>Thanks for the response - looks like you were up kind'a late. From what
>I've read in Gillespie's book he talks about it as 2 roll centers and where
>it crosses the center of the car is the height. But I work with stock car
>people and they think of it as where the 2 roll centers intersect each other
>and they will deliberately change it from center to as much as 20"+ to the
>right. Although they typically stay somewhat close to the center - usually
>within 6" static.
>I'm more concerned with ride/roll rate prediction as I think the steady
>state lateral weight transfer should remain fairly consistent as long as I
>put in the correct roll center height.
Hi Joel.
First of all, I am not an expert in this. I'm going stricly on theory as I use
in my own simulator work and have observed from that, which I do not is right
enough to guide real car setup work such as you're doing. It's very possible
that I am missing something that could completely make the rest of this post
bunk. (I.e., if Mario Andretti tells you I don't know what I'm talking about,
listen.)
With my disclaimer out of the way, I'll continue as though what I "currently
know" actually reflects reality (which is quite improbable).
Second, I just got back from the bar. :-D
Third, I'll make this up as I go and throw around calculations helter-skelter
that may be meaningless tomorrow. Either way, this will be a very long, long,
drawn out post that may server more for my own education than anything else.
If it turns out to be useful, cool.
It would be helpful to concretely define some car that we're working with in
order to analyze this, as I do not know the rules of thumb and have no
experience with oval track Nascar type cars to be able to make generalizations
that you might get from crew members. Another reason this might be bunk :-D
You described a Nascar type race car, so I'll just pull some numbers from my
behind that I think would roughly describe a vehicle you might be dealing with.
We're interested in the lateral roll center location's effects on handling.
More specifically, the effect of this on roll/ride rate at one end of the car
May I quote something here?
>I've read in Gillespie's book he talks about it as 2 roll centers and where
>it crosses the center of the car is the height. But I work with stock car
>people and they think of it as where the 2 roll centers intersect each other
>and they will deliberately change it from center to as much as 20"+ to the
>right. Although they typically stay somewhat close to the center - usually
>within 6" static.
The "2 roll centers" are really called "instant centers." The point of
intersection you are talking about is the real "roll center." In other words,
from the diagrams you are looking at there are lines drawn extending from the
upper and lower arms that intersect at a point.
This point is the "instant center," as seen in the front/rear view of the car.
The "roll center" is more indicative of the point where the lines you saw cross
the vehicle centerline.
Either way, I think you know perfectly well what you're referring to, but it's
good to make a distiction between the roll center and the two instant centers.
I'll expand on the roll center just to make sure we're talking about the same
thing. Look at one side of the suspension in front view. Two lines could be
traced along the upper and lower A-arms (one line each) that would intersect
somewhere. The could intersect outside of the wheel (I've seen this in an RC
car) or inside the wheel. This intersection point is the "instant center."
A line drawn from the center of the contact patch to that instant center will
intersect a line drawn the same way from the opposite suspension at the "roll
center".
On a car that has identical suspension geometry on each side (left and right)
of the car, the lines drawn from the center of each contact patch to its
respective "instant center" will cross the center of the car at the same
height. What's important here is where those two lines intersect. That point
is the roll center, but in a symetrical case, this "point" will be in the
center of the car.
When body roll is present, the instant centers move, so that point can move up,
down, left, or right of course.
Ok, I just explained everything you already knew, but am just making a
distinction between "instant center" and "roll center." Don't forget I've had
a couple and may ramble :-D
What happens if we move this point to the right as seen from the rear of the
car?
Take a look at your diagrams and see where the instant centers are. Forget
about everything except the lines going from the contact patches to he instant
centers. (Also think of roll center location, the intersection of those two
lines.)
All this hoopla about roll centers and instant centers comes down to one thing:
Jacking forces.
Imagine for a moment what happens when the roll center is at ground level.
There could be a net lateral force of 1000 lb acting along the ground plane at
the right tire in the left direction (we're in a left turn and watching this
from the rear). All of this force acts on the car in the lateral direction
(along the ground; the force doesn't point up or down at all).
