Static cross-weight

While I'm at it I might as well get into cross-weight. You might be thinking...

Well who cares on a road racer? Besides I can just corner weight the cross load out.

Just you hold on a minute. Two things to think about...

First, what is it and what does it do? Percentage of load taken up on a diagonal. I do it as the percentage of load taken up by the RF and LR, but either works. On an oval setup it's a good trick to get power down better out of a corner. With a cross-weight > 50%, you are "preloading" load transfer to the outside on the front axle, and the trade is you can "preload" load transfer to the inside on the rear axle. Having extra load on the LR tire in that case will let you get on the throttle earlier and more confidence. Obviously the trade off is the car will understeer more since you're overloading the RF more.


On a road course car, cross-weight > 50% will give you asymmetric balance, particularly on-center. Car will understeer left and oversteer right. Not what you want when trying to tune the car. Having looked at some of the telemetry from my guys' FSAE car last year they had that issue, and I'm kinda curious now if they had a cross-weight problem.

When doing corner weights, you can get rid of static cross-load by lengthening or shortening pushrods and such. Now that I think about it though, I suspect you could be fooling yourself by doing this, particularly if you have asymmetric wheel rates. Asymmetric wheel rates are surprisingly easy to get if your manufacturing isn't perfect or if your spring rates aren't all the same. Having measured springs on the FSAE car, there's a damn lot of variation. Four springs all stamped "300 lb/in" could easily range from 290 to 340.

An interesting way to check would be to take corner weights with and without the driver.

The above example are some representative FSAE numbers. It shouldn't be too hard to position the seat on centerline. While I'd expect the F/R load split to change a bit when the driver gets in, the cross sure shouldn't! Cross changing with vertical load, or acceleration, could lead to some weird stuff... if you put a different driver in, as fuel burns off, or even if you just get onto a section of track with some banking.

In the above example, if everything had been manufactured perfectly and air pressures were set, I'd suspect maybe the RF and LR springrates are a bit higher than the LF and RR. A swap of the LR and LF springs might fix it.

Food for thought.

Hopefully I'll get back to more design-related stuff soon. Been busy with other crap, and gotta drive up to Buffalo at 430am tomorrow morning...

Preload and bump stops

It appeared there was some speculation or confusion elsewhere as to the impact of spring preload on handling. Bump-stops are related. Both are important parameters. Unfortunately I don't think we really appreciated what they all did when I was on FSAE.

Balance is essential to good race handling. Balance inevitably comes down to managing dynamic tire conditions. Load is one aspect.

I think most people get the basics. More front bar (or spring, or damper [momentarily]) = more lateral load transfer relative to the rear = more understeer. The opposite is true for adding rear stiffness.

If you were to put your race car on an SPMM, you could generate a plot similar to what's below... looking at lateral load transfer as a function of chassis roll angle. Rough indicator of cornering balance. Ideally you'd want load transfer as a function of lateral acceleration (Ay)... the two plots are related but not the same.


Anyway. This might be a typical baseline setup with no preload, not hitting bump stops, and linear installation ratios. The slopes, and difference in magnitude between front and rear load transfer are what's important. In this example it's pretty straight-forward. The front has a higher roll stiffness, takes a higher percentage of the load transfer, and all other things being equal (50/50 corner weights, same tires all around) the car would probably understeer slightly. The feel should be very progressive and predictable.

If you were to add a hell of a lot of front preload, it may look something more like this.


If your tires and suspension were infinitely rigid, that initial slope would likewise be almost vertical. The front suspension is locked. Since the tires have a spring rate and inevitably there's compliance in your suspension, the rate is just very high.

There was an article in Racecar Engineering that (I believe) claimed lots of front preload would help a car "cut in" on entry from extra heat into the outside front tire. I find that hard to believe. It's no different than having a stiff anti-roll bar that "switches off" after a given amount of displacement. There are other reasons I won't get into, and I can also vouch for SPMM plots.

