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.

Tire data!

Amazing what you can get when you just ask for it. Managed to get free-rolling cornering, and spring-rate data on both a 20 x 7 front and a 22 x 8 rear, as well as some relevant compound information from one of the manufacturers I've been looking at. Excellent!

Unfortunately... the quality of data is not that good. It's a belted bias construction and has some of the same somewhat questionable things I've seen in similar tires (from FSAE). Even contains Pac '96 coefficients, which I may be able to tweak to get to more reasonable values.

Not the best, but it may give some insight for initial mass distribution, alignment, spring and bar rates.

Revised kinematic... ideas

Did some thinking. The scallops were bangin, by the way. I'm tempted to make some ravioli now. (Edit - I'm doin it!)

Anyway. Was thinking, and rambling to Grant about how the hell I'm gonna do this analysis. You can look at any variable vs any variable with a suspension. It's an overload of information. It's ridiculous. It's overwhelming.

There's a school of thought that you can't really do suspension design without tire data. I used to even agree with this myself, but realize now it's at least half bullshit. True, without tire data I'm not gonna know what camber and inflation to keep a tire at mid-corner, for a given load, to generate the most cornering force. But some shit is pretty clear.

Roll-steer, probably particularly front to rear balance of roll-steer, is always going to do the same thing to a car on entry. Over- or under-yaw (though I can think of situations that might be beneficial). Diabolical amounts of bump-camber or bump-steer while at the limit of traction, is going to upset the balance of the car. As such, those two items I can probably work to minimize and then leave static alignment settings for when (if) I do get tire data.

The plan is now as follows. Evaluate a set of metrics at each of the following "snapshots" in time This allows for a few quasi-steady state pictures of what the car is going to do through a corner. It's not the full "movie," it's not just a "picture," but it's at least a couple slices that you can hopefully interpolate between:

• Static (baseline)
• Straight-line braking
• Trail-brake entry
• Pure cornering
• On-throttle exit
• Straight-line acceleration

These are the metrics, to be evaluated at each corner:

• Load
• Inclination angle
• Steer angle
• Bump-steer (linear fit for +/- 0.5" wheel movement.. or some arbitrary amount)
• Bump-camber (linear fit for +/- 0.5" wheel movement.. etc)

At this point you might think that I don't give a damn about roll centers. And you're right! At least in and of themselves. Their effect is wrapped up into "load." Ultimately it all comes down to the tires, and the tires react to loads and angles imposed on them. They don't care about imaginary points and lines in space. If when its all said and done it looks like the setup favors something where the kinematic roll center (KRC) moves around a whole inch or two or three, so be it! I don't care what it does so long as it makes my tires happy. Designing around low KRC migration because some old men said so, is silly. Doing anything just because some old men said so (even Carroll Smith or Claude Rouelle), is silly. Prove it to yourself, and screw anything else. I bet the late Mr. Smith would even support that.

Not to mention supposed KRC's are kind of a load of crap anyway, particularly at high loads, deflections, and compliances. Roll Center Myths and Reality (W.C. Mitchell) is a good read for those interested.

The advantages of small tires

Got some time to kill while my scallops dethaw. Drove all the way up to Cleveland to go the damn Whole Foods hoping they'd have dry scallops. Fresh out, did get a bag of frozen ones. They may turn out to be legit, we shall see.

Anyway. Seems these days that everyone and their brother is all about megawide tires.

Yea brah, think I'm gonna put some 325's on my Z28 Camaro. Gonna be wicked fast and everyone knows it. That'll get me some respect. That and the T-tops.

A lot of the time wider is better, but there's a limit.. particularly on light, low-power cars. At some point you can have too much tire and not enough load and speed to get it working right. There are definite advantages to using small tires in open wheel, since uncovered tires generate lift and drag. Yea, lift.

Tommy Sizzle... that's crazy, brah! So like, how significant are we talkin' bout with the lift and drag?

Glad you asked. I was thinking about that earlier today! I don't personally have test data, so I'll reference some values from Race Car Vehicle Dynamics, and we'll pick 120 mph as our test speed. Pretty sure these numbers only hold true for being in relatively clean air, but since I don't have any sort of reduction for the rears I got nothing better than to use the same assumption all around. It is what it is.

• 20.0 x 7.0F, 20.0 x 7.0R (FSAE): 26 lbf lift, 83 lbf drag (27 hp @ 120 mph)
• 21.5 x 8.0F, 22.5 x 11.0R (Star Mazda): 39 lbf lift, 124 lbf drag (40 hp @ 120 mph)
• 22.0 x 9.0F, 26.0 x 12.5R ('70 Ferrari 312 B): 48 lbf lift, 155 lbf drag (50 hp @ 120 mph)
• FSAE with flat wheel caps: 25 lbf lift, 70 lbf drag (22 hp @ 120 mph)

That's a significant quantity I'd say. Non-trivial at least. Essentially an extra 23 hp @ 120 mph by going from original spec wheels to FSAE size, and an additional 5 hp on top of that with caps.

There are a couple 13" radials I'll be looking at which might be good for this application. Light construction, and relatively soft compound that I can probably get away with. The thought is that with increased footprint efficiency I can get equivalent or better grip than a big bias slick, with a little better wear rate, and smaller profile. Win win win.