Choose spring rate by ride frequency

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Source path: content/lms/vehicle-dynamics-and-setup/02-suspension-fundamentals/01-springs-rate-frequency.md

Course: Vehicle Dynamics & Setup

Module: Suspension Fundamentals

Estimated duration: 55 minutes

The skill in one sentence

You do not choose a race-car spring because the catalog number sounds stiff. You choose the spring that gives the tire the wheel rate the car needs for its weight, motion ratio, surface, speed, aero load, and available travel. Ride frequency is the driver-friendly name for that normalized stiffness problem: how quickly the sprung mass wants to move on its springs. The supplied corpus gives one direct frequency frame, low-frequency sprung-mass motion in the 1-3 Hz range and high-frequency axle motion in the 10-15 Hz range, but it does not provide an explicit ride-frequency equation. So this lesson teaches the grounded method the sources do provide: start from corner weight and target wheel rate, convert through motion ratio to spring rate, then validate on the actual track.

That distinction matters because the spring is not bolted directly to the tire contact patch in any simple universal way. Lopez warns that wheel rate is what matters for cornering balance, and that two cars can run very different spring rates while producing similar wheel rates because their suspensions move the spring by different amounts. Smith gives the same warning in engineering form: when the wheel travels farther than the spring, the wheel rate is the spring rate divided by the motion ratio squared. Haney gives the alternate convention using spring movement divided by wheel movement, but the physical result is the same. The tire and chassis do not care what number was printed on the coil. They care how much vertical resistance appears at the wheel centerline and tire contact patch.

The first mental reset is this: spring rate is a part number, wheel rate is what the car feels. Ride-frequency thinking pushes you one step farther. A 300 lb/in wheel rate under a 300 lb corner is a different animal from the same 300 lb/in wheel rate under a much heavier corner. That is why Haney starts spring selection by measuring static weight at each tire contact patch and then choosing an approximate ratio of wheel rate to measured corner weight. A small non-aero formula car can start near a front wheel-rate-to-corner-weight ratio of 1.0 to 1.1. A Trans-Am type car starts higher, around 1.2 to 1.3. Formula 2000, Formula Atlantic, D Sports Racer, ALMS LMP, and CART or IRL examples step progressively higher, with the highest-downforce cars needing much larger ratios to keep the platform from bottoming on the straights.

That is the practical ride-frequency method inside this lesson. You normalize the stiffness to the load the corner carries, then you adjust for the job that spring must do. A low-downforce car on a rough track needs the tire to follow the surface. A car with significant downforce needs enough rate, or enough ride height, to keep from using up the travel at speed. A smooth track lets you carry more rate before tire contact becomes the limiting problem. A bumpy track pushes you back toward compliance because a tire that is not in contact with the pavement cannot make grip.

What springs are actually for

Springs exist because the tire contact patch needs continuity with the road while the chassis is being pushed around by acceleration, braking, cornering, and bumps. Smith describes the sprung mass moving under longitudinal acceleration, lateral acceleration, and load transfer, while unsprung wheels deflect relative to the chassis over road irregularities. That movement changes camber and stores energy in the springs. Dampers handle the stored energy afterward, but the spring choice sets how much wheel deflection occurs for a given load transfer.

For this lesson, separate three related but different ideas. Ride rate is the vertical resistance measured at the wheel centerline. Roll rate is the resistance to chassis roll, supplied by the springs and anti-roll bars together. Spring rate is the coil stiffness measured at the spring itself. You can change one and not get the change you expected in another. A spring mounted near the wheel with a favorable motion ratio may deliver a large portion of its catalog rate to the tire. A spring driven by an inboard rocker with a large motion ratio may deliver only a small wheel rate even if the catalog number looks enormous.

