I had a thought the other night and never got any sleep.
I came up with a dimensionless comparison tool with which to compare the aerodynamic efficiency of automotive shapes.
I'll call it :
' Length- to- Square-Root of Frontal Area Cylinder Ratio'
--------------------------------------------------------------------------
1) A list of vehicles of same drag coefficient, along with their L X W X H measurements are required. ( for the USA audience I'll use inches )
2) Width X Height ( in inches ) are multiplied for gross frontal area in square-inches.
3) This value is divided by 144 to get the units into square-feet of area.
4) This gross frontal area is multiplied by 0.85 to get an estimated 'net' projected frontal area ( Af ) in square-feet.
5) The square-root ( in feet ), of the Af is calculated on a pocket calculator, to achieve the average width dimension of an imaginary cylinder of air displaced by the vehicle, in units of feet.
6) This cylinder width dimension is multiplied by 12, to achieve the width in inches.
7) Finally, the vehicle length, in inches, is divided by this square-root of frontal area cylinder width ( inches), to derive the ratio of Length-to-Width
--------------------------------------------------------------------------
8) The calculation is run for each vehicle.
9) Since drag is directly related to fineness-ratio, the vehicle from the list with the smallest (L/ square-root of Af ), by default, is also the shape of greatest efficiency.
-------------------------------------------------------------------------
EXAMPLE:
* A list of vehicles with Cd 0.32 are compared.
* The 1997 McLaren F1 has a ratio of 3.22686-to-1 to achieve 0.32.
* The 2014 Chevy Spark EV has a ratio of 2.5104-to-1 to achieve the same Cd.
* As the Spark has the smaller ratio, it's streamlining capability,per body length, is superior to that of the McLaren.
* A cursory glance at the two cars reveals that the Spark is a 'Kamm' form, known, historically for aero efficiency, the first clue to an investigator.
-------------------------------------------------------------------------
Of course, absolute drag of a vehicle will include the consideration of its frontal area.
This exercise is only for investigating 'shape drag', or 'profile drag.' A dimensionless coefficient. All one needs are the L,W,and H of a vehicle to proceed. Ground clearance and tire width are hidden within the calculation.
-------------------------------------------------------------------------
The fun begins when trying to figure how one shape beats another.
