Suspension Geometry and Kinematics

Track width

This has 4 main considerations:

• If the track is too narrow, the car may fail the 60deg tilt test
  • The minimum track width for a vehicle can be found with some trig and your vehicle's CG height
• Narrower track increases load transfer, reducing maximum potential lateral grip
• Narrower track reduces rear wing, front wing, and undertray width, reducing aero potential
• Narrower track tightens the racing line - can be very beneficial on a maneuverability emphasized course, such as the autocross and endurance.
  • Narrower generally makes a more compact car, that will at least in theory be lighter and have less yaw inertia

These need to be analyzed for an adequate tradeoff.

Track width is regulated in FSAE by rule V.1.3. Beyond the tilt test, if the vehicle has different track widths between front and rear, the smaller can be no less than 75% of the larger.

Wheelbase

Considerations:

• 1525mm minimum set by rules
• Shorter generally makes a more compact car, that will at least in theory be lighter and have less yaw inertia
• Shorter reduces steering angle requirement per a given corner radius, geometrically speaking
• Shorter makes the car less stable at high speeds, but the minimum set is well above any sort of safety concern
• Longer can allow more downforce, at least in theory, from undertray and side aero. But, is it worth the penalty?
• Longer can allow more flexibilty with CG longtitudonal location

An adequate compromise must be made.

Camber

Camber Justification

Camber is the front view angle of the tire from the vertical axis. The top of the tire pointing inwards is referred to as "negative camber". Most cars in the automotive industry, motorsports and FS/FSAE have negative camber.

The tire's camber will change as the suspension articulates. The tire will also see camber change due to body roll seen in a turn. This is known, unsurprisingly, as Camber gain. With 0 camber gain, a vehicle that rolls 1 degree will see 1 degree of camber change in the tire. On a double-wishbone car, there are two simple ways to achieve camber gain. The first is to make the upper a-arm shorter than the lower a-arm. The second is to place the inboard pickup points vertically closer than the outboard points are.

By making the upper a-arm shorter than the lower, and the inboard points closer together than the outboard, the wheel will gain negative camber with wheel travel canceling out part of the camber lost in roll. An easy way to quantify the camber gain is the Front-view swing arm length (FVSAL) - the line from the wheel center to the Instant Center (IC) of the 2 arms, found at the intersection of the extension of the arms line of action. This can allow for a simple sin/cosine relation for camber gain, although it is idealized since the FVSAL doesnt stay constant through the travel. For reference, the 2018 Ryerson car had a 45inch FVSAL, allowing it to run relatively minimal static camber.

Why would that be desirable? static camber could cause the inner part of the tire to overheat on the straights, and so even if the camber during a corner is ideal, the tire wear and tire temperature would say otherwise. So, general considerations in the solution:

• Minimize roll, to reduce the need for static camber. However, a stiffer car will be more upset by bumps, which is difficult to quantify.
• Use camber gain, but remember that in pitch camber gain will reduce the longitudonal grip (for longt, you want 0 camber)
• Account for camber deflection sources, and build in adjustabity of at least static camber.

The "ideal" compromise of these factors has requires detailed analysis.

As a note: positive camber is undesirable from a traction POV. Positive camber has the potential to improve drivability, as seen on 1950s F1 cars.

Toe

A minor adjustment. A stability fine tuning tool, to make the car feel better for the driver. Not a major performance item. Generally, toe out (front of wheels pointing outwards) is for response, and toe in is for stability. You would almost never see toe out on the rear, while the front is likely to be toe out.

However, that is within the usable range (-1:1deg?). Compliance that is often present, especially on the rear, can turn an otherwise decent car into an unpredictable deathtrap. Take into consideration:

• Toe base (mechanical advantage of the toe arm)
• Bolted joint tolerance
• Anything that is not axially loaded or not a direct line of action

As Claude Rouelle said:

“Nothing is rigid; 0.2mm of deflection here and 0.3mm of deflection there, and suddenly your front camber or you rear toe is far, far away from what you thought it was. From the driver input (steering wheel, brake pedal, throttle) to the tyres’ contact patch, there are dozens of non-linear springs, dampers, and hysteresis that compromise the racecar’s response to that driver input. Compliance is the biggest enemy of your driver’s Control and Confidence.”

Kingpin

Not that important for vehicle handling - Its main effect is on reducing scrub radius - but, scrub radius as well is less important on a racetrack with no major curbs/bumps where the steering wheel can be jerked around.

Kingpin adds a VERY minor self centering effect (can be usually neglected relative to caster, even at 10+ deg), and an also minor but not neglegible positive camber gain in steer. This is a symmetric effect left to right, but not once caster is taken into account.

However, to give an example, on a car with 4deg of caster and 8deg of kingpin, the negative camber gain from caster would overpower the kingpin by at least ~2-3x. There are equations to calculate this, but you can also set up your solidworks sketches correctly, and observe the effect in the sketches (if they are made movable), or in the assembly.

Caster

Caster Offset

Caster is the side-view angle of the steering axis to the vertical. It affects:

• Mechanical trail
  • Steering effort
  • "sense of direction the wheels want to go to" - i.e, where would the wheels steer if you let go of the steering wheel
  • High speed stability
    
• Jacking
  • Low speed oversteer inducing, as a tuning mechanism
  • Another variable in steering effort
  • Consider it as adding roll also!
• Steer camber
  • Negative camber on outside wheel, positive on inner - both good!
    • But, do you want more camber for a tight hairpin than for a wide sweeper? I dont think so! in practice, this can be neglegible if caster is low enough, but it is a factor.

Remember, you can have "Caster offset", to independently affect mechanical trail (the most important one) from the other 2.

Also, you dont want to drown out the pneumatic trail with too much mechanical trail. Youll just end up with super heavy steering all the time, instead of giving the driver a signal of understeer like the pneumatic trail should.

CAD Tips

Its helpful to set the CAD up for easy adjustment.

That can be done by:

• Integrating the suspension geometry sketches into the frame file
• Having a few levels of sketches, set up for ease of parameter adjustment:
  • A 2D "geometry sketch", that isnt movable, and has all the critical angles and dimensions set, as well as static roll center visible with driven dimensions
  • A 3D "geometry sketch", adding in caster
  • A 3D "linkage sketch" - movable, with equal length relations to the "geometry sketch" - so that it can be cycled through travel, while getting geometry updates from the geometry sketch.

It can look like this:

Movable Sketch

These sketches would then have in-context relations to the bellcrank, a-arms, uprights etc to have their geometry update accordingly to geometry sketch changes.