Visual representation of vector information
October 25, 2002 | Lee Kamentsky
3 Comment(s)
I was wondering if you know of good designs that represent direction and magnitude of a continuously varying vector function in 3-dimensional space (imagine velocities of gas atoms or the strength of some field)?
Aeronautical engineers must do this all the time; see what they’re up to.
Thanks, I found this while I was looking:
http://www.tfd.chalmers.se/~lada/postscript_files/sinisa_edinburgh.pdf
If you can open it (it takes quite a while for my computer to display it), please look at fig 13 with the hydrogen bubbles. I think that is a really compelling image – you can see the flow speed up as it goes over the top of the cube, like an airplane wing.
BTW, your work and found examples are an inspiration. Thanks again.
There turns out, not surprisingly in retrospect, to be an
enormous literature on flow visualization, often with wonderful
pictures. Such issues must be of particular interest to Boeing, for
example.
It is important to get out of 2-dimensional analysis and escape
flatland in thinking about flows–and maybe for most everything
else as well. Beginning pilots are sometimes taught that wings
achieve lift because of a longer flow-path (in 2-dimensional
cross-section) over the top of an arched wing compared to the
bottom. Based on a theory about Bernoulli effects, this popular
story would, if true, render inverted flight impossible! A more
complete explanation is based directly on Newton’s laws, with
the lift resulting from forces generated in 3-space by a moving
wing powered through the air. For more on this, see Wolfgang Langewiesche, Stick and Rudder: An Explanation of the Art of Flying (New York, 1944, 1972); and David Anderson
and Scott Eberhardt, Understanding Flight (New York, 2001).
Also see the amazing website http://www.hq.nasa.gov/office/aero/
I have written about these matters in my new book, Beautiful
Evidence, in a discussion of the work of the founder of
aeronautical engineering, Otto Lilienthal.