Aerodynamic Streamlining Template: Part-C

[Tesla]

Originally Posted by ChazInMT

Here's an analysis I did for someone messing with a MGB GT top view with template overlays. This was my understanding as to how they are to be applied.



Oh, and if you hold the Alt key and type 0176, you get the "°" 22° thingy to appear.

My understanding was that the vertical centreline forms the 0 point for the horizontal axis, so the templates overlayed from above would be half the size you have shown and the base line for both would be the centreline of the vehicle.
This also raises the point of where the maximum width/height is aligned to, the way it has been described and used for the side views, aligned with the max height of vehicle is fine, but this suggests a wing application and that the vehicle profile continues that way for a much wider distance, where as in real world vehicles the greater effect in most cases is from the sides, so maybe we should be concentrating primarily on the top view, not the side view.

If we think of it in the sense of the mirror effect of the ground principle, then the verticle centreline is ground for the side taper,
Otherwise, the way you have drawn it would suggest another mirror on either side of the vehicle, suggesting a 3x width, which doesn't make sense.

Basically the side flow acts to a degree, as a "flow in free air" model, because this air has nothing to push against, but the top air has the ground to push against to clear room for the vehicle to pass through, this is what I am seeing as the ground effect.

Just for analogies, just like a boat traveling on the water, inverted view, it is much easier to push air to the sides. If the boat was forced to hold it's vertical position on the water, which one would be more streamlined, curved bottom with parallel sides or curved sides with a flat bottom?

[aerohead]

Originally Posted by Tesla

I thought about that initial slope being steeper, but there are a number of reasons I don't think it will be too much of an issue.

1 / As per your comment above, the overall picture in this field seems to be much more important than the sum of it's parts.

2 / No disrespect here, I think nearly everyone here would still be floundering without your imense input, but I still have a bit of a question about the angles attached to the template, they do not seem to conform to a continuous curve, this suggests to me that some errors have been introduced in the process of transcription. So we know the template numbers quoted do get a positive result, but as there is discrepancy sugests that there is some room to play around these numbers, how much?, who knows?

3 / Many so called "streamlined", & proven vehicles seem to fall below the template curve enough to suggest they shouldn't be as good as they are.

I haven't got access to Hucho's book, but if I continue this hobby it may well get on the Buy list.

Copiers are great for a single copy without magnification, once you start magnification & copy of copies, the errors start to multiply out, fine for a visual representation, but not for a scale model, but as you said, if that's all you have to work with then you do what you can.

The whole math noodling thing, thanks, but I do it all through excel, PITA working out all the formula's and error checking, but once it's done, all you need to do is adjust paramaters and dimensions and it does all the calculations. Be great if I had some of those flow programs, but this takes too much of my time anyway, so probably better of without them.

Aerohead
If you wouldn't mind, can you elaborate on how the template angles were derived
and
Your opinion on how to apply template to sides of vehicle, as I have found it produces a very aggressive vertical profile which would suggest seperation.

If you'll go back to permalink#1 on page 1 of this thread,underneath the 'Template' are a number of images.
The 3rd image from the left is Hucho's drag table,and if you'll look towards the bottom you'll find his image of a streamline body of revolution.of L/D= 2.5 and Cd 0.04.
*From Jaray's research,this body,in ground reflection,as a 'half-body' would have Cd 0.08.
*Adding narrow wheels/tires would bump the drag to Cd 0.12.
*Wheel fairings would allow sub-0.12 drag coefficients,as the wheels are better integrated into the body.
* This represents the drag minimum for ground effect for a door-slammer which you could walk up to,open a door and get into.(the 2012 Bochum University solar racer would be a fast-roofline version,@ Cd 0.14).
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From boundary layer theory it is crucial that aft-bodies taper very gently to protect the fragile boundary layer which is operating in an adverse pressure environment,and can detach if the pressure increases too rapidly since it is already at zero velocity,and Bernoulli's Theorem would require this flow to decelerate even more as pressure increases.
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Since the 'Template' is based on a streamline body of lowest drag,and cannot produce flow separation,it satisfies Hucho's requirement for attached flow and pressure regain which he says is the entire premise for automotive streamlining.
Since the 'Template' also respects W.A.Mair's maximum boat tail tangent angle of 22-degrees for attached flow with a bluff body it represents the shortest,lightest,strongest,and lowest drag,generating an automobile of L/H= 5,which is L/D= 2.5 in mirror-image,effective bluffness/effective fineness ratio,which Hucho reports as the ideal for low drag.
Any shorter and pressure drag goes up,any longer and surface friction drag goes up.
If you had to fail,you'd want it to be on the side of skin friction,as it plays such a minor role with road vehicles.So 'longer' vehicles would be preferable to 'shorter.'
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There are shapes which will yield lower drag,but you can't walk up to them and open a door,get inside and go.And these shapes don't lend themselves to production automobile streamlining whereas the 'Template' does.
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The 'Template' is rough although with a number of major bulkhead stations established,a 20' length of 1" scedule-40 PVC pipe is all that's needed to produce a near-flawless contour.Sure it's low-tech but it will get you in the winner's circle.

