Would appear that you're another one looking for that elusive Volume 3, Number 5 of Racecar Engineering.

I cringe, however, when the word "theory" is used in regard to an engineering problem. Hopefully, by the time we engineers receive the problem, the theories have already been proven. As for trailing link suspensions, I would assume the goals are a minimum of links (while maintaining the requisite strength with minimum weight) and a minimum change in geometry within travel limits. (The strength/weight comment is necessary as someone is sure to point out that a Panhard, with a single trailing link solidly attached to the axle housing, is all that's required. True, but that single trailing link ends up being quite heavy.) So, I would recommend that which is commonly used with oval track cars (NOT NASCAR)in the US: 2 symmetrically positioned lower trailing links and a 3rd trailing link above, positioned as close to the car centerline as possible. If the 3 links are all parallel to the car centerline, in plan view (the desirable situation, from a weight viewpoint), a Panhard rod is also required, of course. The IC should be on the no squat/no rise line and all links should be as long as possible. This simple design was used on the Jaguar C-Type (early non-IRS versions), except that the single upper link was offset to the right to dynamically cancel the unloading of the right rear by driveshaft torque.

Why do manufacturers opt for more complicated designs for production cars? As Natalie Wood was told in that movie about the life of the famous American stripper, Gypsie Rose Lee: "You've gotta have a gimmick."

More interested in the Mumford link as this has the effect of lowering the roll centre of the back axle.

Here are some excellent pictures of the Mumford axle location system:
 
http://www.clubcobra.com/t41392--1.html

Personally, I don't see that much value in locating the rear RC any lower than that achievable with a simple Panhard rod. If the Panhard is long and nearly horizontal, RC height variation is minimal. And, of course, identical tire loadings can be achieved, in either case, with an adjustment of front/rear roll stiffness values. About the only argument I can see (for a lower roll axis) is that it can improve the driver's "seat of the pants feeling." This was the argument fifty years ago, anyway. But, with the high spring rates required by modern aerodynamics, I doubt if this is still a valid reason for such a small change.

In my Google search, I noticed that someone had been critical of a new edition of a suspension book because it didn't include the Mumford design. I would point out that the Millikens also didn't mention it in "Race Car Vehicle Dynamics." Rather than being critical of the omissions, I applaud them!

I've seen the picture of that linkage on several sites, I think it must be the most popular Mumford link pisture out there.

Its's more of an interest thing than practical use, my car has four equal length trailing arms and a Panhard. I've seen the question on other forums and would like to know more, with a view to maybe using them in a future project. I've asked the question on here because all the other forums I have seen haven't been able to give any more information other than the above pictures.

How are you going to evaluate what RCH you want? How do you want it to change with jounce and roll?

Dixon's book includes a description of the Mumford linkage. You should be able to find a shareware program on the web that analyses 4-8 bar linkages. Using this you should be able to invent a linkage with any desired RCH characteristic.

Cheers

Greg Locock

The three link and panhard rod set up works fine, but what happens if you no space or a latter chassis to work with? I am looking to convert a Morgan to a 4 link, with 2 links forward and 2 links backwards. Any idea about the angles and possible problems?

The only major problem with the two leading links is that small ride height variations will result in large displacements of the IC. The "odd" link (for the trailing 3link) can be on the bottom, you know. Has to be of a healthy diameter and wall thickness, though. I'd ponder the problem for a long time before I'd go to the trouble of fabricating a rotatable mount for a 4link (to avoid binding).

Perhaps you need to sit down with a 2x4 and whittle yourself another crossmember. (Hope you can take a joke about that wood frame in the Morgan.)

With regard to "Trailing Arm Magic" utilised on Mallock Sports race cars, does anyone know how to go about implementing this? I gather it induces anti-squat, but getting things wrong will result in a rear suspension setup that binds.

How can optium link lengths / spacings be obtained to implement "TAM" or anti squat?

Regardless of the type of rear suspension, the car will neither squat nor rise if the instant center, as viewed from the side, is located on the no squat/no rise line. For a beam axle, this line passes through the rear tire patch and the intersection of two other lines, one a horizontal line through the center of gravity and the other a vertical line through the front tire patch. If the instant center is above this line, the car will rise; if below, squat. For an IRS, the equivalent line is parallel to that just described and passes through the rear axle centerline.

I'll leave the "magic" to the magicians.

Billy,

Do you know of any diagrams on the web for reference to your description? I'm particularly interested in getting the geometry correct for a car with 4 trailing links and a panhard to locate a beam axle.

John

...with the Morgan its only the body structure. The chassis is a steel 'Z' shape. On top of it its not very high. The three link doesn't work on my car, because of a chassis cross member. Hence, I have to find something different. Has some ever tried unequal length 4 link radius arms where by the upper link is shorter than the lower.

Thought as well of having 4 links (forward), but on the same side of the axle, in this case below the axle.

What do you think guys?

John: Not on the web, but, if you're working in the industry, your company library might have a copy of the Millikens' "Race Car Vehicle Dynamics." The diagram is on page 619, Fig. 17.15.

tommog: There's no requirement that upper and lower links be the same length. The general rule is that all links should be as long as possible (within the limits of practicality) to minimize IC movement with suspension deflection.

And, yes, the "lower" link could actually be above the axle centerline (or the "upper," below). It's only necessary that sufficient vertical spacing be maintained for structural integrity.

Finally, I've got to ask a question that's been bothering me throughout this thread: Why fool around with these "trick" suspension schemes for an antiquated rear drive (the beam axle) when, for the same fabrication effort, you can have an IRS? I consider the early Jaguar C-Type to be the ultimate in beam axle competition car suspension, but even this was quickly replaced with the IRS C-Type. Unless the sanctioning body requires the beam axle (e.g., NASCAR) or IRS components lack the required strength (e.g., NHRA Pro Stock), I see no reason to fool with the beam axle.

