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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: email@example.com. Readers are invited to subscribe to this newsletter by e-mail. Just e-mail me and request to be added to the list.
DESIGNING AN OFF-ROAD/ON-ROAD BUGGY
Iím a fairly young mechanical engineer with an interest in motorsport. I built a Lotus-7 style car during my degree, using an MX5 as a donor and making the necessary design modifications.
Iím working on a new design now: a road-licensed buggy based on a Mazda 3 donor: transverse mid engine, relatively light weight, in a similar vein to the 60s beach buggies or the modern Ariel Nomad.
In the course of this Iíve been trying to teach myself the fundamentals of suspension geometry and design. I feel like I have a handle on the basics from the first car (castor, bump steer, camber gain, static roll centre placement etc.).
Iíd be very interested to know what you consider the most important concepts in making a car with relatively soft, long-travel suspension handle predictably and enjoyably on bitumen, especially considering the rear weight bias which this vehicle will have. Outright speed and traction is obviously not the objective, rather something Ďplayfulí which can be thrown around without presenting nasty behaviours.
The highlights are:
Tyres: 225/75/16 (approximately 30x10in)
Wheel offset 38
Wheel travel: targeting 200mm bump/100mm droop on front and rear axles
Fabricated uprights, re-using the factory bolt-on hubs/spindle from a Mazda 3
Mechanical Trail: 30mm
Scrub Radius: 35mm
Caster: 5.5 degrees (adjustable)
Static camber 1 degree (adjustable)
Roll centre vertical: 157mm at 0 degrees roll. 154mm at 2.5degrees roll
Roll centre horizontal: 100mm from centreline at 2.5degrees roll
Camber gain: 0.5degrees per degree of roll
Static camber 1 degree (adjustable)
Roll centre vertical: 146mm at 0 degrees roll. 142mm at 2.5degrees roll
Roll centre horizontal: 200mm from centreline at 2.5 degrees roll
Camber gain: 0.25degrees per degree of roll
Iím trying to stick with the MacPherson strut rear for simplicity/ease of fabrication, but I can see that itís quite compromised: camber gain is very low, and the roll centre moves across the car quite a bit. Do you have any suggestions about whether this path is worth pursuing, or will the handling simply be too compromised with this design to be a fun, playful car?
Iím also interested in the effects of a roll centre moving Ďacrossí the car. What is the real-world outcome, especially if thereís a disparity front-to-rear?
One thing that jumps out at me immediately here is that the questioner plans on building a markedly tail-heavy car with equal size tires at both ends. Unless there is some compelling reason to do that, I would advise following the usual practice in rear-engined buggies of making the rear tires larger than the fronts.
Probably the most likely reason to use equal size tires would be to have a single spare wheel that will fit any corner of the car. A common approach is to have the rear tires wider than the fronts, but similar diameter, and use a front tire for the spare. The car can then use that on the rear as well, temporarily, without creating undue wear on the diff. That matters a lot less with an open diff than with a limited slip. It is necessary to have room to carry the larger flat rear home, of course.
Within certain limits, an engine-over-drive-wheels car with equal size tires can be made to handle decently by giving the light end a disproportionate share of the total roll resistance. The tires at the light end are then less equally loaded when cornering and the tires at the heavy end are more equally loaded. This can give an acceptable understeer gradient Ė acceptably neutral cornering Ė up to the point where the inside wheel on the light end lifts. Beyond that point, the light end has 100% load transfer and any further load transfer must occur at the heavy end.
This means that there is a relationship between the total load transfer the car will exhibit and how successfully we can compensate for having equal size tires yet a lot of the weight on the driving wheels. Weíd like the car to have low-grip tires, a wide track, and a low center of gravity. That will allow the largest percentage of weight to be on the drive wheels, while still giving decent handling with equal size tires.
The questionerís car apparently will have tires optimized for dirt, with a high aspect ratio and therefore tall, compliant sidewalls. They will therefore probably have relatively low grip on pavement, with a gentle breakaway, occurring at relatively large slip angle. They probably will also be relatively insensitive to camber. They will most likely prefer to be inclined into the turn a lot if possible, but their lateral force capability will not change abruptly with camber.
