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Old 10-09-2010, 04:18 PM   #1 (permalink)
aerohead
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Surface-drag calculation

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 )


Last edited by aerohead; 10-14-2010 at 06:26 PM.. Reason: Cf off by one digit
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