Fuel Economy, Hypermiling, EcoModding News and Forum - EcoModder.com - View Single Post - Designing a tail extension for the first-gen Insight

3-Wheeler · 02-20-2010, 09:05 PM

EDIT @ 7:39pm The following calculations are assuming the Aero Template is resting on the ground plane, and not lined up with the under carriage.

OK, Robert got me thinking about the accuracy of my first attempt at duplicating the curvature of the AeroHead Aero Template.

So it was time for another take, and this time with a little more precision.

You recall the first graph, which showed the Aero template and Honda Insight. Looks pretty consistent in shape, right?

So let's calculate the change in Y-data, or delta-Y and then graph that relation. Now how consistent does the graph look?

It turns out that picking data points from the Insight photograph posted earlier in this thread, is not so easy to do. So how do we fix the template data?

I graphed the change in curvature of the template data, and found out that the change in angle gave a constant ramp/rate change, and so the plot below shows a curve that was generated from zero all the way to 22 degrees over our length of 183.5 inches, which duplicates the length of the graphic by Metro.

Next, using some trigonometry, I reverse calculated the effective change in the Y-Axis Offset to mimic the ideal curvature change, as seen below. This was done by altering the X-Axis data in steps of 0.100 inches, all the way out to 183.5 inches. This amounts to spreadsheet with about 1800 data points! This gives us very good accuracy.

Lastly, Robert will ask for the R^2 value of this ideal curve, and I shall show him the following error graph. That shows that the error is less than 0.001 inch quite easily. More than adequate for our purposes of making a card board template.

Almost forgot to include the new polynomial that generated the above curve...

y = 0.00149991110386985 * x^2 - 0.0000513899089202675 * x - 0.000105687318828214

The equation gives us the ideal AeroHead Template shape with very low error, of less than 0.001 inch.

Jim.

02-20-2010, 09:05 PM	#53 (permalink)
3-Wheeler Master EcoModder Join Date: Dec 2008 Location: Southern WI Posts: 829 AlienMobile - '00 Honda Insight Team Honda 90 day: 80.05 mpg (US) Thanks: 101 Thanked 563 Times in 191 Posts	EDIT @ 7:39pm The following calculations are assuming the Aero Template is resting on the ground plane, and not lined up with the under carriage. OK, Robert got me thinking about the accuracy of my first attempt at duplicating the curvature of the AeroHead Aero Template. So it was time for another take, and this time with a little more precision. You recall the first graph, which showed the Aero template and Honda Insight. Looks pretty consistent in shape, right? So let's calculate the change in Y-data, or delta-Y and then graph that relation. Now how consistent does the graph look? It turns out that picking data points from the Insight photograph posted earlier in this thread, is not so easy to do. So how do we fix the template data? I graphed the change in curvature of the template data, and found out that the change in angle gave a constant ramp/rate change, and so the plot below shows a curve that was generated from zero all the way to 22 degrees over our length of 183.5 inches, which duplicates the length of the graphic by Metro. Next, using some trigonometry, I reverse calculated the effective change in the Y-Axis Offset to mimic the ideal curvature change, as seen below. This was done by altering the X-Axis data in steps of 0.100 inches, all the way out to 183.5 inches. This amounts to spreadsheet with about 1800 data points! This gives us very good accuracy. Lastly, Robert will ask for the R^2 value of this ideal curve, and I shall show him the following error graph. That shows that the error is less than 0.001 inch quite easily. More than adequate for our purposes of making a card board template. Almost forgot to include the new polynomial that generated the above curve... y = 0.00149991110386985 * x^2 - 0.0000513899089202675 * x - 0.000105687318828214 The equation gives us the ideal AeroHead Template shape with very low error, of less than 0.001 inch. Jim. Attached Thumbnails Last edited by 3-Wheeler; 02-20-2010 at 09:40 PM..