leading edge radii

[aerohead]

freebeard asked about this, and I don't remember what thread it was in, so:
From Hucho's 2nd-Edition:
* Palowski, Figure 1.38, page-31,
For his four velocities tested, all the drag minimum curves intersect at a leading edge radius of approx. 1-2/3rds inch ( 42.3mm ), and remain saturated. No actual vehicle parameters are provided other than 'square'-bodied.
* On page-32, Volkswagen's research for what became the Vanagon, indicated radius optimization with the radius = 4% of the body width.
* On page-181, Figure 4.99, for RV/ caravan trailers, the drag bottoms out @ radius = 40% of the square-root of frontal projected area ( ostensibly, the tow vehicle wake is shielding 60% of the trailer's face, in this specific test scenario ).
* For commercial vehicles, on page-326, Figure 8.5, the optimum radius is @ 5% of body width.
* NASA's best-case-scenario indicated for the trailer to be exactly the same frontal area as the rear of the tow vehicle, with zero gap.

[Piotrsko]

Would the trailer also need the 4-5% radius on the edges? Does explain why V nosed trailers aren't more efficient.

[aerohead]

[QUOTE=Piotrsko;658768]Would the trailer also need the 4-5% radius on the edges? Does explain why V nosed trailers aren't more efficient.[/QUOTE
* Kamm- Fachsenfeld's research at FKFS indicated a delta- Cd = 16% for a 'softened' upper body vs 'square.'
* According to FIAT's research, on an flat-roofed automobile ( NASA's Ford Econoline ), behind the A-Pillars, there's no change in drag, with, or without the radii.
* If rear downslope is introduced, then there's a drag advantage to having the C-Pillar radii ( 4.37% delta-Cd with a 28.5-degree fastback ).( FIAT )
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* Hucho, page 318, Figure 8.37, Daimler-Benz' aerodynamic concept semitrailer, clearly has all-upper-edge radii.
* Hucho, page-320, Fruehauf's aero concept semi, ditto.
* Hucho, page-321, Ford of Europe, box-truck, ditto.
* Hucho, page-324, Figure 8.46, an 11% radius on a rectangular cylinder, of 3:1 length / diameter ratio, shows Cd 0.20, vs Cd 0.85 without.
* In Hucho's 2nd-Ed, page-332, Figure 8.63, for the motor bus / RV motorhome, they didn't test for longitudinal edge radii, so no info there.
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* General Motors', 1980s, Class-8 semi-trailer 'Optimum' boat-tail is predicated upon the trailer van 'HAVING' upper edge radii.
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Seems like we'd have to say that it's 'conditional', but for my money, I'm going all-in on upper radii.

[kach22i]

Thank you Aerohead for putting this all in one spot.

I assume all of these radius's are modeled on a 90 degree return angle on a flat plane and not some complex curve tapered teardrop form with a NACA foil number.

Let's say one takes a symmetrical cord foil and cuts the fish head off at the thickest point, then puts a 2 inch radius at corners.

How much would that alter the drag coefficient?

See attached study.

[aerohead]

Originally Posted by kach22i

Thank you Aerohead for putting this all in one spot.

I assume all of these radius's are modeled on a 90 degree return angle on a flat plane and not some complex curve tapered teardrop form with a NACA foil number.

Let's say one takes a symmetrical cord foil and cuts the fish head off at the thickest point, then puts a 2 inch radius at corners.

How much would that alter the drag coefficient?

1) Correct, like on a can of SPAM.
2) Kamm and Fachsenfeld did almost exactly what you're describing, but they analyzed the fish head ( It's been called a 'cod's head' ) without the tail, then started adding increments of the tail back on. I'll have to grab those for next time.
3) Fredrick Lanchester analyzed a streamline body with a blunt nose, but I don't remember if Cds were presented. The schematic drawings focused more on turbulence.
4) The performance of the softened, 2" radius would depend on the thickness of the wing section where the cod's head was removed. It would also depend on 2-D closed test section ( attached to, and spanning both walls ), or 3-D testing, unbounded, out in 'free' air, like a solar racer.
It would also depend on if it's a laminar wing or not. If so, anything but the ogival nosepiece would render completely different Cd. It would destroy the Reynolds number.
I'll try and remember to grab things for two weeks from now. I have out of town company for a week, starting Sunday.

[freebeard]

justacarguy.blogspot.com: the winner of the Red Dot Design Award 2021, the whale trailer concept

Modern practice avoids constant radii.

[aerohead]

Originally Posted by kach22i

Thank you Aerohead for putting this all in one spot.

I assume all of these radius's are modeled on a 90 degree return angle on a flat plane and not some complex curve tapered teardrop form with a NACA foil number.

Let's say one takes a symmetrical cord foil and cuts the fish head off at the thickest point, then puts a 2 inch radius at corners.

How much would that alter the drag coefficient?

See attached study.

* In Walter Lay's 1933 research, he takes his Cd 0.12 long-tail and sticks a near-vertical windshielded forebody onto it. The drag degrades to Cd 0.35 ( his model #10 ).
* His model # 14, with more laid back windshield is Cd 0.30.
* Model # 18, with the most windshield rake is Cd 0.12, same as 'optimum' nose.
This is 3-D flow, and there is some 'forebody' leading up to the maximum cross-section, so it's conditional.

[aerohead]

Originally Posted by kach22i

Thank you Aerohead for putting this all in one spot.

I assume all of these radius's are modeled on a 90 degree return angle on a flat plane and not some complex curve tapered teardrop form with a NACA foil number.

Let's say one takes a symmetrical cord foil and cuts the fish head off at the thickest point, then puts a 2 inch radius at corners.

