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Visual representation of vector information

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)?

-- Lee Kamentsky (email)

Aeronautical engineers must do this all the time; see what they're up to.

-- Edward Tufte

Thanks, I found this while I was looking:

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.

-- Lee Kamentsky (email)

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

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.

-- Edward Tufte

Threads relevant to analytic design:

Seeing Around: New ET essay published

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