Scales, coverage and sheet numbering

Detail

1. Key terms

• Topographical map: a large-scale map of a small area. It shows natural features (relief, rivers, forests) and man-made features (roads, railways, villages) in detail.
• Scale: how a distance on the map compares with the real distance on the ground.
• Representative Fraction (RF): the scale written as a ratio. In 1:50,000, 1 unit on the map = 50,000 of the same units on the ground.

• Large scale (e.g. 1:25,000) shows a small area in great detail. Small scale (e.g. 1:1,000,000) shows a large area with little detail.

• Topographical sheet numbering: a reference system. Every sheet gets a fixed number based on its place in a latitude–longitude grid. A smaller sheet's number is made by adding letters or numbers to the number of the bigger sheet it sits inside.

• Survey of India (SOI): India's national mapping agency, under the Department of Science & Technology. It makes, keeps and gives out the topographic map database of the whole country [2].

2. Scales and the area each sheet covers

Scale	Area covered	Example number	Sheets inside the next bigger sheet
1:1,000,000 ("million sheet")	4° × 4°	63	—
1:250,000 ("degree sheet")	1° × 1°	63K (lettered A–P)	16 in one million sheet
1:125,000	30' × 30'	—	4 in one degree sheet
1:50,000	15' × 15'	63K/12 (numbered 1–16)	16 in one degree sheet; 256 in one million sheet
1:25,000	5' × 7'30"	—	6 in one 15' sheet (3 rows of 5' × 2 columns of 7'30")

• Rule of thumb: a larger scale means a smaller area per sheet and more detail.
• 1° = 60' (minutes) and 1' = 60" (seconds).

3. The numbering logic, step by step

• Step 1: million sheet (1:1,000,000). India is cut into 4° × 4° blocks. Each block gets a number, e.g. 63.
• Step 2: degree sheet (1:250,000).
• The 4° × 4° block is cut into a 4 × 4 grid. That gives 16 sheets of 1° × 1°.
• They are lettered A to P, e.g. 63K.

• The letters run down one column at a time, from north to south. A–D form the first (western) column, E–H the second, and so on.

• Step 3: 1:50,000 sheet.

• Each 1° × 1° sheet is cut into a 4 × 4 grid. That gives 16 sheets of 15' × 15'.

• They are numbered 1 to 16 in the same column-wise order, e.g. 63K/12.

• Totals:

• One degree sheet holds 16 sheets at 1:50,000.
• One million sheet holds 16 × 16 = 256 sheets at 1:50,000.

4. Worked example: placing sheet 63K/12

• Sheet 63 covers 24°–28°N and 80°–84°E.
• 63K:
• Column I–L is the third column, so it covers 82°–83°E.
• In that column, I = 27°–28°N, J = 26°–27°N, K = 25°–26°N and L = 24°–25°N.

• So 63K covers 25°–26°N and 82°–83°E.

• 63K/12:

• Numbers 9–12 make up the third column, so the sheet covers 82°30'–82°45'E.
• No. 12 is the bottom (southern) row, so it covers 25°00'–25°15'N.

• So 63K/12 covers 25°00'–25°15'N and 82°30'–82°45'E.

• On the ground: this sheet covers parts of Mirzapur and Varanasi districts (Uttar Pradesh), on the Ganga (NCERT exercise sheet, Exercises B and C).

5. Exam arithmetic at 1:50,000

• Converting the scale:
• 1:50,000 means 1 cm on the map = 50,000 cm on the ground = 0.5 km.

• So 2 cm = 1 km and 4 cm = 2 km.

• North–south size of a 15' sheet:

• 1° of latitude ≈ 111 km.
• 15' is a quarter of a degree, so 15' of latitude ≈ 27.75 km.

• On the map this becomes about 55.5 cm.

• East–west size of a 15' sheet:

• Lines of longitude come closer together as you move away from the equator and meet at the poles.
• So 15' of longitude is shorter than 27.75 km, and it gets shorter towards the poles.

• Near 25°N (the latitude of the Mirzapur–Varanasi sheet), it is about 27.75 × cos 25° ≈ 25 km.

• Result: in the north of India, a 15' × 15' sheet is a little taller than it is wide on the ground. It covers roughly 700 km² near 25°N.

6. Two series of maps under the National Map Policy 2005

• National Map Policy 2005: SOI was given the job of opening up map data to users without putting national security at risk [2].
• Before 2005: topographical sheets used the Polyconic projection and the Everest datum [3].
• Projection: the method used to show the curved Earth on a flat sheet.

• Datum: the reference model of the Earth's shape that coordinates are measured from.