Until I see instrumented track data that proves otherwise, to me, I'd think front preload will "numb" the handling on-center.

Bump stops I am damn sure of, and the way they behave backs up my thought on pre-load.


If you roll onto a bump stop in the rear, your rear roll rate is going to increase substantially, very quickly, and rapidly shift the balance to oversteer.

The point of all this being, unless you manage it all carefully, going overboard with preload and bump stops and what have you can make for really non-linear or bizzarre handling. If you don't need it, or can't justify the reasoning for it... why bother?

Further clarification on Mz and Mx

Thought about this some more, given that a few people asked about it. Best way I can think of each of them is a dynamic measure of where the force center of the footprint is.

When making a simple vehicle model you might assume tire lateral force acts right under the centerline of the spindle. This isn't the case. Due to the black magic of tires, the lateral force trails the centerline, which is what gives rise to pneumatic trail and aligning torque. Mz is really a measure of how the pneumatic trail is changing, and where that "Fy action point" is moving around. Since yaw moment is dependent on Fy cross-multiplied by the distance from the "action point" to the CG, the fore-aft movement measured by Mz does affect your vehicle balance.

Likewise with Mx, in a simple model you might assume your track width to be constant or just a function of how much lateral scrub your suspension generates. In reality as the tire deflects under lateral load, the center of pressure ("Fz action point") deflects as well and your track width changes length or shifts over (deflects toward inside of turn). That in turn will definitely modify your lateral load transfer!

Bottom line, they're both important and non-trivial.

If I were running a MechEng department... [Some of this stuff is really practical!]

...I'd want a class for "Practical Application of Engineering Tools." 3000 or 4000 level, based heavily in Matlab. Probably 4000 level, since MCEN3030 - Computational Methods, is a junior class and pretty much murders you. Back then I eventually got decent at Matlab from having it thrown at me mercilessly, but when I got to work I couldn't do anything PRACTICAL with it. Like.. how to load a damn Excel file. Matlab has so much built in stuff it's unbelievable and I didn't know about any of it.

On the other hand, a bunch of crap that was just theory without application, as far as I was concerned, is really practical! Bode plots for example, who knew!! I sure didn't. I think I either skipped that lecture to work on the racecar, or it was when I had sliced my finger open on a lathe. (Freak accident, but don't EVER think you're the master of the machine. It can, and will get you).

Anyway. Don't let anyone try to fool you into thinking ride quality isn't important on a racecar. It's critical. There's a reason why professional race teams put a lot of time in 7-post ("shaker") testing.

What is a 7-post test? You put your vehicle on a special contraption, and shake the hell out of it. More precisely you recreate the disturbances and undulations the car is going to experience on a racetrack.


Why? We know that tire load variation is bad for grip. If you didn't know that, it's easy to conceptualize. If your suspension is stiff as a brick, if you had rigid links instead of springs, the car would chatter, skip and bounce over the race track. The whole reason for having a suspension is so it can be compliant and ride easily over bumps without upsetting the tires and chassis. The ratio of input from the ground, to force passed up into the vehicle, is transmissibility.

Where do Bode plots come in? It's a way of plotting signal amplification (transmissibility) and phase lag versus input frequency.


Changing masses, spring rates, and damping rates will change the shape of your curves. If I know what the major frequency content is of my suspension in a critical part of the track (big braking zone, corner exit, whatever) I can adjust my suspension rates to deaden that vibration out and increase my mechanical grip.

Wheel rate, tire rate, and damper rate are easy enough to get, as are the sprung and unsprung mass at a corner. If you knew the tire damping rate (hint hint) you could in theory fire up Matlab, play with some of your rates, and do a form of virtual 7-post testing. The Bode plot is a good way of seeing at a glance if your suspension is doing what you want or if you're moving in the right direction. Up until now I just thought it was some silly thing without a practical use.

