Feathers and leaves
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"Donald G. Shead" u10...@snet.net
It's all too obvious that feathers and leaves fall hither and yon in the gusty autumn air: But it isn't at all obvious that streamlined bodies such as acorns and lead slugs are subject to the same effects: The variations in the density of that air.
They appear to fall straight down; with a uniform acceleration; but like all falling bodies their speed and direction vary depending on the vagaries of the density and currents of the medium they are falling in.
Bodies only fall at the same velocity, in vacuum!
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Donald G. Shead <http://pages.cthome.net/donsr/> Such a tangled web we weaved when first we practiced to perceive.
"Richard Bullock" richardbull...@ntlworld.com
Should this be same acceleration - at a constant gravitational field strength.
They took a feather and hammer to the Moon. Both hit the ground at the same time.
Ric
"Donald G. Shead" u10...@snet.net
Yes Ric!
- at a constant gravitational field You've gone _too_ far Ric!
Yes Ric; in the vacuum of the moon's atmosphere.
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Donald G. Shead <http://pages.cthome.net/donsr/> Such a tangled web we weaved when first we practiced to perceive.
"Everett Hickey" lith...@ev1.net
Maybe I'm missing the point. You've got all this m*** that any falling body has to push past... air. Naturally, this has to affect ANY movement, including gravitation. But this doesn't do anything to violate known principals. Every action has an equal and opposite reaction - and it takes energy to move air molecules out of the path of a falling object. This energy has to fall from somewhere, and it ends up comming from the kinetic energy built up by a falling object... thus slowing it down. The difference is, a feather has less kinetic potential, and in relation wind resistance is much greater... so it falls slower. A rock might have the same force of wind resistance acting on it, but it's kinetic potential is much greater than that of a feather, so the loss is far less noticable.
Where is the point of contention?
josephshor ...@aol.com (JosephShore23)
Wow!! That's deep man! JS
Uncle Al Uncle...@hate.spam.net
[snip] Bullshit. Take two m***ive capped long sewer pipes - hey, even vent them - and drop them vertically from a stratospheric balloon. Inside one sewer pipe is a feather, at the top but unattached. Inside the other is a one ounce lead fishing weight, at the top but unattached.
Release both sewer pipes simultaneously at maybe 70,000 feet. The feather and the lead will fall identically for a nice long time.
Equivalence Principle: All small proximate test m***es fall identically (absent extraneous forces) regardless of composition (experimentally confirmed to one part in ten trillion) and geometry (never tested).
sHead, go e-mail yourself.
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Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) "Quis custodiet ipsos custodes?" The Net!
Sam Wormley sworm...@cnde.iastate.edu
Ref: http://physics.about.com/library/weekly/aa120800a.htm The problem of air flow over falling objects such as leaves or pieces of paper is surprisingly complex. In fact, it is so hard to solve the full fluid dynamics equations that physicists haven't even been able to tackle the problem numerically until very recently.
Determining the flow of air over a falling object essentially comes down to solving the Navier-Stokes equation of fluid flow. It is a complicated non-linear differential equation that has very few analytical solutions so most work on it has to be done numerically. The trouble is that even a numerical approach is hard because of the immense quantity of information that needs to be tracked as the flow progresses.
The general approach to solving the Navier-Stokes equation is to only consider points and motions on a 3D lattice or grid. The smaller the spacing of the grid, the more accurate the results.
Even so, many tricky techniques must be used to come up with a solution.
Takayuki Aoki has developed a couple of new numerical techniques that he has applied to the problem of a falling business card or leaf.
The first of these is called the Interpolated Differential Operator (IDO) Scheme. It works by approximating small pieces of the solution to the flow by relatively simple polynomials which are made to match the real solutions at each of the grid points.
This allows a better approach to the problems of dealing with the gaps between the grid points.
A second technique is called the Cut-Cell Method. It attempts to deal with the fact that a widely spaced grid can't model the shape of the falling object very accurately. The Cut-Cell Method allows the shape of the object in the flow to be modelled much more accurately than the normal chunky shape on a widely-spaced lattice.
A third technique is called the overlapping grid method. Normally, there is just one grid that either represents the laboratory reference frame (i.e. everything moves within the grid) or a frame attached to a rigid object (i.e. the object stays still and the fluid flows over it with extra terms in the equations of flow to compensate for motion of the object compared to the laboratory).
Aoki uses a combination of both of these. He sets up a finely spaced grid attached to the falling object to model the flow in great detail very near the object where the flow is most critical for affecting the object. That whole grid moves within a larger grid representing the laboratory frame of reference. The two grids are made to match up and, in this way, most of the computational power is spent where it is needed, near the object's surface.
At the Conference on Computational Physics 2000, Aoki shows animations of falling business cards and leaves that appeared to match lifelike behaviour very well. However, even using his improved numerical techniques, he still needed to employ an SGI Origin 2000 supercomputer to perform the simulations.
Aoki's next step is to make a quantitative comparison of his computer models and actually falling objects - looking right isn't enough in the world of science! With further development he hopes to simulate objects that bend and deform in flows. This would allow him to model a falling piece of paper that flaps and curls as it falls. It would also allow for more useful simulations like modelling the flow of blood through the arterial system, even as the arteries moved and deformed while a person's heart beats and lungs move.
