Chassis & Handling Calculations

Updated 6/21/98
Background
I’ve always found the handling aspects of race cars to be the most interesting technical part of the sport.  Sure, you’ve got to have a good motor to win, but after a certain point handling is more important than horsepower.  What’s really interesting to me is that this phenomena is true almost regardless of what racing series you run.  I started my racing career over 30 years ago running dirt track midgets....14:1 compression motors on methanol.  You could do ANYTHING you wanted to the motor...the only regulation was displacement.  But, as things turned out, getting a competitive amount of horsepower was easy compared to getting a car that would handle.   Thus was born my interest in chassis and handling.

This article in the Mumm Brothers website will be a little different.  It will not emerge as a fait accompli, but rather, evolve.   Over the years, I’ve collected many calculations on the dynamics of the Spec Racer, and I’m taking this opportunity to review my numbers and then post them as I go.  So there’s good and bad news:  the good news is that you will probably get data (and analysis) you otherwise wouldn’t have obtained, the bad news is that you’ll have to wait for all of it over time.

The Givens
Below are -- as Robert likes to call them -- some “stats”.  These are measurements of the car and the car parts that will be used in the other calculations.  Some are specific to my car.  In that case, you’ll want to either use your own numbers or know that my numbers are grossly correct for the entire class.
Element Value Unit Notes
Wheelbase 92 inches
Track 56.75 inches
Total Weight 1660 pounds Post-race 1997 weight
Rear Weight 1015 pounds Post-race 1997 weight
Right Side Weight 825 pounds Post-race 1997 weight
Unsprung Weight, Front 51 pounds Assumes: Steel fasteners, “Shelby” rims, Yokohama tires, Koni shocks, Renault rear springs, brake rotors at 11 mm.
Unsprung Weight , Rear 67 pounds Assumes: Steel fasteners, “Shelby” rims, Yokohama tires, Koni shocks, brake rotors at 11 mm.   This number averages the two sides (right heavier than left).
Tire & Wheel Weight, Front 28.5 pounds “Shelby” rims and Yokohamas
Tire & Wheel Weight, Rear 32.5 pounds “Shelby” rims and Yokohamas
Front Axle Height 10.5 inches Yokohama 185/60-13 loaded @ 29 PSI
Rear Axle Height 11.0 inches Yokohama 205/60-13 loaded @ 29 PSI
Center of Gravity (CG) Height above ground 12.78 inches Assumes: 3 gallons of fuel, simulated 200 pound driver
CG Lateral Location -0.20 inches Right of car centerline (negative #’s are left of center), same assumptions as CG height.
CG Longitudinal Location 56.25 inches Behind front axle centerline, same assumptions as CG height.
A digression: Determining CG Height
I think you may find this somewhat interesting. The process to determine CG height is basically this:  Put the car on scales and measure the weight on the rear wheels.  Raise the front end of the car a specific distance and re-measure the weight on the rear wheels.  In my case, I raised the front end of the car exactly 2 feet, it was the height of the small stools I had.   Then you do some math...to determine the number above, I used Paul Van Valkenburgh’s method from “Race Car Engineering and Mechanics”, Carroll Smith’s method from “Tune to Win”, and Fred Puhn’s method from “How to Make your Car Handle”.   They individually yielded answers within 0.2" of each other at the worst divergence.  I averaged the result to get the numbers above.
Now, back to our regularly scheduled program.
CG Height movement with fuel load 0.5 inches CG upward movement going from 5.5 gallons of fuel to empty.
Lateral CG movement with fuel load 0.04 inches CG rightward movement going from 5.5 gallons of fuel to empty.
Longitudinal CG movement with fuel load 0.25 inches CG forward movement going from 5.5 gallons of fuel to empty.
Rear Ford Spring Rate (Hypercoil) 423 pounds/
inch		 Calculated rate
Front Ford Spring Rate (Old Renault Rear Spring) 265 pounds/
inch		 Calculated rate
Front Ford Spring Rate (Eibach) 278 pounds/
inch		 Calculated rate
Sway Bar Rate at full stiff 830 pounds/
inch		 Calculated rate.  Don’t forget the sway bar works in torsion.
Sway Bar Rate at full soft 260 pounds/
inch		 Calculated rate.  Don’t forget the sway bar works in torsion
Motion Ratio - Springs 1 : 0.83 Measured ratio
Motion Ratio - Sway Bars 1 : 0.61 Measured ratio
Vertical Wheel Rate - Front (Old Renault Rear Springs) 184 pounds/
inch		 Equals spring rate times square of motion ratio.   No roll bar.
Vertical Wheel Rate - Rear 294 pounds/
inch		 Equals spring rate times square of motion ratio.   No roll bar.
Sway Bar Wheel Rate - Full Stiff 309 pounds/
inch		 Equals sway bar rate times square of motion ratio.
Sway Bar Wheel Rate - Full Soft 97 pounds/
inch		 Equals sway bar rate times square of motion ratio.
Front Roll Center Height. -0.39 inches Height above (below) ground.  Measured with Yokohamas. Ride Height of 3".
Rear Roll Center Height -1.09 inches Height above (below) ground.  Measured with Yokohamas. Ride Height of 3 7/8".
Calculations
Now, here’s what we do with those numbers.
Vertical Wheel Deflection 0.495 inches/
degree		 Vertical movement of a wheel with one degree of roll
Total Roll Stiffness 14,500 in-lbs/
degree		 Half the track times vertical wheel deflection times total vertical wheel rate. (Renault rear springs on front, Hypercoils on rear, front sway bar full soft, rear bar full stiff.
Height of Roll Center Axis at the Center of Gravity -0.82 inches Height of the line between the Front RC and Rear RC at the CG location.
Sprung Weight Center of Gravity above Roll Center Axis 13.93 inches Determines the moment arm for lateral sprung weight transfer calculations.
Total Later Weight Transfer 562 pounds Weight transfer at 1.5 G’s.
Centrifugal Force on Sprung Weight 2,136 pounds CF at 1.5 G’s.
Centrifugal Force on Unsprung Weight 354 pounds CF at 1.5 G’s.
Total Roll Couple 29,755 in-lbs Sprung weight times Sprung Weight Center of Gravity above Roll Center Axis
Front Roll Stiffness 4,996 in-lbs/
degree		 The relationship to the rear roll stiffness is the basis for the push/loose balance.
Rear Roll Stiffness 9,504 in-lbs/
degree
Front Roll Couple 10,250 in-lbs Total Roll Couple times the ratio of Front Roll Stiffness to Rear Roll Stiffness.
Rear Roll Couple 19,501 in-lbs As above, but using the Rear Roll Stiffness in the numerator.
Front Weight Transfer 205 lbs Weight moving from inside wheel to outside wheel @ 1.5 G’s.
Rear Weight Transfer 356 lbs Weight moving from inside wheel to outside wheel @ 1.5 G’s.
Weight Transfer due to Unsprung Weight - Front 30 lbs See assumptions at top.
Weight Transfer due to Unsprung Weight - Rear 40 lbs See assumptions at top.
Chassis Roll Angle 2.05 degrees At 1.5 G’s.
Camber Gain on Outside Wheel 1.7 degrees Amount of positive camber added to outside wheel @ 1.5 G’s.
Vertical Wheel Deflection at 1.5 G’s 1.02 inches Amount wheel moves vertically @ 1.5 G’s.
The Next Installment  
Longitudinal weight transfer and spring frequencies.
Rev. 6/21/98
Feedback
I welcome your comments or ideas on this information.  Feel free to drop me a line via “Comments for the Bro’s”.  

Barry
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