Help me understand aero: rear corner radii, yes or no?
 

This is one question I've never been able to answer to my satisfaction:

Regarding transitions from the side of the rear quarter panels of a vehicle to the rear-facing areas (ie the plane that the licence plate is on), what's better for lower Cd: transitions constructed with generous radii, or transitions that are sharp?

The reason I'm confused is because images I have seen conflict with each other and what I have read. What I see on a large number of ultra-sleek concept cars are side/rear transitions which look literally "chopped" - sharp 90 degree corners where the rear quarter panels meet the rear-facing bits.

EG: VW 1-liter car is a prime example; the PNGV cars; Ford Probe V.

Yet I have read (Barnhard, Road Vehicle Aerodynamic Design) that side-to-rear transitions should be generously rounded for reduced drag. With the caveat that generously rounded side-rear transitions are also less stable in cross-winds than sharp rear angles.

EG: several low drag production cars, notably the Insight, and the EV1, had generously rounded side-rear corners - the bumper covers below the tail lights anyway. Which makes me wonder if, because these are production vehicles, some concession to user-friendliness was made over aerodynamics (ie: round bumpers seem less likely to be damaged in minor scrapes than bumpers which have a sharp 90 degree corner).

Does anyone have any credible information or reasoning to help answer this?

I find the apparent "contradictions" on this design element between these otherwise very slick cars a bit confusing.

Yea...the rounded corners on the sides and sharp cutoff on the top seems to be the usual COMPROMISE used vs the ideal boat tail?

Yet supposedly...the CRV on this page...sharp top...rounded corners...

https://www.airtab.com/Images/gallery/CRV/sDSC05730.jpg

...claims 7-10% mpg gain with airtabs on sides and top?

I think someone could come up with the probable mpg for this CRV with an ideal boat tail and compare that with what would be possible with vgs....vs how it comes from the factory?

Been seeing factors relating mpg with CD values.

That's also my understanding, and you may be right that the problem is semantics, ambiguity, or my misunderstanding of Barnard's writing. The quote(s) in question (Road Vehicle Aerodynamic Design, an Introduction, 2nd ed., MechAero Publishing 2001):

This one doesn't specifically make it clear whether by rear-end rounding he's referring to the side-rear corner, or to plan-view tapering.

This one seems less ambiguous, however it is in a section about commercial vehicles (transports/vans), where the roof line is generally straight from front to back.

Maybe the distinction is that there's some aerodynamic benefit to radiusing the side/rear corner where there is otherwise no taper in the shape in plan/profile view.

But my gut tells me that if you've already achieved an proper tapered/boat tailed shape, the side/rear corner should be sharp, a la Kamm back.

These are all good points that could lead to a compromise vs. proper aerodynamics.

I've realized aero is a much more complicated subject since I decided to make an effort to go beyond "lay" or "pop" aerodynamics (which I like to describe as a general understanding of the fundamentals which I can mis-apply in specific situations :D ).

Good, reply clencher - thanks.

Still don't know the answer for sure though. Perhaps time to track down an expert and ask directly.

I should add these:

In the section Vehicles in cross winds:

and also...

Note the author is referring to separation from the vertical plane (side of the car), not the horizontal (roof or trunk)

Tape some tell tails on the back of the various vehicles you can find and see what is generated back there. You apparently want to avoid tapers that are too aggressive as it created more drag than a chopped off end so if you can't slope it back gradually then chop it off. Still haven't figured out if the roof foil on an xB really helps or just looks good. I do know that it is not cheep!

Just to be clear, I'm not talking about boat-tailing here, but the design of the corner where the side of the vehicle becomes the rear.

Just the last 4 or 5 inches of the length of the car.

Tuft testing is a good idea, but it's time-consuming. I'm trying to find the answer from someone who's already done the work (or knows about it).

I don't think that the side has that much effect on a car vs my "van" xB sides because the major air flow is over the roof and dropping over the trunk / rear hatch and the rear wheel wells totally screw up the air around the bumper region in back. I know my rear quarter is all open underneath and I haven't a clue what the air is doing back there other than the dirt that builds up on the outside lower half of the rear of the wheel opening. Once you put the rear wheel skirts on then things change however but volume wise the top air is much more a factor.

The top is usually clean...but the sides have mirrors...windows...wheel wells?

Might be that the air is so disturbed that round works OK?

As far as crosswind stability...they mention improvements for the CRV with airtabs?

Every once in a while I come back to this question.

Regarding this earlier thought:

... I realized that if you look at actual boats, the corner transition from the side/bottom to the transom is almost universally a sharp corner (with the exception of relatively uncommon double-ended hulls, which I believe are done more for safety in following seas than hydrodynamics).

