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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.
EFFECT OF LATERAL C.G. OFFSET ON LATERAL LOAD TRANSFER
I have been reviewing my lateral load transfer calculations using your July 2009 newsletter which provides a good summary of the applicable calculations and variable notation scheme for presenting the calculations for elastic, geometric and unsprung load transfer.
It has occurred to me that I am not sure where you, if at all, define the neutral roll axis based on your chosen coordinate system. The x axis is defined as one half rear track (at least that is what I usually use with a beam axle rear) longitudinally with positive forward in the direction of travel and the y axis laterally at one half the average wheelbase with positive y to the driverís right and z down with the axis system on the ground plane.
I realize you consider the front and rear roll center height locations to be undefined laterally (undefined in y) and I agree with that.
What puzzles me is the calculation of the sprung mass roll angle phi then used to calculate the front and rear elastic load transfer. It's not the calculation or the resulting load transfer that I question, but where you consider the roll angle phi to be located?
I know phi is considered to be the angle of roll around the x axis by definition (SAE axis system) and is usually presented as being around the NRA on a symmetrical car, but do you still consider the NRA and phi to be on the car centerline for a car with, for arguments sake let's say, a high left side percentage which offsets the CG substantially to the left of center when viewed from the rear?
In your video 'Minding Your Anti' you use two diagrams from RCVD from the chapter on wheel loads, one side view to illustrate the locations of the CG, roll centers, roll moment arm and NRA and another for a wheel pair in a banked condition with an offset CG to illustrate your point about how the forces act on these respective point parallel to the ground plane, very effectively in my opinion, and I agree.
Where I am stuck is should there be a correction added to the calculation for roll angle based on a significantly offset CG? You briefly mention in your video that the author talks about this offset but you do not elaborate on this point which is understandable because that was off the topic being presented in the allotted time.
If the NRA and phi remain on the x axis which we have defined as the car track centerline then the sprung weight of the car is acting, in this example, downward at some distance to the left our x axis as viewed from the rear.
If this is so doesn't mS acting at the CG create a moment that would reduce our total sprung moment MeS = mS*ay*rcgsx by an amount equal to mS*(CG offset distance)? Which would then reduce the roll angle and then by definition reduce the elastic load transfers front and rear? In my long ago education in physics I was taught the Torque= ro*F*sin(theta) or that the torque is the cross product of the position vector ro and the force. I have worked this out with the assumption that the position vector goes from the point intersected on the NRA by the moment arm rcgsx to the CG with two forces acting on the CG, that of lateral inertial reaction to lateral acceleration and that of the sprung mass mS acting downward. This results in substantially different values for the roll angle phi and the resulting elastic load transfer front and rear.
Now, to get all this to square with our total vehicle load transfer delta Fz=m*ay*t we would also have to correct total load transfer by an amount m*(CG offset distance).
Considering a simple two-dimensional front-view half-car model (in the y-z plane), the lateral offset of the c.g. (its y coordinate) does result in a roll torque, but only in response to z axis accelerations. (If we like, we can consider gravity to be a form of acceleration, as has become common nowadays.) Y axis (transverse or lateral) ground plane forces act horizontally, and the accelerations that result from them produce inertial reaction forces at the c.g. that likewise have a horizontal line of action.
We can consider the roll moment about the ground plane, which is reacted suspension geometry and by elastic devices (springs and anti-roll bars). We can also consider only the component reacted by the elastic devices, which is commonly represented as moment of the sprung mass inertia force about the roll axis. Either way, if the acceleration is purely horizontal, the centripetal force acts horizontally, and the centrifugal inertia force does too. The moment arm then is simply the vertical (z axis) distance between the two. It doesnít matter what the y location of the c.g. is.
In more general terms, if we have a force applied to a body at some application point, with some line of action, we can move the application point to any other location along that line of action and the forces and moments on the body will not change.
