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Mitsubishi 4WD Owners Club of Qld (Inc) |
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GPS - What's that? |
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GPS-101 (Cave Men to Albert Einstein) Since man first wandered away from his cave in search of food, he has been trying to find his way home. Then next time he went hunting he wanted to find his way back to the valley where he caught that sabre-toothed tiger for dinner. Then, when he did find his way back to that valley, he found that someone else inhabited that area and wanted to defend his territory. So he went back home and got his family and his mates and so did the other guy and they fought over the valley with the tasty sabre-toothed tigers. Now, hand-to-hand combat can really hurt. So they started throwing rocks at their enemy. This way the guy with the most accurate aim could win the fight (Remember David and Goliath). But, your arm gets pretty tired throwing rocks, and you can only hit one person at a time, so came: bows and arrows, guns and bullets, and then intercontinental ballistic missiles and nuclear warheads. Man now had a new problem. They had some really powerful weapons, but when you’re firing them from thousands of kilometres away, how do you make them land in the right spot (i.e. on the guys that are threatening to come into your valley to take your sabre-toothed tigers). Finally, 1978 years after some men nailed another man to a large wooden cross for suggesting that it would be really great if we could all just get along with each other, the U.S.A. Department of Defence decided that they needed a super precise form of worldwide positioning. And hey, they had a spare $12 billion lying around. Hello GPS! Why did they need GPS? The USA figured it would be really good to be able to blow up the USSR missile silos. This would destroy the weapon and the mechanism of launching them. They could do this with dead-reckoning missile guidance systems because they knew where they were launching from and they knew from their surveillance where the USSR missile silos were. But, if they could do it, then so could the USSR – Doh! So, then the USA decided that it would be a good idea to move their missile launch platforms around, by putting them on submarines. This made it hard for the USSR to target them. But, when the sub surfaced, they hard to work out where the hell they were, so that they could work out where to point the big bomb. Since the early 1990s, GPS has evolved beyond its military origins. Not only does GPS provide such services as guiding troops, planes, tanks, ships and "smart bombs," it is now an information resource supporting a wide range of civil, scientific and commercial uses, including 4WD navigation. Barely a club meeting goes by that I don’t get some questions about GPS. So, I’ve decided to start writing a series for Diamond Torque to try and answer some of the questions. I’ll start off with the basics and then get into some more detail and practical application as we go. I’ll also have a word to Ken about running a practical weekend trip sometime later in the year. It’s a wonder that it works at all ! The current GPS configuration consists of a network of 24 satellites in orbits around the Earth. Each satellite orbits at an altitude of about 20,000 km from the ground at about 14,000 km/hour. Contrary to popular belief, GPS satellites are not in geosynchronous or geostationary orbits. They have to keep moving to counteract the gravitational pull of the earth. The satellite orbits are distributed into 6 orbital planes with 4 satellites each as depicted below (plus a few spares that are in orbit on standby).
You need to be able to receive signals from at least 3 satellites to get a 2-dimensional position fix on the earths surface, as depicted above. In theory at least 4 satellites are always visible from any point on the Earth at any given instant with up to a maximum of 12 visible at one time. Each satellite has an atomic clock that "ticks" with an accuracy of 1 nanosecond (1 billionth of a second). A GPS receiver determines its current position and heading by comparing the time signals it receives from a number of the GPS satellites (usually 6 to 12) and triangulating its position, based on the known position of each satellite. To achieve this level of precision, the clock ticks from the GPS satellites must be known to an accuracy of 20-30 nanoseconds. However, because the satellites are constantly moving relative to observers on the Earth, effects predicted by the Special and General theories of Relativity must be taken into account. This is where Albert Einstein’s work comes in handy. These relativistic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day. This sounds small, but the high-precision required of the GPS system requires nanosecond accuracy, and 38 microseconds is 38,000 nanoseconds. If these effects were not properly taken into account, a navigational fix based on the GPS would accumulate error at a rate of about 10 kilometres each day! The whole system would have been utterly worthless for navigation in a few hours after launching. The engineers who designed the GPS system catered for these effects when they designed and deployed the system by slowing down the ticking frequency of the atomic clocks before they were launched so that once they were in their proper orbits their clocks would appear to tick at the correct rate as compared to the reference atomic clocks at the GPS ground stations. Further, each GPS receiver has built into it a microcomputer that (among other things) performs the necessary relativistic calculations when determining the user's location. I’m not going to get into the maths. I’ll give you a private tutorial if you’re really interested. There are five ground stations with super super accurate atomic clocks and computers to calculate things like atmospheric distortion effects and to keep all of the satellites running on the correct orbits and the correct position in that orbit. They transmit correctional information up to the satellites. As well as transmitting time signals, the satellites transmit an almanac of data, which has information, like the atmospheric corrections, the time corrections for orbital misalignments, etc. Your GPS unit has to triangulate your position from 4 or more satellites from the time signals and then use this almanac information received from the satellites and the inbuilt data about the system to make corrections and give you the answer – your location. And modern GPS units can give you a position every half a second. That’s pretty impressive Physics, Maths, and calculating power. Next Issue, I’ll start to try to answer the most asked question, “What GPS unit should I buy?”. If you can’t wait for the upcoming issues, there is a lot of great information at the following web sites: www.gpsinformation.net; www.gpsoz.com.au References and plagiarism sources for this issue: The Bible, The Hitchhiker’s Guide To The Galaxy – Douglas Adams, Trimble web site (www.trimble.com/gps), Spaceflight Now (www.spaceflightnow.com), Ohio State University (www.astronomy.ohio-state.edu), Georgia State University (www.hyperphysics.phy-astr.gsu.edu) Happy Navigating ... or Read More ... GPS-101 Part 2 (Which One for Me) Greg Conlon |
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