Dead Reckoning

When it is the beginning, the navigator is clearly aware of the position/location. When he starts to move (in the mid-sea or mid sky), he can get some known (measured) factors other than the position/location in terms of a fixed landmark. They are,

1. The direction of movement (by using a compass)

2. Speed of movement

3. Time taken to reach each heading

Using all this information, the navigator calculates the distance and route which he has covered and keeps track of his movement by plotting a nautical chart (also called a sea chart). This technique is known as Dead reckoning.

In brief, Dead reckoning is a process to determine the position of the navigator (sailing a ship or flying an aircraft) using the record of courses that have been sailed (or flown), the distance covered (by using the velocity in which he has traveled and time taken to reach the next course from the previous course), known point (the previous point is the known point) and the estimated or known or approximated drift ( continuous slow movement from one place to another due to the flow of water or air) without using the Celestial references. It is not only for determining the current position. We can advance the (current) position based upon estimated or known velocity over elapsed time and course.

Is it error-free?

Absolutely NO!

We are humans and we make errors. With that, we can’t challenge nature too. At each course, the navigator is just approximating or estimating the things apart from few mathematical calculations using the data he has. This results in a fraction of error and when the course points are increased, the accumulated error may result in a huge difference in the intended destination.

Is the error a huge problem?

Yes?

Don’t forget, we did the greatest discoveries using this method in the very old era when there was no smart assistance or even risking the lives. A new world was discovered using this method by Christopher Columbus, an Italian explorer, navigator, and colonist who discovered a viable sailing route to the Americas, a continent that was then unknown to the Old World.

Let us see clearly how this is being carried out in each phase.

Dead reckoning always begins from a known point (the fixed point). Then the speed of the moving object must be known. In earlier times, the sailors threw a log over the side (tied to a rope) and count how long it took to pass this log (or to pull a rope with knots and count how many knots get pulled out in a certain amount of time). Through this, they calculated the speed of the ship. They used a compass to find the direction of their movement. From these two numbers, an estimate (a predicted value) was made about the current location of the ship. However, the wind pushes the ship to one side (drift) and that can really cause a change in the direction in which we are moving. Sometimes the ship may be traveling in the same direction but it can increase a distance with the actual course direction. So it is important to measure the drift as well. Also, currents in the water even in the middle of the ocean can also affect the readings. Over time this could make errors as well, so charts were made to correct for currents.

If we consider airplanes, they can measure their wind speed easily (how fast they are going through the air). But not how fast they are moving relative to land (called ground speed). Many types of wind can affect the ground speed. They are headwind, tailwind, or crosswind. If we are able to calculate the altitude of the airplane from the ground, then the ground speed can be easily found (by timing how fast the plane goes past an object on the ground). Also, the higher you are, the slower the ground seems to move. There was a window on the floor of the earlier airplanes which was used to find the ground speed and the drift of the airplane.

Dead reckoning in the ground is easier than in water or air as we need not worry about drift from the wind, and there are no currents on land.

In the case of animal navigation, dead reckoning is more commonly called path integration. Animals use dead reckoning to estimate their current location based on their movements from their last known location. Ants can track their locations continuously relative to a starting point and return to it. This is an important skill for foragers with a fixed home. There are many animals that use this technique to keep track of their movements.

In deep-sea navigation, the autonomous robots use dead reckoning with GPS-based points and that reduces the error on a high scale and makes a bit precise navigation in the deep sea.

In computer science also we are using dead reckoning-based activities in a data structure.

Do you know what is it?

If it is “Arrays”, congratulations, you have understood what is a dead reckoning.

Every array element has the same size. Therefore it is always possible to directly access an array element by knowing any position in the array. This is what we are doing in the navigation with the help of dead reckoning.