Simple Kinematic Philosophies
In some cases, these can be oversimplifications.
1. Beginners
Are you a brand new team?
Trace a random FSAE suspension in front view.
Design the parts to prevent binding through travel and steering.
In many ways, that will be good enough.
Suspension kinematics only have minor effects.
Even less on cars where there is not much suspension travel.
Are you brand new to suspension design?
Go make a bunch of parametric sketches.
Ideally the current car is already in CAD.
See where the front and rear have different amounts of toe change, camber change, roll center movement, or spring/damper motion ratios.
See what you have, what you like, what you don't.
Use the following steps.
Learn what the suspension is doing.
Fix what it is not doing well enough.
Repeat for each new design.
2. Aphorism
“Any suspension will work if you don’t let it…”
This conclusion is often a result of trying to hold the body into an aerodynamic position.
Broader: If the suspension is doing something bad, use a stiffer setup.
Trade a small amount of grip over bumps for not letting it move far enough to lose more grip.
Good suspension kinematics will let you use softer setups for slightly more grip.
Good designs reach diminishing returns for consistent grip through travel.
This is the broad plateau philosophy, area under the performance curve, rather than sharp peaks.
There is a wide range of solutions to control toe, camber, and roll centers for consistent grip.
In the case of a car with approximately equal corner weights and tires, I prefer the front and rear suspension to be reasonably matched on camber gain, roll center movements, and spring/damper motion ratios.
A mismatch will not have much effect on ultimate grip or steady state balance.
But it will make the front and the rear respond at different rates.
Different geometries can create equal grip, but feel completely different during the time it takes the car to reach steady state.
The more heavily loaded axle (statically or dynamically) has proportionally more influence in transient grip and feel.
3. Suspension Geometry Is Overrated
In steady state skidpad, peak grip, suspension design does not affect:
Total load on front axle
Total load on rear axle
Total load on outside wheels
Total load on inside wheels
Set toe on the finished car to the nearest mm and absolutely minimize bump and roll steer.
But do not obsess with tenths of a degree of camber, or millimeter changes to roll centers.
For perspective, on a full size racecar, with a center of mass about 350mm above the ground, we tested 3 roll center heights in 50mm steps.
The one we thought would be best turned out to be, but they were all acceptable and adaptable with spring, damper, and anti-roll bar changes.
FSAE cars are smaller and lower, so you can argue slightly smaller steps are significant.
Memo to chassis team:
When the wishbone axis is parallel to the center plane, moving the pickups forward and backward does not affect the kinematics, only the internal and mount forces.
Slip angle, beyond the scope of this geometry discussion, is the last big component of tire grip.
4. No Bump Or Roll Steer
Do not let toe move due to suspension travel or compliance.
The toe needs to stay where you set it.
Toe is almost a single number as opposed to a graph.
You will feel and measure noticeable differences between minimizing toe change to a mm or two and allowing it to move several mm.
You will feel and measure noticeable differences depending on the direction of toe change.
If the rear toes out, the car will refuse to go in a straight line.
Easiest method: Toe link in plane with one of the wishbones, equal to the length of that wishbone.
There are a number of other approaches.
Always sweep through travel in CAD.
Plus a nice, big upright offset to keep the forces lower and tolerance deflections smaller.
Do not try to deliberately change toe in bump or roll for some sort of steering effect.
100x easier to wreck everything than do anything useful.
Four wheel steering would be a better plan.
5. Camber: Moderate (Verb), Moderate (Noun)
Camber affects longitudinal and lateral grip.
And fair enough, camber has some tire temperature and pressure effects.
What range of straightline camber maximizes grip acceleration, and braking?
What range of camber maximizes lateral grip?
Now you can actually start designing something.
Get ready to do a whole bunch of parametric sketching.
5a. Wishbone and upright geometry determine how much camber gains in bump.
Is camber in the optimal range during acceleration, and braking?
Camber is not a number, it is a graph in bump and droop.
5b. Wishbone and upright geometry determine how much camber gains in roll.
The camber gain in bump is there to optimize the outside tire in roll.
Take your geometry model, apply bump to the outside, droop to the inside.
Derive from acceptable suspension data / roll targets.
Chassis roll changes the angle and location of the wishbone pickups.
