The Mark Ortiz Automotive
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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.
DIFFUSERS WITH LIVE AXLE REARS, MUMFORD LINKAGES, AND RELATED MATTERS
Last month I responded to a question from a reader who was considering using a Mumford linkage in a Cobra kit car. I mentioned in passing that the car best known for using this type of linkage was a design by Arthur Mallock and that part of the reason he’d used the concept was to get a smooth undertray leading smoothly into a diffuser, along with a low rear roll center. This prompted a related question from a different reader:
After being out of the seat of a SCCA and other road circuit car or building one for 34 years, and spending the intervening years involved with aircraft, I am helping my son build a SCCA SPO silhouette sedan and you can imagine, struggling mightily to get back into the “modern” era.
In this regard, I just read your October [Racecar Engineering] column and reference to the Mumford linkage of Arthur Mallock. A long time ago, I built Panhard and Watts-link systems but I don’t ever recall the Mumford setup.
Could you send me a copy of your previous review of the Mumford linkage? Hopefully it has some illustrations or photos to help me visualize how it is configured.
I am 68 years old now and been out of the seat of a race car for 34 years and have not built a race car in 35 years. In the years in between I was involved mostly with R&D of aircraft engines and related engine/airframe integration.
Currently I am helping my son build a race car from scratch and man is that humbling after all these years. I have so much catching up to do I should just walk away. While I learned with aircraft possibly a few transferable things to race cars, such as how to configure low drag cooling systems, I am long since removed from building a ground vehicle that goes fast.
The car will be an SCCA SPO silhouette 60’s vintage British hatchback and may possibly run in an occasional NASA race rules permitting. The SCCA interpretation of the SPO and rules appear to me pretty generous except it has to have the open driver’s window. The whole project is an homage to old-school but I am applying as much aero as possible while trying to keep some external visual cues so people know what in the hell model/make car this thing is to represent. I am carving the body plug from which molds will be made for the body.
A tight budget dictates a simple old-school steel tube space frame chassis with coil over suspension front and rear…. with double long arms in front and a three-link, live axle Winters quick change in the rear.
The car on which this car is patterned is relatively small has a good power to weight (approx 700 hp) and target weight of 2100 lbs, but the overall wheelbase/track and wheel/tire combination ratio and layout is that of a BMW Tudor GTLM Z4 but looks more like one of those excessive DTM cars. So the frontal area is inherently large and draggy given the overall small size of the car. It is so wide due to packaging the V8 then long front a-arms followed by very big wheels and tires.
I am working the front body aero shape to get some front downforce, along with double front diffusers, and flat bottom.
This long winded background leads to the problem at hand: due to the live axle, I am struggling to how I can integrate some degree of a useful rear diffuser while locating the housing.
But of course that damned rear axle housing, and most of the related stuff, runs all the way across--smack dab in the way of where a clean diffuser should be.
And of course a low mount Panhard or Watts-link makes this area even more of a turbulent mess. So that is why I would like to see the layout of the Mumford linkage at the rear. My guess is that it probably doesn’t help substantively over the Panhard bar or Watts-link but here’s hoping….
My earlier newsletter didn’t have any illustrations, but I sent it to the questioner anyway, and did a search for images of a Mumford linkage. I replied:
Here’s a link to a picture of one version of the concept: http://www.not2fast.com/chassis/mumford.shtml.
Newsletter is attached.
The link actually is to not just a picture but an article from none other than Racecar Engineering, about five years before my first article in the magazine, authored by none other than Arthur Mallock himself.
It shows the version of the system with the rockers inboard and mounted to the frame. Mr. Mallock mentions the issue of how the rear roll center moves when the suspension moves in ride, which I have also discussed. If the front suspension is independent, it is desirable to have the rear roll center move up and down with the sprung mass in ride, rather than with the axle. That way the rear roll center moves similarly to the front one, and the slope of the roll axis doesn’t change a lot as the car negotiates crests and dips. Cars race adequately without this characteristic, but it’s desirable.
In the Mallock layout, the rockers and connecting link are small and short. The rocker-to-axle links attach to the rockers down as close to the floor pan as possible. The links extend out and up from there to attach to the axle tubes near axle height. Those links then have an instant center slightly below the floor pan, and that’s the roll center. The whole affair sits just behind the axle.
