Quantify the steer hiding in roll
Generated from
content/lms/vehicle-dynamics-ii-theory/05-roll-and-compliance-effects/02-roll-steer-and-roll-camber.md; edit the source file, not this page.
Source path: content/lms/vehicle-dynamics-ii-theory/05-roll-and-compliance-effects/02-roll-steer-and-roll-camber.md
Course: Read the forces that steer the car
Module: Add roll and compliance to the rigid model
Estimated duration: 55 minutes
The skill
You are learning to find the steering input that the suspension adds without asking you. In a rolled car, the wheels do not merely move up and down. The suspension links can change toe, the axle can develop a mean steer angle, the camber can move with the roll angle, and lateral force can deflect bushings, steering arms, and structure. The driver may feel all of that as balance, turn-in, midcorner stability, or rear nervousness, but the engineering task is narrower: separate commanded steer from hidden steer, give the hidden steer a sign, and decide whether it is small enough to ignore or large enough to change the model or the setup.
The clean rule is this: roll steer is an axle steer contribution caused by suspension roll. It is not a tire slip angle and it is not the driver turning the wheel. If the car rolls two degrees and the rear axle steers a tenth of a degree because of the suspension geometry, that tenth of a degree belongs in your handling picture. It may be small in handwheel terms, but Dixon warns that small steer-angle changes can matter because bump and roll steer can make the car sensitive, unstable, and unpleasant when the wheels move through their travel. Van Valkenburgh gives the race-car version of the same warning: uncontrolled steer from rolling or deflections complicates the driver's task, because the driver already has steering and throttle to control tire slip angles.
This lesson sits between the roll-degree-of-freedom lessons and the full handling model. Do not use it to re-learn where roll angle comes from. Assume you already have an estimate of suspension roll angle or a way to measure it. Your job here is to turn that roll angle into three side effects: roll steer, roll understeer, and roll camber. Then you decide what to do with compliance steer, because force-driven deflection can add another hidden steer term that does not show up in a pure geometry table.
Keep the vocabulary separate
The first sub-skill is language discipline. If you mix the terms, the calculation becomes meaningless.
Bump steer is one wheel's steer-angle change as that wheel moves in bump or droop relative to the body. Dixon assigns it a bump steer coefficient, usually in deg per meter, and takes it as positive for toe-out with a rising wheel. That sign convention matters because a left wheel in bump and a right wheel in droop can create a different pair behavior from two wheels moving together.
Roll steer is the mean steer angle of the pair of wheels at an axle when the body rolls. With independent suspension it is closely related to the bump steer curves, but track width also matters because a given roll angle produces vertical motion across the track. With a solid axle, roll steer refers to the steer angle of the complete axle. Either way, the result is an axle-level steer angle, usually modeled with a roll steer coefficient in deg per deg. For small roll, the practical calculation is axle roll steer equals roll steer coefficient times suspension roll angle.
Roll understeer is not a new physical motion. It is the same physical steer contribution expressed in the vehicle-handling sign convention. Dixon is explicit that roll steer is an axle property, while roll understeer is a vehicle property or an axle property only in the context of the vehicle. The advantage is that front and rear roll-understeer contributions can be added when you are building the total understeer picture. The rear sign conversion is the trap. A rear axle steer angle that seems positive in the axle roll-steer convention can contribute the opposite way in the vehicle roll-understeer convention. If you skip that conversion, you can add a rear effect in the wrong direction and talk yourself into the wrong bar, spring, or toe change.
Roll camber is the camber angle change caused by roll. It is not steer, and Dixon keeps the notation separate for that reason. It belongs beside roll steer because the same suspension motion that points the wheels also changes the tire's attitude to the ground. Crahan's suspension summary gives the reason this belongs in a handling lesson: one of the main goals of a competition suspension is to maintain the proper tire attitude to the ground while dealing with chassis motion and load transfer. A tire is not a rigid cylinder under load, and the suspension is trying to compensate for tire deformation and chassis motion so the tire can keep making grip.
