If we calculate the net drift between A and B, which in this example means following a constant heading equal to the direct heading at the start of the journey, our path will be much longer than the direct path, a loop heading out to the left. If we attempt to stay on the “shortest” path from A to B, at the end of an hour, we will still be at A. Over the course of an hour, the perspex moves half that distance to the left of the direct track, then half that distance to the right. You have a toy car which can travel at a speed equal to the distance between the dots over one hour. Over the top you have a much larger piece of perspex. To help with the lay understanding, imagine a rectangular table top, with a dot at each end. Having derived a constant heading, it is flown, and neglecting political geography, with no concern for the position with respect to the position on earth below, other than the destination and not bumping into things. However, there may be jetstreams at less optimum altitudes that could provide considerable net improvement, even if more fuel is used per air mile (meaning movement through the body of air, not the 3D relationship with the earth), but lets not go there. Using these, you can calculate the drift for the entire flight due to pressure differences and Coriolis effect, the net geostophic winds.
#Real world example of altitude geometry plus
For an air routing, you could use the barometric pressure at origin and destination plus the latitudes. Sometimes that will be the same thing, but not very often. A longer path with regard to the earth can yield flight path savings in the order of 30% to 50%, the classic example being North Atlantic flights in the forties, where savings of this order resulted from using Bellamy drift derived constant heading paths instead of great circle routing.Īircraft need to travel the shortest route in the air, not in three dimensional space. The origin and destination are fixed to the earth, if the sea and the air were likewise fixed, a great circle would yield the shortest path. The article fails to understand that aeroplanes travel in the air, which is moving, rather than fixed in relation to the earth. In the real world of long distance air navigation, great circle routes are *not* the shortest *flight* path, but they do make a good start on figuring out what will be the shortest flight path. 3 dimensions or 2… sure, you could look at it that way, but its over complicated… if earth wasn’t rotating, then height wouldn’t matter and straight line would. so as you increase height from the center of a circle, the increase in circumference, with earth’s rotation increase your velocity. but the shorter circumference then has less length to travel in that time, so its technically traveling slower. the earth is rotating at a constant speed, but the circumference between the greater height points travels at length over time just as the shorter one. but its only if you fly against earth’s rotation. so one minute of flight at ground level vs one minute of flight at altitude results in greater distance. but what this really does is multiply the distance you travel at altitude relative to the ground. or vice versa, you can say the ground it traveling quicker as well since two point in the circumference have less distance to travel compared to the greater altitude.
at a great altitude, though you are traveling at a perceived pace relative to the motor function, but you are multiplying that velocity by the increase in circumference relative to the ground’s. this means that at greater radius per starting location, the rotational velocity of a shorter radius vs a larger are varied. the length of a circumference increases by 2 pi r. what matters is the velocity the earth rotates at. it doesn’t matter if these lines are curved or not. then draw two lines, one at altitude and the other at ground level.
if you draw two lines from the center of a circle, each come out of the destinations. the real reason is because of difference of rotational velocity of a shorter vs longer circumference. Maybe thats how they conclude it but its wrong, even if it works.