guido@twitch.UUCP ( G.Bertocci) (05/21/85)
I have been intensely amused at the incredible number of
misconceptions that have been posted in netnews and
printed in the general media on how suspensions work.
These articles come from everyone including so called
authorities such as Car & Driver, Road & Track, BMW Roundel, and
advertisers for suspension products.
These articles often completely contradict each other.
One of the favorite suspension myths is the so called "weight
transfer" theory as a function of "stiff" or "soft" suspensions.
THE "WEIGHT TRANSFER" THEORY IS TOTALLY BOGUS.
I will prove that it is false.
I will simplify the discussion with several assumptions and simplifications.
1. The auto in question does not change mass during cornering, or
braking, or accelerating (forget about fuel and tire wear and
relativistic effects).
2. It is easier to solve the problem for a steady state solution
so the car in question is circling a flat skidpad of a fixed
radius at a constant speed.
3. I will draw the dynamics for the front suspension only, (it is
easier to do 2D drawings than 3D). The identical arguments
can be made for the car as a whole.
Remembering freshman physics, the entire situation can be represented
with ONE point,
CM - center of mass,
However, it is useful to have several additional reference points,
LT - left tire,
RT - right tire.
AR - axis of rotation around which the CM rolls during cornering.
(Coming out perpendicular to screen at about the level of the
subframe of a car, or slightly lower than the center of the wheels).
FmT
|
v CM - center of mass
X <-FcT
AR
FmL ---- FmR
| |
v v
LT <-FcL RT <-FcR
At each point we can represent all forces with a horizontal and a vertical
vector.
FmT - total force down due to mass of car
FmL - force down measured at left tire
FmR - force down measured at right tire
FcT - total sideways force due to centripetal acceleration of car (cornering)
FcL - sideways force at left tire
FcR - sideways force at right tire
In addition:
FmT = FmL + FmR = constant (car does not change mass)
FcT = FcL + FcR
FcT is completely defined by V*V/R where V is velocity and
R is the radius of the turn
The entire problem can be represented with forces at CM, however,
what we really want to know is what is happening at LT and RT,
and in particular FmL and FmR.
For any given speed around a skidpad, FmT and FcT are
constant.
For ANY suspension, if we know the angles and lengths of sides of
the triangle, (CM,LT,and RT) it is simple geometry to compute
FmL, and FmR.
During straight line driving FcT = 0, and FmL = FmR = 1/2FmT.
During cornering the change in FmL will be identically = -FmR,
and the change can be computed by knowing where the CM
is relative to the tires using simple geometry and FcT.
There is NO WAY one can transfer weight from left tire to
right tire or anywhere else unless one moves the CM.
As a matter of fact, there isn't anyway to transfer weight anywhere,
either with springs, sway bars, or spaghetti.
Does the CM move during cornering? Some, but not very much.
The CM does not move up or down (Unless they are so soft they bottom
out). A car rides on springs that obey Hooke's law.
(Forget about progressive springs, expecially since
they tend to raise the CM during cornering).
Since we have shown that FmL = -FmR, then by Hooke's
law, the left side of the car will move down by the same amount
that the right side moves up.
(On progressive springs, the left side would move down less than
the right side would move up, therefore RAISING the CM which deteriorates
cornering ability.)
The CM does move side to side slightly. If the CM were
situated directly on the AR (axis of rotation) then it
wouldn't move side to side either, however, the CM is
usually slightly higher that the AR.
Now for some numbers as to how much things really move. Let's
pick some extremes. Some of you have probably seen the
advertisement for Koni kits with a Camaro that looks
like it is about to flip over, and then with it perfectly flat.
The Camaro has between 7-8 degrees of body roll.
The second photo is a phony since the car isn't moving as fast.
If you look at pictures of race cars such as Ray Kormans BMW, Corvettes, or
other cars with extremely stiff suspensions one will find
that about the best a road car can do is 2-3 degrees. (Ignore Gran Prix cars).
(You will get 1 degree simply from tire deflection, and bushings compressing).
Pick an average car with a front wheel track of about 60 inches
and a CM of 20 inches and a AR of about 10 inches from the road.
