ATPL General Navigation - Class 3: Great Circles and Rhumb Lines.

Summary

In this educational video, Grant explains the concept of great circles and rhumb lines in aviation. Great circles, which are the shortest paths between two points on a perfect sphere, are often used in flight planning despite the Earth's slight imperfections. These paths appear as curved lines on maps due to the constantly changing direction relative to true north. In contrast, rhumb lines offer a constant track, making them easier to navigate but resulting in longer routes. The video clarifies the difference between the two, noting that at the equator and along meridians of longitude, a rhumb line and a great circle coincide, providing valuable insights for understanding flight paths.

Takeaways

• 🌐 Great circles are the shortest possible distances between two points on the surface of a perfect sphere, and they are often considered equivalent to geodesics on Earth due to its near-spherical shape.
• 🌍 The Earth is not a perfect sphere, but for practical purposes in aviation, this slight difference is usually ignored, treating geodesics and great circles as the same.
• 📍 Great circles always pass through the center of the Earth, which means they cross the equator at some point, known as a 'node'.
• 🔺 The highest point of a great circle's latitude is called the 'vertex', and it is where the circle reaches its maximum latitude before descending on the other side.
• 🔄 The direction of a great circle route is constantly changing because it is a straight line on a curved surface, which results in a variable track.
• 🧭 On a map with a fixed north reference, a great circle route would appear as a curved line due to the constantly changing direction.
• ✈️ The curved line seen on long-haul flight progress maps is actually a great circle route, which is the most direct path between two points on Earth.
• 🛫 A rhumb line, in contrast to a great circle, maintains a constant track angle, making it easier to navigate but resulting in a longer route.
• 🌡️ Rhumb lines are only the same as great circles when they follow a line of latitude or a meridian of longitude, such as at the equator.
• 🌎 The difference in distance between a rhumb line and a great circle becomes more pronounced the further one travels from the equator and the greater the change in longitude.

Q & A

Why does the flight path on a long-haul flight map appear as a curved line instead of a straight one?

The flight path on a long-haul flight map appears as a curved line because it follows a great circle route, which is the shortest distance between two points on the Earth's surface, and not a straight line.

What is the definition of a great circle?

A great circle is a circle on the surface of a sphere that has the same center as the sphere, and it represents the shortest path between two points on the surface of the Earth.

How does a great circle differ from a geodesic?

A great circle is the shortest path on a perfect sphere, while a geodesic is the shortest path on the Earth's surface, which is slightly squished. In aviation, they are often considered the same due to the minuscule difference.

What is the term used for the point where a great circle crosses the equator?

The point where a great circle crosses the equator is called a 'node'.

What is the highest point of a great circle called?

The highest point of a great circle, where it reaches its maximum latitude before descending on the other side, is called the 'vertex'.

Why is the direction of a great circle route constantly changing?

The direction of a great circle route constantly changes because it is a straight line on a curved surface, so as the plane travels along the great circle, its angle relative to the lines of latitude changes.

How does a rhumb line differ from a great circle?

A rhumb line differs from a great circle in that it maintains a constant track angle relative to true or magnetic north, making it easier to navigate but resulting in a longer route compared to a great circle.

Under what conditions is a rhumb line the same as a great circle?

A rhumb line is the same as a great circle when the path is along the equator or a meridian of longitude, as these are the only cases where the track angle remains constant.

Why do pilots prefer to follow a rhumb line over a great circle?

Pilots may prefer to follow a rhumb line because it allows for a constant track angle, making navigation simpler without the need to constantly change direction as with a great circle.

What is the main disadvantage of following a rhumb line compared to a great circle?

The main disadvantage of following a rhumb line compared to a great circle is that it is a longer route, which can result in increased fuel consumption and travel time.

How can one visualize the difference between a great circle and a rhumb line?

One can visualize the difference by considering a map where north is always up; a great circle would appear as a curved line due to the constantly changing track, while a rhumb line would appear as a straight line with a constant track angle.

Outlines

00:00

🌐 Understanding Great Circles and Rhumb Lines

This paragraph explains the concept of great circles and rhumb lines in the context of long-haul flights. A great circle is the shortest path between two points on the surface of the Earth, which is why planes appear to follow a curved path on flight maps. The Earth's shape is not a perfect sphere, but for practical purposes in aviation, it is simplified as such. A great circle always passes through the Earth's center, crossing the equator at a point called the 'node' and reaching its highest latitude at the 'vertex'. The direction of a great circle route constantly changes, resulting in a curved line on a map where north is always up. This is in contrast to a rhumb line, which maintains a constant track, making it easier to navigate but resulting in a longer route. The paragraph also mentions that at the equator and along meridians of longitude, a rhumb line and a great circle coincide.

