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Old 01-29-2010, 06:05 PM   #31 (permalink)
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Originally Posted by ChazInMT View Post
Aerohed, the red and green templates are both based exactly on the clock face template you described. I made a circle, found its exact center, then projected a line from the center at 25. I then traced that shape. This yields the templates I made.

I just analyzed these further and found some stuff out.




If I make a teardrop out of your "4 Seconds" diagram, I get a 2.75:1 shape using a semi circle as the front. The circular section on top travels through 25. (Red)

If I make a teardrop that is 2.5:1 using a semi circle front, it yields a top circular section that travels 28 or 4.5 seconds after midnight. (Blue)

More questions & graphics later, I would like to nail this down pat as I'm sure many who are looking in on this would.
Chaz,excellent question and I'll beg your indulgence as I attempt my convoluted logic.
From Fluid Mechanics,the professors will tell you that,below 250-mph,forget about the nose,a hemispherical front is all you need for this incompressible flow.
They'll also tell you that the aft-body is where the action is.If your fore-body prevents separation ( which the hemisphere will provide),then focus your attention on a long tapering tail.
The 2.5:1 L/D ratio body of revolution,as cited by Hoerner( and depicted in the "Aerodynamic Streamlining Template")is the "shortest" body of revolution with a Cd 0.04 that I've run across.
When used with Paul Jaray's "ground-reflection" technique,if the upper portion is used,it creates,from what I can gather,the "minimum" curvature for an aftbody which will maintain attached flow in ground-effect for it's entire length.
So the answer to your question,is that while the clockface will "work",the aft-body of the 2.5:1 teardrop represents,from an engineering point of view,the least amount of structure that will deliver a separation-free flow.
You can chop the tail off wherever you like,just as Koenig/Kamm/Korff/Morelli advocated,and you should be guaranteed clean flow right up to the "chop."
As I mentioned in the preamble to the clock-face thread,this would be something one could use in the face of having no other tool to work with.
My opinion,is that for the time and money,the aft-body architecture of the 2.5:1 teardrop is the most appropriate model we might use to construct with.
And this is the teardrop with the traditional semi-ogival, prolate-ellipsoid nose,something to compare to with the simplified "hemi" nose clockface.

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Old 01-29-2010, 06:12 PM   #32 (permalink)
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Originally Posted by Christ View Post
Phil -

Excellent answer, and very helpful in understanding the purpose of your idea.

Looking at Chaz's images, would the smaller half-drop shapes be ideal for kamm extensions (in profile view only), or could the Kamm extension yield a higher angular slope?
Christ,it's tough for me to do the photoshop magic like Chaz has demonstrated.
Let me answer your question by saying that if the "green" curvature of the shorter drop shape shares the same aft-body architecture of the 2.5:1 teardrop of the "Template",then this would be the maximum curvature the air could follow without separation.
Any "steeper" and it would violate Mair's magical 22-degree departure angle.
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Old 01-29-2010, 08:37 PM   #33 (permalink)
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That's exactly what I was looking for, Phil.

Many thanks!
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Old 01-29-2010, 09:09 PM   #34 (permalink)
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More questions, (really pretty much an assertion) and graphics as promised earlier.

Aerohed, I post this image yet again to question your application of the template. It sure seems like the flow is following down the back of this Audi. I also know that this particular Audi has a pretty incredible Cd at 2.5. Based on this, I'd find it hard to believe that the Green Template has any relevance whatsoever. It also seems as though the Red Template is relevant due to the apparent attached flow and the incredible engineering involved on this particular car. So it seems to me that scaling the Red Template so that the Arching section matches the aft shape we're analyzing, makes it relevant. If the shape ends up falling off the back end, it's done. Separation occurs at that point. If the analyzed shape stays within the template, it's aero baby.

Clearly, no car design which stands taller that 3 feet could make effective use of making the bottom chord of this template as the ground plane under the bottom of the tires. Of course if you do this, the flow separation would never occur, but the roof line would be very long. I challenge this use of the template.

Below are 2 other template overlay examples to further prove what seems to me the logical application of this template.



Above we see attached flow on the back of this BMW, the upper arch of the template follows the roofline at the back, the template runs out into the car, so the flow remains attached all the way back.



On this Benz, the Upper arch of the template matches the roofline again, it needs to be scaled quite small to fit, and as you can see, the rear window goes beyond our template and low & behold, flow separation occurs at this point.

Again, If I'm misunderstanding this, and somehow my logic is not really being supported by real life examples, please let me know. Otherwise, we must look to not apply this template by placing the bottom chord under the tires and scaling the size of it up to match the high point of the roof.

I can, and will, load as many images as it takes showing how my application of the template makes sense. I challenge you to find a real world example of how your use of the template has been violated, while my use of it has not, and flow separation is evident.
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Old 01-30-2010, 03:15 PM   #35 (permalink)
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template

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Originally Posted by ChazInMT View Post


More questions, (really pretty much an assertion) and graphics as promised earlier.

