June 07, 2007

Significantly Insignificant Digits

I design sailboats as a hobby. One of my friends designs flying disks, ornithopters, boats, gliding toys and UAV’s for a living. He shared with me recently regarding some proposed changes I was contemplating in my boat design with advice:

There are certain designs changes that you can implement that make a big difference in how something will move through the air or water. Often times there are orders of magnitude difference between the primary and secondary
It has been my experience agonizing over small changes in the design phase of my boat can become the proverbial case of straining a gnat and swallowing a camel… or, being pennywise and pound foolish.
How much precision is needed to store accurate engineering data? Older versions of CAD and GIS software used a long integer with an offset value to store very large coordinates with very small difference between those coordinates. ESRI 3D Shapefiles, 3D File-based Geodatabases and AutoCAD drawings store coordinates using what equates to essentially double precision numbers. Double precision numbers allow you to store very big numbers with very small differences between the numbers. The new ArcGIS 9.2 ArcSDE technology can store larger numbers than ever before with smaller differences between those numbers. A worth while question is how big or small do these numbers need to be to accurately store objects on our globe…should they support infinitely big and infinitesimally small numbers?
The pessimist says; The cup is half empty. The optimist says; The cup is half full. The engineer says; The cup is TWICE AS BIG as it NEEDS to be!
I was a bridge inspector for a summer, and got to crawl over all different kinds of bridges in Washington State overlooking some pretty scenic places. I reported on the safety conditions and maintenance issues of the structures. One could ask, what would be the safest design for a bridge? The answer I got from one engineer was to fill the valley with concrete; that would be the safest bridge. However, I doubt the bridge engineer would win a design award for such a bridge. Using the high precision geodatabase available in ArcGIS 9.2 and given 40 million meters are the equatorial circumference, you can map to the nearest 4 nanometers. A micron or micrometer is one millionth of a meter. A nanometer is one billionth of a meter.

Relating these sizes to the real world; a human hair is said to be about 50 micrometers wide. Viruses range in size from 20 to 250 nanometers., clay dust particles have diameters less than 2 microns, silt particles range from 2 to 50 microns, and sand-size particles are greater than 75 microns. So as I understand it, you could map viruses on the dust, from the sand, over the entire surface of the globe!?

If you are concerned about the accuracy of your data, likely the precision of the number stored in AutoCAD, Microstation, ESRI Shapefiles or ArcGIS isn’t where you should focus your attention. For more information regarding the intimacies of coordinate data storage for Geographic Information a new white paper on the subject from ESRI.

I'm thirsty I think I'll get a half cup of water...


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