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-   -   flow separation:Tiger Woods meets Cinderella,or 5-seconds to a perfect roofline (https://ecomodder.com/forum/showthread.php/flow-separation-tiger-woods-meets-cinderella-5-seconds-2104.html)

flow separation:Tiger Woods meets Cinderella,or 5-seconds to a perfect roofline

There has been a lot of discussion surrounding both boundary layer separation and also Kammbacks,rooflines,etc.,in the search for the perfect form.There has also been challenges with respect to wording,phraseology,linguistics,terminology,etc.,w hen making descriptions of forms (i.e.:curved,parabolic,cambered,curvilinear,ellipt ical,etc.).

I've been racking my brain trying to come up with a "mind's picture" which might achieve universal recognition and get everybody on the same page with respect to "imagery".And while Henry Landa warns of the use of "rules-of-thumb",maybe we members need at least some basic reference to build off of.

So here's my attempt.

(1) Tiger Woods : Hopefully,everyone is acquainted with the game of golf.And if so,everyone is aware that at this time,Tiger Woods is a major player in the sport.Also,members here at ecomodder have already been acquainted with the role dimples play with respect to a golfball's turbulent boundary layer and its impact on drag and range.

Perhaps members have also had a peek at least an introductory text on fluid dynamics and the iconic images from the U.S.Naval Research facility at Pasadena,California,depicting the bowling-ball in the water tunnel.In the side-by-side photos,one can see the difference in boundary layer separation for both laminar,and turbulent flow.When artificial roughness is introduced to the bowling-ball (they glue sand to the leading face of the ball),a turbulent boundary layer forms early and separation is moved from 80-degrees behind the stagnation point,to 115-degrees behind the stagnation point.This is exactly what the dimples on the golf ball do.

(2) Cinderella: In the fairy tale of Cinderella,she must be home from the Prince's ball at the castle by Midnight, or else her carriage will turn into a pumpkin.Thesis: If one invisions Cinderella's clock face nemesis as a golf ball,and the ball is travelling in the direction of 3-O'clock,then 3-O'clock is also the stagnation point,12-O'clock is the point of the ball's frontal area,and at 5-seconds after "midnight",the boundary layer has separated,and begins the turbulent wake (profile drag).

If you take the image of the clock face,and imagine the line which bisects 12 and 6 O'clock depicts any vehicle body at the point where it's roof "peaks".Then if you draw a horizontal line from the rim of the clock face where it intersects the 5-second mark,left to the vertical 12/6 line,this defines the "ground plane",and the curved line from 12-O'clock,rotating clockwise,around to the five-seconds after point defines the" ideal roofline" of any vehicle.

If a scale form of any vehicle is placed such that the bottom of it's wheels are on the "ground plane",and the "peak" of it's roof is at 12-O'clock position,then the curved line described by the rim of the clock face describes it's "ideal" roofline. The bedcover on the T-100 is basically defined by this" form".You can call the the line anything you want.Perhaps "curvilinear" is the most correct,however I'm no Noam Chomsky.

Perhaps we can refer to it as the clock- face -shape.Interestingly enough,if you "mirror" this form,and add a prolate-ellipsoid nose to it,you basically arrive at the "ideal" low-drag ,free-stream,aerodynamic form,of minimum profile drag and minimum skin friction.

I hope this excercise helps clear up some confusion.I know its "geeky",just that maybe everyone can connect with the "imagery" and make the connection.Happy modding,Phil.

 tasdrouille 05-01-2008 08:12 PM

Thanks Phil!

I'll use this Cinderella version as a bedtime story for my son :p

 Patrick 05-01-2008 09:20 PM

Phil, thanks for that analogy. But I'm a bit confused. If the ball is moving in the direction of 3 o'clock, wouldn't the separation point be 5 seconds BEFORE midnight? Doesn't the air cling to the ball for a short distance past maximum circumference?

Also, since water is 800 times as dense as air, wouldn't the Reynolds numbers for the bowling ball and golf ball be very different? Or was this compensated for in the bowling ball analysis?

