A New Tool for Comparing Shapes
 

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. ;)

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.

Ah. Newtonian method of generating CofD. I grok.

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

'EXAMPLE' is anecdotal.

You've renormalized the data, FWIW.

1) 2) 3)
 

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.:)

Walking back the claim?
Like comparing production vehicles with gow jobs.

walking back
 

I don't understand your comment.

Sorry, I was being obtusely archaic.

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.

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.

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....

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?

https://ecomodder.com/forum/member-f...-w-caption.jpg

I was actually thinking of it in terms of solar energy gain in winter, where in fact you do want a long east-west axis compared with north-south. But of course, as with car aerodynamics, there's a lot more to energy efficient house design than just comparing two dimensions...

The relevant 'dimensions' are the inside and outside. As with fineness ration there is a sweet spot.

A mirror-shuttered ridge cap would want to be N-S. Passive structures want E-W. Heat loss is related to exposed 'frontal area' to the prevailing winds. N-S ridge on an E-W plan was a feature of the Shingle Style.

A compromise between the archaic box and the geodesic future would be an octagon plan.

No, that is 'space utilization'. Nothing to do with energy efficiency, which includes external energy absorption, as well as dissipation.

(And if energy were being solely generated inside, wouldn't a sphere have the best surface area / volume ratio, and thus the lowest radiating area versus internal volume?)

But my point is this: suggesting that for road cars 'drag is directly related to fineness-ratio' (the original Aerohead statement) is unbelievably* simplistic.

We can try to apply such a concept (ie just a dimensional ratio) to houses as well - except of course, in the real world, we can't.

* Yes, unbelievably. In more than 20 years of following web discussion groups, Aerohead is so far my Number One pick for a pseudo-expert disseminating (largely) rubbish. And boy, have I ever seen some doozies.

Not sure what I was getting at, but it was about housing. The toroidal airflow inside a hemisphere is all about energy conservation. As you say the sphere has minimal surface area. The external airflow is also optimal with a compound curve and minimal surface texture.

Do you have the Cd for an icosahedron vs sphere?

fineness ratio
 

1) '... the shape of a body in front of the largest cross-section has only minor influence on the total drag. The main contributions to the drag force originate from the rear part of the body.... it is very important to design a rear body surface which brings the divided streamlines smoothly together. Optimum shapes are 'streamlined' bodies having a very slender rear part.' Hucho
2) ' ... the optimum shape in terms of drag is a half-body, which forms a complete body of revolution together with its mirror image- produced through reflection from the roadway.' Hucho
3) ' OPTIMUM FINENESS RATIO' is presented in Hoerner, Page 70.
4) Maximum aft-body contraction geometry necessary to prevent flow separation is given by Mair and Buchheim et al. in Hucho. ( 22-23 degrees)
5) The lowest drag streamline body which satisfies the aft-body contour limit is a 2.5:1 fineness ratio, provided by Hoerner, and illustrated in Hucho's drag table (derived from Hoerner's data ), page 61, TABLE 2.1, 3rd from bottom.
You're looking at the 'aerodynamic streamlining template.'
By definition, this shape provides the lowest drag, three-dimensional flow, half-body, free of flow separation, with minimum surface friction and pressure drag. It's a known quantity. A sure thing. Defined by Hucho, with supporting evidence by same.
I've given you all this information before.

The normal Aerohead irrelevancies. None of the above has anything to do with fineness ratio.

Yes, Aerohead has written all this before. The trouble is, all this is basically ignored (1 -2 pages max in a whole book, if that) by all the current major authoritative texts on automotive aerodynamics. Even with vehicles where you could argue it could be of significance (solar race cars), the most authoritative book on the subject (Tamai) doesn't even have 'fineness ratio' in the index.

Why do they ignore it? Because it's of so little significance. To listen to Aerohead, you'd think these books would be dominated by the subject.

To restate my original response:

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