Why does The Template have to be a half body of revolution?
 

My understanding is that The Template is a half body of revolution to insure that air doesn't want to move laterally because of pressure differentials between the top and sides, which leads to vortex generation.

If that's the case, wouldn't a half-square cross section serve as well, given equal cross-sectional area? If air is not wrapping across the edge, would no vortexes be created?

Here are three aeroforms, a cylinder, a superellipse and a square. Would their Cd be equivalent?
http://i.imgur.com/GlVjc.png

(These are not dimensionally highly accurate; I just eyeballed the proportions against The Template)

The next question: If the height/width proportion changes, what happens to the respective tapers? If the half revolution form is 7' wide, then it is 3 1/2' high. If the height is proportionally greater, does the side taper increase or relax?

TIA

quote: Here are three aeroforms, a cylinder, a superellipse and a square. Would their Cd be equivalent?

``````````````````````````````````````````````

The frontal areas are different the shapes are different,making it unlikely that they have precisely the same cd.
Why do you feel the model with its corners and sharp edges is as aerodynamic as the curved models? i feel the added mass will increase frontal area and the hard edges will create turbulence from mixing in the opposing airflow from the sides/top.

Your logic looks sound to me until you throw in a cross wind.

I would guess the taper of the sides would relax with added height since air from the top is not helping fill in the void further down the sides.

Nice graphics. I have been rolling some of that over in my mind since I have been trying to get some thoughts down on a tadpole shaped special with seperater wheel fairings in front. I am leaning toward that approach because I can register it as a motorcycle. My basic shape would probably be half of a pumpkin seed, as Phil calls it, with tandem seating and a canopy. Would kinda look like a streamlined CanAm 3 wheeler. Still working out the front suspension and the seating layout.

Jim,

Ohh, this sounds like an interesting project!!

I spent quite a bit of time investigating this same approach about 4 years ago, and my best advice would be......

.........Whatever components you decide upon for the vehicle, make sure they are all DOT approved components.........

The more "custom" components you put on the creation, the harder it is for the inspector to get a "comfort" level about your skill level and so on. He has to sign off on your design, and in case the machine has a "failure" in the future that causes injury to someone else, the inspector could still be held partially liable in certain situations for passing questionable construction methods.

I had many email exchanges with my state inspector about this issue, and to make it "easy" for him/her to inspect and give approval for road use, it's imperative that components are either from a previously DOT approved motorcycle, car, truck, you name it. Keep in mind that ATV's are not road legal in the normal sense of the word. Yes, you see them on the road now and then, but they are not DOT approved for normal road use.

Hope this helps, and good luck with your project.

Jim.

I shrunk the box shaped one to approximate equal frontal area:
and I know the single-curve shape will have more skin drag. No doubt there would be a measurable difference, but would it be a practical difference?

This is where I thought the conversation would go. I read, somewhere, that radiused edges improve crosswind performance. The superelliptic shape strikes me as a middle ground with the 'boxfish' shape:
http://i.imgur.com/smKsa.jpg

But it's all compound curves and loses the construction simplicity of the square cross-section. The Tropfenwagen looses the taper in side view almost completely:
http://i.imgur.com/221z8.jpg

I find The Template is kind of like a straight jacket, and almost nothing practical looks completely, exactly like it (the 1939 Schlörwagen comes close). I'm just looking for the most respectful way to slowly drift astray from it. There must be fifty ways...

Yes, I agree and I don't think anyone would contemplate actually building to that optimized shape. But the template is based on sound measurements of Cd for various shapes, so it is completely ignored at your own peril. I found the VW L1, which you can google, to be an acceptable deviation. It has a pretty and practical body shape and still maintained a very low Cd.

Aptera-like? The always entertaining Autospeed website has a wealth of useful articles. For example:
Zero Cost Modelling of Space-Frames
Blows my mind. I see there're new articles since the last time I visited.

When that car hits the market, it will seriously kick some Prius butt. Did you know the first concept (not the 2nd one) had hollow gears in the transmission to save weight?

The square one would definitely higher Cd. When you include the ground plane (and the wheels) in the picture, that changes things a lot -- the air flow is not symmetrical. That is why the template is a half revolution.

