Gee AMES Type 7000
Accuracy of Gee
One 150 kc /s calibration division corresponds to a time difference of 6.66 uSsec or a difference in distance of 1.24 miles. Under good conditions the position of the pulses can be estimated to the nearest tenth of a calibration division, corresponding to a range difference of 0.124 miles. This is not the accuracy of the fix, except on the base-line. To obtain the accuracy elsewhere is complicated but may be simplified if we consider only cases where the distances involved are considerably greater than the length of the base-line. At such distances the hyperbolae can be considered to be coincident with their asymptotes, which are straight lines through the centre of the base line. One such asymptote is shown in Fig. 17.7; let us consider the accuracy with which a point P can be located.
Let AB = d, OP = R and the angle POB = q, and let t = time difference corresponding to the point P. Then t = t0 + (AP - BP)/c where t0 is the "standard" delay between the emission of pulses at A and B.
But by simple geometry
AP2 - BP2 = 2dR cos q
Furthermore when R is great compared with d, AP + BP = 2R. By dividing this into the previous equation we get AP - BP = d cos q so that
t = t0 + d cos q/c
dt = - d sinq dq/c
or dq= -cdt/d sin q
If dt is the minimum time difference that can be measured, the above relationship represents the possible inaccuracy in the identification of the hyperbola.
At a range R an inaccuracy in q of dq will represent an inaccuracy, at right angles to OP, of Rdq = Rcdt /d sin q.
Under good conditions, as previously stated, cdt is 0.124 miles or ▒ 0.062 miles, say ▒ 1/16 mile. We therefore get that this 'transverse' accuracy is
▒(R/ l6d sin q) miles. For given values of R and d we get the result we expect, that the accuracy is greatest when q = 90o.
For position fixing we rely upon the intersection of two position lines. Each of these position lines will be subject to error and will therefore give rise to a transverse inaccuracy and there will therefore be a rhombus of error whose area will be proportional to R1R2 /d1d2. As R1 will approximately equal R2 in the conditions specified (R>= d) we can say .that the accuracy of fix is inversely proportional to the square of the range.
Gee shares the advantage of all hyperbolic systems that the hyperbolae are fixed in position with regard to the earth and consequently all courses derived from them are true courses and the effects of drift are at once apparent.
Gee may also be used for homing in a manner sometimes referred to as "navigation in advance". If the time-differences corresponding to the home airport are set into the navigator's equipment the two pairs of pulses will not coincide. The pilot has then only to fly a course which tends to bring the pairs of pulses into coincidence. It may happen that one pair will become coincident before the other pair. The pilot will then know that he is on a hyperbola passing through the airport and by maintaining the coincidence of this one pair of pulses he is bound to arrive over the airport in due course, when the second pair of pulses will coincide.
One other characteristic of Gee should be mentioned and that is that although the delays are measured one after another the position calculated is that corresponding to the moment when the two pairs of pulses were lined up. An instantaneous fix is therefore obtained whose accuracy is not dependent on the speed with which the measurements are made.
The radio frequency used for Gee lay in the 20 - 85 Mc/s band and therefore gave a range that was little greater than line of sight range. Each system occupies a bandwidth of about 1/2 Mc/s; the number of channels available in the band 20 - 85 Mc /s, bearing in mind that this band includes many other services, is consequently not very great.
By choosing a cycle repetition frequency of 250 c/s the length of the baseline between transmitters is limited. This fact, in conjunction with the finite range determined by the choice of radio frequency makes it impossible for a Gee system to cover a very large area and renders it unsuitable as a long distance navigational aid for use, say, over a whole continent.
Constructed by Dick Barrett
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ęCopyright 2000 - 2002 Dick Barrett
The right of Dick Barrett to be identified as author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.