Thanks.

Quote:
 Originally Posted by Patrick (Post 22771) Phil, thanks for that analogy. But I'm a bit confused. If the ball is moving in the direction of 3 o'clock, wouldn't the separation point be 5 seconds BEFORE midnight? Doesn't the air cling to the ball for a short distance past maximum circumference? Also, since water is 800 times as dense as air, wouldn't the Reynolds numbers for the bowling ball and golf ball be very different? Or was this compensated for in the bowling ball analysis? Thanks.
Hi Patrick! From the images,with the laminar boundary layer,flow does separate before midnight(90-degrees).If 3-O'clock denotes 0-degrees(the stagnation-point),flow separates at 80-degrees from there (clockwise).With the sand glued to the front of the bowling ball,or dimples with the golfball,a turbulent boundary layer is established immediately,which forestalls flow separation until the bell has sounded for Cinderella at 5-seconds after 12:00.When the flow breaks off,the wake is smaller and has a higher base pressure and consequently lower profile drag.For the golfball,drag is cut in half,and its range (for a club head velocity of 110-mph) is doubled,from 150-yards,to 300-yards.Drag reduction is so remarkable with the turbulent boundary layer,artificial roughening of the golfball is critical to it's performance even at the low Reynold's Number it experiences for it's size and velocity.I should have posted the velocity of the submerged ball.And you're correct that under water,the bowling ball it would see much higher Reynold's Number.

Superimposition ( Rolex meets Big-Ben )

Just greasing the wheels for tomorrow.
I finally put some graphics together for this thread.The "word-pictures" seem to hit dead-ends,so between wearing out Al's copy machines,a pair of scissors,White-out,and Scotch Tape,I've finally got something to sink our eyes into.
There's been enough talk of golf-ball dimples,turbulent boundary layers and critical Reynolds Numbers that maybe we can make a connection to all this now.
THEORY Re-hash:
* All spheres behave identically above critical Reynolds Number,regardless of size.
* Spheres are so well understood that they may be used as calibration models for any wind tunnel.
*The 'fixed' separation point of a sphere offers a naturally defined turbulence-free architecture by employing a single superimposition,as Salvador Dali might do with one of his canvases.
*Familiar forms we can use to visualize the the superimposition are the dial face of both the analog wristwatch,and wall clock.

CONDITIONS:
The "flow" conditions for our example can be interpreted either as a dial face moving horizontally to the left,with the forward stagnation point located at 9:00 O'clock,or the dial face stationary,as in a wind tunnel,with the air blowing horizontally from the left.In both instances,air velocities are such to produce Reynolds Number above critical.
RESULTS:
* In all situations,attached flow exists from the forward stagnation point,up and over,to a point at 115-degrees of rotation,occurring both at 4-seconds after 12:00 and 6:00( down and under ).
* Photographs of this flow can be seen in the FLOW-IMAGES thread galleries for both air and water.Golf-ball images can be GOOGLED.
SUPERIMPOSITION
* The area of the sphere's aft-body,between 12/6 and 4-seconds after is what is of interest to aero-modders
* Enlargement and enhancement of this section can provide the architecture for a separation -free automotive roof and aftbody structure.
* Suitable enlargement and superimposition of a properly-scaled smaller watch dial "leading-edge" creates a proto-teardrop of which the aft-body may serve as a design template.
OUTCOME
* The teardrop created possesses the hemispherical nose reported in fluid texts to provide adequate and minimum low drag,separation-free penetration for up to transonic velocity.
* The teardrop's aft-body is also separation-free and may be used with high-confidence as a template for modeling automotive forms.
-------------------- WILL CONTINUE -------------------------------