Sam Wormley sworm...@cnde.iastate.edu
Ref: http://www.sciencenews.org/sn_arc98/10_31_98/bob2ref.htm The Puzzle of Flutter and Tumble Physicists reconsider the fall of leaves Computer simulations and chaos theory come to the fore in attempts to explain the motions of falling leaves and paper sheets.
References: Aref, H., and S.W. Jones. 1993. Chaotic motion of a solid through ideal fluid. Physics of Fluids A 5(December):3026.
Belmonte, A., H. Eisenberg, and E. Moses. 1998. From flutter to tumble: Inertial drag and froude similarity in falling paper. Physical Review Letters 81(July 13):345.
Field, S.B., et al. 1997. Chaotic dynamics of falling disks. Nature 388(July 17):252.
Mahadevan, L., H. Aref, and S.W. Jones. 1995. Comment on "Behavior of a falling paper." Physical Review Letters 75(Aug. 14):1420.
Mahadevan, L., W.S. Ryu, and A.D.T. Samuel. In press.
Tumbling cards. Physics of Fluids A.
Tanabe, Y., and K. Kaneko. 1995. Tanabe and Kaneko reply.
Physical Review Letters 75(Aug. 14):1421.
______. 1994. Behavior of a falling paper. Physical Review Letters 73(Sept. 5):1372.
Williams, M. 1998. As the leaf falls: A study of the deterministic motion of falling leaves. College of William and Mary Senior Research Final Presentations. April.
Further Readings: Peterson, I. 1997. Exposing chaos in a falling disk's flutter. Science News 152(July 19):37.
______. 1995. Cavities of chaos. Science News 147(April 29):264.
______. 1994. Catching the flutter of a falling leaf.
Science News 146(Sept. 17):183.
Willmarth, W.W., N.E. Hawk, and R.L. Harvey. 1964. Steady and unsteady motions and wakes of freely falling disks.
Physics of Fluids A 7(February):197.
Further information about the work of Franco Nori and his colleagues at the University of Michigan can be found at http://www-personal.engin.umich.edu/~nori/falling.html.
Sources: H***an Aref University of Illinois at Urbana-Champaign Department of Theoretical and Applied Mechanics Urbana, IL 61801-2935 Andrew Belmonte Pennsylvania State University Department of Physics University Park, PA 16802 Reggie Brown College of William and Mary Department of Applied Science P.O. Box 8795 Williamsburg, VA 23187 Hagai Eisenberg Weizmann Institute of Science Department of Physics of Complex Systems Rehobot 76100 Israel Stuart B. Field Colorado State University Department of Physics Fort Collins, CO 80523 Scott W. Jones University of Illinois at Urbana-Champaign Department of Theoretical and Applied Mechanics Urbana, IL 61801-2935 Kunihiko Kaneko University of Tokyo Department of Pure and Applied Sciences Komabs, Meguro-ku Tokyo 153 Japan Melody Klaus University of Michigan, Ann Arbor Department of Physics Ann Arbor, MI 48109-1120 Lakshminarayanan Mahadevan M***achusetts Institute of Technology Division of Mechanics and Materials Mechanical Engineering 1-310 Cambridge, MA 02139 Mitchell Moore University of Michigan, Ann Arbor Department of Physics Ann Arbor, MI 48109-1120 Elisha Moses Weizmann Institute of Science Department of Physics of Complex Systems Rehobot 76100 Israel Franco Nori University of Michigan, Ann Arbor Department of Physics Ann Arbor, MI 48109-1120 Yoshihiro Tanabe University of Tokyo Department of Pure and Applied Sciences Komabs, Meguro-ku Tokyo 153 Japan Maura Williams University of Maryland, College Park Physics Department College Park, MD 20742 William W. Willmarth University of Michigan, Ann Arbor Department of Aeronautical and Astronomical Engineering Ann Arbor, MI 48109 From Science News, Vol. 154, No. 18, October 31, 1998, p. 285.
Copyright ?“ 1998 by Science Service.
"Donald G. Shead" u10...@snet.net
Maybe there is none Everett; if we agree that the terminal velocity of feathers and leaves is obviouly much less than for acorns and lead slugs.
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Donald G. Shead <http://pages.cthome.net/donsr/> Such a tangled web we weaved when first we practiced to perceive.
"Donald G. Shead" u10...@snet.net
What a waste!
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Donald G. Shead <http://pages.cthome.net/donsr/> Such a tangled web we weaved when first we practiced to perceive.
Sam Wormley sworm...@cnde.iastate.edu
Understanding the physics of falling leaves... could possibly contribute to better designs of aircraft and countless other devices that interact with moving g***es and fluids.
-Sam
nowill ...@attbi.com (DickT)
On the other hand, as Weinberg said, we seek not only to describe but to understand.
And as Huxley said, we should sit down before a fact like a litle child.
And as Euclid said, He wants to profit by his intruction. Give him an obol and send him away.
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