ANNEX U.K.

Appendix C Modelling of lateral ground track spreading

It is recommended that, in the absence of radar data, lateral ground track dispersion be modelled on the assumption that the spread of tracks perpendicular to the backbone track follows a Gaussian normal distribution. Experience has shown that this assumption is a reasonable one in most cases.

Assuming a Gaussian distribution with a standard deviation S, illustrated in Figure C-1, about 98,8 percent of all movements fall within boundaries of ± 2,5·S (i.e. within a swathe of width of 5·S).

Figure C-1

Subdivision of a ground track into 7 subtracks

(The width of the swathe is 5 times the standard deviation of the ground track spreading)

A Gaussian distribution can normally be modelled adequately using 7 discrete sub-tracks evenly spaced between the ± 2,5·S boundaries of the swathe as shown in Figure C-1.

However, the adequacy of the approximation depends on the relationship of the sub-track track separation to the heights of the aircraft above. There may be situations (very tight or very dispersed tracks) where a different number of subtracks is more appropriate. Too few subtracks cause ‘fingers’ to appear in the contour. Tables C-1 and C-2 show the parameters for a subdivision into between 5 and 13 subtracks. Table C-1 shows the location of the particular subtracks, Table C-2 the corresponding percentage of movements on each subtrack.

Table C-1

Location of 5, 7, 9, 11 or 13 subtracks

(The overall width of the swathe (containing 98 % of all movements) is 5 times the standard deviation)

Subtrack number	Location of subtracks for subdivision into
	5 subtracks	7 subtracks	9 subtracks	11 subtracks	13 subtracks
12/13					± 2,31·S
10/11				± 2,27·S	± 1,92·S
8/9			± 2,22·S	± 1,82·S	± 1,54·S
6/7		± 2,14·S	± 1,67·S	± 1,36·S	± 1,15·S
4/5	± 2,00·S	± 1,43·S	± 1,11·S	± 0,91·S	± 0,77·S
2/3	± 1,00·S	± 0,71·S	± 0,56·S	± 0,45·S	± 0,38·S
1	0	0	0	0	0

Table C-2

Percentage of movements on 5, 7, 9, 11 or 13 subtracks

(The overall width of the swathe (containing 98 % of all movements) is 5 times the standard deviation)

Subtrack number	Percentage of movements on subtrack for subdivision into
	5 subtracks	7 subtracks	9 subtracks	11 subtracks	13 subtracks
12/13					1,1 %
10/11				1,4 %	2,5 %
8/9			2,0 %	3,5 %	4,7 %
6/7		3,1 %	5,7 %	7,1 %	8,0 %
4/5	6,3 %	10,6 %	12,1 %	12,1 %	11,5 %
2/3	24,4 %	22,2 %	19,1 %	16,6 %	14,4 %
1	38,6 %	28,2 %	22,2 %	18,6 %	15,6 %