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. It removes the error and calibrates your receiver at the same time!!!