Geographical and Mathematical Skills Study Notes

Understanding Map Scale and Measurement

Most Ordnance Survey maps used in geographical studies are produced at either a $1:50,000$ or a $1:25,000$ scale. The scale ratio defines the relationship between distances on the map and distances on the ground. On a $1:50,000$ map, $1\,\text{cm}$ relates to $50,000\,\text{cm}$ on the ground. On a $1:25,000$ map, every $1\,\text{cm}$ on the map relates to $25,000\,\text{cm}$ on the ground. Given that there are $100,000\,\text{cm}$ in every kilometre ($1000 \times 100\,\text{cm}$), the following conversions apply:

• On a $1:50,000$ map, every $2\,\text{cm}$ corresponds to a kilometre.
• On a $1:25,000$ map, every $4\,\text{cm}$ corresponds to a kilometre.

A $1:25,000$ map is considered more detailed than a $1:50,000$ map and serves as an excellent source for specific geographical enquiries. Conversely, $1:50,000$ maps provide a general overview of larger areas. Other scales that may be encountered include $1:10,000$ and $1:2500$. Measurement on these maps is facilitated by grid lines, which are regular horizontal and vertical lines. Horizontal lines are referred to as northings, while vertical lines are known as eastings. These lines are essential for pinpointing the exact location of various features.

Grid and Square References

Grid references allow for the location of precise positions on a map using six-figure codes. The first three figures of a reference are the eastings, which indicate how far across the map a position is. The final three figures are the northings, indicating how far up the map a position is. A common mnemonic for this sequence is ‘along the corridor and up the stairs.’ For instance, according to Figure 4.2 detailing part of Jamaica, the church at Rose Hill is located at $691045$, and the church at Davis Town is found at $737043$.

When a feature covers an extensive area rather than a single point—such as villages or woodland—four-figure square references are used instead of six-figure grid references. In this system, the first two numbers refer to the eastings and the last two numbers refer to the northings. The point where these grid lines meet identifies the bottom left-hand corner of the square. For example, most of the village of Seafield is found in square $7504$. Some larger features may span multiple squares, such as Long Bay, which is found in squares $7006$ and $7106$.

Direction and Compass Bearings

Directions on a map can be expressed using compass points or compass bearings. While compass points (e.g., southwest) are commonly used, sixteen specific points are standard. Figure 4.3 lists several points and their associated bearings:

• North: $360^\circ/000^\circ$
• NNE (North-northeast)
• Northeast: $045^\circ$
• ENE (East-northeast)
• East: $090^\circ$
• ESE (East-southeast)
• Southeast: $135^\circ$
• SSE (South-southeast)

Compass bearings (angular directions) are more accurate than compass points but may be confusing due to variations in north. Map directions are affected by three types of north:

1. Grid North: The direction of the northing lines on an Ordnance Survey map.
2. Magnetic North: The direction showing variations based on the Earth's magnetic field.
3. True North: The specific direction of the North Pole.

Relief, Contour Lines, and Slope Profiles

Relief refers to the shape of the land, which is represented on maps by contour lines. A contour line is an imaginary line joining places of equal height. The spacing of these lines provides information about the land's steepness:

• Flat Land: Indicated by contour lines spaced far apart.
• Steep Land: Indicated by contour lines placed very close together. When the terrain is too steep for contour lines, a distinct symbol for a cliff is used.
• Concave Slope: Suggested when contour lines are close together at the top and become further apart lower down.
• Convex Slope: Suggested when contour lines are far apart at the top and close together at the bottom (as seen in Figure 4.4).

Figure 4.4 illustrates these patterns using the Marmolada Glacier and Lago di Fadala in the Dolomites, northeastern Italy. Figure 4.5 shows a cable car extending from Lago di Fadala to the Marmolada Glacier.

Calculating Gradient

The gradient of a slope represents its steepness. While contour patterns provide a rough idea of gradient, accurate measurement requires two specific values: the vertical difference ($H$) between two points (determined via contour lines or spot heights) and the horizontal distance ($D$) between those two places. Note that horizontal distance may not always be a straight line, as in the case of a meandering stream. It is vital to use the same units for both vertical and horizontal measurements during calculation. There are two primary ways to express gradient:

1. As a Ratio ($1:X$): Divide the horizontal distance ($D$) by the vertical height discrepancy ($H$). If the result is $10$, the gradient is expressed as $1:10$ (‘one in ten’), meaning that for every $10\,\text{metres}$ of horizontal travel, the land rises or drops by $1\,\text{metre}$.

2. As a Percentage: Divide the height ($H$) by the horizontal distance ($D$) and multiply by $100\%$. The formula is: $\left(\frac{H}{D}\right) \times 100\%$.

Activities & Discussion

Based on the OS map of Jamaica (Figure 4.2), the following tasks and questions investigate geographic and mathematical skills:

1. How far is it (a) in a straight line and (b) by road from the school in Goodwill to the school in the middle of Dundee?
2. What is the length of the coastline (to the nearest kilometre) as shown on the map extract?
3. Approximately how long is the airstrip?
4. How wide is (a) the coral in Long Bay and (b) the mangrove forest between Minto and Salt Marsh?
5. What is the six-figure grid reference for (a) the two schools at Dundee and (b) Greenwood Great House?
6. What is found at $705023$?
7. Give the four-figure grid reference for Chatham and for Davis Town.
8. Suggest reasons why there is an airstrip in grid square $6905$.
9. In what direction is (a) Long Bay from Davis Town and (b) Goodwill from Rose Hill?
10. Using the provided information, copy Figure 4.3 and complete the missing compass points.