Continued from previous day

Quote:
 Originally Posted by aerohead (Post 153002) Just greasing the wheels for tomorrow. I finally put some graphics together for this thread.The "word-pictures" seem to hit dead-ends,so between wearing out Al's copy machines,a pair of scissors,White-out,and Scotch Tape,I've finally got something to sink our eyes into. There's been enough talk of golf-ball dimples,turbulent boundary layers and critical Reynolds Numbers that maybe we can make a connection to all this now. THEORY Re-hash: * All spheres behave identically above critical Reynolds Number,regardless of size. * Spheres are so well understood that they may be used as calibration models for any wind tunnel. *The 'fixed' separation point of a sphere offers a naturally defined turbulence-free architecture by employing a single superimposition,as Salvador Dali might do with one of his canvases. *Familiar forms we can use to visualize the the superimposition are the dial face of both the analog wristwatch,and wall clock. CONDITIONS: The "flow" conditions for our example can be interpreted either as a dial face moving horizontally to the left,with the forward stagnation point located at 9:00 O'clock,or the dial face stationary,as in a wind tunnel,with the air blowing horizontally from the left.In both instances,air velocities are such to produce Reynolds Number above critical. RESULTS: * In all situations,attached flow exists from the forward stagnation point,up and over,to a point at 115-degrees of rotation,occurring both at 4-seconds after 12:00 and 6:00( down and under ). * Photographs of this flow can be seen in the FLOW-IMAGES thread galleries for both air and water.Golf-ball images can be GOOGLED. SUPERIMPOSITION * The area of the sphere's aft-body,between 12/6 and 4-seconds after is what is of interest to aero-modders * Enlargement and enhancement of this section can provide the architecture for a separation -free automotive roof and aftbody structure. * Suitable enlargement and superimposition of a properly-scaled smaller watch dial "leading-edge" creates a proto-teardrop of which the aft-body may serve as a design template. OUTCOME * The teardrop created possesses the hemispherical nose reported in fluid texts to provide adequate and minimum low drag,separation-free penetration for up to transonic velocity. * The teardrop's aft-body is also separation-free and may be used with high-confidence as a template for modeling automotive forms. -------------------- WILL CONTINUE -------------------------------
SPECIFICATIONS
* The 'teardrop' represents a separation-free body of revolution of 36% thickness.
* Length/ Diameter = 2.78:1
* Frontal Area occurs @ 18% body length behind nose.
* Aft-body boat tail constitutes 82% of body length.
* At "automotive" scale,critical Reynolds Number is achieved at 20-mph.
* At 20-mph,frontal drag coefficient is constant and estimated at 0.04 in free-air.
* Frontal drag coefficient in ground-effect is estimated @ 0.08.
* Boat tail terminal angle is 22-degrees.
ANCILLARY CONSIDERATIONS
* When viewed in 2-D the superimposition mimics Abbott and Von Doenhoff's,"Transformation of a Circle into a Wing Section."
* By default,the form also satisfies the Kutta-Joukowsky condition for ensuring smooth flow at the trailing edge.
* The form approximates the NACA 0021 Section.
* A coincidence of the Rolex/Big-Ben form,is that it embodies W.A.Mair's critical 22-degree boat tail angle.
* The form also embodies the L/D drag minimum,as reported by Hoerner/Hucho ( see Fig.4.119,p.200,Aerodynamics of Road Vehicles,Hucho,1987.
CONCLUSIONS
* In the absence of more sophisticated streamlining tools,the dial-face may serve the would-be aero-modder with a design template that may be used with a high degree of confidence,much the way Volkswagen AG's handbook:"No Guesswork" aids their factory-trained technicians when entering into an overhaul.
* The "GO/NO-GO" simplicity of the clock-face-derived template makes for expeditious fabrication of pre-test prototypes,providing a historically-proven technological basis for project development.

-------- IMAGES WILL BE ADDED ASAP -----------------------------

IMAGES: Template Development

2 Attachment(s)
Here's the linear progression of the development of the clock-face template.
As you see,there's not much to it.That's the whole point.Perhaps you'll see a similarity to other low drag forms.

SEX for ALL (made you look!) check/respond ????????

Please take a look,see if you could work with it.It took me 35-years to come up with it.

