Drag Racing Chassis Tuning

Written by on August 1, 2001 Contributors: Steve Temple Tactics for Maximum Acceleration With Limited Traction
Drag Racing Chassis Tuning View All 20 Photos

Pure and simple, drag racing is an acceleration contest, not who goes the fastest. You win by being the quickest car through the measured quarter-mile, not the fastest at the end. Of course speed is important, but it is more a by-product of acceleration. Here's some tips on how to accelerate quicker and more effectively than your opponent.

Let's start with some simple physics. Drag racing, in fact most vehicle dynamics, are governed by Newton's Second Law (NSL) with the basic equation, F=ma, stating the relationships of force, mass and acceleration of a body. How does this NSL formula apply to your rear-drive rod, and how can you us the factors under your control to tune for maximum acceleration?

Let's start with some fundamentals. To accelerate your car, you've got to apply the force from your engine to the drive wheels, which grip the racing surface and accelerate the mass of your car. A tire's grip is dependent on the vertical force exerted on the tire and the coefficient of friction between the racing surface and the tires' contact patch. When you accelerate, weight transfers from the front of your vehicle to the rear. This transfer has a direct effect on the vertical force exerted on your vehicle's tires and thus how much grip they have to accelerate your hot rod down the quarter-mile.

Understanding this equation and others, and being able to manipulate them is extremely important. This application will give you the ability to tune your machine accurately for given track conditions and/or observed vehicle behavior. The Limits of Traction
Most hot rods have more power than the traction, at least in the lower gears. As you modify your engine to make more power, this situation gets extreme. Where you used to spin the tires in first gear, now you're spinning them in second and third. This traction-limited acceleration can be made better or worse depending on your setup and combination.

Ultimately acceleration is limited by the tires' coefficient of friction and the vertical force, i.e., the weight on the tire and the mass you are trying to accelerate with drive thrust developed at the wheels. This is expressed in a variation of NSL (see Figure 1 at right):

The equation in Figure 1 is true because the coefficient of friction determines the magnitude of acceleration and the weight of the vehicle is mass divided by gravity. Since the tire's vertical force changes as the chassis transfers weight, we know we have two basic systems we can manipulate to get more grip and therefore more acceleration. Getting the most from each of them is the way to quicker e.t.'s. (Note that in this article we're not addressing the effects of aerodynamic downforce, so all weights referred to are the static weights and the weight transferred under acceleration. For more on weight transfer see the sidebar.)

Stating the obvious, the way to a quicker e.t. is twofold: First, generate more grip by using a stickier tire. In drag racing, drag slicks and various D.O.T. legal drag tires are designed for this very purpose. Second, manage the weight transfer in such a way as to optimize the vertical force on the drive tires while the car is accelerating. The latter is easier said than done, but that is the craft of chassis tuning. It requires doing the math and plugging in the equations to predict the behavior of the vehicle. In other words, good chassis tuners work smarter, not harder, by knowing the influences that the various suspension components have on each other. We'll start by going over the basic formulas used by chassis tuners, and then show how to apply them to your hot rod.

The Formulas You'll Need
The formulas at right (please see Figures 2 and 3, and Figure 4 for and explanation of the symbols) quantify the tractive force limits for rear drive vehicles. The one in Figure 2 is for vehicles with an open differential, the one in Figure 3 is for vehicles with a locking differential.

Both of these equations are further variations on NSL with the dynamics of weight transfer appropriately expressed. The quantity of the numerator of both equations is simply the coefficient of friction multiplied by the static weight on the rear wheels. The quantity of the denominator accounts for the dynamics of weight transfer. The equation describing the dynamics of a vehicle with an open differential are more complex because the effects of weight transferring laterally across the axle in response to driveshaft torque must be represented.

The effect of weight transferring laterally across the axle reduces the amount of tractive force if the vehicle has a non-locking differential. As the driveshaft imposes a torque on the axle, the frame reacts in the opposite direction. The driveshaft torque on the axle and the frame's reactions combine to reduce the weight on one tire. A non-locking differential directs torque to the tire with the least traction, thus the maximum tractive force is limited by the drive tire with the least load. In other words, the weight transferred across an axle is equal to the difference of the torque reactions of the suspension and axle divided by the track width. That dynamic is stated by the equation shown in Figure 5.

Because driveshaft torque is influenced by the final drive ratio and the radius of the tire, these factors need to be represented in the equation. A formula for this dynamic is in Figure 6. This formula states driveshaft torque equals the total drive force from the two rear tires multiplied by the radius of the tire (a lever arm) with the product then divided by the final drive ratio.

Since the driveshaft torque reaction also involves the suspension (the engine and trans are bolted to the frame), the amount of lateral weight transfer is affected by the roll stiffness of the suspension. This is why spring rates and anti-roll bars influence dynamic traction. It is logical that roll torque at the suspension is proportional to the roll angle given that springs are involved. To make the equation reasonably accurate we need to add terms that describe the roll stiffness. (Note Figure7.)

We've just discussed several terms and how they represent the various systems and functions of a vehicle as it accelerates with a limited amount of traction. These are combined in the larger equations we presented further above. Now let's begin to gather the information we'll need to make those equation work for us.

How to Find the Variables
Before we can calculate max force, and from there calculate the potential acceleration rate, we need to fill in a couple of variables. The weight of the vehicle is fairly easy—just take it to a scale and measure it. Be advised that the published figures from the factories are sometimes on the light side, but are good to start with if you haven't physically weighed your car.

The distance from the front axle to the cg can be calculated if you know the front-to-rear weight distribution, i.e. how much weight is on each axle. Typical values for front-engine, rear-drive cars are 55-51 percent front/ 45-49 percent rear.