How much would that alter the drag coefficient?

See attached study.

I had to go back 99-years, but Paul Jaray essentially did this experiment around 1922.
The data is in SAE Paper 700035, 'The Time Tunnel- An Historical Survey of Automotive Aerodynamics, by Karl E. Ludvigsen, Mobility Systems Corporation, SAE Transactions, Volume-79, PART-I, 1970, page-102, Figure 4, by Paul Jaray et al. circa 1922.
* from a square-rectangular cylinder 'brick', Cd 0.902
* they put a 2-D version of a convex-hemispherical nose, and 2-D boat-tail on, achieving Cd 0.255 in 2D flow.
* then removing the nose, measure Cd 0.765
* a 300% drag increase.
* restoring the nose brings it back to Cd 0.255, a 66.6% drag reduction.
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* To predict what a 2-inch radii would do to the nose-less wind section, we'd have to specify the original model dimensions.
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* A clue is found with K. Frey's research of March, 1933, published in Forschung Ingenieurwesen, pages 67-74, a part of which appears in Hucho's 2nd-Edition in the chapter on commercial vehicles, and the full schematic in, Hoerner's Aerodynamic Drag, 1951
- Frey took an airfoil of L/ thickness = 4.8, Cd 0.26 in 2D flow.
- then removed the nose for Cd 0.71, a drag increase of 273%
NOTE: a condition of Frey's model was that its leading-edge included a 7%- thickness radius, rather than a sharp edge, so its Cd may have been more like Jaray's 0.765 without the softening. If so, that would mean a 294% drag increase.
- adding turning vanes, to help flow attachment, top and bottom, the Cd dropped to 0.26, similar to Jaray's 0.255.
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* There's some railroad data available online which shows a streamline locomotive/railcar/ boat-tailed tailcar, of Cd 0.059.
* When the streamline locomotive is removed the drag degrades to Cd 0.432, a 732% increase, in 3D flow.
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I looked at some other ' brick' model studies in 3D flow,( Moller, Lay, Hucho, FIAT/ D.M.Waters- Ahmed ) which showed remarkable drag increase when the nose lost its radii ( 178%, 200%, 244%, 265%, and 299%, respectively.
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It's obvious from the body of past research that, at some degree of softening, leading edges will have fully-attached flow, achieve 'saturation', and no further rounding will lower the Cd.
We'd just need to specify the original 'height' or 'thickness' of the symmetrical section.

[kach22i]

Originally Posted by aerohead

I had to go back 99-years...........

Thank you for doing this research, I trust you enjoyed it a bit. I too like doing research, an obsession or a treasure hunt as it were.

At one time in the last decade the Aerotemplate has been altered slightly as I recall.

One of the changes was elongation of the Cod's head.

If anyone can refresh my memory of why this was done and to what benefit, it would be appreciated.

It gets to the point of what's ahead of the "0" mark having an affect on Cd.

I'm imagining an easing in of pressurizing the air for attachment is better than a blunt face with a radius edge, but it may also be splitting hairs if the actual real life advantages are crosswinds and not numbers in a static section/condition.

I trust Aerohead's company comes first, I'm just getting over a sinus infection and need a low stress distraction while I take some time off work to get better.

[aerohead]

Originally Posted by kach22i

Thank you for doing this research, I trust you enjoyed it a bit. I too like doing research, an obsession or a treasure hunt as it were.

At one time in the last decade the Aerotemplate has been altered slightly as I recall.

One of the changes was elongation of the Cod's head.

If anyone can refresh my memory of why this was done and to what benefit, it would be appreciated.

It gets to the point of what's ahead of the "0" mark having an affect on Cd.

I'm imagining an easing in of pressurizing the air for attachment is better than a blunt face with a radius edge, but it may also be splitting hairs if the actual real life advantages are crosswinds and not numbers in a static section/condition.

I trust Aerohead's company comes first, I'm just getting over a sinus infection and need a low stress distraction while I take some time off work to get better.

* The premise for the series of 'templates' was to emphasize the importance of the aft-body architecture, in relation to flow separation and pressure drag.
* And since the mid- 1980s, all mass-produced passenger cars had already done Hucho et al.'s forebody 'optimizations', I gave no emphasis to the forebodies of any of the 'templates.'
* Also, from fluid mechanics, it's been demonstrated that, for 'subsonic', non-compressible flow, a convex- hemispherical nose is perfectly acceptable to guarantee fully-attached forebody flow. So I de-lengthened the traditional cod's head of a streamline body-of-revolution-based half-body, figuring that it wouldn't impact flow, would reduce overall body length, save weight; and from BELL and Hughes Helicopter bubble canopy technology, provide perfect optical quality to the front screen ( I was allowed to sit in some of these helicopters at Oshkosh, Wisconsin's annual EAA Fly-In, and they give the pilot 'perfect' forward vision ).
If you have D.M. Waters' 1969 research on a rectangular block, you'll notice that he achieved a drag minimum of Cd 0.126 with all edges rounded to 39% of the square-root of frontal area dimension, close to dimensionless 'half-round.'
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As to angles in the aft-body of the different 'templates', as I recognized variations for the L/D= 2.5:1 streamline body of revolution, and their half-body counterparts, I wanted to present them, as they were matching 'high-cube' and 'low-cube' auto bodies, and those with vehicles matching the different profiles, they'd have a ready-made 'solution' for elongation of the roofline. Our only passport into 'Low-Drag Nation.'
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I do enjoy the evolution in fluid mechanics, and re-visiting the 'GIANTS' who's shoulders we get to stand on.