Compliance steer is the force-path version of the same problem. It is not roll geometry by itself. It comes from suspension links, steering arms, bushings, tires, caster trail, aligning torque, lateral force, and structural deflection. Dixon's coefficient list includes lateral-force compliance steer, aligning-moment compliance steer, and related compliance camber terms. Van Valkenburgh explains why this cannot be dismissed as old road-car softness: engineers learned to make compliance work for them, and steering-arm placement can make a hard-corner lateral load steer the wheels. A model that includes geometric roll steer but ignores compliance may still miss the steer the driver feels at high lateral load.
The mechanism in one corner
Imagine a steady right-hand corner. The body rolls left. The left-side suspension is relatively in bump and the right-side suspension is relatively in droop. If the independent suspension has a bump-steer curve, each side moves to a different point on that curve. The left wheel may toe out as it rises. The right wheel may toe in, toe out, or move less as it droops. The axle roll steer is not the toe spread between the wheels. It is the mean steer direction of the pair.
That distinction is why the skill is not just reading total toe. Toe change can affect tire scrub, temperature, and feel, but roll steer asks whether the pair of wheels is now pointed left or right as an axle. If the front axle gains a mean steer that helps the driver turn, the driver may need less handwheel for the same path. If it gains a mean steer that fights the turn, the driver may need more handwheel as lateral acceleration and roll build. If the rear axle steers, the car may yaw in a way that feels like balance change even though spring, bar, and tire load transfer were not the only causes.
On a solid axle, the picture is simpler to describe but not less important. The complete axle can steer as the body rolls. Dixon separates this case from independent suspension because the coefficient refers directly to the complete axle steer angle. You still have to convert it into vehicle roll-understeer convention before combining it with the rest of the handling model.
The camber effect happens at the same time. The wheel may gain or lose camber with roll, so the contact patch attitude changes while the axle steer changes. Do not bundle that into the steer number. Treat roll camber as a partner channel. If you combine them too early, you will not know whether the car improved because the tire stayed flatter, because the axle stopped steering itself, or because both changed.
The calculation workflow
Start with a sign card. Write down the project's convention for toe-out, right steer, front axle, rear axle, roll angle, and roll-understeer contribution. Do this before looking at values. Intermediate vehicle dynamics work fails surprisingly often because the math is done correctly in the wrong sign convention.
Next, gather the geometry data. For independent suspension, your basic data is wheel steer angle versus vertical wheel position. That can come from a kinematics rig, an alignment-rack bump-steer sweep, or a suspension model that has already been validated against rig data. Dixon treats bump steer as the basic data form for independent suspension and roll steer as the basic data form for solid axles. Smith's collected paper on vehicle dynamics emphasizes that dynamics and kinematics analysis should be validated through objective testing and kinematics-rig testing. Use that as the standard: a table you have not measured or validated is a hypothesis, not a setup truth.
Choose the roll input. If you already have suspension roll angle from the roll-degree-of-freedom model, use that. If you are making a first pass, use the roll angle at the lateral acceleration you care about. Keep the units consistent. Roll steer coefficient is commonly deg per deg, so two degrees of suspension roll multiplied by 0.04 deg per deg gives 0.08 deg of axle steer. If the model is using roll steer gradient in deg per g, then you can multiply by lateral acceleration instead, but do not mix the two forms.
For independent suspension, map roll angle to the left and right wheel vertical positions. The point is not to invent precision, but to force yourself to use the wheel's actual travel direction. The rising side and the falling side may not be symmetric. Dixon notes that bump steer is often significantly nonlinear over the full suspension range, so a single coefficient may not be good enough once you leave the small central range. If you only have a linear coefficient, say so on the sheet and limit your confidence.
Calculate the axle mean steer. Take the left and right wheel steer angles in the same coordinate system and average them as an axle steer value. Keep total toe separate. A pair of wheels that toes out equally can have zero mean steer but plenty of toe change. A pair that moves together in one direction can have axle steer with little toe change. Your handling model cares about both, but they are not the same output.
