Quote:
Originally Posted by Michael Moore
I spent some time today in Rhino 3D trying to fit a smooth curve to the Aero Template. I started by using sections of ellipses to make it easy to have all of the curves with a zero angle at the starting/high point. Then I did an "extend line by arc" which starts with the arc tangent to a horizontal line at that maximum height point.
It looks to me like the angle numbers on the template have some problems. Perhaps I didn't find the most recent version of the template, I looked at the A, B and C threads. Maybe someone can spot where I've gone amiss. I've attached a screen capture from my spread sheet.
The small and medium ellipses have a common center (at the origin to match the template and height, the medium is longer in the horizontal axis. The large template is aligned with the origin but the center is dropped a fair bit because both horizontal and vertical dimensions are increased.
It seems to me that all the curves should start at zero and continually increase in angle in a smooth fashion. The template curve eventually stops increasing and goes to a straight, presumably tangent, line of 22 degree angle.
I didn't bother with the tangent line as that would probably start at different places on the different semi-elliptical curves and the anomaly was showing up in the early part of the curve.
On the template the 10%-increment station angles start at a 3.5 degree difference at 10% (3.5-0) go to a 2 degree delta at 20%, jump to a 6.5 degree delta at 30% and then back down to 3, 3.5, 2.5, 1 and 0 when the straight line kicks in.
The angles of the smaller ellipses become more vertical at about the 50-60% stations but the curve on the template is erratic well before that point.
The arc seems a pretty good fit to the template with the delta rising very slightly. It could be truncated at the 60% station where the value is 21.7612 degrees and go straight from that point.
I realize that most people are probably using the template tool and comparing it to photos, but if they are wanting to make something based on the angles shown they may have problem.
On the other hand, maybe if the shape was developed empirically it works better with a few spots where the curve gets rough.
ETA: the arc I used is roughly 162% of the total length of the template. I did it by eye so I'll go back later and make an arc that is an even 1.6x the length to see how that looks.
cheers,
Michael
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The template is derived from two different sources of artwork published for Cd 0.04,2.5:1 streamline bodies of revolution,provided by Franzini et al., and Wolf Heinrich Hucho.
One is 'slow' and one is 'faster'.
Some production car greenhouses lend them selves to one,but not the other so I published two,which hopefully satisfies any given production architecture.
It's not a 'perfect' solution but has a high degree of confidence for users as far as eliminating aft-body flow separation,critical for profile drag reduction.