 ChazInMT 01-24-2010 03:18 AM

1 Attachment(s)
OK here's a response, with graphics.

I guess it's more of a question,

You state somewhere in here that the wheels of the vehicle should rest on the ground plane.
Yet you say that flow separation occurs at 4 seconds after midnight.

It seems to me that these 2 statements contradict in the sense that air will either remain attached to a given shape until it reaches 4 seconds past midnight (115° beyond stagnation) on a curve (Red), or, you need to overlay a huge wing section onto a given vehicle (Green), and if you fall below this line at any point, you have flow separation, even if it occurs at some point less than 115° (which in this case is on the ground 20 feet behind the truck).

Which one is it? Red or Green? Or am I missing something? (Again, as usual)

http://ecomodder.com/forum/attachmen...1&d=1264316383

 mjboks 01-25-2010 09:32 AM

1 Attachment(s)
I'll take the dark red:

http://ecomodder.com/forum/attachmen...1&d=1264426206

I'm not sure if Aerohead is back yet so give him a bit of time to respond.

 ChazInMT 01-25-2010 01:26 PM

The question I have with your dark red is that it is scaled to the size of the vehicle. I think that as long as we're talking about largish objects like cars, trucks, boats & motorcycles, the 115° flow separation rule applies. So as long as we keep our top radius line from going past that 115° point, it really doesn't matter the shape. The reason we use this particular template is that it has the best "surface area/ wake generation" ratio. The segment we use is very similar to section 5.

http://ecomodder.com/forum/member-ch...sssections.jpg

This brings up another point that I think people don't often consider. We spend a lot of time trying to make the tops of our vehicles as aero as possible, and often neglect the sides. The air moving around the sides of our trucks and cars has a large impact as well I say. On my Pickup, the sides are about 22" tall on the passenger cabin, just in front of the bed. The roof width at the top in this area is about 52" so with 2 sides at 22", that's 44" of air surface. So we worry about 55% of the equation and neglect the other 45%. This is why I have designed a taper in the sides of my aerocap when viewed from the top. Doing this results in a fastback design.

More food for thought....It is often said that the best possible Cd we can achieve is .18 based on the .09 holy grail of aero shape in ground effect...The sides of the vehicle are not in ground effect. :rolleyes: Hmmmmmmmmmm.

http://ecomodder.com/forum/member-ch...p-2000-gmc.jpg

http://ecomodder.com/forum/member-ch...-shot-side.jpg

 mjboks 01-25-2010 02:35 PM

Aerohead would be best to respond on that but I think what you've talking about is similar to what the GM EV1 had at the rear. The back of that exceeded the template angle but still had a .19 Cd. That vehicle also curves in on the sides similar to your cap.

 KamperBob 01-26-2010 06:44 PM

Quote:
 Originally Posted by ChazInMT (Post 156578) This brings up another point that I think people don't often consider. We spend a lot of time trying to make the tops of our vehicles as aero as possible, and often neglect the sides. The air moving around the sides of our trucks and cars has a large impact as well I say. On my Pickup, the sides are about 22" tall on the passenger cabin, just in front of the bed. The roof width at the top in this area is about 52" so with 2 sides at 22", that's 44" of air surface. So we worry about 55% of the equation and neglect the other 45%. This is why I have designed a taper in the sides of my aerocap when viewed from the top. Doing this results in a fastback design.
I agree. Look at most trucks' head-on silhouette. Height is comparable to width. But there are two sides to go around and only one top to go over. So my bet is more air pushes around the two sides combined than goes over. Sure some goes under too but that has to be the least given the road constraint. I think side profile analysis (top and bottom flow) is less than half the total. Top view analysis (flow on both sides) cannot be neglected on a truck if the real goal is optimizing in 3D. Cars? Maybe...