Because you keep the tires in contact with the ground.
Study camber where it matters: roll at steady state, combined roll+braking, roll+acceleration.
Factor for tire squish and lateral sidewall deflection if you're feeling ambitious.
Camber is not a number, it is a graph through roll.
5c. Slick race tires are going to use a lot more negative camber than commuter tires.
But it’s still going to be in the low single digit degrees.
Use zero camber for minimum straightline rolling resistance.
FSAE car: no meaningful aero driven ride height/camber changes, no high speed corners affected by aero forces changing the ride height/camber.
Of course, your data and math could prove me wrong on that.
6. Steady-State Balance
Tire grip increases with normal load until the grip limit is reached.
The vehicle acceleration increases until the tire grip limit is reached.
In cornering, lateral acceleration increases until one axle reaches its grip limit.
You cannot use the remaining lateral grip from the other axle.
The vehicle will only understeer or oversteer more on the limited axle.
Use the remaining grip from the other axle for acceleration or braking.
Which will then affect the load on the limited axle.
Roll center height, springs, and anti-roll bars (ARB) are equally effective ways to tune the balance.
All determine whether more or less of the total outside load is on the front or rear outside wheel. Of the three, ARBs are the easiest to adjust.
Any geometry effects can generally be overpowered by spring, damper, and anti-roll bar tuning.
Calculate the Total Lateral Load Distribution.
If you do not have an easy, reliable four wheel calculation, allowing the bicycle model to represent just the outside wheels can be a very powerful corner cut.
In order to minimize tire load variation, it is a generally accepted groupthink that you want the softest suspension you can tolerate.
Actual math and engineering to justify this policy is rare and questionable, and the gains are hard to measure, but I follow the practice.
There is good general agreement that a key benefit is allowing the tire to follow surface irregularities instead of skipping over.
At a minute scale, I argue that allowing more body movement lowers the Center Of Mass (COM) and correspondingly lowers the load transfer.
Reasons a suspension can be too soft:
body hitting the ground
worse, significant lurching Center of Mass movement
aero getting out of position
response time is too long (before reaching steady state)
7. Anti Geometry
You can get really far with this oversimplification:
Geometric anti-squat, anti-dive, anti-lift, anti-roll do not affect load transfer, just feel.
7a. Pitch center height, relative to COM, is the portion of the longitudinal force that is reacted by the suspension links instead of the springs, dampers, and bars.
At 100% anti-squat, no acceleration load transfer goes through the rear spring/dampers.
The entire moment is reacted through the suspension links.
The rear ride height does not change at all despite the higher rear axle load.
At 0% anti-squat, all of the acceleration load transfer goes through the rear/spring dampers.
The rear ride height decreases according to the full amount of rear load transfer.
For anti-squat between 0-20% (typical of double wishbone designs without binding):
The rear ride height decreases correspondingly less than it would if the springs carried the full load transfer.
The Center of Mass (COM) stays fractionally higher, rear load transfer and rear traction are fractionally higher.
7b. Roll center height is the geometric anti-roll percentage.
Roll center height, relative to the COM, is the portion of the lateral force that is reacted by the suspension links instead of the springs, dampers, and anti roll bars.
I steal Danny Nowlen's method of decomposing outer and inner forces.
Take a normal roll center construction method, and apply it to only one side.
That is how to find where the net force and moment from the suspension links is applied to the sprung mass.
7c. The angle of the roll center line from the tire to the intersection of the links is decomposed into the lateral force, and the vertical load carried by the links ("jacking").
Creating the lateral acceleration and the roll moment from COM to tires.
The lateral vector, directly under the COM, creates the roll couple.
Jacking (when positive) means a lateral force takes vertical load away from the springs, dampers, and bars.
A roll center below ground will use the lateral forces to pull the center of mass lower (“jacking down”).
Jacking goes directly into the links which, with minimal compliance, respond basically instantaneously.
Lots of jacking force in roll or pitch will make the car stiffer and peakier, because any change in lateral force changes the load on the part of the suspension that has no damping control.
7d. You intuitively/culturally know this already.
"Solid axles are bad!"
But do you know why?
Most 1900-1980C.E. solid axle designs have a roll center around axle height.