That would seem to lend support to the idea that if you have a the ideal plan & profile taper (VW 1L car), the "transom" transition should be sharp. If it's not ideal (nearly all production cars), the corner should be generously radiused.

With a sharp transition, you're going to form an air pocket behind the car. With a rounded or completely tapered rear, you're not going to have the air pocket.

With a rounded or completely tapered rear, the air moving past the car is going to "stick" to the body (the boundary layer, anyhow). With the sharp transition, you get boundary layer separation from the body. Air slides better past air (the pocket behind the sharp transition) than it does to any "stationary" surface (the rounded/tapered rear).

This is not to say that having the rear taper in before the sharp break is a bad idea...it isn't. This makes the size of the air pocket you're dragging smaller, reducing drag. Something sticking out on the body that could 'trip' the boundary layer before the rear could also reduce the size of the air pocket, thus reducing drag.

Like everything else, you must balance surface area of the vehicle with the size of your separation zone.

Airtabs! This dead horse won't go away! 7 to 10 %??? Do the numbers.... :confused:

Aero drag comes from two sources 1) Disturbing smooth airflow... ,and 2) moving the air out of the way (displacing) as you penetrate it.
(please note: Cd is covered in source 1 ... as is boundary layer disturbances )

Ah! the Kamm Effect! It has been years since I've seen this in print! Remember how he was ridiculed for his idea? As was Jim Hall with his rear "wing" chaparall (did I spell this correctly?)....One of the big advantages of the Kamm Effect was (is?) it makes the cars shorter! Stylists love this!
The more we play with aero mods...the slicker we become...even in our claims. I knew a guy (who was an auto body shop genius) who's last name was Kombach...boy, did he hear about his "square tail"! LOL

I hope you succeed, since the car industry is probably not sharing its cutting edge knowledge on this subject. And besides, most companies don't consider it to be terribly important.
A question, and a theory for the discussion:
1. the rear angle of the EV1 (as for the Probe V) is rather close to the 30 degrees forbidden by theory. Why is that?
2. My gut feeling (not tested, sorry) is that the aerodynamic qualities of a car vary according to speed. The theory goes like this: air has mass; mass is slow (or how do you say this in English). The mass is pushed aside by the moving car, and once the car has passed, the mass comes back, attracted by the low pressure area behind the car. My point is this: because of the slowness of mass, the airflow picture will be different for a car depending on whether it's going 50 or 150. With 150, the wake will be longer, and the 'bow wave' will be stumper in shape. If you take one individual air molecule, and a car at 150, (as compared to car travelling 50) it goes like this: the molecule gets closer to the car before it starts being pushed to the side (by other molecules), it probably travels further outward since it hits a higher pressure area, and takes longer to travel back in the wake of the car - or would the lower pressure (stronger vacuum) cancel out this last effect?

In other words, the air behind an Insight travelling at 50 would be back to normal pressure at a smaller distance behind it, than with an Insight travelling at 150.
Or: does it make a difference for the Cd figure which wind speed is used in the wind tunnel that tests it?

There might be a link between the answer to my two points: namely, that at low speeds (say up to 50 MpH), the rear third of the EV1/Probe is perfect, since air flow remains well attached to the car, from start to finish. But the rear third would not be perfect if the EV1/Probe were to travel at a speed of 130 MpH. At that speed, the air flow would not remain attached to the rear third since the car would be going to fast: and a smaller angle would be needed, like 10 or 15 degrees.

This stuff is not necessarily based on existing (known) theory, but there may be a parallel (in the water, not in the air) that I know of: in windsurfing, the rear fin slices through the water, and prevents the tail from gliding sidewards. There is more pressure on one side of the fin than on the other. At low speeds, no problem. At high speeds however, you may encounter spinout: the pressure difference causes the angle of the fin (in comparison to the direction) to become too large, the water can no longer remain attached to the low pressure side (the wind side) and air bubbles start to form. The back of the board slides away to the leeside.
Now of course the properties of water and air are much, much different, but I see no reason why a small similar effect does not exist for air.

Quick point here - will write more later...

I measured the EV1 rear slope to be 18 degrees. The Probe V is harder to measure because I haven't found an image with a true profile view, but the closest 2 I have found measured 17 and 20 degrees.

So not quite the 30 degree angle of death.

One reason both of these cars can use relatively steep rear angles is the shape of the rear is dramatically more conic than wedge like. There is a very generous curve from the sides to the backlight/decklid, and this would help avoid the formation of lift induced vortices formed at the rear of a more conventional wedge-like rear end shape with the same backlight angle but a sharper side-to-deck transition.