• Two series of maps under the policy:

Feature	Defence Series Maps (DSM)	Open Series Maps (OSM)
Users	Defence and national security needs [2]	General public and development work [2][4]
Datum / projection	Everest or WGS-84; Polyconic or UTM [2]	WGS-84 datum, UTM projection only [2][4]
Content	Heights, contours and full content, with no loss of accuracy [2]	Topographical content [3]; no grid; no classified information [4]
Status	Classified; Ministry of Defence (MoD) makes the rules for their use [2]	"Unrestricted" after a one-time MoD clearance [2]
Scales	Various [2]	1:250,000, 1:50,000 and 1:25,000 [4]
Civilian access	Need MoD permission through Form O.57(a) [3]	Sold at SOI map sale centres and by authorised agents [3][4]

• Key terms used in the table:
• WGS-84 (World Geodetic System 1984): the global datum that GPS uses.

• UTM (Universal Transverse Mercator): a world grid of zones, each 6° of longitude wide.

• What OSMs leave out:

• OSMs must not show any civil or military Vulnerable Areas or Vulnerable Points (VAs/VPs) [2].

• Contours and heights are not shown in restricted zones, as per MoD instructions [2].

• Common source: both DSMs and OSMs are made from the National Topographical Data Base (NTDB) [2]. The NTDB has five data sets [2]:

• National Spatial Reference Frame
• National Digital Elevation Model
• National Topographical Template
• Administrative Boundaries

• Toponymy (place names)

• Sharing rules:

• SOI can share OSMs at scales larger than 1:1 million by sale or by agreement. Each deal is logged in a registration database [2].

• Users may publish value-added maps in print or on the web. If the international boundary is shown, the map needs SOI certification [2].

• New topo maps: SOI stopped producing new topographical maps in the old format after the policy came into force in May 2005 [4].

7. OSM sheet numbering

• OSMs have different sheet numbers from the old topo sheets [2].
• Example: old topo sheet 45D/7 = OSM sheet G43S7, which covers part of Gujarat [3].
• How "G43" fits the international grid (worked out from the sheet's position):
• Old sheet 45D lies at 24°–25°N, 72°–73°E.
• "G" matches the 4°-latitude band at 24°–28°N.

• "43" matches the 6°-longitude zone at 72°–78°E.

• Working unit: the 1:50,000 sheet is still the main sheet for field study and exams.

• Finding a sheet: the SOI website has a search tool. You enter a district or a well-known feature, and it gives the sheet number. An OSM index is also available [3].

Prelims Hooks

• Scale and coverage pairs: 1:1,000,000 = 4° × 4°; 1:250,000 = 1° × 1°; 1:125,000 = 30' × 30'; 1:50,000 = 15' × 15'; 1:25,000 = 5' × 7'30".
• Count trap: one degree sheet = 16 sheets at 1:50,000. One million sheet = 256 sheets at 1:50,000, not 64.
• Letter vs number: degree sheets use letters A–P (63K). Fifty-thousand sheets use numbers 1–16 (63K/12).
• Scale arithmetic: at 1:50,000, 1 cm = 0.5 km and 4 cm = 2 km. 15' of latitude ≈ 27.75 km. 15' of longitude is shorter and shrinks towards the poles.
• Place match: sheet 63K/12 = Mirzapur–Varanasi, Uttar Pradesh, on the Ganga.
• Datum and projection: old topo sheets used Polyconic + Everest. OSMs use UTM + WGS-84 [2][3].
• Restriction status: OSM = unrestricted after a one-time MoD clearance. DSM = classified, under MoD rules [2].
• Form O.57(a): the form civilians use to ask the MoD for Defence Series Maps [3].
• Number conversion: 45D/7 (old topo sheet) → G43S7 (OSM), Gujarat [3].
• Common source: both DSMs and OSMs come from the NTDB. Its parts include the National Digital Elevation Model and Toponymy [2].

Mains Points

• Security vs openness (GS-I mapping, GS-III security):
• The 2005 policy split maps into a full-detail, classified DSM series and a cleaned-up, unrestricted OSM series [2].

• Civilian planners got access to maps, while sensitive areas (VAs/VPs) and some contours stay hidden [2].

• Planning and disaster use:

• 1:50,000 OSMs on the WGS-84 datum line up directly with GPS readings and satellite imagery.
• This makes them useful for watershed plans, road layouts and flood or landslide risk mapping.

• The policy itself names disaster mitigation and infrastructure as reasons for good spatial data [2].

• Limits of the old numbering:

• The Polyconic/Everest topo sheets did not match global systems [3].
• Moving to UTM/WGS-84 with new sheet numbers makes it easier to combine map data with international data sets and GIS [2][4].