis values in the 0.7 zeta range and do what you can tuning the shape of the shocks damping force curve to minimize wheel over damping at high speed.

Rebound/Compression Damping Ratio

A second “rule of thumb” is the ratio of rebound to compression damping should be around 2.0. The thinking behind that rule is on the compression stroke the wheel motion fights both the spring and damping. On rebound the spring adds to wheel momentum so the shock has to do twice as much work in rebound controlling both the spring and wheel. That thinking creates the rule of thumb rebound should be twice as stiff as compression by some vague notion of symmetry.

Fast setups

To prevent bottoming fast setups need more compression damping. More compression damping forces fast setups to run rebound/compression damping ratios less than two.

Plush setups

Bump energy absorbed in the compression stroke is all pounded directly into the chassis. To get a plush ride you have to back off on compression damping and that forces rebound/compression damping ratios that are greater than two. The plush range usually ends up around 2.5 to 3.0.

In practice shock damping ratios run around 2.25. Forks are tuned to be plusher with damping ratios in the 3.0 range. Those aren’t hard and fast numbers – just a baseline setup and the suspension can be tuned from there.

Pack or Jack

When a suspension hits a series of bumps it will either Pack or Jack.

Packing

Stiff rebound damping prevents the wheel from returning to the normal ride height before the next bump is hit. When that happens the suspension packs down in the travel and continues to pack until the spring force becomes high enough to overcome rebound damping to return the suspension to some partially extended position. High spring force at that partially extended position makes the suspension ride like a jack hammer over closely spaced repeated bumps.

Jacking

Energy absorbed by compression damping pops the chassis up slightly when hitting a bump. Closely spaced bumps causes the suspension to jack above the normal ride height making the suspension run “high in the stroke”. Lower spring force at that elevated position makes the suspension ride a little more compliant over repeated bumps.

At low-low speeds, somewhere below 3 to 5 in/sec, suspension systems run rebound/compression damping ratios less then one. That makes compression damping stiffer than rebound forcing the suspension to jack slightly for improved compliance on small bumps.

Suspension tuning "rules of thumb"

  • Chassis rebound damping zeta 0.7 to 0.8

  • Rebound/compression damping ratio 

    • Shocks 2.0 to 2.5

    • Forks 2.5 to 3.5

  • Low speed damping ratio approximately 0.8 below 5 in/sec

"Rule of thumb" tuning

Each “rule of thumb” has a range and that range is used to solve basic suspension tuning ills. If the setup is “too loose” rebound zeta values need to be increased into the 0.8 range. If that causes the suspension to pack you need to go to a stiffer spring and set zeta back to 0.7.

Suspension bottoming can be controlled by increasing compression damping and that reduces the rebound/compression damping ratio. If that doesn’t work out you need to go to a stiffer spring.

Understanding where the suspension setup is relative to those basic suspension tuning rules of thumb helps to identify problems you can solve with damping and the point where a stiffer/softer spring might be the better approach.

ReStackor suspension response tuning 

ReStackor suspension response calculations produce a series of plots comparing the analyzed suspension setup to those basic suspension tuning “rules of thumb”. The crf250 stock suspension setup provides an example and closely follows those basic suspension tuning rules.

Chassis rebound

Chassis rebound (green curve) is close to the target 0.7 rule of thumb zeta value. In detail zeta starts out around 0.62 at race sag and advances to 0.73 at a stroke depth around 9” where the suspension hits the bump rubber.

Zeta values for the wheels (blue curve) are over damped with values near 1.2. The usual remedy is re-tuning of the shocks damping force curve to reduce high speed rebound and bring zeta values down into the 1.0 range. But, the shocks damping force curve (right hand figure) shows the rebound stroke after chassis bottoming is at shaft speeds around 22 in/sec (low speed damping) and the wheels bottoming rebound stroke is at 32 in/sec (high speed damping). Those velocities are marked by the symbols on the curve. Tuning rebound to get high speed damping to be less than low speed requires changing the damping force curve shape from the progressive curve shown to a digressive rebound curve. That requires use of a ring shim in the rebound stack to increase low speed damping.

The other approach is rely on tire compliance to resolve the over damped wheel condition at high speed.

Damping ratio (rebound/compression)

The damping ratio (rebound/compression) at race sag is marked by the symbol on the plot. That value is around 2.25 and hits the target rule of thumb.

Low speed damping ratio

The damping ratio curve is on the trajectory to produce damping ratios in the 0.8 range at low speed. But at 5 in/sec the compression adjuster kicks out leaving damping ratios stuck in the 1.1 range. Fixing that requires hacking around on the compression adjuster or adding a rebound separator valve to get more compression damping at low speed.

Suspension tuning guidelines

The basic suspension tuning “rules of thumb” give some guidelines to get to a basic suspension setup. Those rules are vague in that each rule has a range. That range is used to setup the suspension around your personal preference. If you are looking for a plush setup that soaks up bumps you are going to want low compression damping putting you in the upper end of the rebound/compression damping ratio range. On the other hand if you want a stiffer setup that can take bumps that bottoms every other bike out you want to be in the bottom end of the damping ratio range.

Those same "rules of thumb" also give some guidance on tuning spring rate versus damping. If you need a stiffer setup to prevent bottoming but are already in the bottom end of the rebound/compression damping ratio range you would be better off going to a stiffer spring. The stiffer spring would give the needed bottoming resistance and faster suspension response in comparison to a sluggish over damped setup. On the opposite end of rebound/compression damping ratios a lighter spring might be the better choice to improve suspension compliance over backing off of compression damping to near zero values.

Figuring out where your preferences lie in the range of “rule of thumb” values is the art of suspension tuning. Once you figure that out suspension setups can be transferred from one bike to another in terms of zeta and damping ratios. Matching those values will duplicate suspension response regardless of bike weight, spring rate or differences in link ratio between the suspension setups.