Calculator Accuracy & Usefulness

[Garth Wilson]

Quote:Reading this thread it gives the impression that in engineering there's no need for precision. Far from reality!
Engineers don't only use "measured" quantities. We also use complex algorithms with thousands of computations.

True, but not every application that uses thousands of computations needs a lot of digits to prevent errors from accumulating. And when you do, say you do an FFT on a set of 2K samples taken with an 8-bit (ie, 256-step) A/D converter. Six digits is enough.

Quote:Surveyors are a good example

There will always be applications that need a lot of digits, like surveying and financial calculations with interest. I would say very little of engineering is that way though.

Quote:In electronics, engineers need to count 'ticks' of clocks that are gigahertz in frequency. Lots of digits there.

Crystal accuracy is usually in the range of 5 to 7 sig figs. I have an 8-digit frequency counter with a crystal oven and a trimmer to calibrate it against WWV. The specifications say you can get the error down to 0.1ppm, but by luck I was able to get .01 (although I didn't check to see if that went out the window within the next day or week). Crystals are the most precise components we can get, or at least I can't think of any components more precise off the top of my head. Analog-to-digital and digital-to-analog converters probably come next (if you get the ones with lots of bits, like 24, and even then, the accuracy of the voltage reference may not be nearly that good), but those are often applied to audio myths. For some great lessons and demonstrations on the "golden-ears" baloney, watch http://www.youtube.com/watch?v=BYTlN6wjcvQ . It starts out with a lecture at a conference and then goes to demonstrations from quality digital audio equipment in his studio that let him manipulate the exact amounts of different negative characteristics the golden-ears people said were major problems, and you can see if it is or not. In one part, he searched for the most offensive noise he could find, and superimposed in on a fine string quartet performance, and you couldn't hear it at all if it was more than 9 bits (ie, one part in 512) down from the desired program material. On my less-than-ideal PC speakers on the desk, I couldn't hear it until it was 7 bits down. Yes, it's on YouTube which compresses the audio and loses information, but he gives the URL where you can download the raw wave files if you want to, otherwise see what he does with various experiments right there.

An accomplished man I met on another forum wrote that he worked on Nimbus weather satellite. It had a 250 mW transmitter and their 85-foot dish with Maser amplifier could achieve autolock at -150 dbm at a range of 3000 miles. However, the launch vehicle suffered an early burnout and the orbit was degraded, causing the satellite to be lost to the free world for three days. No one at NASA Goddard or the DEW line or any tracking stations around the world were able to locate any evidence that it existed. They scanned the skies continuously in every sort of random and geometric pattern for days, but no cigar. Finally, he had an idea and whipped out his trusty circular pocket slide rule and came up with a reasonable approximation of what the orbit would look like with a 10-second premature shutoff and suggested to his boss that they point the antenna in a certain direction at a certain time. It worked. They found it. The boss wanted to know where he had studied astrophysics, but he didn't think the boss would appreciate knowing about his plastic slide rule so he simply shrugged it off.