My 2c
KB

where

Quote:
 Originally Posted by ChazInMT (Post 156279) OK here's a response, with graphics. I guess it's more of a question, You state somewhere in here that the wheels of the vehicle should rest on the ground plane. Yet you say that flow separation occurs at 4 seconds after midnight. It seems to me that these 2 statements contradict in the sense that air will either remain attached to a given shape until it reaches 4 seconds past midnight (115° beyond stagnation) on a curve (Red), or, you need to overlay a huge wing section onto a given vehicle (Green), and if you fall below this line at any point, you have flow separation, even if it occurs at some point less than 115° (which in this case is on the ground 20 feet behind the truck). Which one is it? Red or Green? Or am I missing something? (Again, as usual) http://ecomodder.com/forum/attachmen...1&d=1264316383
(1) Yes,the longitudinal centerline constitutes the ground plane and the vehicle would be scaled to fit with it's wheels on the "ground",and the highest point of the roof aligned with the 12:00 O'clock position.The rest of the roofline is defined by the curve.
(2) The very back of the teardrop is the separation point,so all points ahead of that are in attached flow.
(3) Since all vehicles must have ground clearance,it would be impossible(and unnecessary ) to build a body the full length of the drop,as it would end where intersected by the belly line.
Al is closing the store,I've got to close now,will catch up asap.

 Christ 01-27-2010 08:23 PM

Quote:
 Originally Posted by KamperBob (Post 156958) I agree. Look at most trucks' head-on silhouette. Height is comparable to width. But there are two sides to go around and only one top to go over. So my bet is more air pushes around the two sides combined than goes over. Sure some goes under too but that has to be the least given the road constraint. I think side profile analysis (top and bottom flow) is less than half the total. Top view analysis (flow on both sides) cannot be neglected on a truck if the real goal is optimizing in 3D. Cars? Maybe... My 2c KB
Even in cars, side flow interferes greatly with top flow. The effect can be noted in a wind tunnel with multiple smoke streams, where one will suddenly diverge from it's "apparent" path. Without seeing all the other flow lines, one might not be able to explain this, but having seen the "rest of the equation", so to speak, one can then understand that flow does not necessarily proceed in a straight curve or an "apparent" arc over or around an object in a fluid.

I think that many of us fall victim to looking at profile flow as opposed to plan view because some of the most aerodynamic vehicles appear to pay specific attention to profile. I think we neglect to notice that their profiles are also much, much smaller than even our smallest cars.

Since lift can occur in any vector, (you change it's name to understand directionality, but the force remains the same) side flow is just as important, if not moreso, since it represents 2/3 of the exposed aerodynamics equation (roughly).

 doviatt 01-28-2010 12:46 PM

Subscribed.

 winkosmosis 01-28-2010 02:04 PM

Cinderella? Jeez, he even had an affair with a blonde fairy tale character?

 mjboks 01-28-2010 02:14 PM

1 Attachment(s)

 Christ 01-28-2010 02:49 PM

Phil -

I gotta be honest here; I'm not entirely sure I understand exactly what is going on in your mind with this one.

I'm desperately trying to follow, but from what I can tell, your pattern (it's yours, right?) suggests that for attached flow, we'd need something along the lines of a 30 foot long vehicle with a bull nose, which doesn't seem to follow the logic of a 3:1 relationship between length and frontal area.

Could I trouble you to elaborate a bit more?

EDIT: I think I understand a little bit better, after having re-read the text and taking a more detailed look at the images. I do, however, still have a question - since the profile of the divine shape is a curve, at what point do we measure the angle of descent?

I notice in your image that it states a 22* angle at approximately 1/4 of the distance from the tail tip to the "12 o'clock", or the area at which cross sectional diameter is the largest. Is that the proper measurement there, or do we average the slope of the full form against the flat center line?

Also - does this apply as is to a land-vehicle, when given the ground effect?

 ChazInMT 01-28-2010 03:58 PM

Uhhhh.