[ChazInMT]

Yes, you could do it this way.



But I'm 99.5% sure it is an incorrect application.

I didn't just guess on the other one. Others told me that was the correct application.

[Tesla]

Originally Posted by ChazInMT

Yes, you could do it this way.



But I'm 99.5% sure it is an incorrect application.

I didn't just guess on the other one. Others told me that was the correct application.

Not suggesting you guessed,

But until I understand more, the format above using vehicle centreline seems to be more appropriate, hope Aerohead can jump in at some point and clarify this.
Most of the reading I have done has been here and hence is second & third hand information, others have read the actual text books and I rely on them for guidance.

Edit:
For those in the know, I can't get the degrees symbol up, tried the 0176 and doesn't seem to work for me.
Just realised Aerohead just posted will read his response now.

[Tesla]

Originally Posted by aerohead

The 'Template' is rough although with a number of major bulkhead stations established,a 20' length of 1" scedule-40 PVC pipe is all that's needed to produce a near-flawless contour.Sure it's low-tech but it will get you in the winner's circle.

Got all the other stuff, and yes template is a bit rough, but using the right materials as above allows nature to smooth out the inconsistancies.

I suppose my primary query at this point is how to apply the template with regard to top and side views, the 5:1 is the ideal, but on what dimensions should one apply it to, the width or the height or both?

[Sven7]

Tesla, I think I get what you're saying. You're assuming both the side and top view teardrops have to end at the same point like a cone, right? I will continue assuming this... if I'm wrong let me know

You can't scale the template in x and not y- you need to keep the same ratio. When you set the template from the side you need the apex of the template (the 0% mark) at the apex of the roof. When you set the template on the top as in the MG above, you do the same, HOWEVER the car's corners should not stick out of the teardrop like they do above. You need to move the drop back far enough that is tangential to the rear quarter panels. (This actually applies to wagon profiles like your Patrol, too- the template should never "cut off" part of the car)

Yes, the apex from the side and the apex from the top will be positioned differently relative to each other- meaning, if the side apex is in the middle of the front door and the top apex is over the rear axle, that's okay. That's how the air needs to flow off the car.

Here is a Patrol with the ideal template. Since it tapers more on each side than on the top and bottom, the sides meet sooner. This is just fine! It will give you the ideal curvature on side as well as top, dissipating pressure evenly. Of course you'll need as much radius as you can get (the fore-body still has pressure differentials windward of the tail) but inevitably the rear will end in a vertical fin- this is natural if you use the template on all sides.

The boat tail will not automatically fix the pressure differentials- it will only bring the "split" air back together again when your vehicle passes. Looking at the macro I believe you will still have vortex-like airflow patterns, though not as strong as before. The radii aft of the apex are where you get rid of those differentials and therefore the vortexes.

*Image replaced with what should be correct*

Ideal Wagon Form by Tyler Linner, on Flickr

Does that help?

EDIT
Now you guys have me second-guessing the correct application of the plan view tapers, but the concept should still be the same.

Since the maximum taper is supposed to be 22*, shouldn't the tail's rear end meet at that angle? Therefore you would want the "wheels" of the template along the centerline of the car as in post #413. Otherwise your teardrop meets without hitting that golden angle, adding more skin drag than is necessary.

Bringing that tail in without tapering to 22* leaves geometry on the table! (But you still have to move the apexes back to be tangential with the body)

Discuss! (I love EcoModder)

[Tesla]

Originally Posted by Sven7

Tesla, I think I get what you're saying. You're assuming both the side and top view teardrops have to end at the same point like a cone, right? I will continue assuming this... if I'm wrong let me know

You can't scale the template in x and not y- you need to keep the same ratio. When you set the template from the side you need the apex of the template (the 0% mark) at the apex of the roof. When you set the template on the top as in the MG above, you do the same, HOWEVER the car's corners should not stick out of the teardrop like they do above. You need to move the drop back far enough that is tangential to the rear quarter panels. (This actually applies to wagon profiles like your Patrol, too- the template should never "cut off" part of the car)

Yes, the apex from the side and the apex from the top will be positioned differently relative to each other- meaning, if the side apex is in the middle of the front door and the top apex is over the rear axle, that's okay. That's how the air needs to flow off the car.

Here is a Patrol with the ideal template. Since it tapers more on each side than on the top and bottom, the sides meet sooner. This is just fine! It will give you the ideal curvature on side as well as top, dissipating pressure evenly. Of course you'll need as much radius as you can get (the fore-body still has pressure differentials windward of the tail) but inevitably the rear will end in a vertical fin- this is natural if you use the template on all sides.

The boat tail will not automatically fix the pressure differentials- it will only bring the "split" air back together again when your vehicle passes. Looking at the macro I believe you will still have vortex-like airflow patterns, though not as strong as before. The radii aft of the apex are where you get rid of those differentials and therefore the vortexes.


Ideal Wagon Form by Tyler Linner, on Flickr

Does that help?

EDIT
Now you guys have me second-guessing the correct application of the plan view tapers, but the concept should still be the same.

