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