05:01

🧭 The Dynamics of Great Circle and Rhumb Line Navigation

The second paragraph delves deeper into the navigational aspects of great circles and rhumb lines. It emphasizes that while following a great circle, the track referenced to true north changes continuously, which is why the flight path appears curved on maps. Conversely, a rhumb line maintains the same track throughout the journey, simplifying the flight path to a straight line when following a line of latitude. At the equator and along longitude lines, a rhumb line and a great circle are identical. This paragraph reinforces the idea that while great circles provide the shortest distance between two points, they require constant course adjustments, whereas rhumb lines, though longer, offer a more straightforward navigational path.

Keywords

💡Geodesic

A geodesic is the shortest possible path between two points on the surface of a sphere, such as the Earth. In the context of the video, it is mentioned that a geodesic and a great circle are almost the same, except that a geodesic takes into account the Earth's slight oblateness, while a great circle is used for a perfect sphere. The script simplifies the concept for aviation purposes, treating geodesics and great circles as equivalent.

💡Great Circle

A great circle is a circle on the surface of a sphere that has the same center as the sphere itself. It represents the shortest path between two points on the sphere, which is why it is used to describe the most efficient route for an airplane to take. The video explains that, despite the Earth not being a perfect sphere, great circles are used in aviation to represent the most direct route, with the understanding that the slight difference due to Earth's shape is negligible.

💡Vertex

In the context of great circles, the vertex refers to the highest point that the great circle reaches before it starts descending towards the other side of the Earth. The video script uses the vertex to illustrate the changing direction of a great circle route, which is crucial for understanding how a plane's course alters as it follows the shortest path between two points.

💡Node

A node is the point where a great circle crosses the equator. The script mentions the node as a specific point on a great circle route, indicating a change in the direction of the flight path as it crosses the Earth's equatorial line and begins to curve towards its destination on the other side.

💡Track

In aviation, a track refers to the actual path or course that an aircraft follows over the ground. The video explains that the track of a great circle route is variable and constantly changing, which is why the flight path appears as a curved line on a map, even though it is the shortest distance between two points.

💡Rhumb Line

A rhumb line, also known as a loxodrome, is a path on the Earth's surface that crosses all meridians of longitude at the same angle. Unlike a great circle, a rhumb line maintains a constant track, which means the direction of travel does not change. The script contrasts rhumb lines with great circles, highlighting that while they are easier to navigate because of their constant direction, they are not the shortest path and thus result in longer flights.

💡Longitude

Longitude refers to imaginary lines that run from the North Pole to the South Pole and are perpendicular to lines of latitude. They are used to measure the east-west position of a point on the Earth's surface. The video script uses longitude to explain how a rhumb line follows a constant track and how great circles cross these lines of longitude at varying angles.

💡Latitude

Latitude is the measurement of distance north or south of the equator, represented by lines that run parallel to the equator. The script explains that a rhumb line can be visualized as following a line of latitude, which is a straightforward path that heads either purely east or purely west.

💡Equator

The equator is an imaginary line that circles the Earth, dividing it into the Northern and Southern Hemispheres. In the script, the equator is mentioned as a special case where a rhumb line and a great circle coincide, meaning they follow the same path.

💡Top-Down View

A top-down view refers to looking at something from above, as if viewing it from directly overhead. The video script uses the concept of a top-down view to illustrate how the track of a great circle changes as it moves from one point to another, providing a visual representation of the flight path's curvature.

Highlights

Explains the concept of great circles and their application in long-haul flights, highlighting the importance of understanding why the plane's path appears curved.

Introduces the idea that a geodesic and a great circle are considered the same in aviation, despite the Earth's imperfection, for the sake of simplicity.

Clarifies that a great circle has to cross over the equator, resulting in a node and a vertex, which are points of special significance in the plane's path.

Describes the variable nature of a great circle's path due to the Earth's curved nature, explaining how it constantly changes direction.

Illustrates the concept of a rum line, which connects two points with a constant track, emphasizing its ease in navigation compared to a great circle.

Explains the main difference between a great circle and a rum line, highlighting that a great circle is the shortest distance between two points on Earth, while a rum line is longer and requires constant direction change.

Discusses the exception where a rum line and a great circle are the same at the equator and following a meridian of longitude.

Explains the practicality of using a great circle for aviation, as it provides the shortest path, despite the path's constant change in direction.

Introduces the concept of a node, where a great circle reaches its highest point, and a vertex, where it crosses the equator, providing a clear understanding of these terms.

