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Comparing two bodies with the same streamlined longitudinal shape, and the same cross-sectional area, one with a circular cross-sectional shape, the other with a quadratic cross-sectional shape, which one of these two bodies would create more aerodynamic drag?

My prediction would be that it is the one with quadratic cross-sectional shape. As around the sharp edges where the two straight surfaces meet, flow interference would occur, which increases the total aerodynamic drag.

Note that these two bodies have 0 angle of attack relative to the incoming flow.

Related question: Why is the fuselage on an airliner circular-shaped?

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The quadratic body has more surface area compared to the round body, so this alone will guarantee a higher friction drag.

If the angles of attack and sideslip were always zero and no lift is created, the edges would not cause trouble. But as soon as a lift-producing wing is attached, the interference will create crossflow which will result in a higher drag of the rectangular fuselage.

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    $\begingroup$ @MichaelHall Yes, a circle has the minimum perimeter for a given area. Any non-circular shape (with the same cross sectional area) will therefore have more wetted area than a circular shape. $\endgroup$
    – Rob McDonald
    Jun 30 at 16:31
  • $\begingroup$ I had a momentary doubt, but mathed it out to confirm for myself. Thanks! $\endgroup$
    – Michael Hall
    Jun 30 at 18:22
  • $\begingroup$ Lengthwise, I was surprised to learn that the optimum fineness ratio was surprisingly stubby; 3:1 or something? The Questair Venture, the stubby little high perf kit plane, was close to egg shaped and it is supposed to have close to the ideal min drag profile. $\endgroup$
    – John K
    Jun 30 at 20:26
  • $\begingroup$ Thank you for answering! Yet I'm still unsure why the sharp edges don't cause interference, I suppose the pressure difference (high pressure over the straight surfaces, ambient pressure along the edges) would cause some turbulence, even at 0 aoa and sideslip. That's why fuselages with an approximate quadratic cross-sectional shape have their edges rounded to reduce this flow interference. see i.stack.imgur.com/ec4v4.jpg $\endgroup$
    – Frank
    Jul 1 at 15:40

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