For the following examples, we'll split the weight distribution difference and assume the car has a manual trans and so use a f/r weight distribution of 53/47 percent and that the car weighs around 3700 pounds with a1/2 tank of fuel and a driver. In addition we'll assume the car has 108-inch wheelbase. Here's the equation that gives us the length to cg from the front axle (use this formula only if you plan to move your vehicle's cg—see comment below):

cg distance = rear wt.. / total wt.. x wheel base

To find the weight on the rear use this equation:

Wt. rear axle =Total Wt.. x rear distribution percent
1732 lbs.=3700 lbs. x .47.

Once we have that data then we substitute numbers for variables:
cg dist = 1732/3700 x 108

cg dist= 50.56 inches behind front wheel centers.

However, since the numerator on right side of the equation (see Figure 8) is simply the weight on the rear wheel multiplied by the coefficient of friction between the tires and the road surface, if you actually weigh the rear, you can dispense with the above calculations and put the weight on the rear axle into the formula. But if you plan to tune the launch by moving your vehicle's cg, then you should know these extra calculations.

The next variable we need is the height of the cg. This value is difficult to obtain, not so much because of the math, but the physical aspects of weighing the vehicle. You'll see quickly the lengths you have to go to get this value. Here's the equation, or at least one tactic to arrive at the cg's height. We take this equation from John Lawlor's Auto Math Handbook:

cg height = (Wb x raised Wb x Wt. transfer) divided by (height raised x total weight)

If you're up for some trigonometry, get a copy of Fred Puhn's classic How to Make Your Car Handle and just follow along. But perhaps the best and easiest way is to just take the height of the cam as the cg height. This works nicely for most pushrod V engines and will get you close enough to do probably 80 percent of your tuning. Be sure to use inches for your unit of measurement.

You'll also need to measure your track width. Track width is simply the distance in inches between the centers of the tire treads.

The last variables you'll need are the front and rear roll stiffness rates in ft-lbs./degree of roll. Unfortunately these values are very hard to find. Fortunately roll stiffness has only a relatively small influence on vehicle traction.

To estimate roll stiffness rates in ft-lbs/degree of body roll, simply double the spring rates. For example if you have 600 lbs/inch spring on the nose, you'd use 1200 as the value for this equation. This method should be pretty close. However, a good compromise for your modeling efforts is to use the values of the variables you know, then adjust the roll stiffness values to approximate the tested performance of your car. These will give you a baseline from which to model potential tuning changes.

These traction equations are very useful because they show you how changes to your set up affect the system. For example, if you have a car with an open differential, what are the best tuning moves you can make regarding chassis set up? Is installing an air bag or stiffer rear springs the right move? Plug in the numbers and check it out.

A Case in Point
To illustrate how to use these equations, lets plug in a few values for an average car, and see what we get. For this model we'll use the values shown in Figure 9.

After we plug the values into a calculator or spreadsheet program, we get the following value for F in pounds of force available to accelerate the car:

Non-locking Diff

Locking Diff

What should we change to improve that? What if we lower the car two inches? It'll look good, but how will that affect its performance? When we lower the car two inches the cg height drops to 19 inches. Here's the result:

Non-locking Diff

Locking Diff

As you can see from the lower figures for pounds of force, that is not a good tuning move—you lost traction. How about adding roll stiffness to counter the torque reaction that takes weight off one of the drive wheels? This trick is usually reserved for cars with open diffs, but lets see what happens when we increase front roll stiffness in 100-pound increments.

Non-locking Diff:

Locking Diff

This tactic barely improves traction on the open diff car and adds nothing to the vehicle with the locked diff. Let's reverse course and increase roll stiffness to the rear suspension in 100-pound increments.

Non-locking Diff:

Locking Diff

As rising traction levels indicate, this is a much more efficient tactic. We're almost back to the tractive force levels achieved with the cg height at 21 inches instead of 19 inches.

Since the tractive force of non-locker differential cars is affected by gearing, let's take a look at what happens when we install a 3.90 gear, increasing the torque multiplication from the 3.47s used above. All we'll change is the gearing, and we'll leave the roll stiffness where it is.

Non-locking Diff

Locking Diff

The deeper gears made a slight improvement in the non-locker car. Now let's cut to the chase and make a change that'll really increase the launch force of this combination comparison. Let puts some slick on this piece and increase the coefficient of friction. We're using .8 as the coefficient now, about what a reasonable performance radial will give on a street surface. But on a drag strip with average prep of the launch pad and a set of wrinkle walls that'll fit under the fenders, you can expect that value to jump 1.25-1.30 easily and perhaps more. Let's use 1.30 just for fun:

Non-locking Diff

Locking Diff

Very impressive. It's no secret that tires are one of the most cost-effective pieces of equipment. Bang for the buck, a properly chosen set of tires make it happen quick.

Modeling a suspension combination and trying various what if scenarios with a spreadsheet gives you a powerful edge in your pursuit of quicker e.t., s. If you're familiar with spreadsheets you already know this. If you're not, then you may want to learn how to insert spreadsheet performance formulas. You have to type in the formulas in a specific way that isn't necessarily intuitive. For your convenience we've included the formulas for the math used in this story in a sidebar below to help you model and tune your own combination.

Keep in mind that these formulas are inexact models of your vehicle's dynamics. They assume a perfectly stiff frame and zero friction in the suspension bushings, and do not account for rolling resistances such as bearing friction, tire to road contact friction or aerodynamic drag. Even though they are imperfect models, they are accurate enough to give you more power and control over your machine's performance than just about any other method short of a full on computer program. So spend some time changing the variable to see what effect various tuning combinations have on your machine. Then go out and try a few of the changes in the real world. We confident you'll pick up the pace, hopefully in a big way.

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