I'm kind of stuck with the design of my rear suspension setup on my racecar ie live axle (or beam axle), but I want to improve what I have if possible. If I can lengthen links or change their pickup points, I will do so to help then I will try it out.

I gather Mallock used their "TAM" theory to adjust link bar location points to good effect. Its this theory that I am ytying to discover.

All suggestions welcome.

If you ever have seen the space which is available  in Morgan behind the seats and the fuel tank and the concept of the ladder frame you know why they a live axle and actually very narrow leaf springs (which prevents of using composite leafs). The BTR axle is rather strong and I need to have some more axle movement up and especially down. Furthermore, a I will substitute 4 or 5 leafs with a coil spring to improve the ride quality. What do you reckon should be the minimum of the length upper trailing arm (both going forward) when the lower is about 50cm. Axle movement will be about 50mm upwards and 30mm downwards from neutral.  cheers

Didn't mean to offend anyone with my thoughts concerning the "antiquated" beam axle. Just wanted to get you thinking about alternatives. I have a '65 Sprite with modern Jap drivetrain and a shortened Chevy Monza rear axle. Seemed logical at the time, but I certainly wish I had taken the time to install an IRS! With all that torque, a narrow track, and an open differential...well, I think you get the picture.

tommog, the upper links can be quite short, actually. Perhaps the solution would be to determine the maximum jounce/rebound which would accompany fuel load variations, etc., make a drawing with a proposed upper link length, and then see if the rear U-joint angles fall within acceptable limits. The other consideration, of course, is whether there is sufficient length to reliably locate the IC, given foreseen ride height variations.

might try a 1 to 1 model made from wood ...

BTW by how much does the pressure on the coil spring rise when you move it 1 inch to the inside (direction differential).

Billy, actually I put roughly 350 BHP and 400 Nm through the axle ... hence, everything must be rather solid

Wheel rate changes as the square of the link ratio.

And, I'll bet you're running either a spool or a limited slip. Right?

OK - I think I have found some schematic diagrams of how a C type layout is. Am I correct in thinking that it has 2 links on the right hand side ,a 3 link on the left side and a panhard link? The top link on the right side is angled down slightly to equalise tyre loadings on acceleration. The pictures show an assortment of chassis side fixing holes on a constant radius from the axle end location hole to adjust the angle. How can anti-squat be achieved utilising this setup, or do we forget it and use the equalised tyre loading principle instead?

Or is my conception of the C type beam axle layout completely wrong?

John

That's it, John. And, yes, you can still achieve anti-squat.

Many of those who post here have mentioned that they own a copy of the Millikens' "Race Car Vehicle Dynamics." There is a companion book for RCVD, a student workbook. As you might imagine, RCVD is often used as a college text. I used it when I taught a graduate level engineering course in vehicle dynamics. This workbook includes contributions by myself and a Norman Smith, who was employed by Jaguar at the time of the C-Type development. Mr. Smith provides the setup equations for equal tire loading and explains, also, that much of the suspension work was empirical in nature, which would account for the multiple adjustment holes you describe. My contribution was to take Jaguar's work a step further and provide equations that would allow both equal tire loading and no squat or rise on acceleration.

Unfortunately, the student workbooks first published did not contain the answers to the questions posed. These were reserved for a "teacher's copy," which was published in very limited quantities. Now, however, when you order the student workbook (more correctly, "Race Car Vehicle Dynamics; Problems, Answers, and Experiments"), the answers are included and errata corrected. Unfortunately, my note to the Millikens for the addition of a multiplier, to my equation, to account for unsprung weight, did not make it into print. The final term of my equation, at the bottom of page 204, should be multiplied by M/(M-m), where M is the sprung mass and m the unsprung.

I strongly recommend the purchase of both books. (No, I don't make a penny out of this.)                                                             

Billy,

Many thanks.

Regards,

John

Just to make the box we're thinking within a little larger, upper link(s) don't necessarily have to be attached at the axle end at or ahead of the side view vertical centerline.  As one example, Factory Five (Cobra replicas) has a 3-link (plus PHB) arrangement where the bracket for the upper link is upward and toward the rear from just outboard of the pumpkin on the right side axle tube.  It's a way of getting a longer (upper) link without putting the chassis attachment point into the passenger seat.

Would something like that help?

Norm

in the U.S. Steeda has developed a similar link for the Ford Mustang (you find details on their web page 'steeda.com'). I have has build a 1:1 model out of wood to try kind of length and arrangements. Doesn't take long and avoids disappointment afterwards.

BTW Bill I run a limited diff. , but the major problem with the back axle remains the limited axle travel. Actually an other one for the experts in math.: When the engine churns out 400 Nm, how does this divide on the upper and lower links under acceleration (to make the bracketts with the correct material and size)?

Take care

Actually, tommog, I wouldn't start with the driveshaft torque. I'd assume a friction coefficient and, from that, calculate the thrust force at the tire patch. With only 3 links, it's then possible to form 3 equations with 3 unknowns and solve.

...thank you very much, but for me as practioner this could be too complicated as I have no theoretical knowledge about the equations involved (maybe u have a tip on the net - German would be quite handy). As I don't want to take any chances on safety, more material seems to be the answer.

Reading about spherical joints and PU bushes it seem to makes sense to use one end PU and in-line spherical (what ever it means) joints (I think the English say as well 'rose joints') on the other side. Does it matter where you fit the PU part -axle or chassis? What do u reckon is the mimimum size you need in my case.

Thanks guys