
<p><strong>Navigation and the Global Positioning </strong><br><strong>System (GPS): </strong></p><p><strong>The Global Positioning System: </strong></p><p><strong>Few changes of great importance to economics and safety have had more immediate impact and less fanfare than </strong><br><strong>GPS. </strong></p><p>• GPS has quietly changed everything about how we locate objects and people on the Earth. </p><p>• GPS is (almost) the final step toward solving one of the great conundrums of human history. </p><p><strong>Where the heck are we, anyway? </strong></p><p><strong>In the Beginning……. </strong></p><p>• To understand what GPS has meant to navigation it is necessary to go back to the beginning. </p><p>• A quick look at a ‘precision’ map of the world in the 18<sup style="top: -0.58em;">th </sup>century tells one a lot about how accurate our navigation was. </p><p><strong>Tools of the Trade: </strong></p><p>• Navigations early tools could only crudely estimate location. • A Sextant (or equivalent) can measure the <em>elevation </em>of something above the horizon. This gives your <em>Latitude</em>. </p><p>• The <em>Compass </em>could provide you with a measurement of your direction, which combined with <em>distance </em>could tell you <em>Longitude</em>. </p><p>• For <em>distance</em>…well counting steps (or wheel rotations) was the thing. </p><p><strong>An Early Triumph: </strong></p><p>• Using just his feet and a shadow, Eratosthenes determined the diameter of the Earth. </p><p>• In doing so, he used the last and most elusive of our navigational tools. </p><p><strong>Time </strong></p><p><strong>Plenty of Weaknesses: </strong></p><p><strong>The early tools had many levels of uncertainty that were cumulative in producing poor maps of the world. </strong></p><p>• Step or wheel rotation counting has an obvious built-in uncertainty. • The Sextant gives latitude, but also requires knowledge of the Earth’s radius to determine the distance between locations. </p><p>• The compass relies on the assumption that the North <em>Magnetic </em>pole is coincident with North <em>Rotational </em>pole (it’s not!) and that it is a </p><p><em>perfect dipole </em>(nope…). </p><p>Navigation on land was helped by the availability of <em>landmarks</em>, places that could put context to a map and help calibrate a journey. </p><p>Such a technique is worthless at Sea…. </p><p><strong>Navigation at Sea: </strong></p><p><strong>Without any question THE most important maritime dilemma of the Renaissance world was how to determine Longitude. </strong></p><p>• A sextant can be used to give latitude very effectively at sea. • A compass can give you a good idea of your direction. • But unless you can determine how far East/West you’ve gone…. </p><p><strong>Will Eventually Turn into THIS! </strong><br><strong>This </strong></p><p><strong>Dead Reckoning: </strong></p><p>• To determine one’s East-West position, the accepted method was called <em>Dead Reckoning </em>(perhaps aptly named). </p><p>• Dead Reckoning has many sources of error that add up over a long journey. Even <em>95% accuracy </em>in crossing from New York to </p><p>London will <em>accumulate to 175 MILES of error </em>at the end of the trip. </p><p>• These kinds of error were a <em>Serious </em>problem for ships approaching rocky coasts or areas with submerged shoals and seamounts! </p><p><strong>Longitude! </strong></p><p><strong>On October 22, 1707, a dead reckoning error by the fleet of </strong><br><strong>Admiral Sir Clowdisley Shovel led to the death of 2000 sailors. </strong></p><p>• In 1717, Queen Anne authorized a prize of 20,000 £ to anyone who could maintain knowledge of longitude to ½ degree (the equivalent of 30 miles on the equator). </p><p>• Almost all of the methods proposed for solving this problem centered on the 4<sup style="top: -0.58em;">th </sup>element of navigation we haven’t talked about </p><p>much…….<em>TIME. </em></p><p><strong>Why is Time so important? Meridians and Longitude: </strong></p><p>• Your <em>Meridian </em>is nothing more than a circle on the Earth that goes through the North and South Poles and your position. </p><p>• The <em>Prime Meridian </em>is the meridian that goes through an agreed upon zero point. </p><p>• The Prime is located today in Greenwich, England. </p><p>• The angle going west from Greenwich to your meridian is your <em>LONGITUDE! </em></p><p><strong>Longitude and Time: </strong></p><p><strong>So how do longitude and time relate? </strong></p><p>• It turns out that while there may be no landmarks on the ocean, there are fixed reference points…the <em>stars</em>. </p><p>• As the Earth turns, the stars pass by overhead. Each star crosses every meridian on Earth exactly once each day. </p><p>• So the difference between the time a star crosses the prime and your meridian is your longitude. </p><p>• The problem then comes down to knowing what time it is…exactly. </p><p>• Every 4 minutes of error equals 1 degree or 60 miles on the equator. </p><p><strong>John Harrison’s Clock: </strong></p><p><strong>To win the longitude prize one had to be able to maintain accurate time to within 2 minutes over a several months at sea. </strong></p><p>There are actually several ways to do this. </p><p>• Galileo couldn’t win the prize (he was dead), but he <em>had </em>devised a way of determining the time using the moons of Jupiter. </p><p>• <em>This actually worked well, but only for that part of the year when Jupiter was visible at night! </em></p><p>• The astronomers Tobias Mayer and Nevil Maskelyne proposed using the predictable changes in the distance to the moon. </p><p>• <em>This also worked, but was VERY hard to do correctly and didn’t work when the moon was less than ½ full. </em></p><p>• <em>John Harrison </em>went after the prize by building accurate clocks that could survive the weather extremes and motion of