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SIMILAR CARS, EXCEPT DIFFERENT TRACK WIDTHS
I was asked a question by a friend about his short oval car that has me a bit stumped and I wondered if you could guide me in the right direction.
I have been doing some set-up work on several cars over the last few years, specifically two formulas of car that are very similar and grew from a common racing ancestor. It is quite easy to make a judgement of equivalency between these cars by comparing wheel rates, because their geometries are so similar. As they have max track width rules the footprints of the cars are very similar too.
What I normally start with as a setting for wheel positions is to line the inside wheels up, and with the rear track about 20mm narrower than the front, that 20mm shows up at the outside wheels by the outside-rear being inside the line of the outside-front by 20mm at about 6Ē off the ground (string line) -- my theory being that because of independent front and live axle rear, the outside front camber of about 3 degrees will actually negate some of that 20mm in terms of where the front tyreís contact patch averages out, and I donít want the outside-rear farther outboard than the outside-front.
My friendís new car is actually a Ford Anglia ďclassicĒ version of these other two types that Iím used to dealing with (run to pre 1976 rules), and it has some slight differences and the car builder has made the rear track much smaller than the front track (by 110mm overall), and both tracks are narrower than the more modern cars. This is where Iím having difficulty making a comparison between the car types and Iím not totally sure what it is I actually want to compare to try to get to the similar sort of front/rear grip balance.
Delving in my copy of Milliken:
To get equivalency in load transfer in an independent front I compare wheel rates relative to the track widths of the two cars, because load transfer alters with roll rate relative to the track, and roll rate is relative to wheel rate. Hence WR(narrow car) = WR(wide car) x (wide track/narrow track),
at the front. This gives an answer I expected of a slight increase in front WR due to the front track widths of 58.2Ē and 54.8Ē (at centres of tyres).
To get equivalency in load transfer at the rear live axle I compare roll rates based upon track width as before (58Ē and 50Ē respectively), but also take into account the ratio of spring bases squared in order to account for the narrower car having a narrower spring base and the effect this has on roll rate. This gives a reversal in what happens at the front Ė which I still think makes intuitive sense. The result is that my simple calculation gives rear spring rates that are increased from 200lb/in to 263lb/in. I made the spring bases to be 42Ē and 34Ē respectively.
What is really puzzling me is that the calculations would say that by comparison with what Iím used to this classic car should have major understeer. However the driver was asking me about the car because it was a bit loose, with about the same diagonal weight % I would have started the car on anyway (51.5%).
My main questions are: 1) am I doing all of the above right qualitatively? 2) is the lack of expected understeer due to the positions of the wheels (diagram attached)?
I understand that if we take an outside wheel inboard it will make the car lose, but drive straighter, is that simply what is happening here? I am tempted to think that he would benefit from widening the rear axle to get to a situation not unlike where I would start the modern cars (20mm narrower rear, perhaps). Before I tell him he needs a new axle I would be grateful for your input.
Iím not wedded to the idea of making the load transfers equal, but I thought it would be a good basis for comparison. The modern cars are slightly lower in CoG, and the classic cars are on better tyres, so load transfer should be greater for the classic. (Racing is clockwise, ľ mile flat oval. Both cars are about 48% rear with driver).
Right approach qualitatively? Well, partly. Itís okay to try to get similar load transfer distribution to the old car as a starting point for the new car. Even if you get that, some adjustment is likely to be necessary. However, to use this approach correctly, you need to calculate total load transfers for both cases, including the geometric and unsprung components, and pick elastic components that make the distribution of those overall totals similar to the old car. Even if the new car has identical roll center heights to the old car, all load transfer components, including the geometric and unsprung load transfer components, will be different with different track widths.
To keep the elastic angular roll resistance rate Kφ the same for a wheel pair when you change the track, the wheel rate in roll needs to vary inversely with the square of the track, not its first power. Varying the wheel rate inversely with the first power of the track keeps the linear displacements the same, but a given linear displacement at the wheel translates to a greater angular displacement when the track is narrower.
