how to calculate course between two positions in navigation

by Terrill Dooley DDS 5 min read

By applying simple trigonometry principles the course and distance between the two positions can be determined. The formulae for determining the values are :- tan course = difference in Longitude / difference in Meridional Parts

Here is the formula to find the second point, when first point, bearing and distance is known:
  1. latitude of second point = la2 = asin(sin la1 * cos Ad + cos la1 * sin Ad * cos θ), and.
  2. longitude of second point = lo2 = lo1 + atan2(sin θ * sin Ad * cos la1 , cos Ad – sin la1 * sin la2)

Full Answer

What is the meaning of course in navigation?

In navigation, the course of a vessel or aircraft is the cardinal direction in which the craft is to be steered. The course is to be distinguished from the heading, which is the compass direction in which the craft's bow or nose is pointed. 1 Course, track, route and heading.

What is the difference between heading and course in navigation?

Course (navigation) The course is to be distinguished from the heading, which is the compass direction in which the craft's bow or nose is pointed. The difference between the course and heading, known as the drift, is due to the motion of the underlying medium, the air or water, or other effects like skidding or slipping.

What is a course plot in navigation?

Instruments used to plot a course on a nautical or aeronautical chart. In navigation, the course of a vessel or aircraft is the cardinal direction in which the craft is to be steered. The course is to be distinguished from the heading, which is the compass direction in which the craft's bow or nose is pointed.

How does a navigator set a course to steer?

Because water currents or wind can cause a craft to drift off course, a navigator sets a course to steer that compensates for drift. The helmsman or pilot points the craft on a heading that corresponds to the course to steer.

How do you find the distance between two positions?

How to find the distance between two points?Get the coordinates of both points in space.Subtract the x-coordinates of one point from the other, same for the y components.Square both results separately.Sum the values you got in the previous step.Find the square root of the result above.

How do you find the distance between bearings and coordinates?

0:556:23How to Calculate coordinates from distance and bearing ... - YouTubeYouTubeStart of suggested clipEnd of suggested clipLine and line parallel to the North line it will be this much of B D will be the latitude. TheMoreLine and line parallel to the North line it will be this much of B D will be the latitude. The departure is calculated by L sine theta and the latitude is calculated by L cos theta.

What is the distance between two longitude?

A degree of longitude is widest at the equator with a distance of 69.172 miles (111.321 kilometers). The distance gradually shrinks to zero as they meet at the poles. At 40 degrees north or south, the distance between a degree of longitude is 53 miles (85 kilometers).

What is the distance between points?

Distance between two points is the length of the line segment that connects the two given points. Distance between two points in coordinate geometry can be calculated by finding the length of the line segment joining the given coordinates.

What happens when two LOPs intersect?

If two LOPs intersect we can construct a position fix → the ship's position on the earth. Often, however, a triangle occurs when a third LOP is added in the construction. This indicates that there are errors involved in at least one of the bearings taken.

How to obtain a LOP without a compass?

A precise way to obtain a LOP – and without a compass – is to locate two aids to navigation in line. The map of Wildrooz island#N#above#N#on the right shows four examples of ranges, each consisting of two aids to navigation:

How many LOPs are needed to fix a ship?

Line Of Position (LOP): the locus of points along which a ship's position must lie. A minimum of two LOPs are necessary to establish a fix. It is standard practice to use at least three LOPs when obtaining a fix, to guard against the false security, and add accuracy.

What is the modern chart?

The modern chart shows us positions of many recognizable aids to navigation#N#aids to navigation#N#like churches and lighthouses, which facilitate the approach to a coastal area. This concept originated from a chart by Waghenaer and proved a milestone in the development of European cartography.

When wind blows perpendicular against the exposed surfaces of a yacht, it will cause a motion to

When wind blows perpendicular against the exposed surfaces of a yacht it will cause a motion to leeward which can be counteracted by steering upwind → (CTS) Course To Steer.

What is the magnetic variation of the safe water buoy?

Our COG to approach the safe water buoy#N#safe water buoy#N#is 220°; the local magnetic variation is West 5°, meaning 5°; and since the wind is from starboard we add leeway 8°.

What is the difference between latitude and longitude?

Latitude: position property defined by the number of degrees north or south of the equator, varies from 0° to 90°. Longitude: position property defined by the number of degrees east or west of the prime meridian, varies from 0° to 180°. Position: latitude first and longitude second.

How long is 1 nautical mile?

In 1929, the international community agreed on the definition of 1 international nautical mile as 1852 metres, which is roughly the average length of one minute of latitude i.e. one minute of arc along a line of longitude (a meridian). Or to put it shortly: 1 NM = 1'.

What was the obvious place to divide the Northern and Southern Hemispheres?

The obvious place to divide the Northern and Southern Hemispheres was the equator. But the division of the Eastern and Western hemispheres was the source of much political turmoil. Greenwich (England) won, placing for example The Netherlands in the Eastern and Ireland in the Western Hemisphere.

Which two parallels form great circles?

Meridians converge at the poles, whereas parallels run parallel to each other and never meet. All meridians and the equator – which is the biggest parallel – form great circles, and the remaining parallels form so-called small circles. A great circle divides the earth in two exact halves, see glossary below.