Most intermediate drivers make their first spring mistake by comparing their catalog spring number with another car's catalog spring number. That comparison is almost meaningless unless both cars have the same motion ratio, the same spring angle behavior, similar tire rates, similar corner weights, and similar travel needs. Lopez gives the practical warning: a 500 lb/in spring can sound stiff but act soft at the wheel on a particular suspension. Smith's examples make the warning concrete. With a wheel-travel-to-spring-travel motion ratio of 1.5, a 400 lb/in spring gives about 178 lb/in at the wheel. With a 2.2 motion ratio, the same 400 lb/in spring gives only about 83 lb/in at the wheel. To get 178 lb/in at the wheel with the 2.2 ratio, the spring must be about 861 lb/in.

That is why the first question is never simply what spring should I buy. The first question is what wheel rate does this corner of the car need. The second question is what spring produces that wheel rate through this suspension. The third question is whether the tire, damper, track surface, aero load, and travel budget agree with the answer.

A usable workflow

Start by weighing the car at the contact patches. Haney's spring-rate table begins with measured static weight at each corner, not total vehicle weight and not guesswork. If the front tire contact patch carries 300 lb on a small non-aero formula car, Haney's example says a 300 lb/in wheel rate is a reasonable starting point at that end. The exact spring is not chosen yet. You have only chosen the target resistance at the wheel.

Next, pick the wheel-rate-to-corner-weight range that matches the type of car and the load it must carry. Haney's approximate front ratios provide the starting map: Formula Ford 1.0 to 1.1, Trans-Am 1.2 to 1.3, Formula 2000 1.6, Formula Atlantic 1.9, D Sports Racer 1.7, ALMS LMP 2.0 to 2.2, and CART or IRL 2.3 to 2.4. Do not treat those numbers as law. Haney immediately says track speed and bumpiness can move spring rates up or down, and ride height can also be changed to cure bottoming. The table gives you an organized first answer, not permission to stop testing.

Then measure or confirm the motion ratio. You must know which convention you are using. Smith and Lopez describe motion ratio as wheel travel divided by spring travel. Under that convention, wheel rate equals spring rate divided by the motion ratio squared. Haney's bell-crank example uses spring movement divided by wheel movement. Under that convention, the wheel rate is the spring rate multiplied by that ratio squared. The two descriptions are compatible because one ratio is the reciprocal of the other, but mixing the conventions will give you the wrong spring.

The safest way to talk in the paddock is to state both the convention and the movement. For example: the wheel moves 1.5 in for 1.0 in of spring movement. That removes the ambiguity. If the target is 300 lb/in at the wheel and the wheel moves 1.5 times the spring, the spring has to be much higher than 300 lb/in because the suspension has leverage against it. Using Smith's convention, 300 multiplied by 1.5 squared gives 675 lb/in at the spring. If the target is 330 lb/in, the spring is about 743 lb/in. Those are not magic numbers. They are the consequence of asking the wheel to feel a specific stiffness through a specific lever system.

Now check the tire and surface before you install anything. Haney notes that tire rates and suspension deflection interact, and that even a 1 psi tire-pressure change can produce a 50 to 60 lb change in wheel rates depending on the car's design variables, spring rates, and motion ratios. That is not a small tuning noise. If your spring decision is only 50 lb/in apart at the wheel, tire pressure and tire stiffness can be large enough to confuse the result. This is one reason spring testing requires a stable test condition. If you change spring rate, tire pressure, ride height, and anti-roll bar at the same time, you may not know what produced the behavior.

Then ask whether the spring is being asked to solve a roll problem. Smith's anti-roll-bar explanation is the guardrail here. If the suspension springs are stiff enough by themselves to limit roll to the desired maximum, the ride wheel rate can become too high for tire compliance. That is why the car has anti-roll bars. Springs hold the car up, set ride rate, share some roll resistance, and protect travel. Bars let you tune roll stiffness distribution without making the car so stiff in ride that the tires stop following the surface. Haney's front-roll-stiffness guidance and 50 to 65 percent front roll-stiffness range belong in the next sibling lesson on bars. In this lesson, the point is simpler: do not choose springs as if bars do not exist.