ship travel. </p><p><strong>John Harrison’s Clock: </strong></p><p>• Between 1736 and 1764 John Harrison produced 4 clocks for the <em>Board of Longitude </em>(the group that held the prize). </p><p>• Each clock was smaller and more accurate than the previous one. And they <em>ALL </em>met the condition for the longitude </p><p>prize. <em>None were accepted! </em></p><p>• So why were they locked in an observatory instead of saving lives on ships during this time? </p><p>• Because Nevil Maskelyne was chair of the Board of Longitude… </p><p>• It would take an act of King George III to break the logjam and put </p><p><em>chronometers </em>into wide use. </p><p><strong>The (FIRST) Global Positioning System: </strong></p><p><strong>Harrison’s clock changed navigation in a fundamental way. </strong></p><p>• Anyone with a sextant and a chronometer could find their position to within a few miles on the Earth. </p><p><strong>They weren’t perfect though </strong></p><p>• The clocks were incredibly expensive and in fairly short supply. • Since they relied on Greenwich time, they had to be re-calibrated to Greenwich: Usually <em>in </em>Greenwich. </p><p>• Positions could only be determined at sunrise or sunset when both a star <em>and </em>the horizon could be seen. </p><p>• It didn’t work at all if the weather was cloudy….. </p><p><strong>A Modern Solution: </strong></p><p><strong>Harrison’s clock (and its successors) made navigation possible for commercial shipping and the well to do, but it wasn’t for the masses. </strong></p><p>• A universal navigation system would need the following. </p><p>• A way to tell time that isn’t expensive. • A clock that can be calibrated anywhere, not just in Greenwich. </p><p>• A set of references that didn’t disappear whenever it was cloudy </p><p><strong>Enter the MODERN Global Positioning System (GPS): </strong></p><p><strong>The Global Positioning System: </strong></p><p><strong>For all its complexity, GPS still comes down to the same set of requirements that Harrison faced. </strong></p><p>• Find out the time. • Find the reference points. • Use the output to determine Longitude and Latitude to high precision. </p><p><strong>GPS adds a pair of twists: </strong></p><p>• The reference points also serve as the clock. • Everyone uses the same system. The GPS network is effectively a single device, like Harrison’s clock. </p><p><strong>Parts of the GPS Network: </strong></p><p><strong>The GPS system consists of 3 elements. </strong></p><p>• GPS satellites. • GPS ground support. • GPS receivers. </p><p><strong>The GPS Satellite System: </strong></p><p><strong>The first GPS Satellite was launched in 1978. </strong></p><p>• To function properly the network of satellites must contain 24 units. With GPS it is all about coverage. </p><p>• Each satellite has a 12 hour orbit, which means it passes over the same place twice each day. </p><p>• There are 6 orbit ‘<em>planes’ </em>inclined by 55° to the equator and rotated for a 60° spacing between them. </p><p>• Each plane contains 4 satellites. </p><p><strong>The GPS Satellite System: </strong></p><p><strong>The first GPS Satellite was launched in 1978. </strong></p><p>• A <em>Ground Track </em>map </p><p>shows how this scheme covers the Earth. </p><p><strong>The GPS Ground Support: </strong></p><p><strong>The GPS satellites are nothing more than atomic clocks that work because we know where and when they can be found. </strong></p><p>• To maintain the satellites requires a ground support network (called the <em>control segment </em>- CS) that uplink time and radar tracking position data to the satellites (called the <em>space vehicles </em>– SV). </p><p>• There are 5 CS components that update satellites and also communicate data to some advanced GPS reveivers </p><p><strong>The GPS Receiver: </strong></p><p><strong>The receiver units are the backbone of the mass market </strong><br><strong>GPS. The receivers serve 3 purposes. </strong></p><p>• Small handheld units receive signals from 4 or more SVs. The receivers are called the <em>User Segment -US</em>. Decoded signals provide X, Y, Z, and T. Everyone can find out where they are. </p><p>• Via SV-US communication, the exact time can be synchronized worldwide in a matter of a few seconds. </p><p>• By combining signals from nearby receivers, very accurate navigation and surveying data can be obtained. </p><p><strong>The Method of GPS: </strong></p><p>• How does GPS work?. • Your GPS receiver gets signals from satellites that are doing nothing more than repeating the time over and over. </p><p>• Since light travels at a finite speed, there will be a difference between the instantaneous time on your receiver and the time you get from the satellite. </p><p><strong>Time Difference = Speed of Light X distance </strong></p><p>• The time differences are small. 1000 feet of distance translates to only a 1,000,000<sup style="top: -0.58em;">th </sup>of a second! </p><p>• The satellites know <em>exactly </em>where they are in X, Y, Z. So, if you have a bearing to three of them, then you know as well. </p><p><strong>The Genius of GPS: </strong></p><p>• There’s a caveat to this. YOU don’t carry an atomic clock. They are expensive and heavy. YOUR receiver clock is going to be off a some random amount when it compares time with the satellites. </p><p><strong>How do we get around this? </strong></p><p><strong>The Genius of GPS: </strong></p><p><strong>We add a 4</strong><sup style="top: -0.58em;"><strong>th </strong></sup><strong>measurement! </strong></p><p>• If we <em>knew </em>the time, a 4<sup style="top: -0.58em;">th </sup>satellite would be redundant. </p><p>• However, the extra satellite can ONLY match up with the other three at the <em>CORRECT </em>time. It removes the error and calibrates your receiver at the same time!!! </p>
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