Convert axle roll steer into roll understeer. This is the second sign check. Dixon's reason for roll-understeer coefficients is practical: once converted, they add into total understeer without repeatedly rethinking the front and rear sign convention. Front and rear axle roll steer do not enter the vehicle balance sum the same way. Make this conversion on paper every time until it is automatic.
Add roll camber as its own channel. Roll camber coefficient is usually dimensionless in deg per deg. Multiply it by suspension roll angle to estimate camber change due to roll. Then compare that camber change to your tire-attitude goal. The number does not tell you grip by itself, because the tire is deforming under load, but it tells you whether the suspension is helping or hurting the tire's attitude as roll builds.
Finally, make a compliance note. If the car uses rubber bushings, flexible links, long steering arms, soft mounting points, or a chassis that does not meet the stiffness needed to limit deflection, write a separate compliance-steer risk line. The Smith excerpt points out that a minimum level of chassis stiffness must be achieved to control deflection while keeping weight and center of gravity low. Van Valkenburgh's steering-arm example shows that lateral force can steer wheels through compliance even when the geometric roll table looks acceptable. Do not hide that uncertainty inside the roll steer coefficient.
What the number means to the driver
A hidden steer number is useful only if you can connect it to a symptom. If front roll understeer is positive in the vehicle convention, the driver needs more steering input as roll and lateral acceleration build. The sensation is not simply initial understeer. It is the car asking for more handwheel after the roll state has developed. The data clue is a steering-angle demand that rises with lateral acceleration more than your baseline predicts.
If rear roll steer contributes roll oversteer, the sensation may be a rear axle that helps rotate as load builds. That can feel lively or fast until the transition becomes unpredictable. Dixon's warning about poor straight-line stability and unpleasant behavior matters here because the same steer sensitivity can appear over bumps, crests, and transitions. A car that feels calm on a smooth constant-radius skid pad may still feel nervous when roll and bump inputs overlap.
If roll camber is the main problem, the driver may describe grip fading as the car takes a set rather than the car changing direction by itself. The calculation helps because the steer channel and the camber channel are separated. You can ask whether the tires are losing a favorable attitude, whether the axle is steering against the driver, or whether both are present.
Static toe is not a clean cure for a bad roll-steer curve. Dixon notes that static toe settings are constrained by tire wear and should be arranged to produce minimal steer angles when running. Within the low-wear band, there is limited scope to use toe settings as a handling-tuning tool. The lesson for you is practical: static toe can trim feel, but if the car steers itself through roll travel, a static toe change may only move the problem to another speed, load, or ride-height state. Too much front toe-in can also make corner turn-in imprecise and unprogressive, so using toe to cover a roll-steer defect can create a new symptom.
How deep the model needs to be
For a first engineering pass, a linear roll steer coefficient is acceptable if the car stays in a small roll range and the sweep is close to linear. That is often enough to prevent a false balance diagnosis. You do not need a multibody model to discover that a rear axle is adding an unwanted steer angle with roll.
For larger roll ranges, high motion-ratio sensitivity, or push/pull-rod suspension, be more careful. The Crahan summary in Smith notes that some steady-state equations ignore tire and bushing compliance and linearize roll resistance per degree. It also notes that push or pull-rod suspensions can require far more iteration because bell-crank rotation can create large changes in wheel rate and motion ratio. That does not mean the simple roll-steer calculation is useless. It means the simple calculation is a screening tool, and the final answer needs validated kinematics and objective testing if the first pass says the hidden steer is meaningful.
The phrase objective testing matters. A roll-steer spreadsheet is not the car. Van Valkenburgh's advice on whether subtle steering-motion effects matter is that the skid pad or test track will tell. The correct attitude is not to worship the model or ignore it. Use the coefficient method to predict where hidden steer should show up, then look for the symptom in a controlled test.
Calibration cues
A good roll-steer analysis has three signatures. First, the signs are explicit. Anyone reading your sheet can tell whether the front and rear contributions are already converted to roll understeer or are still raw axle roll steer. Second, the geometry and compliance terms are separated. If the car improves after a bushing change, you should not rewrite the geometric roll steer coefficient to explain it. Third, the driver description, objective test, and math point in the same direction.