Finally, verify the result dynamically. Haney gives the cautionary example of a 2700 lb car with 400 lb/in springs and 750 lb/in tire rates. The calculated dynamic ride height under a specific condition was 0.30 in, but the measured racetrack laser ride height was 0.50 in. That difference is enough to matter, especially on a ground-effects car. The lesson is not that calculations are useless. The lesson is that the car gets the final vote. Suspension position sensors and chassis-mounted laser ride-height sensors can show whether the rate you calculated is producing the movement you expected.

How to decide softer or stiffer

There is a lazy version of spring selection that says more rate is more race car. Adams calls out that mistake directly: if 300 lb/in coils are good, 600 lb/in coils are not automatically better. The tire makes grip only while it is in contact with the pavement. A softer spring can let the wheel follow irregularities, and that can produce more adhesion than a stiffer spring that skips the tire across the surface. Lopez makes the same point through the bump case. When the suspension has to move fast over a bump or series of bumps, overly stiff or poorly matched settings may fail to keep the tire in contact with the track.

The opposing mistake is to run so little spring that the car bottoms. Adams gives the practical lower bound: as long as the springs are stiff enough to keep the car from bottoming out, they can be adequate. If the car is lowered and ride travel is reduced, a slight increase in spring rate can compensate for the reduced travel. Haney gives the aero version of the same constraint. Downforce requires higher spring rates to keep the car from bottoming on the straights, although ride height can also be used. High-speed ovals and downforce cars need more load capacity than a low-downforce HPDE car on ordinary club tires.

So the spring decision lives between two failures. Too soft for the speed, aero load, and ride height, and the car uses up the travel or bottoms. Too stiff for the surface and tire, and the tire cannot follow the pavement. The correct rate is not the largest number you can tolerate. It is the lowest useful wheel rate that protects travel, supports the platform the car needs, and keeps the tire in contact with the track.

This is where ride-frequency thinking helps even without doing exact Hz math by hand. You are not asking whether the spring feels aggressive. You are asking whether the sprung mass is being controlled in the low-frequency body-motion world while the wheel and tire still have enough compliance for the higher-frequency surface world. Gillespie's distinction between low-frequency sprung-mass motion and higher-frequency axle motion is useful language here. Your spring choice mostly sets the body-support problem. It must not make the wheel-contact problem impossible.

What good feels like

A good first spring choice does not announce itself with drama. The car takes a set without falling onto the bump stops. It does not hammer the driver over ordinary surface changes. It does not hop or skate across bumps that similar cars can cross cleanly. The balance changes you make afterward with bars and dampers make sense because the underlying wheel rates are known. When you compare your setup notes with another driver, you compare delivered wheel rates and corner weights, not only spring part numbers.

On a smoother track, you may be able to run a higher wheel-rate ratio because the suspension is not constantly being asked to follow sharp surface irregularities. On a bumpier track, the same rate may cost grip even if it felt sharp in the shop. Lopez notes that bumpy racetracks may require softer shock settings so the suspension can move fast enough to keep the tires in contact with the surface. That statement belongs mainly to damping, but it is a useful reminder for spring work: if the tire contact problem is already hard, do not make it harder by chasing a spring number for its own sake.

For an aero car, good also means the platform survives speed. Haney's table raises the wheel-rate-to-corner-weight ratio as downforce rises because the car must resist bottoming under aerodynamic load. Adams says Indy cars at high-speed ovals need more spring rate and load because of tremendous downforce. In that environment, a spring that feels beautifully compliant at low speed may be wrong when the car reaches the end of the straight. The platform requirement changes with speed.

For a production-based HPDE or club-racing car, good often means discipline. You choose the spring based on the corner weights, the actual suspension leverage, the travel budget, and the surface. You leave anti-roll distribution to the bar lesson. You leave rate-of-change control to the damper lesson. You read the suspension afterward instead of assuming the spreadsheet was right.

