Quote:
Originally Posted by Tesla
I've been playing with the Power equation and have come up with a few interesting bits.
The original equation was simple y=ax^b which worked well for the purpose but was limited in adjustment, so I added a correction factor to subtract -cx and after playing with it came up with the following values for the CoEfficients:
0.31801x^-0.39103 - 0.05x, Power 2 equation, this matched the AS-II profile very well, just slightly above at 30-60% area. Using the same equation I tried to match up template angles 6.8-23 it matches ok, bit less 20-40%, then a bit more through mid range to catch up to the 23 at end, this one I called Power 2.2. I've left the original, Power 1, on the overlay as a comparison.
The fact that the Power 2 angles correlate quite well with the AS-II angles confirms the accuracy of the image, but it also confirms through 2.2 that the Template angles are more aggressive and result in less that 1.78 tail ratio.
I also looked at the rate of change of angles and also the calculated fall, the top two do not include Template as they require 100 data points, charts below:
The bottom two are based on 10 data points so I've included the template, the third chart shows how the Power 2 equations match the template much better than the original Power 1.
With the 4th chart, I've reduced the range at the start on both x&y axis because there was no significant distinctions at the start, all the interest was in the tail. As I had found interest in the "Rate of angle changes" I asked myself then what is the Rate of change the Rate of angle change, so kind of like a secondary derivative. The first thing that sticks out is the lines of the template which show an erratic direction whilst both the power equations continue to show a continuous rate change curve, like a typical ballistic trajectory. The other point of interest was that the Power 2 equations resulted in virtually identical values. |
*In the literature for 3-D streamline bodies of revolution,the Bernoulli Equation-related velocity/pressure profile across the aft-body holds the position of authority with respect to drag.
*If the fineness ratio is below 2.5:1,the pressure recovery demands deceleration of the boundary layer,which is impossible,since it's already at rest against the body,initiating burble point,then full-blown, separation-induced turbulence and attendant pressure drag increasing drag above the minimum.
*If the fineness ratio exceeds 2.5:1,pressure drag due to separation is eliminated,however surface friction drag increases,and overall drag increases above the minimum.
*The 2.5:1 profile appears to embody the 'sweet-spot'.There's something about its aft-body profile especially representative of the bottom of the drag 'bucket',when plotted on a Cartesian L/D grid.Kinda like the 'Goldilocks' zone.
*Early airship research indicated 2.1:1 for a drag minimum,but this would be for enormous bodies,in which the sloughing turbulent boundary layer actually fills in part of the wake,following the hull wherever it goes,representing a larger 'phantom' fineness ratio.