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Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers. This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr., Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by e-mail to: firstname.lastname@example.org Readers are invited to subscribe to this newsletter by e-mail. Just e-mail me and request to be added to the list.
CURRENT F1 CARS DO HAVE ANTI-DIVE
I was reading your April article [based on February 2012 newsletter] in Racecar Engineering on, "Questioning the rule makers." You stated, "Most current F1 cars have little or no anti-dive or pro-dive."
I had intended to write to you last year regarding something I observed in a late season F1 race. I noticed that from a roll hoop mounted camera it was evident that the car nose was rising under braking. This would imply greater than 100% anti-dive. I don't recall which constructor it was; however, it seemed it was more than one of them. How is this possible, and what would be the benefit?
I was wrong.
Until recently, my statement would have been accurate, but it appears F1 has suddenly rediscovered anti-dive, and there is a massive “trick of the week” effect going on, with designers going to the opposite extreme and using outrageous amounts of it. In fact, this may have a lot to do with the “prominent nose bridge” (or maybe brow ridge?) noses that have appeared. The front inboard pickup points of the upper control arm are being raised to create anti-dive, and simply having a higher or more convex top surface on the nose may be undesirable for reasons of sight lines, side view area, and lift.
And it may well be that some cars now have more than 100% anti-dive, so that the front actually rises under braking. Why might that be?
I do not think it is desirable to have the car pitch rearward under braking. However, if the rear lifts under braking, it may be aerodynamically preferable to have the front lift similarly, so that pitch remains minimal, even though the ride height increases. It is entirely possible to have 100% anti-lift at the rear as well. That would mean we could have zero pitch without the front lifting.
My consulting clients are mainly hobby racers. Very occasionally, I get calls from top-level NASCAR engineers. I get absolutely no F1 work. Consequently, I have no idea how well F1 engineers actually understand vehicle dynamics. With the money and prestige the series has, one would think they’d be the best, but I don’t have the visibility to confirm or dispute that.
I do know that there is lots of incorrect information published about anti-dive and related effects. I’ve seen one graphic recently that apparently has circulated quite a bit that purportedly shows geometry for 100% anti-dive. It shows the control arm pivot axes in side view – the axes defined by the control arm attachment points to the tub – meeting at the sprung mass c.g. in side view. This replicates illustrations in a number of old chassis books, but it is incorrect in at least two ways.
First, the side-view geometric properties depend on the actual side-view projected control arms. These are the lines where the control arm planes intercept the wheel plane, not the control arm pivot axes as seen in side view.
Second, we do not have 100% anti-dive when the side-view projected control arms intersect at the c.g. We have 100% anti-dive when the side view force line intercepts the side-view resolution line at sprung mass c.g. height. The side-view force line is the line from the contact patch center through the side-view instant center. The side-view resolution line is a vertical line located rearward from the front axle line by a percentage of the wheelbase equal to the percentage of ground-plane retardation force exerted by the front wheel pair when braking. This will generally be a greater percentage than the static front weight percentage, so the resolution line will generally be aft of the c.g.
If the front suspension meets this criterion, the front suspension will neither compress nor extend in braking, as the questioner correctly understands. If the front end is lifting in braking, that implies that the anti-dive is more than 100%: force line slope, and jacking coefficient, are greater than described above.
But it is important to note that sprung mass pitch, and front wing height, also depend on what the rear suspension does. 100% anti-dive only results in zero pitch if the rear suspension has 100% anti-lift. It is quite possible to provide that. There are many production cars that have more than 100% anti-lift. Almost any car with trailing arm or semi-trailing arm rear suspension jacks the rear suspension down in braking. This potentially results in wheel hop or chatter, but in practice, as long as either ABS or the brake bias keeps the rear wheels from approaching lockup, such cars brake just fine.
With SLA or double wishbone rear suspension, 100% anti-lift requires a lot of inclination of the side-view projected control arms – more than is needed for 100% anti-dive at the front. The need for extreme-looking geometry results from the fact that the ground plane force we have to work with is smaller at the rear than at the front.
So it is possible that a designer could deliberately make the front end lift in braking because the rear lifts, or it is possible that even an F1 designer might have read the wrong literature, and miscalculated.
