The body shape of minimum drag
 

I'm quoting Antonio Morelli's 1976 SAE technical paper #760186

"The historical development seems to indicate that an optimization of the body shape should be sought for through the reduction to a minimum of the sum of the profile and the induced drag, the third term of the sum expressing th total drag, the friction drag, being practically not variable and negligible (7).
In fact, till now, either a low profile drag was obtained (but not a low induced drag) as with the Jaray body, or a low induced drag (but not a low profile drag) as with the "Kamm" body or with the adoption of spoilers and dams.
...The scope of this work is to determine a shape, suitable for motor cars, having a low profile drag and zero induced drag.
The following conditions were imposed:
A) total aerodynamic lift equal to zero;
B) gradual variation of the area of the transverse sections of the body
C) gradual shape variation of the transverse section of the body.

In order to meet other minor requirements, the following additional conditions were also imposed:
a) aerodynamic pitching moment equal to zero, for stability reasons
b) an oval contour of the transverse sections of the body (mainly of the "basic body" which will be defined further on) in order to reduce the "wetted" area and, as a consequence, the friction drag."

I think it's most important to note that Morelli got close, but didn't achieve his goals. The final shape had a Cd of 0.23.

Figure 5 shows that a "drop shape" in free air has a Cd of ~0.09, while in close proximity to the ground (9-14% of the body thickness) it rises to ~0.14.

A beneficial shape is a "banana" with ~9% camber - the mass centroid peaks at 9% of the length of the body.

His shape is NOT "reverse aerodynamics". He states that a gradual pressure gradient is beneficial on the front and back of the body. You can mess up the air flow in a short distance, and spend the next 10 ft to settle it down, and Morelli believed that this method "increased the car length without contributing much to the usable space."

I learned that you can super impose various bodies and sum the Cd of the individual shapes.

Jaray's aero philosophies are 80 years old. Even this paper is 35 years old. Stay tuned.

Bub speed record motorcycle Cd .09.

banana car
 

*The banana car achieved Cd 0.161 without wheels in ground proximity.
*23% of the tail was chopped off with no measurable drag increase.
*When wheels were added the Cd jumped to 0.35.
*The rest of the time at Pininfarina's wind tunnel was spent anguishing over detail optimization to shave the drag finally achieving a Cd equal to Kamm's K-3 of 1939.
*And I believe it is 'Alberto' Morelli.

It is indeed Alberto...I must have had Banderas on the brain :)

Morelli's figures for the basic shape are:
Cx 0.071
Cz -0.044

The wheeled body:
Cx 0.177
Cz 0.166

The 0.23 figure is an estimate to include surface and underbody details.

This is all just a preface to his more recent work.

figures
 

What's really tough,is that he pours his soul into this work ( it was an absolute coup in its day),throws it out there for everyone's benefit,and is rewarded with little or no enthusiasm from automakers,maybe until Aptera comes along.

Are we talking about this? It's so difficult to understand many things on here without images.

http://img.photobucket.com/albums/v7...2at15322PM.png
http://ecomodder.com/forum/showthrea...hape-3746.html

That's the one Sven. I have been busy doing simulation for the last week. When I took a break to post this I was unable to post pics. Soon!

The shape might be fine from an aerodynamic viewpoint, it's a dog from a practical PoV.

Adding wheels is problematic - both from an aero viewpoint (see above) as well as from a practical viewpoint (see Aptera).
The shape is very complex to build.
The shape has little internal volume, and even less practically useful volume.
The shape is awkward in everyday vehicle use.

Is a 20' long 2 passenger vehicle practical?

The basic shape is an idealisation. The better the basic shape, the better the final car. One of Morelli's stipulations was that it have practical internal volume for passengers and their baggage (his main reason for avoiding the tear drop). I've uploaded the basic shape (Cd 0.071) and the wheeled car (0.177).

I want to reemphasize that this paper is 35 years old. I'll get to posting his 2000 paper. I'm intrigued by his "fluid tail technique".

I did some CFD with a shape inspired by his latest work. I got a wedge shape within a few counts of a 2.5:1 ellipse (0.174). however, I've come to believe that the results were invalid. I'll post a full report when I can.

Like the MB bionic car pointed out, current frames are inefficient. Neural networks and genetic algorithms are whittling away at frame/body to decrease weight, maximise internal volume, and reduce drag. Technology that has not yet been created will shape the cars of the future. Reading over recent SAE papers, they're still struggling to model rotating wheels, and how air moves within internal cavities. It will happen within a few years imo.

a few years
 

I agree on the timeline.Theoretical mathematicians worldwide are networking and building off the state-of-the-art as soon as it is published or lectured.
Just a few years seems to make quantum leaps.Snow-balling!
And wind tunnels are very expensive to operate when the same work can be done in a virtual domain.
It's a really exciting time to be around.:)

No, and we're having very few of them on the road.
20' might work in the US, it won't work here.

Same goes for the teardrop - you'll get most of its benefits even if you cut it short a bit.
But you get more practically useful volume - we just need to rearrange things compared to our current cars.

Smaller more efficient engines need less cooling, take less space, and are lighter so they could go back to where they caused some issues in early teardrops : in the back.
It would help unload today's overburdened front axles .
(driven wheels + engine weight + most of the driver / front passenger weight in typically lightly loaded cars).

Or as Mercedes did in the previous B class and Toyota in the iQ : tilt the engine and put it up front, low down. PLenty of space in a bulbous teardrop nose.

Electric drive solves the whole issue instantly.

The Bionic shows that you can have practically useful volume and good aero together.
The boxy new B class puts it into practice : 0.24 is a good value for this kind of car.

