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Old 12-15-2008, 05:23 PM   #40 (permalink)
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Coefficient of aero.drag(Cd):origin and use

For those without access to fluid mechanics text is the following development of the coefficient of aerodynamic drag(Cd),and it's use in the drag force and aerodynamic power calculations.This is the most important tool any aero-modder can use to predict potential performance based on theoretical changes to an automobile.---------------------------------- The aerodynamic drag coefficient (Cd) = Drag force/ dynamic pressure(q) x area(S).------------------------------ Dynamic pressure(q)=(rho) x (v)squared /2----------------------- or (1/2)x( rho )x(v)squared.------------------------- Therefore, Cd = D/[ 1/2 rho (v-squared) S].------------------------ Substituting A for S(which is used more in aeronautical work),formula becomes Cd =D/ [1/2 rho A (v-squared)].-------------------------- The Cd is calculated from measurements in windtunnels,and also determined from coastdown tests.Windtunnel results are preferred although can vary from tunnel to tunnel.+++++++++++++++++++++++++++++++++++ For examining drag, based on theoretical changes to the shape of a vehicle, drag force calculations can serve as barometer for potential results of modifications.---------------The frontal area is known,or estimated,and"standard air "values for density can be plugged into the formula along with any speed.By making the Cd the only variable,one can estimate drag reduction or gain as a function of the changing Cd.************************** EXAMPLE: The T-100 pickup. With original Cd0.44,and Af @ approx. 29.6-feet-square,and a velocity of 70-mph(102.667 ft/sec)and standard air,the drag force D=[1/2 x 0.00238 x 0.44 x 29.6 x 102.667(squared).= 163.362 pounds resistance at 70-mph.^^^^^^^^^^^^^^^^^^^^^^^^ To calculate the power requirement to overcome the aero drag force,then P = DV/(force per unit of time per power unit)------- or [163.362 pounds x 102.667 ft/sec/ 550 pound-feet per-sec per horsepower= 30.494 Horsepower,necessary to overcome aero drag at 70-mph.--------------------------If you know the mechanical efficiency of your driveline,your power requirements for rolling resistance,and the BSFC of your engine,you can predict your mpg for different values of Cd.***************************** A relationship between mpg and Cd is firmly established which offers a "back-door" in which to calculate Cd based on a vehicles "baseline" performance at a constant 55-mph driving.-------------------- If you do a reliable test of your car's mpg,at a constant 55-mpg before modifications,the following relationship may be used to estimate your new Cd.------------------ A 2% drag reduction will provide a 1% improvement in mpg,at a constant 55-mph.----------------------------------- If you were to modify your car,and after testing,realize a 5% improvement at 55-mpg,then,it follows that you've reduced your Cd by 10%.-------------- So ,for say the T-100,if I put some silly-looking device on it,and after testing,the mpg goes from 23.3mpg,to 24.465mpg,then from the formula,the Cd has dropped from 0.44,to 0.396.------------ That's all there is to it,and no expensive windtunnel needed!----------------- For extensive modifications,it is claimed that a gear change may be necessary to wring out all the MPG from drag reduction.That is a very complicated situation and for a discussion on that I would refer you to Hucho's for a full explanation.
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