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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.
In searching for a simple physical explanation for the inherent maneuverability/agility advantage smaller cars seem to have – they always seem more responsive, nimble and communicative than larger cars – a simple physics model was used. In this model yaw acceleration was taken as the index of agility, the car taken as a rigid body, and then the torques and inertia scaling investigated. The inertia of a rigid body about a vertical axis through the C.G. scales as the mass multiplied by the square of the dimension. Since mass scales as the cube of the dimension, the MOI scales as the
fifth power of the dimension. The torques about the C.G. have two components: The distance of the tires from the C.G. scale as the dimension, while the loads on the tires that determine the tire frictional forces scale as the mass or the cube of the dimension. Thus the torques scale as the fourth power of the dimension. Hence the yaw acceleration, T/I, scales as the fourth power/fifth power, or as the inverse of the dimension, i.e., as the size increases the inherent yaw acceleration capability decreases. (Alternatively, since mass appears in both the numerator and denominator of this quotient, the effects cancel, and the dimensional scaling alone remains and determines the scaling result given.) That seems reasonable, and tire load sensitivity would add some additional scale effect in the same direction. Diminutive athletes now dominate gymnastics and diving sports for similar physical reasons, probably. Conversely, large cars should be inherently more stable than small cars. Excellent engineering can camouflage these inherent characteristics, of course. I still rate a 1,500 pound 1965 Lotus Elan as the most responsive car ever, but after 50 years it may only be in relative terms, then versus now.
Are these conclusions from this simple physical model qualitatively correct? If so, it suggests that of the various car types rear engine cars (rearward C.G.) are inherently more nimble than other types because they have the longest lever arm to the front tires that provide turning torques about the C.G. It then follows that mid-engine cars (central C.G.) are next most nimble and front engine cars (forward C.G.) the least nimble. This all seems qualitatively consistent, but excellent engineering etc. Again, is this qualitatively correct?
At the other extreme of the handling spectrum, spin or oversteer skid recovery, or control, these rankings would be reversed. Here the rear tires would be key in regaining traction. Front engine cars with the longest lever arm to the rear wheels would seem to be quickest/easiest to control or recover from spin/oversteer conditions. This ease of control perhaps explains why drifters and sprint cars are typically front engine/forward C.G. machines – they are inherently easier to control. Then mid-engine cars next in terms of recovery/control and rear engine cars last – they have the least leverage from the rear tires. And, yes, that was indeed a snap spin in the 911 RS America! Again, this seems consistent with experience and common understanding. If so, why do scribes commonly state regarding mid-engine cars that “they are very difficult to spin, but once initiated they are GONE quickly and can’t be recovered”. Perhaps since many mid-engine cars handle very well the tendency may be to overdrive and when the spin occurs it indeed is very difficult to detect or control.
So, is this simple physical model a reasonable basis for making the conclusions reached? Are the conclusions reasonable? Couldn’t find any such macro summary of vehicle design characteristics on handling in my modest library. The answers are undoubtedly contained in Milliken, for example, in all the math, but a concise summary is not offered. Your views would be highly valuable. If not this model and conclusions, then what simple basis is appropriate?
Actual designs are more complicated than the simple model proposed. One never can simply scale anything up or down. However, that said, the simple model proposed is not unreasonable, and the questioner has correctly understood its physics.
· We have a mass that we are angularly accelerating about a center of rotation with a known force;
· The mass’s radius of gyration and the force’s moment arm are in a constant ratio to each other;
· The magnitudes of the force and the mass are in a constant ratio to each other;
· We vary the radius of gyration and the moment arm, maintaining the above conditions,
· The linear acceleration of the mass will be constant.
· The angular acceleration of the mass will be inversely proportional to the radius of gyration.
If we double the size of the car, and the coefficient of friction at the contact patches doesn’t change, then the car will have half the yaw acceleration at the limit of tire adhesion.
With real cars, there are a number of other considerations.
Sheer bulk makes a car harder to manage in the confines of real-world road situations, and requires us to slow down to avoid hitting things. The wider the vehicle is, the less we are able to straighten out the turns. One of the big advantages of motorcycles is their ability to take much straighter lines through turns, especially tight ones, than cars can.
As we lengthen the wheelbase, we get more off-tracking. In tight turns and at low speeds, the rear wheels track further inside the fronts. In sweepers, the rear wheels track further outside the fronts. This increases understeer in tight turns and oversteer in fast ones.