Looks like he copied the profile of a dolphin.

As near as I can tell, this early model of the Boxfish / Bionic has a Cd of 0.095:

http://img.photobucket.com/albums/v7...ar-Body-lg.jpg

Here's a series of screen captures from a video of the same model, that are the only other images I know of:

http://img.photobucket.com/albums/v7...4at83911PM.png

And the Bochum University SolarWorld GT car has a Cd of 0.137.

These papers aren't even mentioning some pretty important aero considerations, namely:

-lift produced
-cross wind stability
-wind noise
-centre of pressure changes due to changes in pitch

Low drag is great, but they would be sacrificing real world fuel economy if the powertrain and suspension have to be compromised to achieve it. The driver would be fighting the car all the time and probably waste fuel in the process.

I think that is why cars like the insight and prius are still pretty 'aerodynamically conservative', so to speak.

airfoil
 

There is a (Richard) von Mises airfoil section with reflexed-camber tail, kinda similar to Morelli's form.
Morelli has borrowed from NACA (now NASA) for his computational fluid dynamics and he has probably been acquainted with this section.'Could have been an inspiration.

considerations
 

*The CNR 'banana' car produces zero lift
*The CNR 'banana' car is one of the most stable forms ever tested,requiring no stabilizing fins.
*The CNR 'banana' car,by default,would be very quiet,as it has no flow separation over its entire length
* The CNR 'banana' car was critically designed with CP/CG considerations as a premise for its creation,and remains an extremely stable design under all wind conditions for pitch/roll/yaw.

Yaw stability is handled pretty well on modern cars. Any better is a bonus, and imo not a driving factor for design. I CFD Phil's aero template, expecting high lift, and it was CL 0.069 or so. Even the 2.5:1 ellipse is very low. Even though they appear to be wings, optimal shapes are better in every way than non optimal shapes (maybe I'm stating the obvious).

Okay, I didn't read enough into that article.

I do counter that all of those benefits fall apart when wheels, mirrors and drivetrain components are attached - it might be even worse than a conventional 'non-optimal' design.

An SAE paper is available for sale online for $16. There's lots more said in the paper that I won't post.

Morelli's newer paper 2000-01-0491: a new aerodynamic approach to advanced automobile basic shapes. There's so much information, that I have to break it up into several posts.

"tests in scaled down models gave, in the best cases: Cx ~ 0.15.

Taking into account that the frontal area of a wheel Sw, is approx. one twentieth that of the body, and assuming Cxw ~ 0.5 the drag coefficient of an isolated wheel, the interference coefficient, CxI, results:

CxI = Cx - CxB - Cxw (Sw/S)*(4/3)
= 0.15 - 0.07 0.5*(1/20)*(4/3) = 0.047

The factor 4/3 stays for the number of wheels (4) multiplied by the area ratio of the wheel not covered by the body (1/3)."

Morelli doesn't define CxB, so I'm unsure of its relevance. My main interest is that Cxw can estimate drag due to wheels. Instead of the 1/20 assumption, it should generally be Afw/Af (the ratio between wheel frontal area and total frontal area). the 1/3 term should be Afw/Af. Since the tire area is width times ground clearance; hG*tire width/Afw.

i.e. 0.5*Afw/Af*hG*tire width/Afw

this simplifies to 0.5*hG*tire width/Af.

To minimize wheel drag, you need to have minimum ground clearance, minimum tire width. Although a larger frontal area minimizes the wheel drag contribution, it hurts overall drag. Wheel fairings hide the tires, without increasing overall frontal area. Lowering ground clearance also affects drag in mysterious ways.

Morelli also cites a paper which analyzed centrifugal fans on the rear wheels. They saw a drag reduction of 18-20% - substantially higher than simple wheel fairings.

fall apart
 

I don't have enough data to agree with your assessment or not but I certainly understand your train of thought.
In 1976,when the 1/2-scale CNR body was tested,after slicing successive pieces off the back,they were able to see Cd 0.161,in ground proximity,but without wheels.
In 1978,when they got financing for the full
scale project,when wheels were added to the body,the Cd jumped to 0.35.
Much work was done with the cooling system and wheel integration to get back down to Cd 0.205 or so,and they figured that when all features were added,that they'd end up with around Cd 0.24.
Here we are in 2012 and we're finally at a point where we could purchase a car with Cd 0.24.So Morelli deserves some credit.
When I GOOGLE'd for 'Aptera drag coefficient/frontal area' a website reported it at Cd 0.11.I don't recall the Af.
Love the car or hate the car,Cd 0.11 is around 1/3rd of typical Cds,or 66% lower.On a frontal area -based comparison,at 55 mph,we'd be looking at a 33% HWY MPG improvement.
With the lower frontal area we'd be looking at even larger savings.
It's certainly body-in -white ecomodding!:)

There are two SAE papers and two shapes being discussed. The earlier 1976 model was featured in Popular Science that year. The car was to be somewhat adaptable to a Fiat 131 and compared to the Chevy Citation. Image such a car with a 3 cyl. turbodiesel. The newer shape (Aptera) has potential as a fairing for a long wheelbase recumbent bicycle.

I don't know where else to put this (and I'm too lazy to check). It's from another paper. I know Aerohead has shown a graph of Cd versus backlight angle. The quadratic equation is:

y = 0.7762x^2 - 0.2612x + 0.2502

y is in radians

If we recall high school calculus, to find the minima, you differentiate, and equate to 0. Short answer = 30.276* (from the horizontal). hth

I may quote the original Jaguar SAE papers where I found this info. 2008-01-0737