On other pages, I have presented methods for directly measuring parameters
important to a dragracer. There are times, however, when a calculation will point you in the right direction and/or prevent
a serious mistake.
As a for instance, consider a "typical" RWD beam axle car with a 108 inch wheelbase, front and rear tracks of 60 inches,
having 1632 pounds statically on the front wheels, a 4.11 axle, rear tires with a 14 inch radius, and a center of gravity
height of 18 inches. Now, suppose we want to know how the difference in left and right rear tire loadings varies during the
launch.
One means would be to instrument the car and analyze the readings after a run. Another would be to use the traction dyno.
But, this is an occasion when calculated values will provide some helpful results. An essential parameter missing from the
car's description is the relative roll stiffness, front-to-rear. This will be used to determine the distribution of the driveshaft
reaction torque. For a production car, the front roll stiffness is about 60% of the total roll stiffness and, as you'll see,
this proves to be accurate enough for some worthwhile calculations.
The weight transferred to the rear wheels, during launch, must vary between zero and the full 1632 pounds. For any given
value of weight transfer, the force pushing the car forward (at the rear tire patches) must equal the weight transfer times
the ratio of wheelbase to CG height. That force, when multiplied by the rear tire radius, provides the torque at the axle.
Finally, division by the axle ratio provides the driveshaft torque. The percentage of this reaction torque taken at the front
must be balanced by the rear wheel loading difference multiplied by the rear track.
So, we have everything we need to plot the rear wheel load difference versus the weight transfer. The plot marked "A" below
represents the stock configuration:
The peak value represents the point at which the left front tire leaves the track surface. The abrupt
change in direction...from a line going up to one coming down...is characteristic of calculated values. Remember, time does
not enter into these calculations, so the oscillations seen during an actual launch are not present. This would also mean
that the zero load difference...at the end of the line...would not be present in a time plot of the actual launch. Instead,
there would be a time of oscillatory loading before the car "settled down."
The plot marked "B" represents a change to an anti-roll bar. The assumption is that the front roll stiffness percentage
would decrease to about 40%.
Obviously, the plot marked "C" would represent a significant launch performance increase over either the stock configuration
or the anti-roll bar setup. But, before we consider plot "C," the following plot is significant:
I mentioned, above, that these calculations could prevent a serious mistake and this last plot is an
excellent example. I have suggested, in the past, that an improvement in rear tire loading, and, consequently, an improvement
in launch performance, could be achieved by limiting the rebound travel of the right wheel. The idea is that, if the right
front suspension goes "solid" before the left front, the shift in weight transfer to the right rear would act to equalize
the rear tire loading. Well, after seeing the results of these calculations...which are for the anti-roll bar car with a chain
(or some other means) limiting the right front rebound..., I would no longer make such a suggestion! As you can see, the car
really gets "jerked around" with such an arrangement and, though the peaks are slightly reduced, I seriously doubt if the
results would be beneficial. (The first peak represents the point at which the chain goes taut; the second the point at which
the RIGHT front tire leaves the strip surface.)
So, back to the plot marked "C": This is really an extension of the "chain" idea, but with a "gentler" approach. Instead
of the right front spring rate abruptly going to infinity (as it essentially would with a chain), a higher rate spring is
used at the right front than at the left front. With this arrangement, the weight transfer is again biased toward the right
rear, but this bias is present throughout the launch. In this case, the right front spring is 600 pounds per inch and the
left front is 400 pounds per inch. Obviously, there are spring rates which would have provided a perfectly horizontal (equal
rear tire loading) line, but I chose values which are more likely to be found in a spring catalog.
For those who might be interested in such things, I would point out that more generalized plots could be presented if both
the abscissa and ordinate values are divided by the static front wheel loading, resulting in dimensionless parameters.
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