With 7 degrees of roll the CM will move sideways 1.23 inches,
while with 3 degrees the CM will move .52 inches a whopping difference
of .7 inches!
It turns out that the CM is usually lower which makes the difference
even smaller.
Using geometry, the car with 3 degrees of roll will enjoy an advantage
of 2 percent in the loading of the outside tire over the one with
7 degrees of roll.
Since the cornering force is more or less a function of the weight on a
tire a generous assumption that 2% translates to an increase of 2%
in cornering means that a your car goes from .800g's to .816g's
on a skidpad. (The actual effect would be much less.)
Since acceleration is the square of the velocity, if you
were able to corner at 60.0 mph then you would be able to do 60.6 mph
with your "rock" suspension.
To reduce body roll from 7 degrees to 3 degrees, assuming 1 degree
comes from tires and bushings, one must increase the effective
spring rate (spring rate + sway bar) by 300%. For those of you,
who drive BMW's, aftermarket stiff springs are advertised as 30% stiffer.
Going from a 23mm sway bar to 25mm sway bar would increase the
coefficient for the sway bar by about 20%.
The point is that 300% is a hell of a lot stiffer than any normal
individual is willing to tolerate, and therefore, going to
a tolerably stiffer suspension is not even going to come close
to the 2% we computed above.
In conclusion, your springs, sway bars, cannot transfer weight
anywhere, the best they can do is hold the CM stationary
Even the difference between a racing suspension and a mushy
suspension in terms of CM moving is maybe 2-3 %.
People might be wondering just why do people want stiff suspensions anyway
since weight transfer really isn't significant.
The reason that they work is complex.
Usually stiff suspensions are accompanied with a lower ride, which lowers
the CM. In our example, lowering the CM from 20 to 19 inches decreases
the load on the outside tire by 5.2% for any given turn.
If the CM where at ground level the load on the inside and outside
tire would always be 1/2 the weight of the car.
Avoiding body roll is not so bad because of "weight transfer"
but because it changes the suspension geometry, in particular
camber.
For example, a 2 degree change in camber will raise the inside of
a 205 mm tire by 7 mm which will dramatically change the load
pattern on a tire.
By the way, all of this would be irrelevant if tires where linear devices.
In other words if you doubled the load on a tire you would be able
to generate twice sliding friction (Remember freshman physics).
If tires worked that way, it wouldn't matter what you did.
There is also an improvement during dynamics situations, (ie. a slalom)
where the the car is not in a steady state. With a stiffer
suspension, the chassis + body achieves a steady state position
quicker, with less overshoot in body roll.
One last note, that stiffer is only better on flat roads.
As soon as you introduce any bump in the road, then one must deal with
trying to maintain optimal tire contact with the road which is a
2nd order problem (the famous LCR circuits).
The result is that there is a different optimal solution given
amplitude of the road distortion and the spacing of the bumps and
the speed of the car. Which means that you would really want
a different suspension for each turn.
And this is in addition to suspension geometry changes as a function
of body roll and shock compression.
Even on relatively smooth tracks, racing teams spend an incredible
amount of time changing the suspension between different tracks.
So to our friend who was worried about the softer Corvette
suspension, I suggest that he not worry so much unless he
wishes to spend to rest of his days going around a 300ft
skidpad.
The moral is that people tend to do the right thing for the wrong reason.
