General Navigation - Lines on the Earth Flashcards
What do all children know about the shortest distance between two points?
It is a straight line.
How might children define a straight line?
As a line that does not bend or deviate or perhaps a line that has a constant direction.
What do we find about the definition of a straight line when looking at lines on the Earth?
The definition is no good; there are lines of constant direction, but they are not the shortest distance between two points.
What must we look back at to find out why lines of constant direction are not the shortest distance between two points?
The way direction itself is described.
How is direction in navigation measured?
As an angle from a datum.
What causes the change of direction on a straight line on the Earth?
The converging meridians.
What is the effect called when the change of direction on a straight line is a result of the converging meridians?
Convergency.
Where are true directions most obvious according to the diagram?
Near the pole itself.
What are directions referenced to the geographic north pole called?
True directions.
How are directions measured?
In degrees in a clockwise direction from the north datum.
How are true directions shown?
With the letter T after the degrees sign, as in 070°T.
What is the proper name for lines that, if extended, would form circumferences on the Earth?
Great circles.
What do great circle tracks mark?
The shortest distance between two points.
What do great circles usually have because of convergency?
A changing track direction along their length.
What tracks are considered great circle tracks?
Tracks that run north/south along a meridian and the equator.
What are small circles?
Any circle that is not a great circle, such as parallels of latitude.
What is true about the plane of a small circle?
It does not pass through the center of the sphere, and its radius is less than the radius of the sphere.
What is a great circle?
The intersection of the surface of a sphere and a plane passing through the center of the sphere.
What does a great circle represent on a sphere?
The largest circle that can be drawn on the surface of the sphere, and the shortest distance along the surface between any two points.
What is the shortest distance between two points along the surface of the spherical Earth called?
A geodesic.
How many great circles can connect any two points on Earth?
Only one, unless the points are antipodal (180° apart on the Earth).
What does every great circle do to every other great circle?
Bisects it.
What is the point of greatest latitude on a great circle called?
The vertex.
What happens to the direction of a great circle at its vertices?
The direction changes progressively until the intersection with the equator is reached.
What is an advantage of taking the shortest track between two points using great circle tracks?
They are used for navigation whenever possible.
What is a disadvantage of great circle tracks?
The constantly changing track direction.
What systems are needed to fly great circles?
Inertial navigation systems, FMS, or GPS.
What is convergency?
The change of track direction between two points.
On what is convergency dependent?
Latitude and how far we travel.
What is the formula to calculate convergency?
Convergency = change of longitude x sine mean latitude.
How does the convergency formula work best?
For calculations between two positions relatively close to each other (within 30° difference of longitude).
What happens to convergency at the equator?
It is zero because the meridians are parallel.
How can convergency be tested for the poles?
Convergency equals the change of longitude.
What happens if you change your longitude by 180°?
You change your track direction from north to south.
How do you find the mean latitude?
Add the two latitudes together then divide by two.
How do you calculate convergency?
Convergency = change of longitude x sine mean latitude.
How do great circle tracks change direction over long distances?
More significantly than over short distances.
How do you find the convergency between London (51°30’N 000° 00’W) and Bristol (51°30’N 002°30’W)?
Use the formula: convergency = change of longitude x sine mean latitude.
How does convergency affect short distances?
It is minimal.
What must you do to calculate the final track direction?
Calculate the difference between the initial great circle track direction and the convergency.
Are you expected to calculate convergency between a point in the northern hemisphere and a point in the southern hemisphere?
No.
What does navigation along great circles require?
Advanced navigation equipment.
What can aircraft that do not have advanced navigation equipment only fly?
A constant direction between two points.
What is true about lines drawn with a constant direction compared to great circles?
They are longer tracks than the great circle.
When can the rhumb line be used for plotting the course of an aircraft?
Over the Earth’s surface at low latitudes or over short distances.
When is the great circle route significantly shorter than the rhumb line?
Over longer distances and/or at higher latitudes.
How does the distance compare for an East-West passage at 20 degrees north for great circle and rhumb line?
Great circle distance is 4997 nautical miles (8042 km), rhumb line distance is 5074 nautical miles (8166 km), about 1.5% further.
What is a more extreme case for rhumb line vs great circle distance?
Air route between New York and Hong Kong. Rhumb line path is 9700 nautical miles (18,000 km), great circle route over North Pole is 7000 nautical miles (13,000 km), 5 1/2 hours less flying time.
Where does the rhumb line always lie compared to the great circle?
On the equatorial side of the great circle.
What is the definition of a rhumb line?
A line of constant direction.
What is the conversion angle between the great circle and rhumb line tracks at either end?
Half the convergency.
What is the formula for the conversion angle?
Conversion angle = 1/2 convergency.
What are the basic rules for drawing sketch diagrams for great circles?
Draw the meridians sloping in to the top in the northern hemisphere and sloping out in the southern hemisphere; look at the given track, if it is generally easterly draw it left to right, if generally westerly draw it right to left; put in the angle you are told about and check it looks roughly correct; make sure the great circle is poleward of the rhumb line.
What are great circles?
The shortest distance between two points with a constantly changing track direction except for meridians and the equator.
What are rhumb lines?
Lines with a constant track direction.
What is convergency?
Change of longitude x sine mean latitude.
What is the conversion angle?
1/2 convergency.
How do rhumb lines compare to great circles?
Rhumb lines lie on the equatorial side of great circles and never follow the same path over the Earth as great circles except for meridians and the equator.