Is there a penalty in the car’s ability to absorb bumps while braking when there is that much anti-dive? Yes. However, when the track is very smooth, that may not matter so much. And when the alternative is to use stiffer springing instead, some anti-dive may be deemed preferable to that.
My own default recommendation regarding anti-dive lies somewhere between the recent former practice of using little or none, and the current fashion of using a huge amount. I generally suggest that the side-view force line should have a slope at static of around four degrees, and no more than eight degrees in any condition. Depending on brake bias, wheelbase, and sprung mass c.g. height, this will generally result in somewhere between 25% and 60% anti-dive.
EFFECTIVE UPPER CONTROL ARM PLANE IN STRUT SUSPENSION
From all of the books I
have read regarding finding the swing axle length on strut suspension, they say
that you project a line from the top of the strut, square to the centerline of
the strut until it intersects with the line of the lower control arm.
I understand this 'in the old days' when struts were in line with the lower ball joint; however I am confused with modern suspension where the strut is bolted to the side of the steering knuckle. Should the upper line project square to the strut? Or should it be square to the 'virtual' strut (line between strut top pivot and ball joint)?
To really be accurate in finding front view geometry, it is necessary to find the front-view projected control arm. This will not contain the top pivot of the strut, although it will come fairly close to doing so. The effective upper control arm plane is the plane perpendicular to the strut axis, containing the top pivot center of rotation. The front-view projected control arm is the line where that plane intersects the front axle vertical plane. Ordinarily, in front view this line will pass slightly above the top pivot center of rotation. However, with two-dimensional drafting, a line through the pivot center and perpendicular to the strut axis will do as an approximation.
Correspondingly, the line where the effective control arm plane intersects the wheel plane is the side-view projected control arm. In side view, this line will usually be further above the pivot center than the front-view projected control arm is in front view.
It is the strut tube axis that we use for this, and not the steering axis. The line containing the ball joint and the top pivot center is the steering axis. We use that for determining front-view steering axis inclination, front view steering offset or scrub radius, caster, trail, and pin lead or trail. We use the tube axis for determining camber change, caster change, anti-dive, and anti-roll properties.
The lower control arm plane is determined the same way as in SLA suspension. It is the plane containing the lower arm pivot axis and the ball joint center of rotation.
Using the upper and lower front-view and side-view projected control arms, thus defined, we are able to find the front-view and side-view instant centers.
THREE-LINK GEOMETRY TO COMPENSATE FOR DRIVESHAFT TORQUE
For a 3 link solid axle, how is the offset of the upper link determined in order to minimize the effects of drive shaft torque on tire loads?
The offset of the upper link relates to a number of other factors. Most commonly, we know the height of the lower links, the tire radius, the height of the upper link attachment to the axle, and how far we can offset the upper link laterally from vehicle center or spring center. We then have a means of adjusting the angle of the upper link, and possibly its height, and we need to determine what that adjustment needs to be.
There is an equation for this. We may define the variables as follows:
LyU is the lateral (y axis) offset of the upper link from vehicle center, or from spring center.
HL is the height of the lower links from ground level, at the axle vertical plane.
HU is the height of the upper link from ground level, at the vertical axle plane.
NRP is the ring and pinion ratio, or the overall rear end ratio in the case of a quick-change.
RT is the loaded radius of the tire.
ϴU is the angle of the upper link from horizontal.
Tan ϴU = (RT (HU – HL)) / (NRP * HL * LYU)
It will be apparent from the equation that we can get the required compensation many different ways, but the upper link angle needed increases as we spread the upper and lower links apart. It increases as we reduce the lateral offset of the top link. It increases as we go to taller rear end ratios.
We may want to use less upper link inclination than the equation calls for, so the suspension doesn’t jack so much diagonal percentage into the car under braking. The equation should be considered to define the upper limit for top link inclination, when the top link reacts braking torque from both rear wheels.
Rules permitting, it is possible to have full compensation for driveshaft torque under power, and also have symmetrical behavior in braking. This involves the use of a birdcage or brake floater on the left. Barring that, there is a necessity to compromise between the conflicting objectives of minimizing roll and diagonal percentage change under power and minimizing these in braking.