Coefficient of Friction( Cf): calculation and use
From time to time,members have asked about automobile surface roughness/skinfriction related issues.For those without fluid mechanics text is the following.A scientificcalculator 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 T100 at 70mph ( 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 boxshaped 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 freestream,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 surfacearea. In that case,the formula becomes Drag(friction) = [Cf x 1/2 x rho x Vsquared x 10 Af ]. EXAMPLE: T100 at aprox. 29.6 feetsquare 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 163.362pounds resistance total for the truck.Subtracting the friction force leaves 152.345pounds aero drag force. The drag, do to skinfriction constitutes 6.74 % of the overall drag. If skin friction could be eliminated,at a steady 55mph,mpg would gain 3.3%.However,do to the nature of typical surfaceroughness 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 "DEADEND" for ecomodding.And as I mentioned in my "DIMPLING" thread,any surface roughness added near the leadingedge of a vehicle(golfballing) will only aggravate drag and lead to lower mpg.For cars,the transition to turbulent boundarylayer occurs at around Nr=500,000 (impossible for a car to avoid at or above 20mph).Bugs stuck to the leadingedge of an aircraft wing are enough to significantly compromise the performance of some laminarflow wings.
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