Keith is right about lighter cars having more grip relative to the normal force. Performance tires generate grip through different mechanisms as load increases. The most efficient method is adhesion through the Van der Waals force. To generate that grip, you just need to press the contact patch into the ground (in the micro sense). Once your little pits and valleys are keyed in, you're not going to get much more adhesion. Grip after that comes from mechanical keying to the road surface and another thing called bulk deformation hysteresis, which have limits and are less efficient for the normal loading. I have driven a 398 lb car capable of a sustained 1.8g with no aero (actually some lift), while 3000 lb racecars with the best slicks can be expected to pull about 1.3-1.4 without aero. I have seen Michelin racing's tyre dyno data, it really is shocking how much grip you have when the weight goes down. In high-school-physics terms, the friction coefficent goes up as the weight goes down. (Please realize that "friction coefficients" are a criminally simplified term in the world of non-linear tire dynamics).
While it may seem contradictory to my argument above, the Miata also has better weight transfer characteristics and static balance than a Mustang. It's going to put more of it's weight on the driven tires. Without drivers, the GT500 is 57.5% front, while a turbo or LSx Miata is around 52.5-54% (stock Miatas are around 52.5%). Since the wheelbase is shorter on the Miata compared to the CG height, the Miata will put a larger proportion of its weight on the rear tires. Any weight still on the front tires can't help you accelerate, and Mustangs leave a lot. Static weight balance is very important, since it increases your ability to induce weight transfer and overall grip. You want something between ~51 to ~45% front weight to maximize your weight transfer characteristics without compromising handling. Obviously this changes with CG height, wheelbase, diff characteristics, and the ability to accelerate harder, which is why you see some high power nose-heavy cars lift the fronts at the strip. On a road course, more rear bias will give you more accelerative traction (up to a point). The downside is fundamental instability and other characteristics that need to be dialed out. If you design the suspension for it, you can run 60% rear weight and still maintain forgiving handling characteristics. Once you get past that, you end up in P-Car Widowmaker territory, which can be faster for very experienced drivers at the expense of predictable-to-the-layman handling.
Another thing that hasn't been discussed is suspension kinematics and geometry. Dampers can make a huge difference. Also, anti-squat is something that affects traction on imperfect surfaces and with transient loads. Basically, it means that the force of acceleration is transmitted through the suspension links themselves rather than the coilover. Most cars have a small bit of anti-squat, since it can be annoying to have the nose pitch up when you get on the gas. The downside is in compliance. When you transmit force through the suspension links, the effective spring rate is dictated by your suspension bushings. Medium-frequency vibrations are not absorbed as well as if they were routed through the shock. The contact patch of the tire is less "cusioned" when you have a lot of anti-squat, but the rear end won't sit down as much with the same springrate.
Mustangs have a lot of anti-squat (~60%). Miatas were never designed for power, so they have very little. Again, this means the Miata resolves a lot of the vertical acceleration load through the coilover rather than the suspension arms and bushings. In general, on road course tires and street tires, traction is maintained when you are relatively gentle with the contact patch. Think of the tire as a big spring dragging across the ground; when you change accelerations, you want to keep it from vibrating as much as possible. (That said, the forefront of tire tech today actually involves controlling and inducing vibration, but we'll ignore that). Another big factor is unsprung mass. Mustangs have a ton in the rear, including the diff. Miatas have less, so the suspension can do a better job at keeping the tires happy. Ignoring the entire IRS vs live axle kinematic comparison, you won't be able to compare accelerative traction between a V8 Miata and V8 Mustang just due to the anti-squat differences.
Why do cars come with anti-squat? To reduce the amount of squat during acceleration, and in the case of racecars, keep the aero trimmed level. It's not for overall grip, except when used to keep the rears off the bumpstops. While the grip is less, a lot of anti-squat can make a car "feel" like it has more traction. You'll see this in autojournals, the testers will champion anti-squat and anti-dive as "feeling" planted and fast. While a proper amount of antis is important in real racecars, that's mainly for aerodymanic performance. For mechanical grip, you want a bit more movement. Go flog around an Elise and tell me it handles poorly despite its body motion. :) Antis, along with tons of rebound damping, are the bodybuilding-Synthol of street car handling.
Some drag racers will contest because 100%-120% anti-squat is fastest on the dragstrip. Drag tires are different and work to cushion the contact patch themselves, so applying a great shock to the tires (compared to radial road course tires) during launch is ideal. It loads up the tires faster, since they act as a radial spring. This is one of the big reasons why drag racers prefer solid axles, it's easy to get 100%+ anti-squat with a four-link setup. While loading up a drag radial is important at launch, it is worth mentioning that a lot of anti-dive can cause traction issues down the strip. It's only useful for launching on very compliant drag tires.
TLDR: light cars can pull harder than heavier cars, especially if they have forgiving suspension geometry. This is why Atom 500s can do 0-60 in the low 2 second range with 245 rears. (Now you might understand my annoyance when we have customers wanting to put 335s on Exocets, which have the same rear weight loading under acceleration as an Atom 500.)
- can be difficult to find someone to work on one
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