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Old 12-15-2008, 04:14 PM   #39 (permalink)
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Coefficient of Friction( Cf): calculation and use

From time to time,members have asked about automobile surface- roughness/skin-friction related issues.For those without fluid mechanics text is the following.----------------A scientific-calculator is handy for this,as the exponents are "unconventional",and also,the memory functions are a real help.--------------------------- It's necessary to first calculate the Reynolds Number for your car in order to use the formulas.This has been covered above in the aero sticky.------------------------ For Reynolds Numbers greater than 10(to the 7th power) Cf =[ 0.455/( log Nr)to the 2.58 power].------------------------------ For Reynolds Numbers less than 10(to the 7th power) Cf =[ 0.0775/ ( Nr ) to the 1/5 power].----------------------------------- EXAMPLE: My T-100 at 70-mph ( 102.667 feet per second) and length of 16.5 feet,has Reynolds Number:[( 16.5 ) x ( 102.667 ) x ( 6380 )]= 10,807,720.---------- Since this value is more than 10(7), then I use Cf= 0.455/[( log 10807720 ) to the 2.58 power]----------------------- or 0.455/[ ( 7.0337) 2.58 power]---------------------- or, 0.455/ 153.369 = 0.002966686513.----------------------- So my Cf = 0.002967(rounded).******************************** To use the friction coefficient is much like the drag force calculation,although you are concerned with the surface- area of your car instead of frontal area.--------------------- If you have a simple box-shaped vehicle like a van,you can use the height,width,and length to calculate the area.-------------------In my fluids class,the underside of the vehicle was ignored,as the flow there was unlike that in the free-stream,being dragged along the ground by the "dirty"undercarriage.---------------------------------- For passenger cars,the shapes vary so much that S.F.Hoerner recommends we simply multiply the frontal area by 10,to get an approximation of surface-area.----------------------- In that case,the formula becomes-------- Drag(friction) = [Cf x 1/2 x rho x V-squared x 10 Af ].---------------------------------- EXAMPLE: T-100 at aprox. 29.6 feet-square and 102.667 feet/sec,and standard air,--------------- Drag(f) = 0.002967 x 1/2 x 0.00238 x 102.667 (squared) x 296 feet squared = 11.017 pounds resistance.^^^^^^^^^^^^^^^^^^^^^^^ Plugging Cd 0.44(the original drag coefficient) into the drag force equation gives me 163.362-pounds resistance total for the truck.Subtracting the friction force leaves 152.345-pounds aero drag force.----------------------- The drag, do to skin-friction constitutes 6.74 % of the overall drag.-------------- If skin friction could be eliminated,at a steady 55-mph,mpg would gain 3.3%.However,do to the nature of typical surface-roughness and Reynolds Numbers effects,any additional "smoothing" to the body of a car will not reduce it's skin friction at all.It's basically a "DEAD-END" for eco-modding.--------------------------And as I mentioned in my "DIMPLING" thread,any surface roughness added near the leading-edge of a vehicle(golf-balling) will only aggravate drag and lead to lower mpg.For cars,the transition to turbulent boundary-layer occurs at around Nr=500,000 (impossible for a car to avoid at or above 20-mph).Bugs stuck to the leading-edge of an aircraft wing are enough to significantly compromise the performance of some laminar-flow wings.
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