As the wheelbase gets longer, we need to steer the front wheels more to make a given turn. As the car gets heavier, we need to use slower steering to maintain a given level of steering effort, or we need to add power assist, or use stronger power assist. Good power steering can be pretty nice, but it’s hard to beat the feel of well designed unassisted steering in a small, light car. In any case, for a given steering ratio (hand wheel degrees to road wheel degrees), a smaller car will need less steering wheel movement to negotiate a given turn, at any speed.
Are cars with low yaw inertia are more or less inclined to spin, and are they harder or easier to catch? Well, they accelerate in yaw faster. That means it takes less to destabilize them but also takes less to catch them. The car will do a bigger wiggle when it hits a slick spot while cornering. It will oversteer less on exit in a chicane or lane change. It takes a smaller correction to catch a slide, but you have to be quicker with it.
Sprint cars are required by the rules to be front-engined. They are not nose-heavy, thanks to ample engine setback. They are actually quite tail-heavy.
Drift cars are required to be sedan-bodied. That rules out anything mid-engined. They have hydraulic handbrakes using a second set of rear calipers. The drivers use these to get them to turn in and get sideways. Drift cars are helped by more rear percentage, mainly to help forward bite. I’d be interested to see what one of those four-door Porsches could do, or whether a 911 could be qualified (they do have back seats, sort of) – or maybe a Corvair? Engine swaps are legal, long as the new engine is from the same corporate family.
FSAE/FORMULA STUDENT IDEAS
I am currently a member of my school’s Formula SAE club and would love to ask you some questions to possibly help us design a better car. I’m not in charge of chassis so I don’t have any specific questions but I know a big issue for us this year is trying to save weight. I was wondering if you had any tips on materials or designs to help save weight in regards to chassis? Also, would there be any other relevant design features you think worth mentioning?
I haven’t been to an FSAE competition since 2006. They’ve changed the rules quite a bit since then.
One always wants to take weight out of a race car. In FSAE/FS, this is compounded by the fact that the event is partly a judged competition, and one criterion traditionally used to make the cut for the design finals is car weight.
If a team goes with a steel tube space frame, the diameters and wall thicknesses of most of the tubes are prescribed by the rules. About the only way to save any large amount of weight there is to eliminate parts of the frame entirely.
The big place to save weight is the engine. The really light cars use singles or in some cases twins, rather than fours. The UNC Charlotte car is using a KTM single this year. They’ve used Aprilia twins in the past as well.
In terms of actual performance, making the car compact is probably as important as making it light, at least for the autocross and endurance events, because the courses are so narrow and tight.
If I were doing an FSAE/FS car, I’d give a lot of thought to laying it out like a go-kart: engine beside the driver, probably on the right, rather than behind. The engine and the driver would then be in the same bay of the frame, and the engine bay would be eliminated. The driver’s head and the rear roll hoop would be in the region of the rear axle. The driver’s feet would be offset from his body, toward the center of the car.
It would probably be possible to have the driver entirely within the wheelbase this way, while getting the wheelbase down to the 60” minimum or very close. The front bulkhead and the impact attenuator would be just ahead of the front axle. This would maximize plan view area available for a front wing.
Plan view area for the rear wing would be reduced. Under current rules, the rear wing can’t be forward of the rear roll hoop and it can’t extend more than 250mm (9.8”) aft of the rear tires. However, the front is where an FSAE car needs more wing. For autocross with full-size cars it makes sense to have the center of lift (downforce) fairly far back, set the car up mechanically loose, and use the aero to stick the back end if there are high-speed turns. But in FSAE there are no high-speed turns and the cars all fight understeer because of the very small radii of most of the turns.
A big overhead wing, as on a sprint car, would work very well, if it were legal. One person has told me that somebody tried that years ago, and the car was fast. However, such wings are no longer permitted.
A go-kart layout would lend itself to beam axle suspension. At the rear, the chain would be off-center. At the front, there would be room for a beam axle if the driver’s feet are behind the axle line. Beam axle cars tend to be lighter overall than cars with independent suspension.
With an offset drive chain, there is a question of what to do for a diff. The simplest, lightest, cheapest approach would be to use a locked axle consisting of a simple tube with a spool, as in a mini-sprint. The car would have to corner with the inside rear tire airborne or very lightly loaded, but FSAE cars all do that anyway. Driving style with a spool and a tight course involves unloading the rear for turn-in by trailbraking. Drivers vary in their ability to drive a spool car. I also think it would be possible to create a beam axle incorporating a locker: a device like a Detroit locker that lets
either wheel overrun the sprocket individually, but not both at once. That would improve turn-in.
Diffs for FSAE get a lot of discussion on forums, and would make a good topic for a future newsletter.