The frontal area is a separate issue from the Cd -- greater frontal area increases the CdA, but it does not change the Cd, per se.

Edit: I may be misunderstanding your question. All three of the shapes you are proposing are "flat bottomed", right? Elsewhere in this forum, someone did a CFD study of the round shape with a slightly curved underside (I think, and air comes out from under the bottom an spirals up and around the sides, if I recall correctly? So, the template is a general guide for shaping the upper side, but the interface of the wheels and the ground with the car chassis have to be worked on more.

That Boxfish model had an amazing Cd of just 0.095, if I am not mistaken.

box fish
 

dang you! I came on here to post my pics of my latest CFD testing. I'm trying to replicate the box fish, which MB used to shape the bionic car. My very first iteration, which was 80" long from peak to the kamm back, came to 0.143. My second iteration is 120" long, and came to 0.101. MB said the box fish came to around 0.005 with excellent yaw stability.

I used a convex rectangle section with rounded corners, approximating Morelli's later designs, instead of the "X" type shape of the box fish (I actually took a video of one at the local aquarium today). I was surprised how easily it obtained such a low Cd, considering how much more work I did to get Aero's template to 0.092. The body falls away from the streamlines much quicker, yet there's no delamination.

This answers my question of whether we "need" the tear drop shape for a low Cd. A box is certainly roomier, and easier to fit/hide wheels, and it's much shorter than the template.

Note that any body will work better with a rounded bottom - not flat - and generous fillets on the rocker panels, and a raised tail. Anything to equalise pressure around the perimetre of the body helps prevent vortices. Morelli discusses elliptical shapes to minimise wetted area, hence, skin drag.

discuss amongst yourselves :)

Yes. I put 'half body of revolution' in the title and showed full bodies in the illustration. In my defense I posted at 4 am. I realized at 2 am I wasn't going to sleep, so I got up and prepared the models. By 4 am, I was sleepy and didn't truncate them properly. I thought I scaled the square sectioned one in all three dimensions, but the length looks the same, so ??????

What I was getting at was if the frontal area is the same, and there is no air movement except out and then back into the center (i.e., no lateral movement that would lead to vortexes), would compound curves be necessary? Or would the simplified construction of the (half) square section carry an aerodynamic penalty?

What strikes me is that even though the superellipse is half way between the square and circle, it looks closer to the circle. That may be because I didn't subdivide the square section equivalently. There are a whole class of superelliptic curves, some would be very close to a square with radiused edges.

I understand that the underbody is a whole separate can of worms, until they re-merge at the rear.

ERTW -- Thanks for sharing. That is precisely on-topic. Consider it a preview and do your own separate post if you like.

Is the line at the bottom a ground plane or are they in free air? And if so, why do you think the stream-lines from the top cross the stream-lines from the bottom in the side view? Wasn't that a no-no in Ghostbusters?

Does anyone have a reference for the study done on a body shape with a pronounced arch to the underbody? I know I've seen it referenced here but I didn't save and can't find it now. My recollection is an Italian-sounding name in the 1960s. I wanted that for MTrenk's underbody thread, and the 'Aero concept car -- Bugatti Stratos' thread the mods spun out of that one. TIA

Did someone say car shaped like a fish? :)
http://i.imgur.com/kVIcf.jpg

http://ecomodder.com/forum/showthrea...-pdf-1028.html

pininfarina banana car

My memory is that the computer model of the boxfish was a Cd of 0.06:

http://www.speedace.info/solar_cars/...fish_model.jpghttp://www.ecofriend.com/wp-content/...ncept_car2.jpg

The blue quarter scale model has a Cd of 0.095 and the diesel powered concept car has a Cd of 0.19:

http://img.photobucket.com/albums/v7...ar-Body-lg.jpg
http://www.thedivesite.co.za/files/1...-bionic-07.jpg

Edit: here's a series of screen captures I got from a video about the Boxfish, that show many more angles of the early model:

CarBEN EV Concept :: Mercedes Bionic/Boxfish clay model picture by NeilBlanchard - Photobucket

half body
 

The streamline bodies of revolution are of the lowest drag 3-dimensional bodies known.
