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February 26, 2007
Calculating Aero Downforce Benefits
It's time to add some downforce to the Camaro, and rather than trial and error, I'd like to design it first. I figured the Liebeck LD104E airfoil is a good shape to start with, since it was used in TransAm and now Daytona Prototype (http://www.grand-am.com/ARCHIVE/daytona_prototype/rules.html). They used a 10.75" chord x 72" width wing, and 12" long x 6" high end plates. The airfoil shape coordinates can be found at http://www.aerodesign.ufsc.br/teoria/perfis/outros/liebeck104e_dat.htm, and entered into the JavaFoil applet at http://www.mh-aerotools.de/airfoils/javafoil.htm.
The reynolds number (Re) is 6300*Velocity(ft/sec)*Chord Length(ft)
V@100 mph is 146.67 ft/sec
Re=6300*146.7*.896=827,750
I put the data into JavaFoil, had 15% thickness, and max CL (coefficient of lift) was right around -1.9 at 16 degrees. At that point, the CD (coefficient of drag) is .100. Reducing the thickness to 10% changed the max CL to 1.52@ 11 degrees, and CD down to .026. Using those numbers:
Air Density at 0 ft and 59 degF Rho (p) = .002378 slugs/ft^3
Wing Area = .8958 ft * 6 ft = 5.375 ft^2
Velocity V = 146.67 ft/s
Downforce = p/2*A*CL*V^2 = .002378/2*5.375*1.52*146.67^2 = 206 lbs
Most race cars seem to have 55%-65% front downforce relative to rear, so I'll assume 60% rear downforce balanced by a splitter.
206 lbs / 60% rear downforce = 343 lbs total downforce at 100 mph
Next assumption is a 1.4 coefficient of friction for moderate race tires at my vehicle weight.
Cornering Force = Coefficient of Friction * Normal Force = 1.5*343lbs = 481 lbs additional cornering force
F=m*a, or a=F/m = 481 lbs / 3700 lbs = .13 g's more cornering force
If you were cornering before at 1.1 g's, you can now corner at 1.1+.13 = 1.23 g's, which is 11.8% more cornering force (1.23/1.1=1.118)
Your speed increases by the square root of the cornering force (F=m*v^2/r)
1.118^.5 = 1.057, or 5.7% more speed
On a 70 mph corner (such as the downhill corner at LimeRock), I'll now be able to hold 74 mph, and use the added 4 mph down the entire front straight. Another way of looking at it is you'll increase your average speed for the entire lap (your laptime gains depends on if the track has more or less fast/slow corners). With a 64 second laptime, 5.7% faster gets you down to 60.5 seconds. Time to get the aero done...
Posted by Z28tt at February 26, 2007 5:01 PM