This does not mean that the y location of the c.g. has no effects. It does influence yaw moments in response to x axis accelerations. It does influence roll moments in response to z axis accelerations. It affects roll moments through dips, over crests, and in banked turns. It affects what the right and
left wheel pair loads are in cornering on a flat surface, but only because it affects what their values are statically. It does not affect how much they change from static. Having the c.g. toward the inside of the turn is definitely beneficial, because it result in more equal tire loading when cornering. However, it does not accomplish this by reducing load transfer, or roll. It merely introduces a static inequality of loading that partially compensates for the dynamic load transfer.
The action of gravity on the offset c.g. does introduce a moment about the track midpoint, or a greater moment if we take moments about the further contact patch than about the nearer one. This shows up as higher scale readings on the nearer wheels. But this moment does not change in response to a pure y force at the c.g.
With independent suspension, the amount of geometric anti-roll usually varies somewhat depending on the distribution of y axis ground plane force at the contact patches. Since c.g. offset affects this distribution, it can affect front and rear lateral load transfer distribution. However, it is impossible to generalize about such effects. They will depend on the geometry of the particular car.
EFFECT OF RAISED TRAILING LINKS ON LIVE AXLE REAR END
We race ARCA/Main Event Racing Series outlaw late model oval track asphalt race cars throughout Michigan, Indiana and Ohio. One of the newer chassis builders has been very successful. One of the main differences on their cars is the design of rear 3 link suspension. The trailing arms are much shorter, they attach to the rearend axle tube housings and they also float on the tube similar to a dirt car bird cage suspension. They also run the rear springs in front of the rearend with large spring rates 650LR, 750RR or soft 150lb springs with bump stops on both the LR and RR. I have attached a few pictures to show. My question is do you think this is a advantage over the traditional 3 link suspension, if so why? By running the trailing arms and springs this way whatÖhow does it change wedge or wheel loads?
The questionerís pictures show what appears to be a conventional three-link pavement car rear end with a long Panhard bar and coilovers, except that as he notes, the links are all raised compared to most such layouts, and the lowers are about two feet long. The lowers attach to a small birdcage with a clevis at the front of it. The front of the link has a regular rod end.
The top link is shown very high above the axle, but this is adjustable. The front end heights of all three links appear to be adjustable.
The brake calipers appear to be on clamped brackets, which is customary on such cars.
I donít see any big advantage or disadvantage to making the lower link pivot exactly about the axle tube center. Without the clevis, the link would try to locate the axle laterally and a bind would result, but with the clevis I donít see any reason it should create any problems. On the other hand, I
donít see that it does anything that couldnít be done with a clamp bracket and a conventional link with rod ends front and rear, and itís a little less adjustable.
Raising the lower links increases the loads on them and on the top link under power and braking, for a given top link height. This can be addressed by mounting the top link higher, but the entire system gets taller. Thatís acceptable if thereís room, but thereís no advantage. There is some advantage in mounting the lower links as low as possible and the upper as high as possible, in terms of reduced friction and wear at the rod ends. In general, any desired combination of anti-squat, anti-lift, and roll steer can be had with high or low mounting of the lower links.
Thereís a slight weight saving in keeping the brackets short, but the brackets donít weigh much compared to the rest of the axle.
The links shown appear to be around two feet long. There isnít any huge difference between two feet and three feet, for the amounts of wheel travel seen in pavement cars. When you start getting up to four feet, sometimes the links will bend instead of the rod ends moving. The angle and height of the link are what matter. The length just affects how much the angle changes as the suspension moves.
Mounting the coilovers ahead of the axle has more effect when we use a compliant pull bar for the top link, or a compliant torque arm. But the setup in the pictures has rigid links. If the side view swing arm length is short, the spring to axle motion ratio in ride gets smaller. That makes the wheel rate in ride softer compared to the wheel rate in roll, a bit like having a wider spring base or having an anti-roll bar. However, this effect is dependent on the adjustment of the side view swing arm length, and that complicates adjustment of the car.
Overall, Iíd have to say that this design is more of a harmless gimmick than a real advantage. It doesnít do anything that canít be done by other means, but it doesnít do anything awful, and it looks different. If a builderís cars are well supported and set up, and have a feature that just makes them visibly different, that feature can sell cars, because people will tend to assume that the difference they can see is what makes the cars successful.