A New Tool for Comparing Shapes

[aerohead]

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'
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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
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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.
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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.
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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.
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The fun begins when trying to figure how one shape beats another.

[JulianEdgar]

Just popping in for a quick look and some comments.

1) I don't understand the point of the tool - how does it help people actually achieve anything?

2) There seems to be a lot of oversimplification happening here - eg "Since drag is directly related to fineness-ratio". No, that's not the case on any real-world car.

3) You say: "The fun begins when trying to figure how one shape beats another." I am afraid I think that is just rubbish.

[Piotrsko]

Ah. Newtonian method of generating CofD. I grok.

[freebeard]

2)....
3)....
4)....
5)....
6)....
7)....

This is a teensy bit verbose. One might reduce it to a mathematical expression for purposes of evaluation. IMHO, of course.

'EXAMPLE' is anecdotal.

The fun begins when trying to figure how one shape beats another.

You've renormalized the data, FWIW.

[aerohead]

Originally Posted by JulianEdgar

Just popping in for a quick look and some comments.

1) I don't understand the point of the tool - how does it help people actually achieve anything?

2) There seems to be a lot of oversimplification happening here - eg "Since drag is directly related to fineness-ratio". No, that's not the case on any real-world car.

3) You say: "The fun begins when trying to figure how one shape beats another." I am afraid I think that is just rubbish.

Thanks,
1) It may take until you've completed your 3rd year of mechanical engineering studies, when you'e completed fluid mechanics before you understand. $ 75,000 ( US ) ought to get you there.
2) If you'll ask your world-class aerodynamicists for assistance, they ought to be able to walk you through Hucho's text, especially the part where fineness ratio is probably the single-most important criteria for the drag coefficient, and has been well established with empirical testing in the real world since 1922.
3) You can take 25 different homes, of identical size, built on the same street, by 25-different builders, maintained at identical indoor temperatures, year-round, exposed to the same weather, yet yield 25-different energy bills each month. This would be a direct analog for what the L/ square-root of Af offers.
Perspicacity is the game.

[freebeard]

...fineness ratio is probably the single-most important criteria for the drag coefficient...

Walking back the claim?

3) You can take 25 different homes, of identical size, built on the same street, by 25-different builders, maintained at identical indoor temperatures, year-round, exposed to the same weather, yet yield 25-different energy bills each month. This would be a direct analog for what the L/ square-root of Af offers.

Like comparing production vehicles with gow jobs.

[aerohead]

Originally Posted by freebeard

Walking back the claim?

Like comparing production vehicles with gow jobs.

I don't understand your comment.

[freebeard]

Sorry, I was being obtusely archaic.

Originally Posted by DDG

GOW JOB? | The H.A.M.B. - The Jalopy Journal
/https://www.jalopyjournal.com/forum/threads/gow-job.34415/
Gow Jobs and Other Stuff Here are the answers to your questions about the origin of terms like hop-up, gow job, soup-up, etc. The origin of these terms seems to puzzle everyone but I believe I know where they came from and what they mean. In California in the '40s and early '50s hot rodders despised the term "hot rod" and never used it.

[JulianEdgar]

Originally Posted by aerohead

Thanks,
1) It may take until you've completed your 3rd year of mechanical engineering studies, when you'e completed fluid mechanics before you understand. $ 75,000 ( US ) ought to get you there.

In the decades over which I have been writing about cars, I've met many people with undergraduate engineering qualifications who know very little, so it doesn't much surprise me to find another.

2) If you'll ask your world-class aerodynamicists for assistance, they ought to be able to walk you through Hucho's text, especially the part where fineness ratio is probably the single-most important criteria for the drag coefficient, and has been well established with empirical testing in the real world since 1922.

Hucho (1987) page 200 for anyone who wants to look. There's just one index reference to fineness ratio in the whole book! And the current - fifth edition - drops 'fineness ratio' entirely from the index. So as I said:

There seems to be a lot of oversimplification happening here - eg "Since drag is directly related to fineness-ratio". No, that's not the case on any real-world car.

If we were striving for shapes with the lowest drag in free air, then I'd imagine fineness ratio would be important. (Say, in the design of airships.)

But we're talking here about cars, so more misleading material from Aerohead.

3) You can take 25 different homes, of identical size, built on the same street, by 25-different builders, maintained at identical indoor temperatures, year-round, exposed to the same weather, yet yield 25-different energy bills each month. This would be a direct analog for what the L/ square-root of Af offers.
Perspicacity is the game.

What a great analogy! And so, using your logic, the parallel to fineness ratio would be the house's north-south versus east-west length ratios! That's all we need to do to assess the energy efficiency of these houses - just measure their shape....

[freebeard]

What a great analogy! All things being equal (), the hands down winner for efficiency is an hemisphere with an oculus.

Can I sell you on a Dymaxion-esque motor home?