To reduce the unserviceable area as compared to serviceable area a hexagonal model is proposed and analyzed as follows. Let us consider an area to be covered is having a hexagonal shape is shown in fig (3). We place six WRS station at six corners, only the shade region is service area. Other area is not under service area due to bowing effect. The service area covered by each satellite on average for hexagonal shape with six satellites is 21.63* 10 6 Km 2. The service area covered by each satellite on the average for square shape with four satellites is 13.414942*10
6 Km
2. This is very clear
that increases of WRS in number will increase the service area
drastically and also indicates the reduction of the bowing effects. By
placing the reference station at all the corners of Hexagon,
calculation for service area is as follows.
Side of the hexagon (rs) = 7900Km
Total service area = Area of the Hexagon
From fig (4), Area of the equilateral triangle ABC = Ö (3)/4 * side
2 = 27.02 *10
6 Km
2
Area of the sector = (
q/ 360) *
p* rs
2
Area of the sector = 32.667106*10
6 Km
2
Deepest point (segment depth) d = 7900-6814.6 = 1058.4 Km
Uncovered area (unshaded) each station BDC = sector area – triangle area
Total uncovered area =6* 5.657 *10
6 Km 2 = 33.942*10
6 Km2
Total area covered by hexagon= 162.12*10
6 Km2
Useful coverage area = Hexagonal area – total uncovered region= 128.178*10 6 Km2
Service area of each station =21.630 *10
6 Km2
Adding two WRS, the service area of hexagon model is increased by 37.33 *10
6 Km2
Table 1
| | Rectangle (4) | Hexagon (6) |
| Area of the WRS | 124.81*106 Km2 | 162.12 *106 Km2 |
| Uncovered due to bowing effect | 71.153816 *10 6 Km2 | 33.942*106 Km2 |
| Useful service Area | 53.65*106 Km2 | 128.178 106 Km2 |
The above methods suggest that increase of WRS station will reduce the bowing effects as well as increase in the monitoring area in turn service area will get increased. In the case of regional coverage, total area get reduced depending upon the size of the country as well as controlled airspace. Hence the distances between
WRS get reduced to counter the bowing effect. The concept of the
optimization to place the WRS is discussed below.
WRS placement for satellite Integrity monitoring over Indian Airspace:
Geographical condition of Indian air space is versatile in nature. The positioning of the WRS stations for providing monitored air space and reliable correction signal to user in all the phases of flight is challenging task. The coordinate of the place, accessibility to the point for installation of the equipment and also should fulfill the siting criteria defined in International Civil Aviation Organisation (ICAO) document for navigation equipment. For sake of simplicity, the coordinates of Doppler Very High Frequency Omni-Range (DVOR) and Distance Measuring Equipment (DME) Stations, Non Directional Beacon (NDB) and Airport Reference Point (ARP)
have been taken into consideration . The coordinates of the navigational aids are published in Air Radio of Airports Authority of India (AAI) and used by pilot for navigation of the aircraft in all the phases of flight. The coordinates of the proposed WRS placement over Indian Airspace are placed in the Table –II as plan I &II.
Table - II (Proposed Plan - I)
| Place | Latitude (N)Deg Min Sec. | Longitude (E)Deg Min Sec | Site / facilities |
| Srinagar (1) | 34 00 12 | 74 45 23 | DVOR |
| Delhi (12) | 28 34 00 | 77 05 46 | DVOR |
| Jamnagar (2) | 22 29 35 | 70 03 30 | NDB |
| Bhopal (13) | 23 16 56 | 77 20 13.5 | DVOR |
| Mumbai (3) | 19 07 01 | 72 50 04 | NDB |
| Hyderabad (14) | 17 26 59 | 78 21 13 | DVOR |
| Kavatati (4) | 10 30 00 | 72 36 00 | NDB |
| Nagarcoil (5) | 20 42 45 | 70 55 20 | NDB |
| Port Blair (6) | 21 38 26 | 69 39 46 | NDB |
| Chennai (7) | 12 59 30.50 | 80 10 09 | DVOR |
| Bhuneshwer (8) | 20 14 38 | 85 49 02 | DVOR |
| Aziwal (9) | 23 44 32 | 92 48 22 | NDB |
| Itanagar (10) | 27 06 01 | 93 44 37 | Proposed Airport |
| Gagtok (11) | 27 21 03 | 88 56 41 | Proposed Airport |
(Proposed Plan - II)
| Place | Latitude (N)Deg Min Sec | Longitude (E)Deg Min Sec | Site / facilities |
| Srinagar (1) | 34 00 12 | 74 45 23 | DVOR |
| Jamnagar (2) | 22 29 35 | 70 03 30 | NDB |
| Hyderabad (9) | 17 26 59 | 78 21 13 | DVOR |
| Kavatati (3) | 10 30 00 | 72 36 00 | NDB |
| Nagarcoil (4) | 20 42 45 | 70 55 20 | NDB |
| Port Blair (5) | 21 38 26 | 69 39 46 | NDB |
| Jodhpur (8) | 26 14 00 | 73 03 00 | DVOR |
| Itanagar (6) | 27 06 01 | 93 44 37 | Proposed Airport |
| Gagtok (7) | 27 21 03 | 88 56 41 | Proposed Airport |
Source: Air Radio AAI SEcond Edition
The Plan -I has 14 number of WRS where as Plan- II has nine number of WRS stations. The positioning of WRS station to cover the Indian Airspace have nonlinear pattern of triangles or squares. It is very difficult to calculate the total / Actual monitored area for users. The methodology adopted for calculating the monitored area is as follows.
Calculate the circumference of earth where radius of earth is 6378Km (taken)
Calculate the distance between 1 degree, 1 minute and 1 second in KM
Calculation based on:
Radius of the earth = 6378 Km, Circumference of the earth = 2ð * 6378 = 40,054 Km
One degree = 40,054/360 = 111.3 Km
One Minute = 111.3/60 = 1.855 Km