User:Guy vandegrift/Chuck's little critter

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The small circle represents the center of volume, while <math>\ell</math> is the distance of the center-of-mass from the center of buoyancy.

I propose we model the problem hyrdodynamically and calculate the torque, lift, and drag of a cone in a moving fluid as shown in the figure. Using the fact that the center of buoyancy of a cone is one fourth the height of the cone,[1] we can establish this as a convenient reference point for calculating the torque (not the center-of-mass as one might ordinarily think).

From this figure, we can calculate the lift, drag, and torque exerted by the fluid. The little critter can "adjust" it's parameters to create this scenario. The lift is matched by combining the mass of the critter and the vertical component of its thrust. The drag is compensated by the horizontal component of the thrust. Finally, torque due to the fluid is balanced by the location of the center of mass, as well as the horizontal component of the thrust. At the moment, we assume the thrust is applied at the center of the base.

I propose that the lift, drag, and torque can be modeled in one of two ways:

  1. Use a hydrodyamic code, which I am certain that the university affiliated with Wright Patterson (if it's not classified).
  2. Experimentally measure using a water tunnel, or even a wind tunnel (if you adjust for the samy Reynold's number[2]

From Wikipedia:Reynolds number[edit]

Qualitative behaviors of fluid flow over a cylinder depends to a large extent on Reynolds number; similar flow patterns often appear when the shape and Reynolds number is matched, although other parameters like surface roughness have a big effect.

Personally I think it's OK to begin with Wikipedia since it is almost always correct, and with the understanding that all this needs to be verified. The following was lifted from wikipedia:special:permalink/819903847:

If we are lucky, our Reynold's number is much smaller than unity, since it is likely that our critter is slower than a "small" fish. From Wikipedia:

Typical values of Reynolds number
The Reynolds number is defined as
<math>\mathrm{Re} = \frac{\rho s L}{\mu} = \frac{s L}{\nu}</math>

where:

  • <math>\rho</math> is the w:density of the fluid (SI units: kg/m3)
  • <math>s</math> is the speed of the fluid with respect to the object (m/s)
  • <math>L</math> is a characteristic linear dimension (m)
  • <math>\mu</math> is the dynamic viscosity of the fluid (Pa·s or N·s/m2 or kg/m·s)
  • <math>\nu</math> is the kinematic viscosity of the fluid (m2/s).

Opportunity to "wiki-publish"??? NO!!![edit]

The beauty of Reynold's number is that different systems with the same value of <math>Re</math> are essentially equivalent. For example the study of a small airplane at high speed in a wind tunnel can be made to match the behavior of a large airplane at a lower speed (provided both speeds are subsonic). I am considered the "founder" of the WikiJournal of Science[3], and wondered if an explanation of this might be suitable for this journal. The answer is No because there is a Wikipedia article that seems to explain it:

I haven't bothered to carefully read this article, but am confident that it wouldn't be on Wikipedia if it was wrong.

Footnotes[edit]

  1. See Wikipedia:Special:Permalink/813978061#Center_of_mass. While we can't reference Wikipedia, someday perhaps we should think about referencing to "approved" permalinks to such wikis.
  2. See wikipedia:Water tunnel (hydrodynamic) for an (inverified) statement that water/wind tunnels can be used interchangeably.
  3. See wikiversity:WikiJournal of Science/About#Guidelines