Since the maximum taper is supposed to be 22*, shouldn't the tail's rear end meet at that angle? Therefore you would want the "wheels" of the template along the centerline of the car as in post #413. Otherwise your teardrop meets without hitting that golden angle, adding more skin drag than is necessary.

Bringing that tail in without tapering to 22* leaves geometry on the table! (But you still have to move the apexes back to be tangential with the body)

Discuss! (I love EcoModder)

That's it, and thanks for the Patrol images, still haven't worked out how to do the overlay's.

Regarding starting point 0, we tend to agree that there should be some flexability that it matches as close as possible to the max camber point and the natural taper which all vehicles have to some degree, so there are some compromises to be made here, because unless you drive a template, these two points wont be the same on any regular road vehicle.

As for the scaling, that's where my bigger question lies, I've read numerous times that the width dimension is used as the whole mirrored effect, so the template must be applied from the vehicles vertical centreline as the base for the template.

I've also read numerous times that the narrower of the two dimensions, length & 1/2 width is the major player, so this suggests we either apply that to both dimensions, resulting in a significantly reduced tail, or we have to apply different scaling to the sides and the top.

My thinking is that the x coordinate applies from the centre line and the y coordinate applies from ground level.

So like in my case with the Patrol, a point somwhere around the rear axle best conforms to a balance between max camber and start of natural body taper, I then took the measurements at multiple points up the sides and on top creating a 2d profile then tabled these coordinates and applied the same equation to all coordinates, some fade to 0 very quickly others take longer, but ultimately as your image shows a full tail would end up as a vertical fin.

It kind of came to me when I was thinking about the angled surfaces on a vehicle, are these vertical or horizontal or do both apply causing both narrowing and lowering, this seems to be the way to do it, because the air will want to go down as well as come in.

If we think of the ideal 5:1 tear drop body of rotation, it is tapered from all perspectives, not just vertically or horizontally, so therefore both coordinates must get the same treatment.

Still getting my head around this stuff, so well prepared to be wrong.

[Sven7]

You're on the right track, IMO.

Since it seems we need to scale the "height" of the top template between the vehicle centerline and max camber point/apex, this will appear much smaller than the side application. I believe this is correct. (I'll try to edit the image and re-post).

Yes, it will end in a much more prevalent fin shape in the rear, and I think this is also correct. You would want to continue the natural top-to-side (of the truck) radius along the edge of the boattail. If you change it to a larger radius the angles will be altered.

So, imagine the right form here, with radii on the edges and the sides brought together enough to form that fin.


Updated Patrol templates... hopefully these are correct


Ideal Wagon Form by Tyler Linner, on Flickr

[Sven7]

Originally Posted by ChazInMT

Oh, and if you hold the Alt key and type 0176, you get the "°" 22° thingy to appear.

As soon as I press 1, it bumps me out of the thread and into the forum page. Never could make those icons work

Vista, Chrome

[Tesla]

Originally Posted by Sven7

Updated Patrol templates... hopefully these are correct


Ideal Wagon Form by Tyler Linner, on Flickr

That's what I was thinking,
And thanks for the pic, saved both versions.

I am not trying to manipulate the concept to get a shorter tail, just trying to work out what is most right.
Aerohead has mentioned a number of times, longer is safer as skin friction is minimal, so we know the outer limit is the taper predicted by the larger dimension, usually height, if this is applied to the sides as well then we get a longer tail that should maintain attachment, but becomes impractical for real life application, except as a basis for a Kamm back.

The side rule predicts a shorter tail with the vertical fin finish, but this all works fine from top and side, just becomes an issue when you hit the corners.
You can't leave them sharp as this will lead to vortex issues, but if you merge with a good radius, then this leads to a sharper finish over the top, resulting in more than 22* when viewed from the side.

We are after something like the centre image below, I think??.

Originally Posted by Sven7

Yes, it will end in a much more prevalent fin shape in the rear, and I think this is also correct. You would want to continue the natural top-to-side (of the truck) radius along the edge of the boattail. If you change it to a larger radius the angles will be altered.

So, imagine the right form here, with radii on the edges and the sides brought together enough to form that fin.

Looking at that centre image, because it is squareish the diagonal measurement of the max camber is greater than the vertical measure, this means that the path length along that corner from tip to tail is longer than that when measured over the top, so that means the angles over the corner must be greater than those over the top.
So should the template profile be applied to the diagonal dimension which is greater than either top or side?
or
Is it ok to have a greater degree of curvature along the corners, because we are filling it with air from two sources, both above and from the side?,

The more I think about it the more I think this is how it should be for a basic square form profile.

A round profile like the image 1 must maintain the template curvature because it's entire surface has equal competition for the air, but the square profile has an excess, so to speak on the flatter side & top surfaces, which should allow for, and need greater curvature on the corners to give minimal turbulance.

Edit:
Sorry to all, for thinking out loud, am just exploring and testing the principles as I understand them.

I am sure the template needs to be applied in three dimensions, we have length and height or length and width, I'm just trying to merge all three with the limited tools I have at my disposal.