The sub-skills

Sub-skill one is translating spring rate to wheel rate. You need the suspension's motion ratio and the convention being used. If the wheel moves farther than the spring, the spring must be numerically stiffer than the target wheel rate. If you only know the catalog spring and not the motion ratio, you do not yet know the wheel rate.

Sub-skill two is normalizing wheel rate to corner weight. A 300 lb/in wheel rate is not automatically soft or stiff. It depends on how much weight that wheel supports and what type of car it is. Haney's ratios give a defensible starting point by car type and aero demand.

Sub-skill three is separating ride support from roll tuning. Springs contribute to roll resistance, but Smith explains why bars exist: using spring rate alone to limit roll can make ride rate too high for tire compliance. If your complaint is mostly cornering balance after the car is supported correctly, that belongs with the anti-roll bar lesson.

Sub-skill four is respecting travel. Adams and Haney both put bottoming into the spring decision. If the car is lowered, has reduced travel, or sees high downforce, it may need more spring or more ride height. If it is not bottoming and the tire is struggling over bumps, more spring may be the wrong direction.

Sub-skill five is validating against the real car. Tire rates, pressure, motion ratios, and dynamic loading can make the measured ride height differ from the calculated value. Haney's laser ride-height example is the warning label. Use calculation to choose a starting point, then use measurement and repeatable track feedback to decide whether the starting point survived contact with reality.

Where this lesson stops

This lesson is not the damper lesson. Dampers control how quickly the sprung mass and wheel motions are allowed to change and how stored spring energy is dissipated. Springs choose the load-deflection relationship. If the car takes a good set but oscillates, packs down, or cannot follow a rapid bump sequence, the next lesson on dampers becomes the main tool.

This lesson is not the anti-roll-bar lesson. Bars tune roll stiffness distribution and balance after the ride-rate foundation is credible. If the car has enough support and travel but needs more or less front roll stiffness, go to the bar lesson instead of ruining tire compliance with spring rate.

This lesson is also not the suspension-reading lesson, although it depends on it. Once the spring is installed, you still need to read dynamic ride height, bottoming behavior, tire contact, and balance. Haney's data-acquisition example is the advanced version. The same principle applies at club level: trust the car's evidence more than the confidence of the spreadsheet.

Worked example: small non-aero formula car front spring

Start with Haney's small non-aero formula-car example. The front tire contact patch carries 300 lb. For a Formula Ford type car, the starting wheel-rate-to-corner-weight ratio is about 1.0 to 1.1, so the front wheel-rate target begins around 300 to 330 lb/in.

Now bring in the motion ratio. Suppose this suspension uses the Smith and Lopez convention, wheel travel divided by spring travel, and the wheel moves 1.5 in for 1.0 in of spring movement. Smith's formula says wheel rate equals spring rate divided by the motion ratio squared. Turn that around for spring selection: spring rate equals target wheel rate multiplied by the motion ratio squared. The square of 1.5 is 2.25. A 300 lb/in wheel-rate target needs about a 675 lb/in spring. A 330 lb/in wheel-rate target needs about a 743 lb/in spring.

The important lesson is not the final spring number. The important lesson is the order of operations. You did not start with a spring catalog. You started with corner weight, chose a wheel-rate ratio appropriate for the car type, converted through the suspension leverage, and only then looked for a spring. If the track is unusually bumpy, Haney's guidance lets you adjust down from the starting point. If the car bottoms, Adams and Haney both allow more spring or more ride height. If the car has a balance complaint after the rate is credible, that becomes a bar or damper question rather than another blind spring change.

Worked example: the inboard rocker trap

Smith's inboard-suspension example is the cleanest warning against copying catalog rates. With a motion ratio of 2.2 using wheel travel divided by spring travel, a 400 lb/in spring produces only about 83 lb/in at the wheel. That spring may look serious on the bench, but the tire sees the softened result after the rocker leverage does its work.

