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Old 09-16-2020, 10:45 AM   #1 (permalink)
aerohead
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Six - 'Optimum' templates

From Daugherty and Franzini, drag minimums ( optimums ) occur when both friction drag and pressure drag are at their minimums for a given shape.
R. Barth conducted the dimensional analysis for 5-shapes, and the results are presented in Figure 8.46, page 324, Hucho's 2nd-Edition. ( I presented these materials years ago, but they're now lost to the photo-bucket black-hole.
Barth presented a Cartesian grid, with drag curves for five geometric bodies:
* square-rectangular-cylinder
* circular-cylinder
* 11%-radii, soft-edged square-rectangular cylinder
* round-nosed circular cylinder
* and ellipsoidal cylinder
From the curves, it's easy to find the bottom of the 'bucket' for each shape, where each achieves their drag minimum. Their 'optimum.'
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In order of appearance in the above list, the shapes attain their drag 'optimum' at a Length/ Width ( or Height ) of:
* 2.473
* 2.210
* 4.978
* 5.042
* 6.263
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Number- 6 template appears in, ' AERO- HYDRODYNAMICS OF SAILING,' by Marchaj, page 244, for a symmetrical wing section. Again, a Cartesian grid is offered whereas the friction and pressure drag components are given, and the ratio of 'optimum' can be obtained directly from the chart's 'bucket', @ ( 3.92 :1 ) ratio of Chord / section thickness. I published this information also, years ago.
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The take-away, is that because of dimensional analysis, anyone desiring to know the state-of-the-art for some specific body forms, has available to them, off-the-shelf technology, from which to streamline their project from the get-go.
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There are also, 'templates' for piping and duct work in the professional literature, denoting 'optimums' derived from laboratory measurements of contained flows, which illustrate where friction and pressure drags reach their minimums also. These are germane to induction, exhaust, inter-coolers, air-to-air and water -to- air heat exchanger ducting and manifolds.

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