When was the kamal invented

The gyrocompass is more accurate than the magnetic compass because it points in the direction of the earth's axis and cannot be disturbed by nearby metal such as the hull of a ship. The first radio was created in Italy. They are used on board ships to communicate via long-distances. Echo sounding was invented by Alexander Behm. Echo sounding is a device that determines depth and distance by using sound waves.

It is currently used on most modern ships. In , researchers in the Naval Research Lavatory started experimenting with the way that radio waves would bounce off objects, after they noticed that occasionally other ships would block the path of the radio while at sea. In Robert Page created an instrument able to detect nearby aircraft and ships for navy boats.

The first long-range navigation device was created so a ships position could be located from land by using radio waves. With the introduction of an electronic chart system, it has become easier to navigate by pinpointing locations and attaining directions. ROTIs are mostly used upon naval ships. In Section V Regulation 19 of the Convention, it states that "All ships of 50, gross tonnage and upwards shall, in addition to meeting the requirements of paragraph 2.

January GPS was created when 22 satellites were built specifically for the purpose of sending position and coordinate data to ships at sea. These satellites have been replaced since, as they eventually stopped working.

Modern satellites launched into orbit around Earth mean that countries around the world have access to service such as internet and data, which can be used to transfer information across the globe instantaneously. GPS, or global positioning system, is a satellite-based navigation system. The GPS system is controlled by the U. The angle between an object in the sky and the horizon is the altitude or elevation. In navigation, this is also called the bearing. The meridian is the line that connects North and South at the horizon and passes the zenith.

Figure 4: Illustration of the horizontal coordinate system. At the equator, it would just appear at the horizon, i. Figure 5 combines all three mentioned coordinate systems.

For a given observer at any latitude on Earth, the local horizontal coordinate system touches the terrestrial spherical polar coordinate system at a single tangent point. The sketch demonstrates that the elevation of the celestial north pole, also called the pole height, is exactly the northern latitude of the observer on Earth. Figure 5: When combining the three coordinate systems terrestrial spherical, celestial equatorial, local horizontal , it becomes clear that the latitude of the observer is exactly the elevation of the celestial pole, also known as the pole height Credit: M.

Nielbock, own work. From this we can conclude that if we measure the elevation of Polaris, we can determine our latitude on Earth with reasonable precision. The concept of the kamal relies on the relations within triangles. Those are very simple geometric constructs that already the ancient Greeks have been working with. This depends on whether the angles are measured in degrees or radians. One radian is defined as the angle that is subtended by an arc whose length is the same as the radius of the underlying circle.

The sides of a triangle and its angles are connected via trigonometric functions, e. The hypotenuse is the side of a triangle opposite of the right angle. In Figure 6, it is c. The other sides are called legs or catheti. The leg opposite to a given angle is called the adjacent leg, while the other is the opposed leg.

In a right-angled triangle, the relations between the legs and the hypotenuse are expressed as trigonometric functions of the angles. The Pythagorean Theorem tells us something about the relations between the three legs of a right-angled triangle.

It is named after the ancient Greek mathematician Pythagoras and says that the sum of the squares of the catheti is equal to the square of the hypotenuse. Early seafaring peoples often navigated along coastlines before sophisticated navigational skills were developed and tools were invented. Sailing directions helped to identify coastal landmarks Hertel, To some extent, their knowledge about winds and currents helped them to cross short distances, like e.

Soon, the navigators realised that celestial objects, especially stars, can be used to keep the course of a ship. A very notable and well documented long distance voyage has been passed on by ancient authors and scholars like Strabo, Pliny and Diodorus of Sicily. Pytheas already used a gnomon or a sundial, which allowed him to determine his latitude and measure the time during his voyage Nansen, At these times, the technique of sailing along a parallel of the equator or latitude was used by observing circumpolar stars.

The concept of latitudes in the sense of angular distances from the equator was probably not known. However, it was soon realised that when looking at the night sky, some stars within a certain radius around the celestial poles never set; they are circumpolar.

When sailing north or south, sailors observe that the celestial pole changes, too, and with it the circumpolar radius. For them, it was sufficient to realise the connection between the elevation of stars and their course. Navigators had navigational documents that listed seaports together with the elevation of known stars.

On order to reach the port, they simply sailed north or south until they reached the corresponding latitude and then continued west or east. Its purpose is to measure stellar elevations without the notion of angles.

If you stretch out your arm, one finger subtends an angle. This method appears to have been the earliest technique to determine the elevation of stars. Figure 7: A simple wooden kamal. This method was standardised by using a wooden plate, originally sized roughly 5 cm x 2. When held at various distances, the kamal subtends different angles between the horizon and the stars Figure 8.

Knots located at different positions along the cord denote the elevations of stars and, consequently, the latitude of various ports. Figure 8: Illustration of how the kamal was used to measure the elevation of a star, in this case Polaris. The lower edge was aligned with the horizon. Then, the distance between the eyes and the kamal was modified until the upper edge touched the star. The distance was set by knots tied into the cord that was held between the mouth and the kamal. The knots indicated elevations of stars Credit: M.