As an aside, since at each corner of the car you have a sprung and unsprung mass, you'd think one would be acting as a mass damper relative to the other. For a long time there's been the phrase that you want to "always reduce unsprung mass." Generally I think this is true. There may be the case though that you could tune your unsprung mass to go along with everything else and really zero in on the frequency response you want.

Aw snap.

Ohhh... yea...

I gotta give it up to the folks at the F1-Info site, wow. Some amazing photos and drawings.

This... is a beast. 1972 flavor of the 312B-2. I do kinda like that extra fairing that blends the roll hoop into the rear wing, and the NACA ducts which feed the oil coolers.

Also the '70-'71 312B-1...


And the '69-'70 312B

FVSAL Decisions

Allright enough screwin around. Time to decide on a few things, namely baseline FVSAL and how it progresses through heave and roll. In case it has been a while since the last time you designed an independent suspension, we'll go through a refresher. Take a look at the following graphic I stole off a Google image search:

You can see the a-arms, and if you virtually extend them out they intersect at a point, A. The distance from A to the center of the spindle (NOT to C) is your "swing arm length." Basically when the wheel moves it's going to act like it's just on a beam that pivots around A. This length defines your camber gain in ride and in roll simultaneously. You cannot change one without changing the others.

Really long FVSAL: Very small camber gain in heave. At FVSAL = +inf, bump-camber = 0 degrees per inch, and roll-camber = 1 degree (wheel) per degree (chassis).

Conversely, short FVSAL (near half your track width): Small or zero camber change in roll, and high camber change in ride.

You can also have a negative FVSAL... it's all summarized here:

The equations to generate the above are very simple, and can be found in RCVD around page 625 (plus or minus).

Essentially how parallel or non-parallel your a-arms are, defines your FVSAL. To make things more difficult though, your FVSAL changes as your suspension goes through travel.

Equal-length a-arms: no change.

Top a-arm shorter than bottom: outside FVSAL shortens in roll, inside FVSAL extends (and can go negative). FVSAL also extends in heave, shortens in squat.

Top a-arm longer than bottom: outside FVSAL extends in roll (and can go negative), inside FVSAL shortens. FVSAL also shortens in heave, extends in squat.

By the way I figure

• I want the integral of the roll-camber curve to be relatively small. I don't necessarily care what it is on-center, so long as when the car takes a set in a corner I haven't lost too much camber.
• Going down a straight, when not grip limited, I can probably stand to have some bump-camber (while still having little bump-steer). The benefit is I pick up some roll-camber control.
  
• When mid-corner I want to take care of the outside tire more than the inside tire, as it is going to be most heavily loaded and dominating grip level.

As such I believe I want a positive, non-infinite FVSAL on center, with the top control arm longer than the bottom so as I go into a corner my outside tire bump-camber control gets progressively better. Additionally, under braking when the fronts are highly loaded my FVSAL will extend for progressively better camber control over bumps... and if I do the same in the rear, under acceleration I will have the same effect for when the rear tires are heavily loaded!

Bits of drivetrain

Got to working a bit more on the rear wheel assembly and drivetrain layout. I'm still on the fence for differentials, though I'm leaning toward the chain-drive Salisbury offered by Williams Racing Development. The other option is the chain-drive Quaife ATB from Taylor Race Engineering. In any event I'll be using tripod joints on both ends of the axle.

Craig Taylor's FSAE and DSR tripod housing is billet steel. Bullet proof in that application, but also weighs in at about 1 pound. There are some alternatives for Formula Fords that are billet aluminum with steel sleeves to take up the load from the tripod rollers. We played around with this on the '07 FSAE car, but the trick is getting the sleeves to stay in place. I suppose I could bond them in there. In any event, if I remember right it saves about 1/4 lb per unit.

In other news... got camber? I do. Got all the wheel mates set up properly so I can adjust track width and maximum static camber fairly easily. I'm assuming I won't throw more than -4 degrees of camber at the tires. Certainly won't on belted bias slicks, but I'm keeping the option open to run radials as well.