Re: What is the maximum gravities of accelleration a race car can achieve?

I assume you are speaking about the ability of an automobile to generate speed by rapid acceleration and not necessarily some sort of free fall or turning on a bank experiment.  I will not use equations but give you a short list of concepts to keep in mind when considering the maximum acceleration or other performance desires of an automobile.

A pretty good technical (but overly so), Camaro webpage is
http://brl.ee.washington.edu/BRL/people/phm/fbody/cartest.html
This page has some number to go along with the some of the concepts I mention below.  A web search with the keywords power to weight ratio or your favorite make of car can produce some useful technical information if you know what the numbers measure.

The limits on self-propelled acceleration of a car are set by several factors.  Some of which are: engine power to car weight ratio, gear ratio, friction between the tires and the roadway, and weather conditions.  I will briefly discuss each of these in turn.  I suspect I have listed these in order of most important to least important, but that is debatable.
 

Engine Power to Car Weight Ratio:
Simply stated the more power from the engine produces better acceleration and faster top speed.  One thing to be careful about is that the terms power, energy, work, force, and torque get thrown around by advertisers and enthusiasts as synonymous terms.  When I speak of power I mean the physics term of energy produced or used per time.   It is often convenient to think in terms of power because the task of the operation of the car can be broken down into time intervals of nearly constant actions based on events.  For example, the event of passing another car is different than cruising along on a lonely road or starting from a traffic light when the light turns green.  We should expect that the energy consumption will be different during these three events because the car is performing different actions.

A running car is constantly losing energy to the environment through friction while the engine is furiously asked to produce energy to propel the car.  If the engine is capable of producing more energy in a given time than the car is losing in the same time, then the additional energy can be spend on acceleration or towing.

The amount of energy lost is nearly directly related to the weight of the car.  A heavier car takes more energy to keep moving than a lighter car with the same engine (and basic setup).  So many cars will have a power-to-weight-ratio listed somewhere.   The power-to-weight-ratio has remained nearly constant for the average passenger car since the late 1960's.   The trend has been for lighter cars with less powerful engines, but consumers demand a certain level of acceleration performance so the ratio has remained pretty constant.

An important thing to remember is that power output of an engine is not linear with engine cycles (revolution per minute - RPM).   I will just mention that most passenger cars are designed to have maximum fuel effeciency around 2000 to 2500 RPM, but have their best acceleration between 2500 and perhaps 3500 RPM.   Higher RPM can produce better acceleration at significant risk to the engine and the moving parts of the drive train.
 

Gear Ratio
Gear Ratio is sort of a measure of the cycles of the engine per turn of the drive shaft.  This gives a relative measure of the torque on the different gears of a car.  The higher the number the more torque that is provided to the tires which means better acceleration. However, top speed in a given gear is inversely related to gear ratio.  Think about riding a bicycle.  The lower gears on a bike correspond to high gear ratio -- more turns of the crank per wheel revolution.  It is easy to accelerate from rest in first gear but your top speed is severally limited.  In tenth gear it is difficult to get started from rest, but a much higher speed can be maintained for the same number of crank cycles per time (pedaling).

Drag racing (hotrods, funny cars, stock cars) is greatly effected by the driver's ability to change gears at the appropriate moment and as smoothly and quickly as possible.   The driver must change gears at the peak moment so that the car does not flip or wheelie because of the change in tire angular acceleration cause by a change in torque from the sudden re-application of the clutch plate to the flywheel or so that the engine does not over-rev and cause engine failure (some times explosively).

Friction between the Tires and the Roadway
The friction between the tires and the roadway make the car move.   If the wheels spin without grabbing the road the car cannot move.   Just about everyone who as ridden in a car has experienced a skid or a slide in wet or icy weather.   It is possible to given the wheels too much torque such that the tires spin more rapidly than they grab the road.  In the normal condition a tire rolls in what is referred to as the "no-slip" condition which means the point of contact of the tire with the road is effectively stationary.

When the tires spin faster than the no-slip condition acceleration is limited.
Again, I am envisioning drag racing.  At the start of a race the wheels actually spin multiple times per rotation of forward motion.  Or a more common experience is watching a car "peel out" or "lay rubber" from a full gas start.  The tire actually melts from the friction between the tire and the road since the car is not moving as it should (no-slip).

Weather Conditions
I lump all sorts of environmental effects into this category.   It is more difficult to accelerate into a headwind because there is more drag on the car.  Drag is the force that opposes forward motion.  It is friction between the air and the car.   Since drag opposes forward motion, it also opposes forward acceleration.  Reducing drag is key design element in all cars.  Drag is a complex function of shape, relative speed of the car in the wind, and air density.  Usually drag can be reduced by "streamlining" the car -- reducing the front cross sectional area of the car.  The drag function can only be solved for in a few simple geometric cases but not to shapes like automobiles that have shape limits imposed by functionality (it has to carry people, the engine can only be so small, etc.).

The density of the air affects the compression ratio.  Compression ratio is a measure of how much squeeze the cylinder does on the incoming air-gasoline mixture.  It is directly related to engine power, which I stated earlier is a key factor in acceleration.   Lighter air in the moutains reduces the effeciency of an engine because less air is sucked in during the engine cycle.   Humid air also can reduce the effeciency of an engine as anyone (like me) who has driven a 4-cylinder car in the Midwest can tell you -- the car losses some of its "giddy-up" during a humid summer day.

There many other weather related effects that can be considered (beside wet or icy), but I leave that to the reader to consider for himself or herself.
 

Conclusions
These are just some factors that are important in the top acceleration available in an automobile.  Except in testdrive laboratory conditions it is difficult to separate the effects.   I recommend further reading on drag racing like

http://www.lm.com/~hemi/
http://www.telusplanet.net/public/vavy2/gbr.htm
http://www.nhra.com

Just follow the links around to get a feel for what the people involved in racing say about their sport.  They are the experts in acceleration.

Sincerely,

Tom "Blown Head Gasket" Cull