Guido Bertocci
P.S. Next week, I will give on a dissertation on the myth of
"More rubber on the road with wide tires".guido@twitch.UUCP ( G.Bertocci) (05/24/85)
After posting my original article on the weight transfer myth, I received some replies wondering about cars, usually racing, with the inside tire in the air. My original article does not say that the inside and outside tires have the same load. Only that one cannot change the distribution of the load by changing the stiffness of the suspension. The load on each tire is completely determined by the radius of the turn and the speed around it, not the junk connecting the tires. For example, pick your favorite entrance ramp and go around it at 40 mph. Do this twice, once with a "soft" suspension and once with a "stiff" suspension. If you could put a scale under each tire you would read almost exactly the same thing both times. (For example, for your two front tires you might have 1000 lbs on the outside and 400 lbs on the inside). By changing your swaybars, springs there is no way to change the readings to say 900lbs and 500 lbs or 1100 and 300 lbs. This is what I mean by saying that you cannot transfer weight by changing the suspension stiffness. Your body roll will differ depending on the stiffness on the suspension, but the load on each tire will not, because the center of mass does not move much when the body rolls. Cars with a wheel in the air, (assuming they haven't hit a bump) have simply increased the point at which they lose traction, to the point where the load on the inside tire is zero. Most cars slide before this point is reached. Once the inside tire starts to lift, the camber on the loaded tire changes dramatically, causing the tire to slide. This is most fortunuate for drivers. Otherwise, they would find themselves upside down a lot more ofter than they do already. -- Guido Bertocci AT&T Bell Labs Holmdel, NJ ...!ihnp4!houxm!twitch!guido
gvcormack@watdaisy.UUCP (Gordon V. Cormack) (05/24/85)
> The load on each tire is completely > determined by the radius of the turn and the speed around it, > not the junk connecting the tires. > -- > Guido Bertocci > ...!ihnp4!houxm!twitch!guido The jist of the original article was correct; that you cannot alter "weight transfer" on cornering much with suspension stiffness. However, this statement and the original article are misleading in a couple of areas. First, the relative front-to-rear roll stiffness (which certainly IS affected by sway bars etc.) has a great effect on how much of the total weight trasnfer is borne by the front vs. rear wheels. The reason that racing cars sometimes lift the rear wheel is that, because the front outside wheel is heavily loaded anyway the rear is given a lot of roll stiffness to offload the front tire a bit. Lifting the rear tire is a symptom of a bit too much roll stiffness in the rear. Second, it is not true that the center of mass of a car cannot go up or down due to lateral force. It depends on the suspension geometry. The simplest way to explain this is to consider the swinging half-axle geometry. If the hinge point is anywhere above the ground, the centre of gravity LIFTS with weight transfer. This is called JACKING. If the hinge is below the ground (obviously impossible, but there exists suspensions with equivalent geometry) the CG will LOWER with weight transfer. Most cars exhibit some jacking; extreme cases were cars like the Corvair and VW Beetle, both of which had swing-axles and were known to tuck-under from time to time. Stiffer suspension limits jacking and therefore reduces weight transfer. Weight transfer also occurs on front-to-rear acceleration. "Squat" on acceleration and "Dive" on braking result from the suspension lowering the CG on acceleration. Geometry changes can result in anti-dive and anti-squat suspensions. Finally, who said weight transfer had anything to do with increased or decreased cornering power? I do not understand the argument that begins: assuming tires have a constant coefficient of friction... Assuming that, the weight distribution makes absolutely no difference. Of course, tires are not perfect frictional devices, and that is why one tries to transfer roll stiffness to the lighter end of the car. But there is no simple formula for what that does. The real reason that one wants to limit body roll is to try to keep the wheels perpendicular to the road (0 camber). This can be done in spite of body roll with perfect suspension geometry. But, for various reasons, few cars have perfect suspension geometry. So any limit on body roll will keep the wheels closer to the proper camber. -- Gordon V. Cormack CS Department, University of Waterloo gvcormack@watdaisy.uucp gvcormack%watdaisy@waterloo.csnet
allgair@fritz.UUCP (Ed Allgair) (05/30/85)
You still haven't convinced me that there is no significant weight transfer affecting cornering. Imagine a car that is conering so hard that one or both of the inside tires no longer is touching the ground. You see this photograph all the time in car rags, tv ads, in real life if you go to the racetrack, or by scaring yourself to death in an unexpected decreasing radius turn on some mountain road :-). What happened to the weight that was on the inside tires in this condition? Ed Allgair
nrh@lzwi.UUCP (N.R.HASLOCK) (06/05/85)
An apparently neglected point is the discussion is the effect of stiff suspension refusing to lift the tyre off the road when it hits a bump. Having driven large cars with soft suspension around bumpy corners at speeds adequate to scare me as the car bounced ever closer to the crash barrier, I have a distinct preference for hard suspension systems. You pays your money, you takes your choice. Nigel The Mad Englishman in exile.