The questioner does not say what the track width is going to be, but the use of Mazda MX-3 components, with somewhat wider wheels, would put the track somewhere around 60 inches, or about like most cars. The fact that the car is to be off-road capable and has 200mm (almost eight inches) of bump travel suggests that it must sit fairly high. I would caution that it is important that the suspension bottom before any part of the frame or floor gets too close to the ground, and that the suspension bottom gently, on good snubbers. The high ground clearance and correspondingly high c.g. work against us in trying to make a tail-heavy car corner neutrally with equal size tires.
Itís not too bad to have a strut suspension in back and double A-arm in front. Colin Chapman designed a number of successful cars that way in the 1950ís and 1960ís, including the original Lotus Elite, Elan, and Europa. He even tried it on his last front-engined single-seater, the Lotus 16 of 1958, which he designed at about the same time as the Elite. He was so known for this that a MacPherson strut system used at the rear is commonly called a Chapman strut. Whether Chapman should be credited with an invention there can be debated. Certainly Chapman was the first I know of to use strut suspension at the rear. However, Ford was using it at the front of passenger cars first. Chapman was pretty much just applying prior art to the rear of the car. His designs did incorporate some features not seen in front suspensions. The Elite and the 16 used the driveshaft as the lower control arm, with just one additional diagonal trailing arm for toe and longitudinal location. Brakes were inboard. Later versions used separate lower control arms and outboard brakes.
In the Lotus designs, the strut was inclined more than is generally seen in front suspensions. That tends to provide more camber recovery in roll; the front view projected upper control arm has more inclination and the front view swing arm length is shorter, for a given lower arm configuration. The original Elite had the struts inclined at around twenty degrees. The Lotus 16 had them at around thirty degrees from vertical. Such inclinations canít be used in front suspensions because the front-view steering axis inclination becomes excessive.
Roll center heights in the neighborhood of six inches would be a bit high for a pure pavement car, especially on sticky tires. They would cause the car to jack noticeably, although not really severely. On the tires contemplated for this car, they are probably okay but I wouldnít go any higher.
I have written pretty extensively on the subject of roll centers. Long-time readers will be aware that I am not of the opinion that the concept should be dispensed with entirely, in favor of exclusive reliance on multi-body simulations that can only be done with computers. Nor am I of the opinion that the force line intersection, sometimes called the kinematic roll center, is actually what should be taken as the roll center. My opinion is that the concept of the roll center is useful, provided that the
roll center is thought of not as a pin in a hole but rather as a roller in a vertical slot. The height of that notional roller is such that the portion of the lateral inertia force acting through the suspension linkage, times the roller height, equals the geometric roll or anti-roll moment.
For cases where the force line intersection or kinematic roll center is near the center of the car, the height of that point will very nearly satisfy this requirement. For cases where the force line intersection is far to one side, the height of that point will generally not come anywhere near satisfying that requirement.
When the system has little geometric anti-roll (low roll center), the force lines will be close to horizontal and close to parallel. In such a case, very small changes in force line slope, or jacking coefficient, will cause the force line intersection to laterally migrate wildly. It doesnít matter. With a higher roll center, the same variation in jacking coefficient will create much smaller lateral migration of the intersection. That doesnít mean the system will behave better.
What does matter is how much the force line slopes, or jacking coefficients, themselves vary. That is what determines the variation in actual geometric roll resistance.
In that regard, strut suspensions are not very good. The jacking coefficient decreases a lot in bump and increases a lot in droop. The jacking coefficient of the outside wheel diminishes in roll and the jacking coefficient of the inside wheel increases. Thatís why the force line intersection migrates toward the inside wheel in roll.
Bottom line: double A-arms in front and struts in back arenít too bad. The rear loses and gains geometric roll resistance more than the front as ride height changes, but that is not really cause for alarm Ė just something to be aware of, particularly if you like to set the car up higher or lower for different applications.