The 27/28 Mz "LONG PATH" TECHNICAL NOTICE (English only)

The real meaning of the word "Tz" is for hours "Time Zone", then there is 24 Tz (for 24 hours) on the horizontal axis. The Earth is a 360 degree sphere, then one Tz is also 15 degree, and as the Earth circumference is 40.000 Km then one Tz is also about 1666 Km at the equator level as weel as for each meridian. Then there is also 12 Tz on the vertical axis !!! The Tz marking is very interesting for Ham radio using Time or Distance as Angle. To trace Tz on your own world map symply trace lignes at each 15 degree and mark them 1 to 24 in horizontal axis, and 1 to 11 in vertical axis.

Arc AB = ArcCos ((Cos TzA x Cos TzB) + (Sin TzA x Sin TzB x Cos TZ)) Angle A = ArcCos ((Cos TzB - (Cos AB x Cos TzA)) / (Sin AB x Sin TzA)) Angle B = ArcCos ((Cos TzA - (Cos AB x Cos TzB)) / (Sin AB x Sin TzB))

Mexico is about LATITUDE 4.5 Tz then TzA = 4.5 x 15 = 67.5 Mauritius is about LATITUDE 7.5 Tz then TzB = 7.5 x 15 = 112.5 Time Zone is about 10.5 Tz then TZ = 10.5 x 15 = 157.5 Arc AB = ArcCos ((Cos TzA x Cos TzB) + (Sin TzA x Sin TzB x Cos TZ)) ------ C 67.5 C 112.5 S 67.5 S 112.5 C 157.5 = 159 degree length (then the distance is 159 x 1666 / 15 = about 17.600 Km) Angle A = ArcCos ((Cos TzB - (Cos AB x Cos TzA)) / (Sin AB x Sin TzA)) ------- 112.5 C 159 C 67.5 S 159 S 67.5 = 95 degree (direct Azimuth toward East) Angle B = ArcCos ((Cos TzA - (Cos AB x Cos TzB)) / (Sin AB x Sin TzB)) ------- C 67.5 C 159 C 112.5 S 159 S 112.5 = 85 degree (for West Azimuth you must compute 360 - 85 = 275 degree)

France is about LATITUDE 3 Tz then TzA = 3 x 15 = 45.0 New Caledonia is about LATITUDE 7 Tz then TzB = 7 x 15 = 105.0 Time Zone is about 11 Tz then TZ = 11 x 15 = 165.0 Arc AB = ArcCos ((Cos TzA x Cos TzB) + (Sin TzA x Sin TzB x Cos TZ)) ------ 45 105 45 105 165 = 147 degree length (then the distance is 147 x 1666 / 15 = about 16.300 Km) Angle A = ArcCos ((Cos TzB - (Cos AB x Cos TzA)) / (Sin AB x Sin TzA)) ------- 105 147 45 147 45 = 30 degree (direct Azimuth`toward East) Angle B = ArcCos ((Cos TzA - (Cos AB x Cos TzB)) / (Sin AB x Sin TzB)) ------- 45 147 105 147 105 = 20 degree (for West Azimuth you must compute 360 - 20 = 340 degree)

Brasil is about TzA = 6.5 Tz x 15 = 97.5 France is about TzB = 3 Tz x 15 = 45 Time Zone is about TZ = 4 Tz x 15 = 60 Arc AB = ArcCos ((Cos TzA x Cos TzB) + (Sin TzA x Sin TzB x Cos TZ)) ------ 97.5 45 97.5 45 60 = 75 degree length (then the distance is 75 x 1666 / 15 = about 8.000 Km) Angle A = ArcCos ((Cos TzB - (Cos AB x Cos TzA)) / (Sin AB x Sin TzA)) ------- 45 75 97.5 75 97.5 = 40 degree (direct Azimuth toward East) Angle B = ArcCos ((Cos TzA - (Cos AB x Cos TzB)) / (Sin AB x Sin TzB)) ------- 97.5 75 45 75 45 = 120 degree (for West Azimuth you must compute 360 - 120 = 240 degree)

