Surface-drag calculation

[aerohead]

Calculating a vehicles 'skin-friction' drag requires a 2-step process:
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First,a surface friction coefficient Cf must be calculated using the formula:
Cf= 0.455/ ( log of Reynolds number ) raised to the 2.58 power.

Using the Reynolds number calculated for the 3rd-gen Prius in the Reynolds number thread, Cf= 0.455/ ( log 8,213,333 ) 2.58

Cf = 0.455/ ( 6.914 ) 2.58

Cf = 0.0031
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Second,now knowing the Cf we can solve for the skin-friction drag force ( Ff )with the relationship:

Ff =[ Cf X (specific weight/gravitational constant)X (Velocity-squared/2) X ( H+W+H) X L ]

at specific weight = 0.0763 lbs/ft-cubed
g = 32.2 ft/sec-squared
V = 88 ft/sec
H = 4.89-ft
W = 5.725-ft
L = 14.633-ft
we have: Ff = [ 0.0031 x ( 0.0763/32.2 )x( 88-squared/2 ) x ( 4.89+5.725+4.89 )x 14.633 ]

which yields, Ff = 6.45-pounds force at 60 mph
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Using the aerodynamic drag force formula,and using Toyota's published Cd 0.25,and an estimated frontal area ( @ 80% gross ) of 22.39 square-feet,the aerodynamic drag of the Prius at 60 mph on a 50-degree-F day is 52.45 pounds.
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Subtracting the calculated friction drag of 6.45 pounds leaves the Prius' pressure drag of 45.99 pounds (87 % of drag).
Skin friction constitutes 13 % of drag.
( I'm bundling internal drag,interference drag,form drag,and induced drag all together to segregate friction drag )

[3-Wheeler]

Originally Posted by aerohead

.....at specific weight = 0.0763 lbs/ft-cubed....

Just want to mention that the density of air listed above, is obviously at sea level and 70°F, and varies based on barometric pressure and absolute temperature.

Jim.

[Patrick]

I don't know where this equation came from, but the H+W+H x L portion seems to be calculating the surface area of the car. If so, shouldn't there be another W for the bottom of the car? Or is that just ignored for the equation?

[aerohead]

Originally Posted by Patrick

I don't know where this equation came from, but the H+W+H x L portion seems to be calculating the surface area of the car. If so, shouldn't there be another W for the bottom of the car? Or is that just ignored for the equation?

Patrick, this equation is from Daugherty's Fluid Mechanics text.
The 'mirror image' surface below ground is ignored.
The 'bottom' surface of the vehicle is ignored ( it will be a component of the pressure drag ).
Only the above the belly perimeter ( sides and top ) along with length are used in the surface area.

[aerohead]

I'd made a mistake at the Reynolds number thread which carried through to this thread.
I've gone back and corrected both threads and believe both are error-free now.
My apology.

[aerohead]

Patrick raised the question of the origin of the formula I'm using for the surface-drag calculation.
It comes from an example problem published in my college text,"FLUID MECHANICS with Engineering Applications," by Daugherty and Franzini.
On page 62 of the text the authors make the comment:"..a rigid mathematical treatment of turbulent flow is impossible,and instead statistical means of evaluation must be employed."
From the authors' comment,I infer that the drag of the underside of a 'typical' automobile would be 'impossible' to calculate,and that this explains the deletion of the vehicle underside surface area from the surface-drag calculation illustrated in their work.
If your car car has an extremely well detailed,full bellypan,which under flow visualization demonstrates fully attached flow over its entire length then you'd want to include its area in a surface drag calculation.
Short of that,you could just ignore it,keep things simple,which is the spirit of the formula.

[jime57]

[QUOTE=aerohead;199198] If your car car has an extremely well detailed,full bellypan,which under flow visualization demonstrates fully attached flow over its entire length then you'd want to include its area in a surface drag calculation.[QUOTE]

Has anyone here been able to demonstrate this level of modding of a "real" car? Has any manufacturer achieved this? If so, I missed it.

[aerohead]

[QUOTE=jimepting;199200][QUOTE=aerohead;199198] If your car car has an extremely well detailed,full bellypan,which under flow visualization demonstrates fully attached flow over its entire length then you'd want to include its area in a surface drag calculation.

Has anyone here been able to demonstrate this level of modding of a "real" car? Has any manufacturer achieved this? If so, I missed it.

I think it was the belly of Ferrari's F-40 which made the cover photo of AUTOWEEK back in the 1990s.There might be a shot of it in the Phil Knox's Aerodynamic photo albums in the archive.
It's as good as I've seen.
The old Citroen ID 19 also had a pretty sweet underside.