Cartographic map projection principles are fundamental to land survey professionals in Kenya, enabling the accurate transformation of the earth's curved surface into flat maps suitable for measurement, analysis, and planning. Mastery of these principles ensures that survey data is correctly represented, facilitating infrastructure development, land registration, and resource management. This chapter focuses on essential projection systems such as Mercator and the World Geodetic System, as well as the criteria for selecting appropriate map projections in diverse surveying contexts.

2.1 Cartographic map geographic area is identification.

This topic introduces how the geographic area to be mapped is identified and described before any map projection is chosen or applied. Knowing exactly where the area lies, how large it is and what shape it has is critical, because these properties decide which projection will keep distortions in shape, area, distance and direction small enough for the map's purpose. Kenyan surveyors, for example, require precise definition of the mapped area for county boundary demarcations and urban planning, where even small errors can lead to disputes or inefficient resource allocation. Example: before producing a land-use map for a county planning department, the cartographer recorded the county's bounding latitudes and longitudes, its north-south length and its east-west width from the gazetted boundary and the 1:50 000 topographic sheets.

Characteristics of the geographic area to identify

• Location: The position of the area on the earth, given by the latitudes and longitudes of its centre or corners.
• Extent: The bounding coordinates, that is, the most northerly, southerly, easterly and westerly points.
• Size: The north-south and east-west distances and the total area, which decide the map scale and sheet size.
• Shape and orientation: Whether the area is compact or elongated, and whether it runs mainly north-south or east-west, since projections handle each differently.
• Latitude band: Areas near the equator, such as most of Kenya, suffer different distortion patterns from areas near the poles.
• Boundaries: Administrative, property or natural boundaries such as rivers, ridges and coastlines that define the edges of the map.
• Existing reference systems: The datum, grid and map sheets already used for the area, so the new map fits existing records.

Steps for identifying the geographic area

1. Define the purpose: Confirm what the map is for, since this decides how precisely the area must be defined.
2. Gather source materials: Collect topographic maps, boundary descriptions, previous surveys and imagery covering the area.
3. Delineate the boundary: Mark the limits of the area on a base map or in GIS, using gazetted or surveyed boundaries.
4. Determine bounding coordinates: Record the northernmost, southernmost, easternmost and westernmost latitudes and longitudes.
5. Find the centre point: Calculate the central latitude and longitude, which is used later when setting projection parameters.
6. Measure size and shape: Work out the north-south and east-west extents, the area and the main orientation.
7. Note the reference system: Record the datum and grid used by the source data.
8. Document the findings: Write a short area description to guide projection selection and map design.

Worked example: centre point of an area

Central latitude = (northern latitude + southern latitude) ÷ 2

Central longitude = (eastern longitude + western longitude) ÷ 2

A catchment lies between 0.5° S (−0.5°) and 1.0° N, and between 36.0° E and 37.0° E.

Central latitude = (1.0 + (−0.5)) ÷ 2

Central latitude = 0.5 ÷ 2 = 0.25° N

Central longitude = (37.0 + 36.0) ÷ 2

Central longitude = 73.0 ÷ 2 = 36.5° E

Worked example: extent of the area in kilometres

North-south distance = difference in latitude × 110.6 km

East-west distance = difference in longitude × 111.3 km × cos(central latitude)

Using the same catchment:

North-south distance = 1.5 × 110.6

North-south distance = 165.9 km

East-west distance = 1.0 × 111.3 × cos 0.25°

East-west distance = 111.3 × 1.0000

East-west distance = 111.3 km

The catchment is longer north-south than east-west, a shape that is recorded when the projection is chosen.

Chapter Summary

This chapter explored the fundamental principles of cartographic map projection, emphasizing the importance of accurately identifying the geographic area to be represented. It addressed how different projections serve various purposes depending on the nature and extent of the area under study. The discussion then moved to the selection of appropriate map projection types, highlighting the characteristics and applications of the Mercator projection, which preserves direction and shape but distorts size, and the World Geodetic System, a global standard for geospatial referencing. Finally, the chapter examined the concept of cartographic map projection itself, explaining how the curved surface of the earth is transformed onto a flat map while managing distortions inherent in this process. Understanding these principles equips learners to choose and apply projections that best fit the intended use of their maps. This foundation is essential for producing accurate and functional cartographic products in various professional fields.