Aerodynamic Streamlining Template: Part-C

[freebeard]

Paging Aerohead -- [found it, see below] I've looked for and can't find an illustration that has been posted here. IIRC it was from a naval architect, about torpedoes. It employed a profile that consisted of the straight line of the forebody, a simple curve transition, and a straight line for a terminating cone. Again IIRC, it transitioned to a straight cone around 22°

here is an irrelevant example:


Depending on your needs a more easily built shape might have a place. Optimum is optimum. The perfect is the enemy of the good.

[Tesla]

Originally Posted by freebeard

Depending on your needs a more easily built shape might have a place. Optimum is optimum. The perfect is the enemy of the good.

Seen this written a few times and it is sinking in.
I suppose my goal is to be able to do close to perfect, then make appropriate compromises for utility.

Still about 8 pages back on the thread, want to get up to date today, taking notes all the way.

I may be Over-Anal-Izing this, but do usually find my way back to solid ground, sometimes in a roundabout way though.

[freebeard]

Try this:
A geodesic dome, because of its mathematical purity, can be accurate to 6—20 decimal places. However much you need. An octahedral geodesic has axes at 90°. The frequency determines how closely it approximates a sphere. A prolate spheriod is cigar shaped.

Air flows around a sphere to 115° from the stagnation point before it separates. That's 25° in template terms. It might as well be a conic shape after that.

I wrestled with this object in two different programs, flipping normals and such. I guess this is all we're getting tonight. It is a 4v octahedral prolate spheroid stretched in the Z-axis to a 3.2 fineness ratio.

With the nose drooped to lower the stagnation point and the rear tip extended it would closely approximate the template. The template is truncated to 50% vertically. Truncating to 5/8ths or 3/4ths would yield more useable interior space for a given width.

Edit: And here's the illustration I couldn't find:

[Tesla]

Originally Posted by freebeard

Try this:
A geodesic dome, because of its mathematical purity, can be accurate to 6—20 decimal places. However much you need. An octahedral geodesic has axes at 90°. The frequency determines how closely it approximates a sphere. A prolate spheriod is cigar shaped.

Air flows around a sphere to 115° from the stagnation point before it separates. That's 25° in template terms. It might as well be a conic shape after that.

I wrestled with this object in two different programs, flipping normals and such. I guess this is all we're getting tonight. It is a 4v octahedral prolate spheroid stretched in the Z-axis to a 3.2 fineness ratio.

With the nose drooped to lower the stagnation point and the rear tip extended it would closely approximate the template. The template is truncated to 50% vertically. Truncating to 5/8ths or 3/4ths would yield more useable interior space for a given width.

Edit: And here's the illustration I couldn't find:

I think there is an issue with the 25* assumption on separation,
There is enough back pressure to push the air down to the 25* mark, but once that point is passed lengthwise air will not stay attached on a cone, more than likely you will need a cylinder and it will not attach to the surface again until a certain distance has passed, this may well be the intersection point with template profile.

If one is only doing a short Kamm/boattail, then a more agressive angle can be used as the air will stay attached for the short distance, but for the full length something more like the template is the only real solution to get the best results.

With that said, I do wonder if we are only doing a 50% boattail, how much can we sharpen it to get the maximum benefit, somewhere between a point and the template 50% mark I imagine, probably biased to the 50% mark more so and observing the "no more than 22*" rule.

I assume the Geodisic dome concept is only for modeling purposes, with all the varying panel angles that would be probably be more complex than doing compound curves.

With the image posted, the top row is that the angles along the tail, they look to be steeper than the image is drawn, along with that the 1.9d ratio indicates they should be even shallower than the templates 1.78d ratio?

[Tesla]

I have been playing with some numbers & charts,
trying to determine a template equation, I thought I'd look at the angles listed and the rate of change as this will express the derivative of the curve, as the angles are obviously approximations for real world application they aren't going to be perfect.
When I charted the rate of change, seems to me the angles could do with some adjustment, primarily at the 30-60% range as this seems to be where the rate of change peaks, but there is a number of peaks where I think there should only be one.

If the rate is changing, then there will be undulations in the surface which are not good for the airflow, I know the angles are just a guide and the final result needs to be finished by hand & eye, but getting a bit closer to the ideal at the start may make it easier to emulate the template profile.

I did another series with proposed adjustments, here is the data & chart, open for critique, is this the right approach?

[freebeard]

I assume the Geodisic dome concept is only for modeling purposes, with all the varying panel angles that would be probably be more complex than doing compound curves.

Actually just the opposite. The 4v octahedral dome has 512 vertexes, and the shape I evolved has a void on the bottom so it's only 448 vertexes. That would fit in a spreadheet, higher frequency means smoother shapes although the count goes up fast. I think at 4v it would be like the dimples on a golf ball, but I can't find any info on frequency vs Reynolds number. Think F-117.