On the skid pad, look for steering-angle demand as lateral acceleration builds. Increased understeer that appears with load transfer, aligning torque, lateral force on caster trail, and steering compliance is consistent with Dixon's discussion of measured skid-pad behavior. If the driver says the car takes a set and then needs more handwheel, and the front roll-understeer contribution is in the same direction, you have a coherent explanation. If the numbers predict the opposite, either the sign is wrong, the data is wrong, or another effect is dominating.
On a bumpy straight or a fast transition, look for steer sensitivity that does not match driver input. Dixon warns that bump and roll steer can hurt straight-line stability and make behavior unpredictable. If the car hunts over bumps with no steering command, do not call that a pure tire or aero issue until you have checked the bump-steer and roll-steer curves.
In the paddock, look for whether a setup answer is doing the correct job. If you add static toe to make the car feel calmer, but the running toe or roll-state steer still points the axle the wrong way, the symptom may return at another ride height or speed. If you stiffen a bar and the car changes because it rolls less, you may have reduced a roll-steer input rather than changing only lateral load transfer distribution. That is not a failure. It is exactly why this lesson belongs after roll as a working degree of freedom.
What good looks like
Good work is a short table, not a vague opinion. For each axle, write the roll angle, raw roll steer, roll-understeer contribution, roll camber contribution, and confidence level. Add a separate line for compliance risk. If the coefficient came from a central linear sweep, mark it as a central linear value. If it came from a full nonlinear table, mark the exact travel points used. If it came from an unvalidated model, mark it as unvalidated.
The result should let you answer four questions before changing the car. Is the hidden steer large enough to matter relative to the driver's steering demand? Does it add understeer or oversteer in the vehicle convention? Does it grow in the roll range where the symptom appears? Is compliance likely to be adding another steer path under load? If you cannot answer those four questions, you do not yet have a roll-steer diagnosis. You have a suspicion.
The discipline is especially useful because it keeps setup conversations honest. A driver may report understeer, but the car may be adding front roll understeer, losing roll camber control, gaining rear roll steer, or deflecting through compliance. Those are different mechanisms. The repair may be a geometry correction, a bushing or link stiffness correction, a static toe trim, a roll-stiffness change that reduces the roll input, or simply better data before any change. The coefficient method does not choose the setup for you. It prevents you from choosing one while blind.
Worked example: independent suspension from a bump-steer sweep
Suppose your front independent suspension has been swept on a rack. At the roll state you care about, the outside wheel is at the bump point that measures 0.10 deg of steer in your positive direction, and the inside wheel is at the droop point that measures 0.02 deg in the same positive direction. The axle mean steer is 0.06 deg. That is the front roll steer for this roll state. It is not the total toe change. Total toe would ask how far apart the wheels point. Roll steer asks where the pair points as an axle.
Now convert it into vehicle roll-understeer convention. If this is a front axle and your sign card says that this steer direction requires less driver-applied handwheel, then it is not a positive roll-understeer contribution. If it requires more handwheel, it is. The important part is not memorizing this example's sign. The important part is doing the conversion deliberately, because Dixon separates axle roll steer from vehicle roll understeer for exactly this reason.
The track-width point enters before the average. For the same roll angle, a wider track produces a different vertical separation between left and right wheel positions than a narrow track. That is why Dixon says independent-suspension roll steer is closely related to bump steer but also influenced by track width. Do not take a bump-steer coefficient from one geometry, ignore track and travel, and pretend it is the roll-steer coefficient for another car.
Add roll camber after the steer calculation. If the same roll state gives the outside tire a camber change that hurts tire attitude, the driver may feel a grip loss on top of the hidden steer. Keep the two columns separate so a later camber-link change does not get credited with fixing a steer problem, or the reverse.
