Honda Insight Tail Extension Project

[HydroJim]

So does this mean that the template is wrong and that flow will stay attached at a more aggressive angle?

[aerohead]

Originally Posted by 3-Wheeler

Phil,

The more I dig into this, the more interesting it is becoming.

When you talk about the optimum length/width ratio being 2.5:1, I automatically assumed that the Streamlining Template had these ratios.

Well from the drawing below, you can see that the 2.5L dimension is at this location while drawn on top of the "template" and the yellow line representing this length is much shorter than the rendering???

If one were to extend the tail of the rendering all the way to the ground level, I'm guessing the length/width ratio would be closer to 3:1. Whoops, I'm off a little bit. Just fired up the CAD and checked. It's 3.58:1. And this length/width ratio does *not* include the nose.

If the rendering *was* actually drawn 2.5:1 in length from the maximal height, the 22 degree angle would be the predominant *curve* from the ground up towards the maximal height. Not sure what to make of it?

Unless.... your 2.5:1 ratio is for a fully revolved shape above the ground, and when this revolved shape is cut in half and brought to the road surface, the length/width ratio then becomes 5:1. If one includes the shape of the nose, then maybe the rendering is pretty close to this ratio. It's getting late, and I will check tomorrow.



Since it can be assumed that Honda did a good job designing the roof of the Insight, I went ahead and worked up the geometry of the roof shape, stopping where the tail starts.

Here is what that geometry looks like. You can't tell from this small picture, but I zoomed in real close with the CAD program to make these curves/angles, so they are very close to the actual shape of the roof.

By the way, this particular picture was shot from about 100 feet with a zoom lens, so the perspective is at a great distance, minimizing parallax error.



Jim.

*There are a range of streamline bodies of revolution which in free flight have a frontal area-based drag coefficient of Cd 0.04.
*The shortest streamline body which will produce Cd 0.04 has a L/D ratio of 2.1:1.Hoerner identifies this as the 'ideal' although there are reasons not to use it in aviation.Hoerner says the 'optimum' will be a bit longer.
*W.A.Mair's research on boat tails established the rear slope tangent angle of 22-degrees as the maximum angle which would maintain attached flow.
*Later,Buchheim figured 23-degrees might be accepted as the 'steepest' angle we'd want to use.
*When I put the 'Template' together I tried to respect a 'minimum' streamline body of revolution which was just long enough to also include no more than a 22-degree rear slope tangent angle.
*The 'original' 'Template-C" shows the 2.5:1 streamline body which I chose,in 'ground-reflection' as per Jaray,Prandtl,and Rumpler.This Cd 0.04 body is shown in Hucho's book.
*Technically,the body of the vehicle would have exactly the same profile in plan as in elevation.Working with 'production' automobiles,we'd have something more narrow.
*Our cars,and also one underneath the ground is what the air 'see's'.This is borne out in the original 'Template'.
*Using the 'above ground' portion of the 'Template' produces a minimum drag body of Cd 0.08 in the ground proximity as identified in the wind tunnel.
*This minimum drag body has L/H=5 at the ground plane.
*If the aft-body portion is 'shorter' it will suffer separation and higher pressure drag.
*If the aft-body portion is 'longer' it will suffer a drag increase due to increased wetted area and it's skin friction.
*The rear contour of the 'Template',according to wind tunnel investigations will guarantee attached flow and produce the lowest skin friction.
*When you add wheels to the 'Template' body the drag increases to about Cd 0.13 (from wind tunnel investigations).
*If we fair in the wheels,we can get drag coefficients below Cd 0.13.
*From the empirical data derived in the wind tunnel,if we want the lowest drag we need to stay close to the 'Template' profile.
*If you do anything,go longer.The added skin friction will pale in comparison to increased pressure drag from flow separation.
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I reduced the forebody curvature of the streamline body since all the major aerodynamicists say that a convex hemisphere -based nose is plenty good for below 250 mph.

[aerohead]

Originally Posted by HydroJim

So does this mean that the template is wrong and that flow will stay attached at a more aggressive angle?

So far,the data from the wind tunnels suggest that we're not going to beat this contour for the aft-body.
We can take liberties in the front of the car but we shouldn't gamble at the rear which is the foundation of streamlining.