Aerohed, I post this image yet again to question your application of the template. It sure seems like the flow is following down the back of this Audi. I also know that this particular Audi has a pretty incredible Cd at 2.5. Based on this, I'd find it hard to believe that the Green Template has any relevance whatsoever. It also seems as though the Red Template is relevant due to the apparent attached flow and the incredible engineering involved on this particular car. So it seems to me that scaling the Red Template so that the Arching section matches the aft shape we're analyzing, makes it relevant. If the shape ends up falling off the back end, it's done. Separation occurs at that point. If the analyzed shape stays within the template, it's aero baby.

Clearly, no car design which stands taller that 3 feet could make effective use of making the bottom chord of this template as the ground plane under the bottom of the tires. Of course if you do this, the flow separation would never occur, but the roof line would be very long. I challenge this use of the template.

Below are 2 other template overlay examples to further prove what seems to me the logical application of this template.



Above we see attached flow on the back of this BMW, the upper arch of the template follows the roofline at the back, the template runs out into the car, so the flow remains attached all the way back.



On this Benz, the Upper arch of the template matches the roofline again, it needs to be scaled quite small to fit, and as you can see, the rear window goes beyond our template and low & behold, flow separation occurs at this point.

Again, If I'm misunderstanding this, and somehow my logic is not really being supported by real life examples, please let me know. Otherwise, we must look to not apply this template by placing the bottom chord under the tires and scaling the size of it up to match the high point of the roof.

I can, and will, load as many images as it takes showing how my application of the template makes sense. I challenge you to find a real world example of how your use of the template has been violated, while my use of it has not, and flow separation is evident.
The clock-face template is a thought exercise which might find application if a person had no other resources to work with.Using the aft portion would provide a separation-free aftbody for a vehicle,albeit,very long.
I'd like you to do a search for "Aerodynamic Streamlining Template:Part-C ,and look at the 2nd image.
This is the template that I advocate members use as a go-no-go minimum for attached flow.I believe the smoke flow traces over the two cars you have shown will be in better agreement with this template.
I repeat,I do not advocate that any member or lurker actually use the clock-face template.I presented it as a way to illustrate the evolution of streamlining.And as your intuitive instincts are rebelling against it you are correct in assessing that we can do better.Which is the whole point of the 2.5:1 teardrop template.
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Old 01-30-2010, 06:59 PM   #36 (permalink)
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OK, Got it, clock template thing is a strict section from a circle, your Fig 2 template is not, it is relatively flat towards the back. Still, when you apply even this 2.5:1 teardrop template, it flies in the face of reason to use it by putting it "under the wheels". I have overlaid it (Gold shape on top of the BMW) onto the Beemer as an example.



What do you have to say about scaling these templates down to match the curves of the roof?

It seems to me that the limiting factor is getting the air to try and pull past 22, the end of your tear drop template is very close to that.

It still seems you are creating a far to conservative "go-no go" by scaling the template to go under tires/top of roof.

Also, I'm not rebelling, I just want to educate myself as much as possible. I am also inherently a skeptic, meaning if it doesn't quite make sense to me, I really want to get to the bottom of things and understand it in principle. I really don't take "That's just the way we do it." as an answer. I'm sure you understand that.

I am so grateful to have found this forum where these aerodynamic ideas are bantered about. I have learned a ton in the past month. I really want to understand why you don't think the template should be scaled to match the roof line.
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Old 02-01-2010, 04:00 PM   #37 (permalink)
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Originally Posted by ChazInMT View Post
OK, Got it, clock template thing is a strict section from a circle, your Fig 2 template is not, it is relatively flat towards the back. Still, when you apply even this 2.5:1 teardrop template, it flies in the face of reason to use it by putting it "under the wheels". I have overlaid it (Gold shape on top of the BMW) onto the Beemer as an example.



What do you have to say about scaling these templates down to match the curves of the roof?

It seems to me that the limiting factor is getting the air to try and pull past 22, the end of your tear drop template is very close to that.

It still seems you are creating a far to conservative "go-no go" by scaling the template to go under tires/top of roof.

Also, I'm not rebelling, I just want to educate myself as much as possible. I am also inherently a skeptic, meaning if it doesn't quite make sense to me, I really want to get to the bottom of things and understand it in principle. I really don't take "That's just the way we do it." as an answer. I'm sure you understand that.