And their half-bodies lend themselves okay to a 2-door coupe or sedan and such.
Today's Bochum University', Cd 0.14 solar car would be a recent example.
There has been a tremendous interest in the 1948 NACA mathematical algorithm which became the 1976 Morelli shape as used by Aptera,although,with ground proximity and wheels,the Morelli form has failed to demonstrate lower drag than a half-body 'pumpkin seed.'
If you'll look at the full-boat-tail trailer thread there should be some pictorial drag tables which demonstrate the drag increase when side radii are lost on the streamline half-body.
An example would be the square fuselage of the 'Spirit of St.Louis' with Cd 0.247 and the 'round' fuselage of the Arado 'Smooth' of similar fineness ratio,at Cd 0.06.
You will never see a high performance,low drag fish,bird,airship,fuselage,submarine,torpedo,etc., with square edges.
There are a lot of graphical drag coefficient tables in the public domain from which to compare architectures.
I believe that if you will exhaust all avenues,you will come to the realization that you're not going to beat the 'Template.'I've been actively looking since 1973.

boxfish
 

It would have been really instructive had Mercedes published a plan-view image of the fish.This decides the flow path and the side view makes it as difficult to understand as if they offered a photo of panties when speaking of brassieres.

It's not called a bodyofrevolution fish ;). Mb was surprised at the low Cd. They also mention that it's very stable and maneuvrable. We can't say for sure what the most streamlined animal is until we test them. In the meantime we just have to drive cigar shaped cars.

I was at the big al's the other day and noticed the shark's head is elliptical. The body is almost triangular.

Imo as long as the air on the top and side is the same, sharp edges won't hurt. It's when there is a pressure differential that sharp edges will accentuate it and create vortices. In that case a round edge will allow a gradient, and not feed vortices

Aerohead -- Thanks for you thoughts. Have you posted your Bonneville stories anywhere? I have a post at Project the third that I would appreciate your comments on.

I'm not looking so much to beat it, as to find some way to accommodate it into my life. Life full of compromise, if you take the half body of revolution and hang a license plate on it, you've already compromised. :)

Now that right there is what I was looking for. One would expect the superllipse to have Cd ~0.15.


ERTW -- This is how I'm seeing it:
So we have a preferred shape (or shapes), with the wheels spats and departure angles; we know that surface dirt and duct tape are trivial. That leaves the scale from drip rails and door handles up to rear view mirrors to think about. Maybe air scoops behind the rear view mirror to eat its vortex?

Aerohead -- I found your Bonneville post. I also rediscovered this picture this morning. Perhaps it is what started my thought process. It out-boxes the boxfish.
http://i.imgur.com/4zkgI.jpg

picture
 

It would be nice if Honda published a Cd for the pictured car,then we'd know what we were 'looking' at.Have you seen the Honda P-NUT?
Some of the current minis are running on the order of Cd 0.3.
If you wanted lower drag you'd have to extend the rear.
--------------------------------------------------------------------------
If you'd like to depart from the 'Template,' you might want to find out all you can about Wolfgang Klemperer's 'minivan' of Cd 0.16 (in naked model form) which he tested in 1921.Klemperer was a doctoral student working under Paul Jaray at the Zeppelin Werke.This 'minivan' is what VW used as the basis for the VW 2000 concept car.
I might be more excited about it if there was more data available on it.After extensive shaping in their new wind tunnel,VW got a 'production-ready' model to about Cd 0.25.
If you weren't interested in going below Cd 0.16 it would be a good way to go.

It looks like it's got a lot of taper in plan, and the lower nose seems to be handled well; but yeah, that's not a number.

I'm familiar with the VW Auto 2000 concept; but I'm not finding much on Klemperer. I searched on combinations of 'Wolfgang Klemperer 1921 windkanal minivan', etc. Google points to page 25 of the Aerodynamic Streamlining—Part C thread but the trail goes cold there.