Your most recent post is all about the limitations of 3rd hand Cartesian coordinates. The solution used in naval Architecture is loft lines. Those are still only accurate to the limitations of the drafting methods. One could define the shape geodesically, then use software to slice it into layers like NeilBlanchard has. The octa symmetry has 90° corners at the middle sides so you could stretch it a little to the front to get the bluff body, then droop the nose to lower the stagnation point and stretch more to more to the rear with a truncation. Width and height can be de-coupled. And the 'equator' can be lowered, all because of the octahedral symmetry.

As for the 22° vs 25° debate, I start blocking it out. A gathering angle at the rear of 45° means 22 1/2° and that's close enough for me. I don't get what you mean by the cylinder to reattach flow, but that's OK.

[Tesla]

Originally Posted by freebeard

Actually just the opposite. The 4v octahedral dome has 512 vertexes, and the shape I evolved has a void on the bottom so it's only 448 vertexes. That would fit in a spreadheet, higher frequency means smoother shapes although the count goes up fast. I think at 4v it would be like the dimples on a golf ball, but I can't find any info on frequency vs Reynolds number. Think F-117.

My comment was more related to complexity of construction, not the aerodynamics of the shape, I'm not up to speed with all the programs used or the knowledge of those shapes, I know the basics of geodisic domes, but only in the sense of dwellings. As for the F117, I expect the primary aim was stealth, not aerodynamics and we all know that if you put enough thrust behind it a house brick will break the sound barrier.

Originally Posted by freebeard

Your most recent post is all about the limitations of 3rd hand Cartesian coordinates. The solution used in naval Architecture is loft lines. Those are still only accurate to the limitations of the drafting methods. One could define the shape geodesically, then use software to slice it into layers like NeilBlanchard has. The octa symmetry has 90° corners at the middle sides so you could stretch it a little to the front to get the bluff body, then droop the nose to lower the stagnation point and stretch more to more to the rear with a truncation. Width and height can be de-coupled. And the 'equator' can be lowered, all because of the octahedral symmetry.

Understand about the limitations you mention, but I think it is just a simple observation, the angles along the spine are changing rate up and down, this will create a wiggly line, not a continuous curve in one direction, in the table from 20to 40% you go from 4 to 3 to 3.5 then 2 in rate change, surely this should be all in one direction, either up or down for the template type curve.

Originally Posted by freebeard

As for the 22° vs 25° debate, I start blocking it out. A gathering angle at the rear of 45° means 22 1/2° and that's close enough for me. I don't get what you mean by the cylinder to reattach flow, but that's OK.

I think you referenced the sphere and 25* seperation at 4 seconds analogy, then suggested a 25* cone behind this, my point was it probably wouldn't matter if you attached a 1* cone behind that the air is gone. From what I have read & as I understand things so far, there are some ideal shapes to keep flow attached and the template is one of them, but in general they are all in the same family. With a sharp bend the air can hold on for a bit, but there will be payback, once you pass the 4 second mark you're into the turbulance and this will not settle or re-attach for quite some distance.
With freight trailers, they are limited to length, so they dive in hard with the angle and can get a good benefit, most likely better than if they followed the template to the same distance, but I suspect if they extended the full length with that steeper angle, there would be nothing further to be gained and the result may even be worse. So for a short cut off tail, you can go a bit steeper, for a longer tail greater benefits will be seen by sticking to the template. That,s what I think I know, but still learning.

[freebeard]

As are we all. Since my last post I found aerohead thread on Cinderella and the 4° past midnight analogy. The F-117 example is related to golf ball dimples. The Tiger Woods part.

I think this method would incrementally approach the theoretical ideal contour (it is a B-spline curve, lathed; nothing more) with a mathematically rigorous foundation. But I personally don't care; I'm more interested in eyeball engineering. The hot rodder maxim: "If it looks right it is right."

The thing I've been thinking about is this—people talk about air moving or being moved. What actually happens is the air occupies the space and sound waves, i.e., alternating highs and lows, move. At our levels of sensation and Reynolds numbers it's silent, but once you get to the sound barrier—boom. But people talk about air 'relaxing' back into the low pressure area.

[Tesla]

It is both, the air molecules do physically move, they have to otherwise you would have to re write some new physics theories, then there is also the pressure waves which are on the same spectrum as sound waves, but the big boom won't really be a concern for most of us.
I am slowly getting my head around the fact that the air is stationary and the vehicle is moving at the point of impact, so visualising the movement of boats is coming into play for me. I think a number things govern the aerodynamic solution, which includes the air volume moved, frontal area, shape & body length all have a bearing on how the air will return to the space vacated by the vehicle, different shapes will create different pressure profiles.
I don't know anything about B-Spline curves, but have been looking at some interesting stuff recently.

[Tesla]

I went down this track and plotted the equation for the 0040 airfoil below:


I tried to get it to scale as best I could on screen with a ruler, 300mm long and 60mm high at apex.
It fits the 2.5:1 ratio, has Apex to tail ratio of 1.7729.....

Could someone try to overlay it on the template, I haven't done that yet, too busy playing with the numbers.
The plot was done with 110 data (extra 10 on nose to get nice curve) points, but I could easily go more.

The equation does not go to 0 at tail, but there is some additional stuff to add to the equation to fix this, just thought I'd post this up now.