3 Attachment(s)
MJ, I am using exactly what Aerohed described. I have analyzed the shape you posted here and have the results below. I hope it makes sense.

http://ecomodder.com/forum/attachmen...1&d=1264706143
In this image I have placed your teardrop ideal and the ideal that Aerohed presented earlier. Your shape is the bright green one in this image. My shape is red. I have been extremely careful not to mess with any of the proportions of these shapes at anytime. Also, I have made a circle in my drawing program and have marked a point which is 25° past center and then I trace this shape to get my template, I did not simply trace Aeroheds foil shape.

http://ecomodder.com/forum/attachmen...1&d=1264706143
In this image I have overlaid my shape (bright green) with the foil cross sections which I got from somewhere. You can see that my shape closely approximates the shape # 5 on this chart, your shape (red) is pretty close to #7.

I have noticed that the nose shapes on Aeroheds foil, your template, your ideal foil, and these foils on the chart are all quite different. This I suppose could be the subject of a new discussion.

 ChazInMT 01-28-2010 04:20 PM

1 Attachment(s)
http://ecomodder.com/forum/attachmen...1&d=1264709957

Again, Red or Green?

 mjboks 01-28-2010 04:32 PM

1 Attachment(s)
The shape I'm using is what most of the other streamline templates on this forum have used. It originates from aerohead's photo album called "perfect streamlined shape". I haven't used the simpler "clock face" shape which is very close.
Fuel Economy, Hypermiling, EcoModding News and Forum - EcoModder.com - aerohead's Album: Book illustrations - Picture

I'm sure the exact shape, give or take a degree is just nit picking. These shapes are basic guidelines for those that haven't studied aerodynamics. My one semester of Fluid Mechanic only gets me a little dangerous.

I cropped your image and scaled it keeping perfect proportions to the template I'm using. I think your scale might be just a bit off.
http://ecomodder.com/forum/attachmen...1&d=1264710095

Cont'd from yesterday

Quote:
 Originally Posted by aerohead (Post 157232) (1) Yes,the longitudinal centerline constitutes the ground plane and the vehicle would be scaled to fit with it's wheels on the "ground",and the highest point of the roof aligned with the 12:00 O'clock position.The rest of the roofline is defined by the curve. (2) The very back of the teardrop is the separation point,so all points ahead of that are in attached flow. (3) Since all vehicles must have ground clearance,it would be impossible(and unnecessary ) to build a body the full length of the drop,as it would end where intersected by the belly line. Al is closing the store,I've got to close now,will catch up asap.
I'm trying to pick up where I left off yesterday,but all the original graphics and questions didn't get included in the new"quote".
(3)(cont'd) This 'clock-face' template is more liberal than the "Aerodynamic Streamlining Template",at about 2.78:1 L/D ratio as opposed to 2.5:1.And with the hemispherical nose instead of the prolate ellipsoid,it has more aftbody.It's more akin to the one Darin first posted with "Permanent Metro Kammback." They all will provide attached flow.The 2.5:1 has the least drag,with lowest friction drag,as it has the least "wetted-area"(i.e. skin friction).
The spirit of the clock-face template,is that,in light of it's origins,it could be used with an extremely high degree of confidence to construct a roof-line of any length(or boat tail or trailer )which maintains attached flow,working with virtually no other reference.
This line of reasoning was the foundation for Kamm's,von Fachsenfeld's,Jaray's,Klemperer's,Lay's,Heald's,Re id's,and others development of low-drag cars,including Hucho,for the VW 2000 concept.
Today,university teams are using this form to win solar car and HPV competitions,whether on land or underwater.

Green

Quote:
 Originally Posted by ChazInMT (Post 156279) OK here's a response, with graphics. I guess it's more of a question, You state somewhere in here that the wheels of the vehicle should rest on the ground plane. Yet you say that flow separation occurs at 4 seconds after midnight. It seems to me that these 2 statements contradict in the sense that air will either remain attached to a given shape until it reaches 4 seconds past midnight (115° beyond stagnation) on a curve (Red), or, you need to overlay a huge wing section onto a given vehicle (Green), and if you fall below this line at any point, you have flow separation, even if it occurs at some point less than 115° (which in this case is on the ground 20 feet behind the truck). Which one is it? Red or Green? Or am I missing something? (Again, as usual) http://ecomodder.com/forum/attachmen...1&d=1264316383
For this template,it would be the green.It's "clean" but LONNNNNNNNNNNGGG!
For this reason I prefer the 2.5:1.