Most racecars have the COM around axle height.
Geometric anti-roll ~100% = violent oscillating springs/dampers/bars having no effect.
(If you don’t pay attention, it’s also easy to create lots of bump/roll toe out = oversteer.)
Move the roll center low, cut in camber that is permanently where you want it (except for changes in tire deflection), and solid axles can provide excellent tire and body control.
Unsprung mass is just a tuning problem.
7e. Roll and Pitch Accelerations
Just like yaw acceleration takes up part of the traction circle, sprung mass roll and pitch acceleration modifies load.
Tires have lower normal load while the sprung mass is accelerating towards them.
The couple around the roll/pitch center is unbalanced.
Tires have higher normal load while sprung mass is decelerating towards them.
The couple around the roll/pitch center is unbalanced.
Dampers and springs control the acceleration, and transmit the load due to net roll and pitch acceleration.
Underdamped overshoot means the load is increased for the whole, long deceleration.
8. Roll and Pitch Center Movement
Roll and pitch centers are taught with the car at ride height, going straight ahead.
You need to follow the both from braking, through turn in, midcorner, and exit.
Roll center and pitch centers are not single numbers, they are graphs.
8a. From your camber roll sweeps above, the outer and inner roll center heights are not in the same place.
The outer dominates, and is the one to focus on.
The unloaded suspension only has a little bit of grip force to work with.
The unloaded tire usually has less to gain from optimum camber, and its anti-effects can only affect a small amount of movement.
8b. With a double wishbone corner, the roll center gets lower in bump, higher in droop.
The shorter the arms, generally the more camber gain.
But the more the tire/instant center/CoM intersection point moves.
If "longer arms better", it is because the geometric anti-roll/anti-squat/anti-dive move less.
And the spring/damper see less load variation from changing anti percentages.
Lots of roll center movement will make the car less consistent in trail braking, corner exit, and over bumps.
8c. Your roll center will move more at the extremes of travel.
Trying to keep it in exactly the same place is not the answer.
(Congratulations, you've invented the swing axle, with its terrible and terrifying camber control. You'll see.)
I believe in reducing the rate of movement when going from static to loaded.
Let the inevitable bigger movement happen in droop when that tire/axle is not particularly loaded anyway.
With higher roll center in droop, the unloaded wheel(s) will be more responsive, but actually soften up as the roll center lowers when it gets loaded.
8d. From trigonometry, we know that the roll center will move the least when the lower links are closer to level.
Keep this technique in mind less for straight ahead, and more for roll at steady state, combined roll+braking, roll+acceleration.
Lateral movement of the intersection between the inner and outer roll center lines, even if the roll couple does not change, will affect the movement of the sprung mass and feel to the driver.
9. Spring/Damper/ARB Motion Ratios
Assuming 50::50 ish car with driver:
Keep the motion ratios as similar as possible in the front and rear designs.
I would prefer the same dampers front and rear.
This makes tuning changes equally effective and easier to understand.
Don't mess with rising or falling motion ratios until you know what you're doing.
Ratio changes are inevitable with direct acting spring/dampers, try to reduce it.
Ratio changes are easy to accidentally do with rockers.
Really watch the input/output ratio through suspension travel in rocker design.
My opinion: ARBs are the first place to start playing with nonlinear rocker ratios.
Where rockers make it much easier to control than direct acting.
10. Component Design
The upright has to fit inside the wheel, with brakes.
That will rule out some of your geometry desires.
The chassis, driver, templates, and powertrain will limit your pickup locations to a certain range.
A lot of it will wind up "designing itself".
10a. The worst design decision you can make is causing binding.
Even worse than bump and roll steer.
Not only dynamically terrible, it also breaks everything.
10b. Make the links and uprights super easy to make.
Make an effort to keep them flat on the jigs and machining setups.
10c. Make the springs/dampers/ARBS super easy to adjust.
Make any camber or toe adjustment super easy to do.
Ideally, no disassembly or even bolt removal.
How did I just learn about this?
You might even be able to 3D print them.
And do a full spring change later.
11. Congratulations, You’re Ready To Start Vehicle Dynamics!
You have designed mechanisms to control toe, camber, and total lateral load transfer.
They should all be adjustable as you start thinking about slip angles.