The EV1 side-to-top rear radius is most obvious when seen from above:

https://www.geencommentaar.nl/media/ev1.jpg

I think the EV1 went beyond typical boat-tailing. Maybe a distinction is called for:

A pyramid is "boat tailed". But a cone is far more aerodynamically efficient owing to the elimination of the sharp angles where the pyramid's planes meet.

I would say that most cars - even those which employ boat-tailing - retain distinct side & top "planes", like a pyramid.

The EV1 did "conic" boat-tailing. Better.

(EDIT: of course it's not really a cone, since the edges are curving in 2 dimensions, but the analogy still works.)

The effects that make a pointy nose more aero than a blunted one are associated with traveling at Mach numbers near or over 1. Has alot to do with the speed of the vehicle in relation to the speed that pressure waves travel (ie: mach 1).

Not very applicable to highway speeds though, or even speeds attainable by street-legal cars. At speeds any of us are likely to travel in a car, the classic teardrop shape is supposed to be the most aerodynamic as mother nature has been telling us for years.

re sharp vs blunt, all I can tell you is that on rc sailplanes they prefer NOT to round off the trailing edges, if you cant bring them to a point then leave them square. rounding will create control surface flutter and other noises. Granted the back of a car isn't exactly a trailing "edge". A boat too has a sharp transition to verticle at the back, if any verticle, don't know if it's for the same reasoning.

Good link. Thanks. One day I will find an aerodynamicist to talk this over with.

Get a block of foam and a big fan - shape the foam to the teardrop shape first and place in the fan air stream and measure the force on the shape . . . repeat as you cut the rear taper off.

MetroMPG,
I haven't seen this referenced to anywhere on this forum yet.

https://www.nasa.gov/centers/dryden/p...ain_H-2283.pdf

Big file, 3.35 MB. It does give hard experimental evidence of whether radii help or not, at least for a van. It ought to rank at least "for kicks and giggles".

I'd seen that PDF before, but forgot about the rear radii reference. (How's that for alliteration :D)

Comparing tested Cd values for configurations E & F, all else being equal:

0.350 (rounded rear corners)
0.365 (square rear corners)

So: if you've got a square shape, and no boattailing, rounded rear corners are better.

But boattailing is better than rounded rear corners:

0.238 - 0.242 (tests with full vs. partial boattail - although this isn't directly comparable to E & F because they were using a 3/4 length undertray on E & F vs. full-length undertrays on the boattail runs).

What it doesn't answer is whether rounding the ends of an otherwise properly boat-tailed or Kammback shape would net a similar reduction in Cd (I think not).

BTW, welcome to the site NewsFlash.

Thanks MetroMPG.
Another archived NASA file (1.61 MB) shows the details of that same boattail seen in the previous pdf file. It doesn't give a degrees radius, but does show the lengths at the base of each curved surface as well as the overall length.

https://www.nasa.gov/centers/dryden/p...ain_163113.pdf

Obviously, the truncated boattail is the way to go as the Cd ratio of the truncated isn't much different than the full boattail. Hope this helps.

MetroMPG,
I've thought about it and agree that the sides of the boattail do not need to be curved when the height of the boattail is reduced from being as tall as the one on the van referenced to above. Then you would wind up with a boattail like on a boattail nozzle on a jet. File is 400 kb.

https://techreports.larc.nasa.gov/ltr...aa-99-2670.pdf

I reference this file mainly for the boattail's shape, they put air pressure through the open nozzle, and airspeeds around the nozzle are at least 0.6 Mach and greater (supersonic).

Imagine a boattail nozzle shape on the back of a pickup truck!

Another good link, thanks.

It seems to me one reason their full boattail didn't work as well as it could have (you could see flow separation in the telltales) is they continued to curve the planes away from horizontal/vertical as they were extended; the tip of the tail was dramatically more than the often-quoted 10 degree optimum angle.

Their results are consistent with what Kamm discovered though: a properly shaped, truncated boattail will be nearly as effective as a full boattail.


You should post a thread in the "introduction" forum to say hello and tell us a bit about yourself. Obviously aero is one of your interests. ;)

Basic advice
 

I'm new here, but I just wanted to say something that should cut through all the confusion. A famous quote: "Most cars would be more aerodynamic if driven backwards." That is, a big flat rear surface (such as a hatchback) creates the most drag.

Question, what is the most aerodynamic object in the world? An airplane wing. How is it designed? BIG in front and TAPERED in back. It doesn't matter how you split the air, but you have to *put it back together* properly.

https://img299.imageshack.us/img299/4...ock2ediiq2.jpg

Let's use the Geo Metro as an example. The air going over the top suddenly gets sucked down by the flat hatchback and swirls around. That's drag.

https://img440.imageshack.us/img440/8...forwardai4.jpg

Now let's drive the car backwards. The sloped engine body forms a smooth airflow at the "rear" of the car.

https://img440.imageshack.us/img440/5...ackwardbz8.jpg

Thus, the rear of the car should ALWAYS be tapered. I guess you call this boat-tailing?

