Transcript File
Navigation Alan Altschuler (Mr. A) 13 April 2012 1 Why is Navigation Important? • You need a path to get to your destination – That requires you to know where you are to start and updated locations while on the trip • Sometimes, it is also important to just know where you are – So someone can send help – So someone can avoid you (another aircraft) – So you can build something if location is important • Property ownership • Political boundaries • Precise measurements to align objects 2 How can you navigate? • Sun – If away from the tropics, north/south at noon – Approximate east/west at sunrise/sunset • Moon – Some insects use it • Celestial – – – – • North Star (Polaris) Southern Cross Stars / Planets with charts Eclipses with charts Inertial – With an original location – With acceleration • Maps – With landmarks – With signs 3 How else can you navigate? These methods are particularly good when there are no landmarks • Sun and a clock – Declination from zenith at noon (maximum height of sun) and a calendar provides latitude – Time offset between local noon and noon at a reference point gives relative longitude to reference point – Doesn’t work well near poles (either difficult or impossible to determine maximum height of sun). – Doesn’t work when sun is obscured by clouds. • Global Positioning System (GPS) – Knowing distance from your location to multiple satellites (whose locations are known) provides your lattitude and longitude. – Doesn’t work when line-of-sight to satellites is obstructed – GPS was enabled by the space program, fast computers and the use of a universally invariant value (the speed of light). 4 How does GPS work? • Each satellite orbits the earth twice a day. Their locations are always known. They are positioned in their orbits to provide coverage across the earth at any given time. • The satellite continuously broadcasts a signal that includes its identification number and the time. • A GPS receiver listens for satellites. – If it knows the time, it needs info from each of 3 satellites. • 3 equations in 3 unknowns (lat, long, alt) – If it does not know the time, it needs info from each of 4 satellites. • 4 equations in 4 unknowns (lat, long, alt, time) – However, the more satellites the better, in order to reduce the error. Inevitably, some the satellites will be near the horizon. As such, the error associated with altitude is the greatest. 5 How does GPS work? • Light travels a distance of 186,000 miles per second. If a computer can “listen” – 1,000,000 times per second (1 megahertz), it can estimate the distance to a satellite within 0.186 miles (about 1,000 feet) – 100,000,000 time per second (100 megahertz), it can estimate the distance to a satellite within 0.00186 miles (about 10 feet) 6 How does GPS work? • If we are a certain distance from a satellite, we can say we are at one of a set of points Satellite Our possible location In blue ring • The more accurate the clock, the better our prediction can be Satellite Our possible location 7 How does GPS work? • With 2 satellites, we can significantly make our prediction better Satellites Our possible locations at intersections of rings 8 How does GPS work? • With 3 satellites, we can make a much better prediction of where we are Satellites Our possible location • More satellites can reduce the error further9 Even more satellites Our possible locations 10