New Caledonia is about TzA = 7 Tz x 15 = 105 Mexico is about TzB = 4.5 Tz x 15 = 67.5 Time Zone is about TZ = 7 Tz x 15 = 105 (you compute 24 Tz - 17 Tz = 7 regarding the Tz world map) Arc AB = ArcCos ((Cos TzA x Cos TzB) + (Sin TzA x Sin TzB x Cos TZ)) ------ 105 67.5 105 67.5 105 = 110 degree length (then the distance is 110 x 1666 / 15 = about 12.000 Km) Angle A = ArcCos ((Cos TzB - (Cos AB x Cos TzA)) / (Sin AB x Sin TzA)) ------- 67.5 110 105 110 105 = 70 degree (direct Azimuth toward East) Angle B = ArcCos ((Cos TzA - (Cos AB x Cos TzB)) / (Sin AB x Sin TzB)) ------- 105 110 67.5 110 67.5 = 100 degree (for West Azimuth you must compute 360 - 100 = 260 degree)

France is TzA = 3 Tz x 15 = 45 Indian Ocean is TzB = 7.5 Tz x 15 = 112.5 Time Zone is TZ = 4 Tz x 15 = 60 Arc AB = ArcCos ((Cos TzA x Cos TzB) + (Sin TzA x Sin TzB x Cos TZ)) ------ 45 112.5 45 112.5 60 = 87 degree length (then the distance is 87 x 1666 / 15 = about 9.600 Km) Angle A = ArcCos ((Cos TzB - (Cos AB x Cos TzA)) / (Sin AB x Sin TzA)) ------- 112.5 87 45 87 45 = 125 degree (direct Azimuth toward East) Angle B = ArcCos ((Cos TzA - (Cos AB x Cos TzB)) / (Sin AB x Sin TzB)) ------- 45 87 112.5 87 112.5 = 40 degree (for West Azimuth you must compute 360 - 40 = 320 degree)

France is TzA = 3 Tz x 15 = 45 SE Australia is TzB = 8.5 Tz x 15 = 127.5 Time Zone is TZ = 8.5 Tz x 15 = 127.5 Arc AB = ArcCos ((Cos TzA x Cos TzB) + (Sin TzA x Sin TzB x Cos TZ)) ------ 45 127.5 45 127.5 127.5 = 140 degree length (then the distance is 140 x 1666 / 15 = about 15.500 Km) Angle B = ArcCos ((Cos TzB - (Cos AB x Cos TzA)) / (Sin AB x Sin TzA)) ------- 127.5 140 45 140 45 = 100 degree (direct Azimuth toward East) Angle B = ArcCos ((Cos TzA - (Cos AB x Cos TzB)) / (Sin AB x Sin TzB)) ------- 45 140 127.5 140 127.5 = 60 degree (for West Azimuth you must compute 360 - 60 = 300 degree)

Brazil is TzA = 6.5 Tz x 15 = 97.5 Mauritius is TzB = 7.5 Tz x 15 = 112.5 Time Zone is TZ = 8 Tz x 15 = 120 Arc AB = ArcCos ((Cos TzA x Cos TzB) + (Sin TzA x Sin TzB x Cos TZ)) ------ 92.5 112.5 92.5 112.5 120 = 116 degree length (then the distance is 116 x 1666 / 15 = about 13.000 Km) Angle A = ArcCos ((Cos TzB - (Cos AB x Cos TzA)) / (Sin AB x Sin TzA)) ------- 112.5 116 92.5 116 92.5 = 115 degree (direct Azimuth toward East) Angle B = ArcCos ((Cos TzA - (Cos AB x Cos TzB)) / (Sin AB x Sin TzB)) ------- 92.5 114 112.5 114 112.5 = 105 degree (for West Azimuth you must compute 360 - 105 = 255 degree)