With the caveat that generously rounded side-rear transitions are also less stable in cross-winds than sharp rear angles.

Well, that makes sense, if you taper the rear, you're making the car longer, and thus the side larger, so crosswinds would have a bigger area to hit. But how often are crosswinds an issue in everyday driving?

What I see on a large number of ultra-sleek concept cars are side/rear transitions which look literally "chopped" - sharp 90 degree corners

Market forces. A "sharp" trunk is what customers *expect* to see, but it's not aerodynamic.

Ford Probe V:

https://img264.imageshack.us/img264/9...forwardwg3.jpg

Probe driven backwards:

https://img237.imageshack.us/img237/5...ackwardku2.jpg

I can't vouch for the validity of this, but more than once I read that the Pro Stock Pintos of the early '70s were more aerodynamic when going backwards. Given how high they sat in the rear, I don't know. Does it sound plausible?

Maybe you Pinto fans can find some better photos.:D I wonder if the same aero peculiarity applied to Gremlins and Vegas, those other members of the economy car elite.:rolleyes:

Is the AMC pacer the ultimate drive backward aero car ?

/ https://www.gassavers.org/garage_imag...ia5whehwjq.jpg

Well, here's a quick reply:

https://www.av8n.com/how/htm/4forces.html

"A non-streamlined object (such as the flat plate in figure 4.9) can have ten times more form drag than a streamlined object of comparable frontal area (such as the one shown in figure 4.10). The peak pressure in front of the two shapes will be the same, but (1) the streamlined shape causes the air to accelerate, so the region of highest pressure is smaller, and more importantly, (2) the streamlined shape cultivates high pressure behind the object that pushes it forward, canceling most of the pressure drag, as shown in figure 4.10. This is called pressure recovery."

"Any object moving through the air will have a high-pressure region in front, but a properly streamlined object will have a high-pressure region in back as well, resulting in pressure recovery."


Another quote from the same article:

"At high airspeeds, parasite drag is dominant and induced drag becomes almost negligible."

I'm pretty sure that everyone here already accepts that a boat tailed rear is the best for low drag, but that's not always practical in the real world. Things like the need to fit four people and luggage in a car that will also fit in a garage get in the way...

The main point if the thread topic is that when the ideal shape cannot be used, what should be done with the trailing edge. Since tapering the rear at the ideal angle is usually not possible, a hatchback is actually a very good shape for a car of a given length and useful interior volume but should one chop the edges off sharply or with an asthetic (but not always aerodynamic) rounded edge.
I find it interesting that you use pics of one of the Ford Probe concept cars. It was designed specifically as an exercise in aerodynamic design and has one of the lowest (if not the lowest) Cd values for a car. I'm also not sure that it would better driving that car backward. Given that it has a nice sharp Kammback cutoff I would expect to see some disturbance caused by driving that tail into the wind. That disturbance would then lead to 'dirty' airflow over all the rest of the car causing excess drag. I'm also curious about your example for the Metro. The angle from the roof to the windshield isn't exactly an ideal boattail and might cause turbulence over the entire hood area. Are there any Metro owners intrepid enough to try coastdown tests forward and reverse?

>I find it interesting that you use pics of one of the Ford Probe concept cars. It was designed specifically as an exercise in aerodynamic design

I used the Ford Probe because GeoMetro mentioned it in his article, and because the pics were easy to find. The Probe is an extremely aerodynamic car, but the chopped-off rear is disturbing to me, and noteworthy to make a point.

>I'm also curious about your example for the Metro. The angle from the roof to the windshield isn't exactly an ideal boattail

That's true, it isn't ideal. There's a sharp angle between the hood and the windshield that could be a problem.

After all, there's more to mileage than just aerodynamics, such as weight and number of cylinders. On the latter two points, hatchbacks win.

While we're on this subject, I've been looking at what's being done with semi trailers--that may be related to driving an xB. It seems that FE is improved when the vertical side/corners are rounded, often with attached fairings. This has led me to wonder about the old station wagon deflectors that diverted air downward to keep the rear window clear. Would a similar deflector mounted vertically at the rear corners of the xB would help fill in behind. Sounds too ugly to contemplate. Interesting idea, though.

IMO a flat back (such as an 18-wheeler or Scion) is the worst scenario drag-wise.

Anything you can do to round the rear end is going to help aerodynamics at high speeds.