Similar distribution of Kφ to the old car will not give similar load transfer distribution when the tracks are changed by dissimilar percentages, nor will keeping linear displacements the same give similar load transfer distribution. The end where the track was narrowed more will see an increase in its percentile share of the load transfer.
Yes, moving the inside rear wheel inboard (or the outside one outboard) tends to add oversteer, particularly power-on. Exactly how big a factor that is in your case is harder to say, but we can be confident that there is some effect, and it is in that direction.
One other thing that happens when you narrow the rear track is that a given amount of tire stagger acts like more, or at least the theoretical neutral or least-drag stagger for a given turn radius is less.
Aligning the inside rear wheel to the inside front wheel, and using the resulting line as a datum, is popular but I donít recommend it. Cars aligned this way will run well in some cases, but the method presents problems. It results in changes to the aim of the rear wheels any time you change wheel offsets, track widths, or camber settings. I recommend having two parallel strings or lasers, one on either side of the car, positioned from some feature on the frame, not from the wheels. You then measure the alignment of all four wheels with respect to those lines.
From a practical standpoint, I guess you can just be glad the car was halfway decent on the first cut, and adjust from there, even if it was a bit different than you anticipated. Even with the best theoretical basis for an initial setup, you donít expect perfection the first time you run the car.
Thanks for your answer - I had a feeling I was doing something wrong. I'll work it through more thoroughly like you say. I was hoping that I could short cut that but I guess I can't. The driver did report power-on oversteer as the problem, and he does have quite a lot of inside % when he's in the car, so I think we could space the inside rear outboard some more and pretty much stick with the spring rates he has now as a first guess before further testing. The tyres that are used don't have much stagger available, but I will certainly get the driver to check what sizes he has been using on the car.
As an aside, I measured the front geometry for "roll centre" purposes, and calculated based on your method with a 70% resolution line. The anti-roll height was 3.5" static and 2.9" rolled 2 degrees. Whilst looking at the car (on MacPherson struts) we decided that it could be lowered 1" at the front, which would bring it more level with the rear. So, I recalculated for the lowered condition and got much lower anti-roll heights of 0.5" static and 0.15" with 2degrees roll. I know that basically, independent suspension should have low anti-roll height to avoid jacking, etc., and I'm not worried by have so little anti-roll, because it has removed a lot of the side-scrub that was happening at the outside front, but this strut layout seems very sensitive to ride height change. I think that by reducing the ride motion (stiffer springing) we might make the car more consistent during pitch motion. I could try to alter the lower links to take the roll centre back up a bit, but that could lead to packaging problems with the rack and tie rods to eliminate the bumpsteer it would give. So my current plan is to stiffen the front springs to compensate for the lower anti-roll from the links, and
bear in mind that the whole car may need to go stiffer in the future. Can you see any holes in my reasoning here?
It certainly is true that strut suspensions produce big changes in roll center height with ride displacement. They have what I call a Mitchell index of considerably greater than one: with ride displacement, the roll center moves the same direction as the sprung mass, and a considerably greater amount.
I donít know if Iíve mentioned this previously, but Bill Mitchell calls this quantity an ďincline ratioĒ. For a long time I couldnít understand why, but I finally found out. The term does refer to the slope of a line, as the name suggests. It just isnít a line that would appear on a geometry layout of the suspension. Itís the line you get on a graph when you plot roll center height as a function of ride height.
The camber recovery in roll also diminishes to a very low value when we lower a strut suspension. In some cases it may even go negative Ė the wheels lean more with roll than the body does.
I would agree with just accepting lower geometric roll resistance at the front, and less camber recovery, especially for an oval track application. Remember that when you only have to turn one way, not only can you use stiffer elastic components to control roll and camber, but you can also set the car up with any static tilt and camber you need to get the body and wheel attitudes where you want them in the turns. On production-based cars, available adjustment range may limit this. That will depend on the car, and the rules.
You can also control wheel load distribution with static settings. The static settings have relatively greater influence on entry and exit, and the elastic values have their greatest influence mid-turn. Knowing this, you can optimize balance in different parts of the cornering process, once youíve got the general balance reasonably good.