Describes the practical application of a great circle in long-haul flight maps, where the reference to north is maintained, leading to a curved appearance.

Explains the concept of a vertex, where a great circle reaches its highest point, and how it is used in navigation to calculate the path of the plane.

Discusses the practicality of using a rum line for navigation, especially at the equator and along meridians of longitude, where it offers the same path as a great circle.

Summarizes the key differences between a geodesic and a great circle, emphasizing that while they are almost the same, a geodesic accounts for the Earth's slight squished nature.

Explains the practicality of using a great circle for aviation, as it provides the shortest distance between two points on Earth, despite the path's constant change in direction.

Introduces the concept of a node, where a great circle crosses the equator, and its significance in the plane's path.

Summarizes the practicality of using a great circle for aviation, emphasizing its use in long-haul flight maps and the constant change in direction it implies.

Explains the practicality of using a rum line for navigation, especially at the equator and along meridians of longitude, where it offers the same path as a great circle.

Transcripts

have you ever wondered why on a

long-haul flight the little map shows

the plane flying along a curved line

instead of just a straight line from

point a to point b

why is the plane wasting so much time

fuel and energy flying along this curved

line instead of just going from point a

to point b

let's find out

[Music]

hi i'm grant and welcome to the third

class in the gnab series

today we're going to be looking at great

circles and run lines what they are and

what the main differences are between

the two

the shortest possible distance between

two points

on the surface of the earth is what is

called a geodesic a great circle will

connect two points

in the shortest possible distance on a

perfect sphere

so that means

that on earth a geodesic and a great

circle are slightly different because a

great circle only applies to a perfect

sphere and the earth is not a perfect

sphere but

in hpl's and in aviation in general we

like to simplify things

so we kind of ignore this squished

nature because it's only minuscule and

we would call a geodesic and a great

circle as being the same thing

so great circles by their very nature

have to have their center at the center

of the earth so it means at some point

they must cross over the equator and

this point that that happens is called a

node

and where the great circle reaches its

highest or lowest latitude and then

starts returning back down the other

side we call this highest point the

vertex

so due to a great circle

being a straight line on a curved

surface

the track of the great circle is

variable it's constantly changing so

what do i mean by that

if we take a look

at a top down view from this point a to

this point b

we start off with a track always

reference to north

of 30 degrees

and you see as we travel along the line

of the great circle

the reference point of north slowly

comes around

but we still reference it to north so

about halfway we're looking at the great

circle track of being about 90

and then out the other side at b

it's going to be much larger than 30

it's going to be

much larger than 90 and that's what

we're going to look at in the next class

how to actually calculate this value

so because the great circle doesn't

cross every line of latitude at exactly

the same angle that means that

its

direction is constantly changing and if

you think of this as a

map where

north is always up

if you've got a constantly changing

track you would see a curved line

which is why when you look at the

progress maps on long-haul flights it

appears to be a curved line that you're

flying across

it's actually a great circle but instead

of changing the reference for north like

we're doing in this case

the reference from north stays the same

and our line curves instead

a rum line

is a line that connects two points with

a constant track

this is the main difference between the

great circle and a rum line it makes it

far easier to fly as you don't need to

constantly change your direction to fly

along the right circle you just pop in

one track and then you fly along it but

it is a longer route

apart from the only cases are if you're

at the equator

and if you're following a meridian of

longitude

at that point a rom line and a great

circle are the same thing

so in this example here

the simplest run line would be to follow

a line of latitude around

so you'd follow the line of latitude

around like that

heading purely east or purely west if

you're starting at b you can clearly see

just from this example that that line is

a lot longer than that line

and this difference is more obvious the

further from the equator you go

and the larger the change in longitude

so a very quick one today but in summary

geodesic is almost exactly the same as a

great circle but there is a difference

because a geodesic

is on earth with that slightly squished

nature and a great circle as a perfect

sphere we think of them as being equal

for aviation

when it reaches its highest point it is

called a vertex and when the great

circle crosses the equator that's called

a node

and the great circle being the shortest

distance between two points on the

surface of the earth

that means that if we follow a great

circle

our track is always meant referenced to

north

so our track is going to constantly

change

as we fly along the great circle

we're always going to have our compass

pointing north and as we move along it's

going to constantly point north and our

track is going to change

the in the opposite to that or something

a bit different is a rum line

run lines follow

the same track the whole time and the

easiest way to think of it is just

following a line of latitude from one

point to the other at the equator and

along the lines of longitude a rum line

and a great circle are actually the same

thing

you