Smith also gives the reverse calculation. If the desired wheel rate is 178 lb/in with that 2.2 motion ratio, the spring has to be about 861 lb/in. That number can sound extreme to a driver used to production-car coilover catalogs, but it is simply the spring needed for the wheel to feel 178 lb/in through that linkage.

This is why two cars in the paddock can both be correctly sprung with very different catalog numbers. An outboard spring near the wheel and an inboard rocker spring do not have the same mechanical leverage. If you copy the other driver's spring without copying the wheel rate, you have copied the wrong thing.

Worked example: dynamic ride height does not have to match the calculation

Haney's 2700 lb car example is the validation example to remember. The car had 400 lb/in spring rates and 750 lb/in tire rates. Under a specific condition, the calculated dynamic ride height was 0.30 in, but racetrack measurement with a laser ride-height sensor showed 0.50 in. That difference was large enough to matter, especially for a ground-effects car.

For an intermediate club racer, the lesson is not that every car needs a laser ride-height sensor. The lesson is that the calculation is a starting model, not a verdict. Tire stiffness, tire pressure, suspension motion ratio, track surface, speed, and actual load can move the real car away from the simplified answer. If the car's dynamic ride height matters to aero, bottoming, alignment, or driver confidence, you need some repeatable way to confirm what happened on track.

This example also explains why spring testing should be narrow. If you change springs and tire pressures together, the tire-pressure change may alter wheel-rate behavior enough to confuse the result. If you change springs and ride height together, you may fix bottoming with ride height and blame the spring. Make one meaningful change, repeat the same kind of run, and compare the car's evidence.

Common mistakes

Mistake one is shopping by catalog rate. The bad version sounds like choosing the bigger spring because it sounds more race-oriented. The good version starts from wheel rate at the contact patch, normalized to corner weight, and then converts through the suspension's motion ratio.

Mistake two is mixing motion-ratio conventions. Smith and Lopez use wheel travel divided by spring travel. Haney's bell-crank example describes spring movement divided by wheel movement. Both can be correct if you keep the convention straight. The good version writes the actual movement sentence first, such as the wheel moves 1.5 in while the spring moves 1.0 in, then applies the matching formula.

Mistake three is using springs to fix every roll complaint. Springs do contribute to roll resistance, but Smith explains that springs stiff enough to limit roll by themselves can make ride rate too high for tire compliance. The good version uses springs for ride support and travel, then uses anti-roll bars for roll-stiffness distribution and balance.

Mistake four is assuming stiffer means more grip. Adams warns that a soft spring can help the wheels follow road irregularities so the tires can generate adhesion. Lopez gives the same tire-contact warning for bumps. The good version asks whether the current rate protects travel while still allowing the tire to stay on the track surface.

Mistake five is ignoring bottoming. Soft enough for grip is not the same as soft regardless of travel. Adams says the spring must be stiff enough to keep the car from bottoming, and Haney adds that downforce cars need higher rates to avoid bottoming on the straights. The good version treats bottoming as a hard constraint, then chooses the least excessive rate that satisfies it.

Mistake six is forgetting tire rate and pressure. Haney notes that a 1 psi pressure change can produce a large wheel-rate change depending on the car. The good version controls tire pressure during spring tests and avoids declaring a spring change successful when the tire condition also changed.

Mistake seven is trusting static math without dynamic evidence. Haney's calculated-versus-measured ride-height example shows that even a sensible calculation can miss what the car does on the racetrack. The good version calculates first, measures or observes afterward, and revises the setup only from repeatable evidence.

Drill: the two-rate spring worksheet and validation run

Do this drill before and during your next event. The count is two candidate wheel-rate levels, one baseline session, and one validation session. The duration is about 45 minutes of prep before the event, 15 minutes between sessions, and 20 minutes after the day. The success criterion is a completed worksheet that names the target wheel rate, the motion-ratio convention, the resulting spring rate, and the on-track evidence for whether the choice protected travel without costing tire contact.