The Mallock doesn’t have a quick change axle. The Mumford linkage sits where the quick change gears would be with the Winters. It wouldn’t be impossible to move the linkage back far enough to clear the quick change. Many cars run Panhard bars that pass behind the quick change. However, it might make more sense to put the Mumford linkage ahead of the axle instead, with the rockers longer than in the Mallock and straddling the rear U-joint or the front of the rear end housing. The connecting link would then pass above the U-joint or housing.
Or, if the rockers are made long enough, they could also straddle the quick change gears.
Another possibility would be to have the rockers outboard, mounted to the axle, a long central connecting link, and right and left links running down to frame anchorage points about where the lower ends of the Mallock’s rockers are. This makes more of the linkage unsprung mass, but it potentially simplifies frame construction and may package better in some layouts.
Winters also makes a version of their quick change that has the quick change gears in front. It’s a bit harder to change gearing with those, and in some cases the driveshaft can get really short, but that configuration does get the quick change gears out of the area behind the axle. Other considerations permitting, from the standpoint of diffuser design we’d want both the gears and the lateral locating linkage in front.
According to the Winters catalog (http://www.wintersperformance.com/catalogs.htm), the large (10” ring gear) quick change hangs just over 6” below the axle centerline. The front cover on the front gear unit hangs a little lower – almost 7” below axle center. Depending on tire radius, that gives something like half a foot to the ground. If we have a continuous panel under the diff, we have room for about 3” of droop travel and about 3” of ground clearance. This means that for a road car, we cannot run a panel under the diff, but for a pavement race car, we can – just barely, if nothing else is in the way.
We need to keep in mind that the rear axle needs to be cooled. If we isolate it from undercar air flow, it will definitely need a cooler. However, the downforce gained from a highly effective diffuser can be substantial, and we may be resigned to providing a cooler anyway.
We can use almost any kind of lateral locating linkage, provided that any part that moves with the axle is at least six or seven inches above the ground at static condition. Even a Panhard bar seven inches above the ground will work. That gives a fairly low roll center. Lateral tire scrub on one
wheel bumps won’t be huge. The roll center rises and falls about half as much as the sprung mass in heave. That doesn’t really match the front end, but it’s not too bad. And the whole linkage is just one simple lateral member.
The only really compelling reason why road racers strive to get extremely low roll centers on live axle rears is suppression of torque roll and torque wedge: the roll movement and change in diagonal percentage due to driveshaft torque acting through the suspension. The amount of diagonal percentage change depends on the relative elastic roll resistance at the front and rear. The greater the elastic roll resistance at the rear relative to the front, the less torque wedge results. To maximize rear elastic roll resistance without getting oversteer, rear geometric roll resistance has to be minimized. That is, the rear roll center has to be lowered as much as possible.
But all of this goes out the window if we understand how to cancel torque roll and torque wedge using the longitudinal locating linkage. This is not as difficult as many suppose. It does require that we react brake torque differently than engine torque. Otherwise we get roll and wedge in braking.
The simplest way is to have two trailing links at each end of the axle, with the right side ones on a clamped or welded bracket and the left ones on a rotating birdcage that also carries the left brake caliper. For minimal bump steer, the instant centers of both link pairs need to be at or near axle height. The longitudinal location of both instant centers needs to be the same. The longitudinal location of those instant centers – the side view swing arm length – needs to be approximately consistent with this rule: the side view swing arm length, divided by the lateral distance of the link pair from center of the vehicle, needs to equal the overall axle gear ratio.
For example, if the rear end ratio is 4:1, and the longitudinal links are two feet from center, the side view swing arm length should be eight feet. If the links are a foot and a half from center, the side view swing arm length should be six feet.
An alternative would be to use a torque arm and put both calipers on birdcages or brake floaters. In that case, a similar relationship governs the lateral offset of the torque arm and its length: the length of the torque arm divided by its lateral offset should equal the final drive ratio.
For example, if the rear end ratio is 4:1, and the torque arm is four feet long, the arm should be offset one foot. If instead the arm is three feet long, it should be offset nine inches.
Obviously, the ideal geometry will vary as we adjust gearing to suit different courses. However, we don’t need perfection on this. Just getting close will put us ahead of competitors who do not use anything but springs and anti-roll bars to deal with driveshaft torque.