I'm stumped, I can't decide if I am interested in sub-0.16 territory. While I'm dithering, how valid do you think the reported Cd of 0.17 is for the Volkhart-Sagitta:
http://i.imgur.com/3xMgg.jpg

Cd 0.17
 

It would help to know where the number came from.Just shooting from the hip,I don't have a problem with it.All the leading edges have generous radii.The windscreen has nice curvature as well as it's header and A-pillars.
The full wheel skirts are a plus.And the side mirrors are well formed and pushed forward into slower air away from the A-pillars.We could presume a full bellypan?
It's very similar to Ferdinand Porsche's personal car of 1939 with which he commuted between Stuttgart and Berlin.

That's the way I see it, too.

The up-kicked cowl on the Talbot-Lago T-150-C was a styling gimmick, here it serves the aerodynamic need. And it has a single wiper. I picture those skirts having the one Dzus fastener at the top and then they could rotate out 90° and pull out of a slot in tube restraints at the bottom corners.

My understanding is that 2 were built, now there's one in a museum. It was a 4-passenger high speed Autobahn cruiser for the Luftwaffe.

VW reproduced the Berlin-Rome racer and characterized it in a wind tunnel. I'd like to see that done here. Imagine if in 1974, someone had re-popped that in fiberglass and sold them as a kit car.

kit car
 

If Fibre Fab had done exactly that in '74,I would have been all over it.I'd just read Crisis Fighter Pinto by Don Sherman and purchased a crashed Karmann Ghia to restore and replace my El Camino as commuter car.
I'd seen Fibre Fab's Valkerie at a North American Rockwell facility in Palmdale,CA where we were working with the B-1 Bomber.They could make anything out of composites! And nice stuff!

You and me both. I was headed toward a Sterling or Amiga kit car until the world changed around me into something I wasn't expecting (still does that); I got as far as the PolyGlas F60-15s on 8" wide rims (front and back, on gravel you could turn or brake, but you couldn't turn *and* brake).

The nice thing about today is there is software that will produce a 3D model from a few 2D pictures. One could recreate and 3D print the Volkhart-Sagitta to within a few tens of microns accuracy.

=============

Oh, and this:http://i.imgur.com/uASDn.jpg
Karmann Ghia Station Wagon in France - Fake Volkswagen

3D
 

With Scaled Composites 5-axis router,a full-scale rendering could be done from which tooling could be generated for wet layups or a chopper gun.
If you shaved the chrome and integrated the bumpers
n stuff,the Volkhart- would appear to most as quite modern.And with seating for 4,more 'practical' than Porsche's speedy little 2-seater of '39.

Since you're dropping names like North American Rockwell and Scaled Composites; I'll just say—somebody needs to do it and I don't think you should wait for me.

I need to catch up on some promises I made in another thread, but I've been thinking about modelling the V-S in 3D, by extracting the cross-sections from the 2D pictures manually in Photoshop. I use a box modeler instead of a subdivision modeller, but the smoothing function can yield the compound-curved surfaces needed.

Did you ever develop this line of thought and exercise further?

Were you talking about this thread in the other thread?

Where I'm at currently is a 6-frequency octahedral symmetry geodesic dome. The octahedral symmetry puts 90° corners at the center of the top/bottom, sides and front/rear. Increasing the frequency approaches a smooth compound curve and the geometry can be calculated to any arbitrary precision.

http://ecomodder.com/forum/member-fr...-w-caption.jpg

Big ol' windshield with skylighting in the living area. I have a donor vehicle and tools, but not the shop space and budget. The basic sphere is 'prolated' front to rear and above the equator and 'oblated' and truncated below the equator. 30/70° split front to rear. As such:
http://i.imgur.com/XtJJdlZ.pnghttp://i.imgur.com/m1VAmt4.png

Interesting stuff, I would love to see more of these studies.

And now that I know about your dome background, this is all becoming clear.:thumbup:

Tell you what. I'm sitting on some intellectual property that I refuse to disclose to the predatory capitalists (i.e., patent) but I have some responsibility to give back to Humanity. I'm curious about Opensource Architecture and Creative Commons Licensing.

Do you have any opinions on that?

some values from K-F
 

I've been chugging back through Aerodynamiks des Kraftfahrzeugs by Koenig-Fachsenfeld and looking at material he worked on under Kamm at the FKFS which is germane to the 'organic' vs 'cubist' teardrops.
