A demonstrator in principle of a flight guidance system whose function is to steer an aircraft from an origin to a destination via a route, where a route is defined as a set of way points joined by 'great circle' arcs using an ellipsoidal model of the earth.
The habitable land of Planet Earth is neither permanent nor stable. Tectonic plates shift. Mountains rise. Coastlines change. In some places, the sea erodes the land and it disappears. In other parts, the sea deposits new land. Volcanic islands appear and disappear. Climates change. Where once there was lush forest and grassland, now there is desert. Frequent tempests destroy all human endeavour in once tranquil river deltas. Weather patterns shift and become more violent. Advancing cold expels populations from their once-temporate homelands. Sea levels rise. Vast cities become inundated. Entire civilizations lose their once-plentiful needs of life while regions yet uninhabited become bounteous. The recent acceleration in climate change has amplified these effects. They have become unignorable. To survive the future, man must once again become a nomad.
Unfortunately, the nomadic life is wholly incompatible with the social and legal frameworks on which modern civilizations are based. The root of this incompatibility is the current notion of property.
I remember many local television news stories in England about houses perched on the edges of cliffs that finally fell into the sea. When the house was built, it was a safe and reasonable distance from the sea. But over the years, the sea gradually eroded the coastline until it undermined the house. The owner obviously paid money to buy an original plot of land that included adequate space between the house and the sea. But the sea "stole" his land and finally consumed his house. Further down the coast, the sea deposited new land. Here, the owner of a home found the area of his land gradually increasing. It would be sand and mud at first. But as plants gradually invaded the new area and took root, soil gradually built up until it became good land.
A fair way to deal with this situation would be as follows. The owner of the land that the sea deposited would move his inland border towards the sea until he had the same about of land as he did originally. Then every other land owner in between him and the owner of the eroded land would move his borders a bit. The owner of the eroded land would then move his border inland so that he had the same amount of land as he originally bought. Then society would collectively help him build a new house. But it doesn't work like that. Under our current legal framework of specific ownership and rigid demarcation, the owner of the eroded land loses all and becomes dependent on social housing and welfare.
Climate change, shifting weather patterns and land erosion effect the same thing on a vast scale. Whole tribes in Africa lose their lands to permanent drought and migrate as unwelcome refugees into the over-stretched economies of other states. The result, under the current notions of law and property, is friction, war and poverty. There has to be another way. In my previous articles in this series, I have outlined my vision of another possible way. My vision is of a world in which every human being has the unalienable right to the sustainable economic use of his fair share of the planet's habitable surface. But for this to work, we must be mobile. When erosion strikes or climate changes, we must be able to move so as to reconfigure the organization and distribution of the use of land smoothly and without upset.
For this reason, I propose that this alternative world should not only have ordinary vehicles, but that the new kinds of homes I describe should themselves be vehicular. They must be able to relocate easily. They do not need to move frequently. Nor do they need to travel at great speed. Preferably, such a home should, for the duration of a move, become some form of airborne vehicle that can move easily and safely when necessary under its own power and guidance. For this it needs a global navigation system which provides fully automatic piloting with the ability to avoid collisions with fixed geographic obstacles and other airborne vehicles.
The Moving Map Navigator applet described herein is my rendering of such a system. It requires an input of current position and provides an output of heading error - the difference between actual heading and required heading. This is, in effect, a steering command.
The input of current position must be acquired from an external reference. In the past, the angles subtended by stars from the horizon were used to determine geographic position. The 20th century saw the introduction of radio-navigation ground stations such as NDB, Radio-Range, VOR/DME, TACAN and ILS. Currently, a Global Positioning System (GPS) using artificial Earth satellites is the most convenient means of determining the geographic position of some object or point on the Earth's surface. The drawback of GPS in my view is that, unlike the stars, it is artificial. Consequently, it can be subject to equipment malfunction and changes in availability policy. I would prefer to see the future development of a navigation system that did not depend on artificial infrastructure. One such possibility would be a system that made use of the known positions and radio signatures of quasi-stellar objects.
The accuracy to which the position of a geographic feature or waypoint can be specified depends on the accuracy of the means used to measure the position. GPS can (at the time of writing) give positions to an accuracy of 15 metres. This is within about 1 second of arc on the equator. Certainly, I think that a global system that can reveal your position to one second of arc is sufficient. This is sufficient to place you well within visual range of an objective.
A more accurate determination of position is only necessary as a vehicle approaches its destination. I think final approach is far better managed by a local navigational aid because its accuracy necessarily increases as you get closer to it. I do not consider the determination of height to be part of navigation. A vehicle simply needs to maintain a safe height above the terrestrial profile and avoid obstacles and other vehicles. Safe height is best determined by equipment that directly measures height above ground. The avoidance of obstacles and other vehicles is best done by on-board sensors such as sonic or electromagnetic radar.
The circumference of the earth is about 40075160 metres at the equator and 40008000 metres through both poles. Call it 40067000 metres. There are 12960 seconds of arc in a complete circle. Consequently, 1 second of arc represents a surface distance of 30.916 metres. A position on the equator specified to 1 second of arc places it precisely within a circle about 31 metres diameter (about 15 metres radius). At higher latitudes the circle becomes an ellipse whose major axis is 31 metres but whose minor axis reduces as latitude increases. This means that a specified position is always within about 15 metres of its "true" position.
For this reason, the co-ordinates of a geographic feature or waypoint that make up the data file for a given route, are specified to a precision of one second of arc. However, to avoid multiple rounding errors, the precision to which calculations of position, distance and bearing are made within the applet is that of an IEEE 754-1985 floating point double, which is vastly more precise than one second of arc.