I am so grateful to have found this forum where these aerodynamic ideas are bantered about. I have learned a ton in the past month. I really want to understand why you don't think the template should be scaled to match the roof line.
I'm looking at the gold template and it's centerline should be right at the bottom of the tires which should reduce the overall height of the upper curve,bringing it more in line with the BMW.
Scaling and lining the template up with the bottom of the wheels,top of the roof camber is the premise behind Jaray's "Ground-Reflection" technique.It's the only parameter that can be shared with all vehicles.
The concept is,given the height of the car,and selecting the roof peak,from there back,the template defines the top and sides of a vehicle which will exhibit zero separation.
Models are horrifically expensive to build and test.Building a full-scale prototype even more.
By engineering a "conservative" roof and aftbody,we can get that part of the build behind us and move on to new business.
Cd 0.04 is the lowest drag form I know of for a structure which can deliver Cd 0.08 in ground-effect.I couldn't find a body of revolution of Cd 0.04 with attached flow shorter than 2.5:1.Hucho demonstrates it to be the form of lowest drag.And,just as a coincidence,it also possesses the 22-degree exit exo-duct architecture which Mair's research determined to provide the lowest drag/minimum structure.
If we had unlimited resources we could pick a styling design and then optimize it to death as an automaker can,and perhaps eventually arrive at an acceptable drag figure.
But I don't know anyone at this site who's in that position.
To go after really low drag,in turbulent boundary layer,the pumpkin seed appears to be the ever-repeating solution for this challenge.And the pumpkin seed is a derivation of the 1/2 body-of-revolution.Hucho states that the target for low drag is a body fineness ratio of 5.0:1,after which if made any longer,will have only higher drag.This form becomes a full-boat-tail 2.5:1 teardrop in "reflection."
This infers that the 2.5:1 teardrop is the only structure which can satisfy this limitation.This is why I believe it to be without peer as far as a starting point.I've never found any science to disqualify it.
Of course,reality intrudes,and for road vehicles many compromises are thrown into the mix,and practicality rears it's ugly head.
So we're left to make our way,best we can.
I'm headed for sub-Cd 0.10 territory and the 2.5:1 teardrop will be my A-Ticket to get there.And not because I wish it to be,it's because all the folks that dedicated their entire careers to aerodynamic research say it's so.
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Old 02-01-2010, 06:19 PM   #38 (permalink)
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So you're saying we can't scale the template to match a feature on a vehicle to determine if it will maintian attached flow (Lime). You say that if the roofline of a vehicle is steeper than the back curve of the 2.5:1 Pumpkin Seed Template which is scaled to match the bottom of the tires and the peak of the roof (Gold), it will not have attached flow, and create drag.
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Old 02-01-2010, 06:33 PM   #39 (permalink)
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I don't know about the L/D ratio from the top of my head, but Hucho's book clearly reference a maximum angle of 22 degrees, at which point you can cut the tail right there else the flow is going to separate anyway.
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Old 02-03-2010, 04:53 PM   #40 (permalink)
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Template

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So you're saying we can't scale the template to match a feature on a vehicle to determine if it will maintian attached flow (Lime). You say that if the roofline of a vehicle is steeper than the back curve of the 2.5:1 Pumpkin Seed Template which is scaled to match the bottom of the tires and the peak of the roof (Gold), it will not have attached flow, and create drag.
The spirit of the template is to serve as a guide for the design of any add-on device to clean up an aft-body already demonstrating separated flow,like a spoiler for a coupe/sedan,or aeroshell for a pickup.
The template might also give insight to potentially "dirty" designs which might require remedy.
Paul Jaray invented the "ground-reflection" technique for auto design.When the "upper" half of his teardrop was used to design his 1922 "pumpkin seed",it produced a "car" with Cd 0.15.By adding a chin spoiler,the drag fell to Cd 0.13.
W.I.Kamm basically did the same thing during development with Fachsenfeld of the famous K-cars.
The Jaray form and Kamm form passenger cars have identical Cd 0.21 with full boat tails.
From Fachsenfeld's "Aerodynamics of Road Vehicles," 1951,the pumpkin seed development models for Jaray and Kamm,in "reflection" create teardrops of 2.28:1 and 2.4:1 respectively.
During WW-II the DVL at Berlin ( Germany's NASA ) came up with a streamline body of revolution of Cd 0.04 with L/D = 2.5.
Hucho depicts this form in Table 2.1.This is the "shortest" structure I've ever seen which can produce Cd 0.08 in "reflection" within ground-effect.
Hucho also demonstrates with Table 4.119 that an ellipsoid of L/D 2.5 also produces the minimum Cd beyond critical Reynolds Number.
This is why I settled on the 2.5 L/D as the "minimum"
To get even Weirder,if you take Mair's wind tunnel model for boat tails and lose the cylinder portion,leaving only the nose and boat tail,you end up with a teardrop of 2.52:1 L/D,and this form embodies the 22-degree exit architecture demonstrated as the maximum angle which will sustain attached flow in an aft-body.
So the short answer to your question is yes.Theoretically,and confirmed by wind tunnel study,if the aft-body roof-line or sides of a car taper in, any more aggressively than the 2.5:1 teardrop/pumpkin seed form, one could have little confidence in it's ability to support attached flow.
A "back door" reverse-logic confirmation of the notion comes from Hucho when he chastises Mercedes-Benz "short" length,with it's C-111-III which fell below the "ideal" 5.0 L/D,something Volkswagen capitalized on with it's ARVW concept car,which in "ground-reflection" produces the 2.5 L/D form.
Of course,it's simplistic,and with coupes,sedans,SUVs,Vans,etc.,it's asking a lot for the template to always perform.
However,since it's origins are steeped in good science,it may be considered as a go-no-go quick assessment tool.

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