[3-Wheeler]

Phil,

After working with the CAD for a few hours, it became apparent that some more extreme radii would allow a nice rendition of the streamlining template.

This first graphic shows the use of 4 radii, namely 3.75H, 7.5H, 15H, and 30H.



Now take a look at the second graphic.

Several things are obvious from this.

First, either my math is off or the template, in it's current form is not drawn 5:1 in length.

Also, the 30H radius is drawn at an ending angle of 22°, just as you have mentioned as the maximum angle that the template should show.







There is probably a mathematical function, or a wing design program out there on the web that would model the streamlining template better than what I have shown here.

Jim.

[Varn]

So your older hypothesis of 5.6h is out the window for the first 21 degrees.

[3-Wheeler]

Originally Posted by Varn

So your older hypothesis of 5.6h is out the window for the first 21 degrees.

Varn,

I'm not sure if you're asking me or Phil the question.

Also, I looked around my and Phil's previous posts and don't see a 5.6H reference.

Can you give a post number to reference to?

Jim.

[Varn]

Hi 3wheeler I was mentioning the 5.64xH=r that you described as a close approximation for the first 21 deg of Aerohead's template. It was in post 427 of this thread.

I plan on making a kamm tail based on this shape.

[3-Wheeler]

Originally Posted by Varn

Hi 3wheeler I was mentioning the 5.64xH=r that you described as a close approximation for the first 21 deg of Aerohead's template. It was in post 427 of this thread.

I plan on making a kamm tail based on this shape.

Varn,

Yes, I would have to say that as short as the Kammback would be, that the info in post #427 would work great.

All the other posts where I'm sketching the full streamlined shape, I'm working with AeroHead on developing a good mathematical process of duplicating one of the ideal airfoil shapes, that's why it's so interesting to me.

Jim.

[aerohead]

The 5:1 L/D ratio is for the 'apparent' ground reflection body,measured at the ground plane.Along with it's sister image below the ground it forms the 2.5:1 streamline body.
A car and it's reflection below the ground is the premise for evaluating it's aerodynamics.
The concept was first realized and introduced by Paul Jaray and gained traction after Ludwig Prandtl's and Edmund Rumpler's wind tunnel work.
The original 'Template'-C illustrates this concept.
Paraphrasing Hucho:" the low drag body is represented by the streamline body and it's reflection below the road surface."
I have cut away the ground clearance of the body based upon SAE 'approach,ramp,and breakover clearance angles.
If you extrapolate the aft-body out and down to the ground plane,it creates the aft-body of the 2.5:1 streamline body,never exceeding Mair's 22-degree angle.
I've essentially ignored the forebody,as mentioned in the 'Template' thread,as Hucho recommends we concentrate on the back of the vehicle for streamlining purposes.

[3-Wheeler]

Originally Posted by aerohead

The 5:1 L/D ratio is for the 'apparent' ground reflection body,measured at the ground plane.Along with it's sister image below the ground it forms the 2.5:1 streamline body.
A car and it's reflection below the ground is the premise for evaluating it's aerodynamics.
The concept was first realized and introduced by Paul Jaray and gained traction after Ludwig Prandtl's and Edmund Rumpler's wind tunnel work.
The original 'Template'-C illustrates this concept.
Paraphrasing Hucho:" the low drag body is represented by the streamline body and it's reflection below the road surface."
I have cut away the ground clearance of the body based upon SAE 'approach,ramp,and breakover clearance angles.
If you extrapolate the aft-body out and down to the ground plane,it creates the aft-body of the 2.5:1 streamline body,never exceeding Mair's 22-degree angle.
I've essentially ignored the forebody,as mentioned in the 'Template' thread,as Hucho recommends we concentrate on the back of the vehicle for streamlining purposes.

Phil,

I thought that's exactly what I did in post #465.

The total length of the shape is drawn 5:1, at the ground plane level. And the trailing angle just touches 22° at the very end.

Not sure of anything I would change to match what you are describing.

From that information, it would appear that the Streamlining Template is slightly too short based on what you are describing above.

Jim.