Worked example: solid axle roll steer as complete axle steer
For a solid axle, do not build the answer from independent left and right bump curves unless that is how your actual test method is defined. Dixon treats roll steer for a solid axle as the steer angle of the complete axle. Suppose the measured roll steer coefficient is 0.04 deg per deg and the rear suspension roll angle at the test condition is three degrees. The raw axle roll steer is 0.12 deg.
That number is small enough to tempt you into ignoring it, but it points both rear wheels as an axle. At the rear of the car, that can change the yaw response the driver feels. Before you add it to total understeer, convert it to the roll-understeer sign convention. Dixon notes that rear sign handling is where roll steer and roll understeer differ. Once converted, the front and rear roll-understeer terms can be added without redoing the sign argument every time.
The driver cue in this example would not be a sharp one-wheel toe problem. It would be a car that changes yaw attitude as roll builds, especially in steady lateral acceleration or in transitions where roll direction changes. If the same car also has chassis or link deflection, keep that as a separate compliance risk rather than folding it into the measured solid-axle roll steer coefficient.
Worked example: GM leading steering arms and compliance steer
Van Valkenburgh's GM leading-steer-arm discussion is useful because it shows why hidden steer is not always geometric roll steer. With traditional rear-mounted steering arms, the steering linkage can be laterally stiffer than the front suspension. In a hard corner, the suspension may deflect inward more than the steering linkage, so the wheels steer inward and contribute to oversteer. Moving the steering arms to the leading side changes how the compliance path works.
For this lesson, the takeaway is not that you should copy that road-car solution onto a race car. The takeaway is that lateral force can steer the wheels through compliance. If your model only contains bump steer, roll steer, roll camber, and roll stiffness, it can still miss the force-driven steer that appears only when the tire is loaded. Dixon's coefficient list names several of these paths, including lateral-force compliance steer and aligning-moment compliance steer.
The correct worksheet treatment is a separate compliance-steer line. If the symptom appears only at high lateral load, if it changes after bushing or steering-link changes, or if the kinematic table looks clean but the car still steers itself, do not keep searching the roll-steer column for the whole answer. You may be seeing force-path steer.
Common mistakes
The first common mistake is treating steer angle as slip angle. Dixon explicitly prefers the steer symbol for bump and roll steer because the effect is wheel steer, not a direct tire slip-angle change. The tire may later develop a slip-angle consequence, but the suspension output you are quantifying is wheel direction.
The second mistake is confusing total toe with axle mean steer. A roll event can change toe without pointing the axle, and it can point the axle without much toe spread. If you only look at toe, you can miss the steer that enters the handling model.
The third mistake is forgetting the rear sign conversion. Roll steer is an axle property. Roll understeer is the vehicle-convention contribution. The rear axle must be handled with the correct sign before you add it to total understeer.
The fourth mistake is using static toe as a blanket fix. Static toe is constrained by tire wear and should aim for minimal running steer angles. It can tune feel within a narrow range, but it is a poor substitute for fixing a suspension curve that points the axle the wrong way in roll.
The fifth mistake is trusting a linear coefficient over too much travel. Dixon warns that bump steer can be significantly nonlinear over the full suspension range. A one-line coefficient near ride height may be fine for a small-roll model and misleading at larger roll.
The sixth mistake is ignoring compliance because the kinematic model is neat. Van Valkenburgh's steering-arm example and Dixon's compliance coefficient categories both point the other way. Loaded parts bend, bushings move, aligning torque acts through compliance, and the chassis itself needs enough stiffness to control deflection.
The seventh mistake is diagnosing the driver before checking the hidden steer. A driver who adds steering as the car takes a set may be compensating for real front roll understeer. A driver who reports rear nervousness may be feeling rear roll steer or compliance steer. Coaching and setup both improve when the car's self-steer is measured before blame is assigned.
Drill: the hidden-steer audit
Run this as a two-session engineering drill, not as a race-weekend thrash. The count is three roll states per axle, two axles, and one short validation drive. The duration is about 60 to 90 minutes if you already have access to bump-steer or kinematics data, longer if you must measure from scratch.