template,sides,Cd

Quote:
 Originally Posted by ChazInMT (Post 156578) The question I have with your dark red is that it is scaled to the size of the vehicle. I think that as long as we're talking about largish objects like cars, trucks, boats & motorcycles, the 115° flow separation rule applies. So as long as we keep our top radius line from going past that 115° point, it really doesn't matter the shape. The reason we use this particular template is that it has the best "surface area/ wake generation" ratio. The segment we use is very similar to section 5. http://ecomodder.com/forum/member-ch...sssections.jpg This brings up another point that I think people don't often consider. We spend a lot of time trying to make the tops of our vehicles as aero as possible, and often neglect the sides. The air moving around the sides of our trucks and cars has a large impact as well I say. On my Pickup, the sides are about 22" tall on the passenger cabin, just in front of the bed. The roof width at the top in this area is about 52" so with 2 sides at 22", that's 44" of air surface. So we worry about 55% of the equation and neglect the other 45%. This is why I have designed a taper in the sides of my aerocap when viewed from the top. Doing this results in a fastback design. More food for thought....It is often said that the best possible Cd we can achieve is .18 based on the .09 holy grail of aero shape in ground effect...The sides of the vehicle are not in ground effect. :rolleyes: Hmmmmmmmmmm. http://ecomodder.com/forum/member-ch...p-2000-gmc.jpg http://ecomodder.com/forum/member-ch...-shot-side.jpg
From the strut chart you see that the drag minimum occurs where form drag minimum intersects the skin friction drag minimum at t/c 0.255,somewhere between shape #4 and #5.These are 2-dimensional flow devices and in 3-dimensions,the minimum appears around L/D 2.5:1
With respect to the sides,BINGO!!!!!!! This is exactly what Kamm was doing with the roofs of his K-Cars,and is the reason your cap will have lower drag.
As far as the Cd minimum,Subaru,and GM(AeroVironment) have demonstrated sub-0.10 forms.

my mind

Quote:
 Originally Posted by Christ (Post 157429) Phil - I gotta be honest here; I'm not entirely sure I understand exactly what is going on in your mind with this one. I'm desperately trying to follow, but from what I can tell, your pattern (it's yours, right?) suggests that for attached flow, we'd need something along the lines of a 30 foot long vehicle with a bull nose, which doesn't seem to follow the logic of a 3:1 relationship between length and frontal area. Could I trouble you to elaborate a bit more? EDIT: I think I understand a little bit better, after having re-read the text and taking a more detailed look at the images. I do, however, still have a question - since the profile of the divine shape is a curve, at what point do we measure the angle of descent? I notice in your image that it states a 22* angle at approximately 1/4 of the distance from the tail tip to the "12 o'clock", or the area at which cross sectional diameter is the largest. Is that the proper measurement there, or do we average the slope of the full form against the flat center line? Also - does this apply as is to a land-vehicle, when given the ground effect?
Christ,This thing is just a thought experiment.The "dimple-hysteria" got everybody obsessing over golf-balls,spheres,laminar and turbulent boundary layers and drag.
The sphere seemed the perfect tool to introduce what would morph into wing theory,fuselage theory,and finally automotive body theory.
The 'clock-face' is a SURE THING.But that's not to say that I's use it.
For attached flow,you need at least the aft-body portion of the 2.5:1 teardrop.It can be longer but the drag will be higher due to increased skin friction.
Will the skin-friction increase make a big difference? No! Skin friction is only about 7% of the overall aerodynamic drag of an automobile.So even if aggravate it with a lot of wetted-area,the overall net increase is negligible.I'm sure Bicycle Bob wanted to throw knives at me when I first introduced the template with 2.5:1 L/D ratio due to it's "shortness".Stretching a body out l-o-n-g-e-r wouldn't really beat you up at the gas pump.
I just wanted to build a consensus on theory which states that there is a point where profile drag and skin friction,together,present the lowest drag,which to the best of my abilities occurs for a body of revolution of 2.5:1 L/D.
As to the 30-foot-long thing,for my T-100,this IS about the length I'll need to hit Cd 0.12 or lower,due to it's height and width,and is why I chose to go the trailer route.A 7-foot boat tail seemed out of the question.By adding some length,I get a trailer I can camp with,and it looks like the trailer will pay me to pull it.
If you have Hucho's book,or have access to it,when you look at Jaray's ground-reflection for a body of revolution in ground-effect,which was the basis of his 1922 Cd 0.13 design,it looks eerily similar to the clock-face segment in reflection which creates the template.Also Kamm's development model for his K-Cars.