When did Portugal use latitude and longitude?

The use of latitude and longitude was understood since the time of Ptolemy the second century CE. During the fifteenth century Portugal led the European world in sea exploration. The golden age of discovery for Portugal lasted almost a century until the Dutch eventually seized their trade routes from them.

What is the time zone in the Northern Hemisphere?

Northern hemisphere, centred on Greenwich and the Prime Meridian. When it is 12:00 UTC ( international standard time) – anywhere in the world – it is 12:00 Local Time in Greenwich and 24:00 Local Time at the other side of the planet: 180° E or 180° W: roughly the International Date Line.

What is the name of the line that crosses all the meridians at the same angle?

The straight line on the Mercator map turns on the globe into the endlessly spinning spiral to the poles. That line is called loxodrome, which means "slanting run" in Greek.

Is the mercator projection still used?

Mercator projection is still widely used for navigational maps. Even the ancient sailors noticed that the rhumb line is not always the shortest way between the two points, and it's self-evident for the long distances.

Where is longitude measured?

Longitude is similar to latitude but it is measured vertically (east - west) from the meridian line that runs through Greenwich, England. The longitude range runs from 0° - 180°. The meridian that is on the opposite side of the globe from Greenwich is known as the International Date Line and is 180° from Greenwich.

How long does it take to sail a 20 mile boat?

You count the miles and from there gauge how long the day’s sailing will take. A 10 mile route might take a couple of hours while a 20 mile route may take 4-6 depending on the conditions and whether you’re only out to get to the destination or to enjoy the journey itself.

How many satellites does GPS use?

The Global Positioning System (GPS) computes your position using up to eight satellites in space. Your GPS unit will have an ultra-accurate clock and will compare time signals from each satellite, the difference in time they tell compared to your GPS system’s time allowing it to calculate your vertical and horizontal position relative to the satellites.

What is the shifting of the magnetic pole?

The shifting of the magnetic pole is known as ‘ Variation ’. Variation is predictable and using your chart’s compass rose you can find the Variation every year for a given location. This might be 7 degrees West for example. In that case, in order to head due North you would have to adjust your course by 7 degrees East.

What is the magnetic north?

Magnetic North is the top of a vast magnetic field that runs from hundreds of miles above the South Pole to hundreds of miles above the North Pole. It protects the Earth from cosmic rays that could otherwise destroy our electronics and give us skin cancers.

Can you see the world on a chart of the Ionian Sea?

On a chart of the Aegean and Ionian Seas, you will be able to see the world you’re travelling on a flat projection. In most cases these days you will use an electronic chart, whether a Navionics app that runs using the GPS in your tablet or phone, or on the vessel’s electronic navigation system.

What is a compass for navigation?

Generally a ‘compass’ is an instrument, which gives you the direction information for navigation . You must refer Haversine distance formula before going through this post.

What is the difference between bearing and heading?

While Heading is an angle or direction where you are currently navigating in.

What is bearing angle?

Bearing or heading angle is used to define navigation generally in the field of aircraft or marine or Vehicle navigation or while working for land surveying.

Can you share data related to bearing?

You are free to share more data related to bearing or any thing that you uses to calculate bearing and how you use navigation with bearing. If you find anything difficulty to understand the bearing calculation, you may comment below, so that we will discuss further on finding bearing or heading angle.

What is the term for the method used to solve the problem of course and distance between two positions?

Sailing is the term used in the maritime world to describe the method used to solve the problem of course and distance between two positions. In broad terms, there are two main types of sailing , namely, the Rhumb Line sailing and the Great Circle sailing.

What is the track on the Rhumb Line?

The constant course track that appears like a spiral on the Earth spheriod is called a Rhumb Line track.

What is the bearing of the destination airport off of your departure airport?

In this instance the bearing of the destination airport off of your departing airport is also 090. This is also the direction you want to track the airplane ...

What is the difference between a track and a heading?

Heading is the direction the airplane is pointed, whereas track is the actual direction of the airplane tracking across the ground. Bearing is the angle between any two points, whereas course is your intended path of travel to your destination. In the rest of this post we’ll elaborate on each of these points and then also provide ...

Why is bearing confusing?

Bearing can be confusing sometimes because has some overlap with course. Bearing is simply the angle or direction between two points. A practical application of this is in VOR navigation. It’s a common thing to hear someone say “we are bearing 090 from the station”.

What happens to your bearing when you fly from one airport to another?

If you are going directly from one airport to the other, your course and bearing will be the same along the route of flight. If you are flying from an airport to a VOR to another airport, your course will change in each leg, as will your bearing.

What is the meaning of heading in airplanes?

By definition though, heading is actually just the direction that the nose is pointed. This does not factor for wind, or the actual movement of the airplane across the ground.

Is "on course heading" a misleading word?

It’s confusing because they are often (incorrectly) used interchangeably in conversation: Heading, bearing, course, and track. Even correctly used by ATC, “on course heading” is still a little misleading because below you’ll see they’re practically referring to “course” and not “heading”.

Does GPS use RNAV?

In contrast, GPS RNAV systems may use an algorithm, which applies the local magnetic variation and may produce small differences in the displayed course. However, both methods of navigation should produce the same desired ground track when using approved, IFR navigation system.

image