What if the roll center is somewhat above ground level? What matters is not
the location of the roll center, but the angle between the contact patch and a
line drawn through the roll center when trying to find what's happening at one
wheel. This angle is the same if you extended the line through the instant
center.
The angle between the line that extends from the contact patch to the instant
center of that wheel's suspension is what dictates the jacking force.
That's so important I'll say it again:
The angle between the line that extends from the contact patch to the instant
center of that wheel's suspension is what dictates the jacking force.
This jacking force is the portion of the vertical force that acts directly
through the suspension links and bypasses the springs, dampers, and anti-roll
bars, and is what causes the change in roll stiffness you get from the roll
center being above or below ground level.
How in the world can we see what will happen if we move the roll center left or
right?
Basically we should be able to figure this out by forgetting about the roll
center location entirely. Instead, we can use the propose roll center location
to give us our "vertical angles" (described in the two repeated statements
above) that are required to calculate jacking forces.
I need a real example now. Let's invent a car. Its front track width (as
defined by distance between center of contact patch locations across each
"axle", or more specifically, the distance between the force centroid locations
across each "axle") is 60 inches, or 5 feet.
Our car's center of gravity is located half way between each wheel and raised
24 inches (2 feet) above the ground.
For simplicity, let's assume our car can accelerate laterally at 1 g. In
addition, we have 50/50 front rear weight distribution. The vehicle's weight
is 3217 lb, or as I commonly say (despite what physicists tell me is proper) it
has a mass of 100 slug. I hope you're not European :-)
If this car is in a steady state left turn in a corner with no banking (not
speeding up or slowing down, and it has "set" into the corner where the
dampers/shocks will not be influencing anything), then the total lateral force
acting on the car is:
force = mass * acceleration
force = 100 * 32.17 (1g)
force = 3217 lb
The same as the weight of the car: 3217 lb. Since the weight distribution is
50/50 front/rear, the front will provide half the cornering force and the rear
will provide half of it. I know you know this already, I'm just doing it this
way for my own mental exercise. Bear with me please :-D
What's all this stuff about the roll center height/location? It's suppose to
effect something, right?
It does, but we won't see exactly where yet.
Let's imagine that the roll center is located precisely in the center of he car
WHILE the car has assumed whatever roll angle it assumes while pulling us
around the corner at 180 mph (usually not the case; the roll center usually
moves left or right).
What effect does the height have? What is this?
The roll center height effects how much of the weight is transferred directly
through the suspension links. I'll cheat and look up the formula for weight
transfer from Fred Puhn's "How to Make Your Car Handle":
Weight tranfer = force * cg height / track width
I'm only concerned with the weight transfer at the front end right now, where
the lateral force is 1/2 of the total force (3217 * 0.5 = 1608.5 lb)
Weight transfer = 1608.5 * 2 feet / 5 feet (60 inch or 5 foot track)
Weight transfer = 643.4 lb
This "weight transfer" is the total vertical force change in both the left and
right rear wheels. We're in a left turn (most of the weight is on the right
wheel), so we can calculate the left/right wheel vertical forces like this:
Front vertical force when stationary : 3217 * 0.5 (50% front weight
distribution) = 1608.5 lb
When stationary, both left and right front wheels would have a vertical force
equal to half this: 1608.5 / 2 = 804.25 lb
Left vertical force when not cornering = 804.25
Right vertical force when not cornering = 804.25
We can now add the weight transfer to find the current vertical force at each
end:
Left vertical force while cornering = 804.25 - 643.4
Right vertical force while cornering = 804.25 + 643.4
Left vertical force while cornering = 160.85 lb
Right vertical force while cornering = 1447.65 lb
For simplicity, let's assume the body only rolls 1 degree in this situation.
We could then say that the roll stiffness is 1608.5 lb*ft/deg for the front
suspension. This would assume the rear is identical.
-------------------------
Let's raise the front roll center now:
-------------------------
There isn't a very
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