ATPL General Navigation - Class 4: Convergency.

Summary

In this educational video, Grant explores the concept of great circles, the shortest paths between two points on the Earth's surface, and their constantly changing direction. He explains how the convergence of meridians, which depends on latitude, affects the great circle track using simple geometry and the sine function. The video demonstrates how to calculate the change in direction, known as convergence, and how to switch between great circle and rhumb line tracks. It also clarifies the differences and similarities between the two, including the fact that they only match at the midpoint of a journey and that the rhumb line is always closer to the equator.

Takeaways

• 🌐 A great circle is the shortest possible distance between two points on Earth, and its direction changes as you travel along it.
• 📐 The direction of a great circle can be determined by simple geometry, comparing angles at different points along the path.
• 🌍 The change in direction of a great circle is influenced by the convergence of lines of longitude, which varies with latitude.
• 📈 Convergence is zero at the equator and increases towards the poles, and it can be calculated using the sine function of the latitude times the change in longitude.
• 🧭 The great circle bearing can be calculated by adding the convergence to the original angle at the starting point.
• 🔢 The average great circle track can be found by averaging the bearings at two points, which is equivalent to the rhumb line track between them.
• 🌟 The rhumb line is a path with a constant direction, which is always closer to the equator than the great circle path.
• 🔄 The highest latitude of a great circle route is reached when the great circle track is at 90 or 270 degrees, indicating purely east or west travel.
• ⚖️ The conversion angle, which is half the convergence, is used to switch between a great circle and a rhumb line.
• 🛰️ The relative position of 'north' changes as you move along a great circle, which is why the direction is constantly changing.
• 📊 The sine function is key to understanding convergence, as it provides a mathematical model that starts at 0 at the equator and reaches 1 at the poles.

Q & A

What is a great circle and why does its direction constantly change?

A great circle is the shortest possible path between two points on the surface of the Earth. Its direction constantly changes because as you move along the circle, the relative position of 'north' changes, necessitating a continuous adjustment in direction to maintain the shortest path.

How can the angle difference at two points on a great circle be determined?

The angle difference at two points on a great circle can be determined using simple geometry by creating parallel lines and comparing the angles at each point. The angle at point B is found by adding the angle at point A to the change in longitude and the convergence angle.

What is convergence and how does it relate to the change in direction of a great circle?

Convergence is the angle by which the direction of a great circle changes as it moves from one meridian to another. It depends on the latitude and the change in longitude between two points, affecting how much the direction of the great circle needs to adjust.

Why is the sine function used to calculate convergence?

The sine function is used to calculate convergence because it provides a value that starts at 0 at the equator and increases to 1 at the poles, which corresponds to the change in convergence from 0 degrees at the equator to full convergence at the poles.

How is the average great circle track calculated?

The average great circle track is calculated by taking the average of the initial and final great circle bearings. This average is equivalent to the rhumb line track between the two points.

What is a rhumb line and how does it differ from a great circle?

A rhumb line is a path that crosses all meridians at a constant angle, maintaining a constant direction from start to finish. It differs from a great circle, which changes direction as it follows the shortest path between two points.

At what point are the great circle track and the rhumb line track the same?

The great circle track and the rhumb line track are the same at the midpoint between two longitudes, where the lines are parallel.

What is the conversion angle and how is it related to convergence?

The conversion angle is the difference between the rhumb line track and the great circle track. It is equal to 0.5 times the convergence, providing a way to convert between the two types of tracks.

How does the latitude affect the convergence of lines of longitude?

The latitude affects the convergence of lines of longitude because the lines converge more as you move from the equator towards the poles. At the equator, there is zero convergence, while at the poles, there is full convergence.

What is the relationship between the great circle track and the change in longitude at the poles?

At the poles, the convergence is equal to the change in longitude. This means that the angle of the great circle track at the poles is determined solely by the change in longitude between the two points.