First, make the sign card. Define positive bump steer, positive axle roll steer, positive roll-understeer contribution, and positive roll camber. Write the front and rear sign conversion on the same page. Success criterion: another person can read the sheet and tell which direction adds vehicle understeer without asking you.
Second, choose three suspension roll states: small, medium, and the largest state you actually expect to use. For each axle, use the measured or validated wheel-position data to calculate raw axle roll steer. If it is independent suspension, use the left and right wheel travel points and average the wheel steer angles. If it is a solid axle, use the complete-axle roll steer measurement or coefficient. Success criterion: each axle has three raw roll-steer values and the units are shown.
Third, convert each raw value into roll-understeer convention and calculate roll camber for the same roll states. Keep compliance as a separate note, with higher concern if the car has soft bushings, flexible links, steering-arm geometry likely to steer under lateral load, or uncertain chassis stiffness. Success criterion: your table has separate columns for raw roll steer, roll understeer, roll camber, and compliance risk.
Fourth, take the car to a skid pad or controlled test-track segment and look for the predicted symptom. You are not trying to set a lap record. You are trying to see whether steering demand, driver feel, and roll state move in the direction the table predicts. Success criterion: after the drive, you can mark each axle contribution as supported, contradicted, or not isolated by the test.
Do not change three things afterward. If the audit says the car has a meaningful hidden steer term, choose the next investigation deliberately: geometry correction, compliance inspection, static toe trim, or roll-input reduction. The lesson is complete when the hidden steer has a number and a confidence level, not when you have guessed a setup change.
When this principle breaks down
The simple coefficient method breaks down when the assumptions behind the coefficient are no longer true. If bump steer is nonlinear through the travel range, a central coefficient will not describe the loaded corner. If the model linearizes roll resistance but the vehicle has large roll angles, the roll input itself may be wrong. If push or pull-rod motion ratios change rapidly with bell-crank rotation, an iterative model may be required before the wheel positions are trustworthy. If bushing, tire, steering, or chassis compliance is large, pure kinematics will not predict the loaded steer.
Those limits do not make the method useless. They tell you when to stop presenting the first-pass number as final. Use the coefficient method to expose the likely hidden steer, then move to validated kinematics, objective testing, and compliance measurement when the first pass says the effect is large enough to matter.
Author Review
No quiz questions are attached to this lesson.
Sources
| # | Document | Chunk | Pages | Score | Collection |
|---|---|---|---|---|---|
| 1 | Tires Suspension and Handling Second Edition Dixon John C | e25d930d-3a2c-f059-a678-86e12d837c0f | 311 | 1 | uio_books_raw_v1 |
| 2 | Tires Suspension and Handling Second Edition Dixon John C | 61c93e47-4f73-9fb8-6d71-872b26d4fd26 | 312 | 1 | uio_books_raw_v1 |
| 3 | Tires Suspension and Handling Second Edition Dixon John C | a994ddea-97e5-1548-22a5-f38121cb37de | 324 | 1 | uio_books_raw_v1 |
| 4 | Race Car Engineering Mechanics Paul Van Valkenburgh | e4ae726c-3875-9085-b434-4ae8c67c5a74 | 25 | 1 | uio_books_raw_v1 |
| 5 | Tires Suspension and Handling Second Edition Dixon John C | 560ef1be-06ef-28ac-b58d-977984b068f2 | 511 | 1 | uio_books_raw_v1 |
| 6 | Racing Chassis and Suspension Design Carroll Smith | cb98cc00-5481-d32d-c43d-18838cb107e5 | 184 | 1 | uio_books_raw_v1 |
| 7 | Racing Chassis and Suspension Design Carroll Smith | 1ac1a126-b9d2-24ff-6133-1843c3554108 | 213 | 1 | uio_books_raw_v1 |
| 8 | Racing Chassis and Suspension Design Carroll Smith | 52047a73-bbbf-e4e8-51ff-bb6cdbc0101b | 134 | 1 | uio_books_raw_v1 |