teardrops

Quote:
 Originally Posted by ChazInMT (Post 157454) MJ, I am using exactly what Aerohed described. I have analyzed the shape you posted here and have the results below. I hope it makes sense. http://ecomodder.com/forum/attachmen...1&d=1264706143 In this image I have placed your teardrop ideal and the ideal that Aerohed presented earlier. Your shape is the bright green one in this image. My shape is red. I have been extremely careful not to mess with any of the proportions of these shapes at anytime. Also, I have made a circle in my drawing program and have marked a point which is 25° past center and then I trace this shape to get my template, I did not simply trace Aeroheds foil shape. http://ecomodder.com/forum/attachmen...1&d=1264706143 In this image I have overlaid my shape (bright green) with the foil cross sections which I got from somewhere. You can see that my shape closely approximates the shape # 5 on this chart, your shape (red) is pretty close to #7. I have noticed that the nose shapes on Aeroheds foil, your template, your ideal foil, and these foils on the chart are all quite different. This I suppose could be the subject of a new discussion.
The lower teardrop image within streamlines is from Baron R. von Fachsenfeld.This drop has a L/D ratio of about 2.72:1 which is a little longer than what is necessary.
Your green line drop would have the lower drag.

green

Quote:
 Originally Posted by ChazInMT (Post 157458) http://ecomodder.com/forum/attachmen...1&d=1264709957 Again, Red or Green?
With this template,the green outline would be proper.This does not suggest it is the lowest drag,only that it will be free of separation.Personally,I would not choose it.

 ChazInMT 01-28-2010 09:23 PM

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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.

http://ecomodder.com/forum/attachmen...1&d=1264742516

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.

 Christ 01-29-2010 01:00 AM

Phil -

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?

yield

Quote:
 Originally Posted by ChazInMT (Post 157517) 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. http://ecomodder.com/forum/attachmen...1&d=1264742516 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.

higher slope

Quote:
 Originally Posted by Christ (Post 157544) 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.

 Christ 01-29-2010 09:37 PM

That's exactly what I was looking for, Phil.

Many thanks!

 ChazInMT 01-29-2010 10:09 PM

2 Attachment(s)
http://ecomodder.com/forum/attachmen...1&d=1264709957

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.

http://ecomodder.com/forum/attachmen...1&d=1264815331

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.

http://ecomodder.com/forum/attachmen...1&d=1264815075

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.

template

Quote:
 Originally Posted by ChazInMT (Post 157757) http://ecomodder.com/forum/attachmen...1&d=1264709957 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. http://ecomodder.com/forum/attachmen...1&d=1264815331 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. http://ecomodder.com/forum/attachmen...1&d=1264815075 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.

 ChazInMT 01-30-2010 07:59 PM

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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.

http://ecomodder.com/forum/attachmen...1&d=1264895382

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.

wheels

Quote:
 Originally Posted by ChazInMT (Post 157914) 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. http://ecomodder.com/forum/attachmen...1&d=1264895382 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.

 ChazInMT 02-01-2010 07:19 PM

1 Attachment(s)
http://ecomodder.com/forum/attachmen...1&d=1265065995

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.

 tasdrouille 02-01-2010 07:33 PM

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.

Template

Quote:
 Originally Posted by ChazInMT (Post 158323) http://ecomodder.com/forum/attachmen...1&d=1265065995 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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