It looks like they tested both images (left) and (right) as passenger car bodies,with wheels,at 'standard' ground clearance.
The (left) body produced Cd 0.12,the (right) body Cd 0.21.
I've contacted a local German tutor to help with translation,but from the tabulated data I think this is what they found.
FIAT,in a 1986 SAE paper investigated fastback bodies and demonstrated how the Cd is corrupted without both tumblehome and edge rounding,something which is a feature of the body of revolution.
Jaray cheated the form with his pumpkin seed of 1922 so we've got 'options.'
I'll try and have something for Saturday at the latest.

some numbers to chew on
 

--------------------------------------------------------------------------
I'm still working through the German-English translation and I haven't heard yet from the tutor but have roughed-in some text and believe that the following is an accurate portrayal of what K-F and Kamm did at FKFS:
*Using a slice of airfoil twice as wide as the section height,with a thickness ratio of 15.38%,with a ground clearance equivalent to standards circa 1938 (around 9.25-inches (235mm)) they got Cd 0.19.
-------------------------------------------------------------------------
*Adding wheels gave Cd 0.24.
-------------------------------------------------------------------------
*Adding plan-view camber to the body produced Cd 0.1938.
-------------------------------------------------------------------------
*Adding rounding to all the upper edges produced Cd 0.161
-------------------------------------------------------------------------
*By restoring the plan-view radius to the nose produced Cd 0.12.
-------------------------------------------------------------------------
*K-F/Kamm did 'remeasuremnts' (Nachmessungen) to a reproduction of Walter Lay's 1933 aerodynamic research model from the University of Michigan.They recorded an identical Cd 0.12.
*Lay's model# 10 with 'JEEP Wrangler' windshield couldn't better Cd 0.24,as with the FKFS compromised nose.
--------------------------------------------------------------------------
FIAT's aeronautical laboratory,in their SAE Paper# 860212 reported that a 'fastback' car (Template) suffered a 32.6% drag increase with compromised forebody leading edges, which reinforces the conclusions of Lay,K-F,and Kamm.
*Fiat's research also showed that of fastback (Template),notchback,and squareback body styles,that the fastback was most sensitive to upper body rounding and suffered the greatest drag increase without it.
-------------------------------------------------------------------------
*Jaray and Kamm were both airship 'Luftschiff' people.
*Jaray was designing Zeppelins at the same time Kamm was serving in military with observation balloons.
*Kamm's doctoral dissertation was on streamlined teardrop-shaped balloons of which he patented circa 1919 as the K-Balloon.
*All Allied barrage-balloons of WW-II were lineal descendants of the K-Balloon.
-------------------------------------------------------------------------
*At FKFS,the half-airship 'halbeluftschiff',Half-streamline body of revolution 'halbestomlinienrotationsk'o'rper',was always the 'Alpha' form from which all the attempts to 'cheat' were done.
--------------------------------------------------------------------------
*The half-body has a good enough forebody for subsonic flow.
*Most importantly,it has the sectional density in the aft-body necessary for the gradual pressure rise which will prevent the reverse-flow that triggers separation and the attendant pressure drag aerodynamicists demand that we avoid if we're to achieve really low drag.
--------------------------------------------------------------------------
*We can push the shapes around in frontal elevation.Jaray did it.Lay did it.Kamm did it.Which means that production automobiles are game.It is a condition of boundary layer 'legislation.'
-------------------------------------------------------------------------
*We can't mess around with it much in side elevation or plan-view.If anything,you'd go hyper-template,but never steeper.
-------------------------------------------------------------------------
*With 'zero' streamlining you're looking at Cd 0.86.
*With ' complete' streamlining Hucho says we can approach the drag of the body sans wheels (0.07-0.09).
*Hucho also says that these lower values will be achieved only through airfoil and half-body forms.
* You can consider the 'practicality' of a 'wing-car.'
*And we've demonstrated above what happens when you 'template' a 'wing-car'.
You can fool most of the people most of the time.You can fool the atmosphere non of the time.;)

Thanks for thinking about this.