Before the event, weigh the car or use the best current corner-weight sheet you have. Write the front and rear contact-patch weights. Pick a starting wheel-rate-to-corner-weight ratio from the closest Haney car type, then write one softer and one stiffer candidate around it. If you are in a low-downforce production-based car on a rough surface, bias the first test toward compliance. If the car is lowered, has limited travel, or is likely to bottom, bias the first test toward travel protection.

Next, measure or confirm motion ratio. Do not write only a number. Write the movement sentence. For example, the wheel moves 1.5 in for 1.0 in of spring movement. Then write the convention. Convert each target wheel rate to a spring rate using the matching formula. If the available catalog springs do not land exactly on the calculated number, choose the closest sensible pair and write the actual delivered wheel rate back into the worksheet.

In the baseline session, do not chase balance with bars or dampers unless the car is unsafe. Drive a repeatable session and focus on evidence related to spring choice: bottoming, harshness over known bumps, whether the car takes a set, and whether the tires stay in contact over the surface. If the car has suspension position or ride-height data, mark the minimum ride heights and the sections where they occur. If it does not, keep the notes disciplined and specific.

Between sessions, decide whether the evidence points to travel failure or contact failure. Travel failure means the car is using up the available motion under braking, cornering, bumps, or straight-line aero load. Contact failure means the car is too harsh or skates across irregularities even though it is not bottoming. If the evidence is mixed, do not change three things. Pick the one rate change that addresses the dominant failure, or leave the spring alone and move the next question to dampers or bars.

After the validation session, score the drill. You pass if the second session answered the worksheet question more clearly than the first. You fail if you changed springs because the number sounded right, could not state the motion-ratio convention, changed tire pressure enough to hide the result, or tried to fix a roll-balance issue that belonged to the anti-roll bar lesson.

Cross-references and boundaries

Go to the damper lesson when the spring rate seems basically right but the car's movement timing is wrong. The sources separate the spring's load-deflection job from the shock absorber's job of damping stored spring energy. Lopez's bumpy-track note about softer shock settings belongs there.

Go to the anti-roll-bar lesson when the car is supported correctly but the front-to-rear balance in roll needs tuning. Haney's front roll-stiffness guidance and Smith's explanation of why bars prevent excessive ride stiffness both point to that boundary.

Go to the suspension-reading lesson when you need to prove what the car did. Haney's suspension-position and laser ride-height example is the advanced data version of this skill. The spring worksheet gives you the predicted behavior. The suspension-reading process tells you whether the prediction survived the session.

Stay in this lesson when the question is still foundational: what wheel rate should this corner feel, and what spring rate will actually produce it through this suspension.

Author Review

No quiz questions are attached to this lesson.

Sources

#	Document	Chunk	Pages	Score	Collection
1	The Racing and High-Performance Tire Paul Haney	18ea2b9d-3955-611b-22e1-4498633f8c8d	252	1	uio_books_raw_v1
2	Tune To Win Carroll Smith	f07d0274-8121-8323-aeb0-8f80bf25afe6	63	1	uio_books_raw_v1
3	Going Faster Mastering the Art of Race Driving - Carl Lopez	e23be77d-2bb8-aef6-5ad2-b5eff9354b3b	228	1	uio_books_raw_v1
4	The Racing and High-Performance Tire Paul Haney	7a28c69f-568c-c56c-d7a0-a2b5d96d3ef8	249	1	uio_books_raw_v1
5	Tune To Win Carroll Smith	8753a79d-fc2a-3e83-88ff-2f45b123ecf7	63	1	uio_books_raw_v1
6	Chassis Engineering Adams	edaf483a-2106-5443-0e17-71fa7ffded40	38	1	uio_books_raw_v1
7	Going Faster Mastering the Art of Race Driving - Carl Lopez	d0604c94-4a94-899b-8b2a-a1a89cc93f37	228	1	uio_books_raw_v1
8	Fundamentals of vehicle dynamics Gillespie T. D. Thomas D.	2dd6d9e5-2331-90c1-9859-7b9107424c55	170	1	uio_books_raw_v1