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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 5:01 PM
February 9, 2007
HP gain from a lightweight clutch
One of the members on FRRAX asked LouisG:
I have a question for ya if it doesn't give anything away, but does using a triple disc move the powerband around at all? None of the modeling software accounts for it, but I have to think that it will increase horsepower since horsepower is a function of torque over time.
And I didn't want to go work outside in the 15 degree cold, so I decided to figure it out:
Maybe it doesn't give a number directly, but it's not tough to figure out. You can model the clutch/discs, and get the moment of inertia (I=lb*in^2) for both the old and new setup, take the difference, multiply by acceleration rate, and get torque (and convert to hp).
To keep my brain from brain from rusting, and avoid losing what I learned 10 years ago, I called Quarter Master, and spoke to a very helpful engineer (Tony), who was able to provide some weights and MOI numbers. MOI numbers are also on their website at http://www.quartermasterusa.com.
LS1 clutch & flywheel (49.916 lbs), 1303.07 lb-in^2
LT1, about 45 lbs, about 1000 lb-in^2
Pro 5.5 3 disc, 13.9 lbs, 159.7 lb-in^2
I figured an acceleration rate of 300 rpm/second, multiplied by 2*pi/60 gives 31.4 rad/sec^2
Angular Torque = MOI*accel
LT1 Torque = 1000 lb-in^2 * 31.4 rad/sec *1/32.2 (convert to slugs) * 1/144 (convert to feet) = 8.8 ft-lbs
Pro 5.5 = 159.7 * 31.4 / 32.2 / 144 = 1.1 ft-lbs
You'll gain 7.7 ft-lbs and lose 31 lbs from the car.
Looking at my data from Limerock, accel rate was around .3 g's in 4th gear, which is a 224.5 rpm/sec acceleration rate. That's a 4.26 ft-lb gain.
I was able to pick his brain about adapting a 3 disc clutch to the LT1 T56 (and I'll just do a dump of my notes, so I have them saved here forever). I'd need their 509-105 button flywheel, 509-121 or 509-180 (lightweight 2.5 lb) flexplate for the 2 piece rear main seal crank, 710-100 or 710-200 (for a lighter pedal) hydraulic throwout bearing, 710-106 2" sleeve, and a machined collar to slip over the T56 input shaft sleeve to space the TO assembly correctly. Looking at the engineering drawings on their website, an individual clutch disc and floater has a MOI 7.8 lb-in^2, in case someone was contemplating using a 2 disc instead of 3 for less MOI. Tony recommended a 7/8" or 13/16" master cylinder bore (I don't remember what stock LT1 or T5 is). Set up the TO bearing with .150" gap from the tip fo the clutch fingers. I'll need an adapter for the GM roll pin to -4AN fitting on the TO assembly (which McLeod might make). Piece of cake, right?
Posted by Z28tt at 2:03 PM