When Vasco da Gama set out to find the sea passage from Europe to India in , he stopped at the Eastern African port of Melinde now: Malindi , where the local Muslim Sheikh provided him with a skilled navigator of the Indian Ocean to guide him to the shores of India. This navigator used a kamal for finding the sailing directions Launer, Since the latitudes the Arabian sailors crossed during their passages through the Arabian and Indian Seas are rather small, the mentioned size of the kamal is sufficient.

For higher latitudes, the board must be bigger to avoid very small lengths of the cord to realise such angles. Figure 9: Excerpt of a world map from showing the Indian Ocean. This is realised by a knot in the cord on the side opposite to the kamal board. In this simple configuration we get:. The kamal has a height labelled h. The length of the cord between the eyes and the kamal is labelled l Credit: M.

However, the measurement is done with the cord between the teeth or just in front of the lips. Eyes and mouth are separated by the length d Figure This more realistic approach leads to:. The difference between l and l' can be a few centimetres. A realistic value for d is 7 cm. This geometry is accurate enough for uncertainties inherent to the measuring method. Note that it is always assumed that the kamal board is held in an angle perpendicular to the line of sight, not the cord.

The kamal consists of a parallelogram, usually made from horn or wood, that is attached to a string. There are many different ways to use the kamal. Then, move the parallelogram along the string so that its bottom edge matches with the horizon, and the bottom edge matc hes with whatever star is being targeted.

This star is usually the North Star also called Polaris. The angle of the star is then measured by counting the number of knots between your teeth and the parallelogram. Why isn't the kamal used as much today? The Age of Exploration Inventions Astrolabe. With these dimensions, the following relations hold. Table 1: Dimensions and relations between the angles and lengths of a kamal according to Eq. For each kamal, prepare a thin piece of ply wood approx. If this is not available, a piece of very stiff cardboard of equal size can also be used.

Determine the centre of the board by drawing or scratching two diagonal lines that connect opposite corners. Drill a hole through the centre that is big enough to permit the cord to fit through. It must also be small enough not to let it slide out again after a knot is tied. Figure The kamal after running the cord through the central hole Credit: M.

Tie a knot at one end of the cord and run it through the central hole of the board. The knot should block the cord from sliding through the hole. Now add knots at distances from the board as indicated in Table 1. Be careful to keep the cord straight. You can restrict the number of knots according to the angular range needed for the activities. Remember that the elevation of Polaris corresponds to the latitude. Introduction The worksheets contain Figure 2 star trails.

There are a few questions to be asked that can help students understand the concept of the apparent trajectories of stars. Q: What does this picture show, in particular, where do the bright curved lines come from? A: As the Earth rotates, the stars seem to revolve around a common point. This is the celestial pole. The long exposure enables visualisation of the path of the stars as trails. Q: How does the picture show us that some stars do not set or rise during a full day? A: Many trails can be followed to form a full circle.

One rotation is 24 hours. Q: Can you identify the star that is next to the celestial North Pole? In this picture, it should be close to the centre of rotation.

A: This is Polaris or the North Star. It is the star that produces the smallest trail close to the centre of the trails. Q: Imagine you are at the terrestrial North Pole. Where would Polaris be in the sky? Where would it be if you stood at the equator? A: North Pole: zenith, i. Preparations Find a spot outside with a good view of the northern sky and the horizon.

This activity can be done as soon as the North Star is visible. Therefore, the summer time may not the best season for this activity. Finding Polaris Finding Polaris in the sky is rather simple. As soon as the stars are visible, let the students look at them for a while and ask them if they knew the group of stars that is often called the Big Dipper. It is easy to find in the northern hemisphere as it is always above the horizon.

A video explains this in detail. Measuring the elevation of Polaris Now the students use the kamal. The cord must be kept straight during the measurements. The board must be held with the smaller edges up and down and perpendicular to the line of sight.

Any tilt would compromise the measurement. As shown in Figure 8 provided in the worksheet , the lower edge of the kamal must be aligned with the horizon. Then, the length of the cord is modified until the upper edge touches the star. The alignment with the horizon and the star should be checked again. The students count the number of knots needed to keep the kamal aligned. Counting starts with the knot closest to the board. They may have to interpolate the position between knots.

They write down the number and read the corresponding angle from the list in their worksheet. They will have determined the latitude. Q: Why are the results not always identical? A: Some aspects are not perfect especially knot positions , and different kamal sizes change the perspective a bit. Further, the kamal may not always be held correctly. Q: How would this affect real navigation on open seas?

A: Small errors of a few degrees can lead to course deviations. One degree in latitude corresponds to 60 nautical miles. Repeated measurements and additional information can mitigate this effect. Analysis This can be done as homework and checked during the next lesson in school. Let the students check their results with a local map that provides coordinates or online services like Google Maps or Google Earth.