That's gold right there. I assert that even though the squircle is mathematically demonstrably half-way between, it is closer to the half-body aerodynamically ...but/and better suited to packaging passengers.
This would describe my approach.

I'll have more to say later but I'm mocking up a Breer's-style stinger on the '58 Beetle body. It will have a three-piece windshield similar to the old Shalako dune buggy (posted as the VLC conncept) and a boattail that extends the interior space straight back. It's an hexagon at the bulkhead 35" across at the top 43" at the center and 30 " deep, i.e., 39x30=1170sq in. This tapers to a line 16" tall 48" back, but truncated to an 8x16" base plate (768sq in). The front and rear wheels and the diffuser enclosing the engine are To Be Determined. I'm learning that the gutter and door cuts are splayed outward. A nice subtle change would be to pie-section the body vertically so the A- and b-pillars are the same width moving the widest point forward half the width of the door.

I notice it's my thread so I will go off-topic with my own permission:
http://ecomodder.com/forum/member-fr...27-9-47-14.png
Here's a screen grab from a few moments ago. I'm seeing a body kit for the Beetle that has front fenders that trade the iconic Beetle crown for a BMW-style shave, a rocker extension that replaces the running board, a panel that mounts on the lower door that swallows the lower door hinge and raises the swage line, and a slot on the inner edge of the fender that exposes the break to the inner fenderwell (opposite to the vent on the Corvette).

Possibly 4 crescent shaped box cavities on the fenders?

Edit: Well, I can't sleep. the whole body kit could be done in PolyMetal as simple curves. With curved scores in the flat sheet and basically a sector bent into a conic section. I made fender flares for a '62 13-window once that way.

The edge in the wheel arch would be wire-wrapped (tests soon) and the edge at the body mounting bolts would be crimped—probably heavily— between the mounting holes.

The rear fenders could start as a scoop at the door opening and terminate in a semicircular arc starting behind the rear wheel openings and canted back at about 30°.

Speed-whiskers off the tops of the front fenders to bury the top door hinges.

squircle
 

The squircle would be real good.So many production vehicles already have a body section like that.
Jaray's was like it in the center of his pumpkin seed.
The FKFS K-cars were like it for the same reasons you mention.
As long as the contours are gentle the boundary layer will be protected.

Guy I used to work with always said "If you were an air molecule..."

So, if you were an air molecule headed straight at the front of the three shapes, where would you like to go?

The left body is easy, any path around it is the same. The ones to the right are different. Superimposing a clock face, the 12, 3, 6, and 9 o'clock paths are the same simple paths from the left body. Anything but those paths is a longer path. And the war is lost...

I should really redo that graphic with the shapes truncated to half-bodies. There is no 6 o'clock.

But, still... I get what your saying, but would not the individual molecules simply be less likely to take a path at 10:30 or 1:30.

aerohead nailed it. The battle is lost in cross-winds, the nominal condition.

Yeah, half bodies, I didn't type 6 when I first typed a response.

Sure, the air molecules would LIKE to take the easy path. But the air molecule before you already did. Easy path isn't so easy. Air molecules bumping into one another. Energy wasted.



Another thought. A .21 Cd for the shape on the right makes things like the Dryden van (which is shaped like the right shape) seem pretty good at a .25 Cd (approx. - from memory) in the real world. Hmmm....

Brownian movement. I think of them as little herd animals in a stampede, or little schools of fish or flocks of birds. Each, though inanimate, trying to reach its happy place. Energy is only wasted when that 'intent' is thwarted.

paths
 

Hucho 'said' that where we get into trouble with the square edges is that as the high pressure under the vehicle will try to seek equilibrium with the lowest pressure up on top.
As the two airstreams collide at differing velocities,they'll whip up into attached vortices on the corners,as rising moist super-cell Gulf air over Colorado would collide with the jetstream overhead,initiating the vorticity that will spawn tornadoes as the vortex rolls eastward eventually rotating into the vertical super-vortex over Kansas.
With any body section closer to a body of revolution,as you say,the pathways are more similar,and so to too with velocities.
With sharp lower edges,and even running boards on a pickup,it's harder for the high pressure underneath to even telegraph itself up onto the sides of the vehicle.