ATPL General Navigation - Class 8: The Mercator.

Summary

This educational video explores the common Mercator projection used in maps like Google Maps, explaining its historical development by the Belgian cartographer Gerhardus Mercator in the 1500s. It highlights the projection's distortion of size and shape at higher latitudes, using Greenland's misleading representation compared to Africa as an example. The video delves into the mathematical principles behind the projection, including scale expansion and the cosine formula to calculate scale changes with latitude. It also discusses the projection's utility for navigation at sea, its limitations at high latitudes, and its properties in displaying true angles and rhumb lines, despite not being ideal for accurate global representation.

Takeaways

• 🗺️ The script discusses the inaccuracies in map representations, specifically pointing out that Greenland appears massive on maps, similar in size to Africa, which is not accurate.
• 📚 The most common type of map projection is the Mercator projection, which is widely used, including by Google Maps, despite its distortions.
• 🧭 Mercator projection was developed in the 1500s by a Belgian cartographer, Gerhardus Mercator, to aid navigation at sea by allowing ships to steer a constant track.
• 🌐 The Mercator projection uses a cylindrical projection with the great circle of tangency at the equator, which results in distortions as one moves away from the equator.
• 📏 The scale of the Mercator projection expands as latitude increases, causing areas far from the equator, like Greenland, to appear larger than they actually are.
• 🌍 The distortion of the Mercator projection means that Africa, which is 14 times larger than Greenland, appears similar in size to Greenland on such maps.
• ⚖️ The script explains how to calculate the scale change at different latitudes using the cosine equation, which is crucial for understanding the level of distortion.
• 🔍 The Mercator projection is not useful for navigation at high latitudes (above 70 degrees north or south) but is suitable for equatorial regions.
• 📐 The script introduces an ABBA formula to compare scales or distances at different latitudes, which is a simplified method to understand scale changes.
• 🛰️ The Mercator projection does not account for the convergence of longitude lines, which means it does not accurately represent the shape of great circle routes compared to rhumb lines.
• 📈 The video concludes by summarizing the properties of the Mercator projection, noting its usefulness within a certain latitude range and its limitations outside of that.

Q & A

Why does Greenland appear much larger than it actually is on most maps?

Greenland appears much larger on maps because of the Mercator projection, which distorts sizes as you move further from the equator. This causes regions near the poles to appear much larger than they are in reality.

Who developed the Mercator projection and when?

The Mercator projection was developed by a Belgian cartographer named Gerardus Mercator in the 1500s.

What was the original purpose of the Mercator projection?

The original purpose of the Mercator projection was to aid navigation at sea by allowing ships to steer a constant track or rhumb line rather than the shortest possible great circle track.

What are the drawbacks of the Mercator projection?

The drawbacks of the Mercator projection include significant distortion of sizes and distances as you move away from the equator, making high-latitude regions appear much larger than they are.

How does the Mercator projection distort the lines of latitude and longitude?

In the Mercator projection, the lines of latitude become more spaced out as you move from the equator, and the lines of longitude are displayed as parallel lines rather than converging at the poles. This causes the scale to expand and objects to appear larger.

What is the formula to calculate the scale at different latitudes in the Mercator projection?

The formula to calculate the scale at different latitudes in the Mercator projection is: Scale at latitude = Scale at equator / cosine(latitude).

Why is the Mercator projection not useful for navigation at high latitudes?

The Mercator projection is not useful for navigation at high latitudes (above 70 degrees north or south) because the scale expansion becomes too large, leading to significant inaccuracies.

What is a rhumb line and how does it appear on a Mercator map?

A rhumb line is a path of constant bearing, which appears as a straight line on a Mercator map. This was useful for navigation as it allowed for a constant compass direction.

What is the difference between a rhumb line and a great circle route on a Mercator projection?

On a Mercator projection, a rhumb line appears as a straight line, while a great circle route, which is the shortest path between two points on a sphere, appears as a curved line that is closer to the poles.

In which regions is the Mercator projection considered accurate enough for use?

The Mercator projection is considered accurate enough for use within about 10 degrees north and 10 degrees south of the equator, where the scale expansion is minimal and the distortion is less than 1%.

What properties make the Mercator projection partly suitable as an 'ideal' chart for certain uses?

The Mercator projection displays latitude and longitude lines intersecting at 90 degrees, accurately displays distances and angles within a limited equatorial region, can display symbols for navigation, and shows rhumb lines as straight. However, it does not have a constant scale and is not accurate at high latitudes.