Whether you travel by foot, using a boat, airplane or space ship there are many common and related techniques and instruments for navigation. Typically we want to either find our own position or the position of some observed object.
While navigation for each of these areas can be studied separately many places, what I find interesting is that there is a lot of overlap between the approaches used. There are a few core concepts repeated in different ways.
Dead reckoning is the absolutely simples form of navigation. It is based on knowing your:
- starting point
- direction towards target
It is essentially what a person does when he determines where he is by estimating position by counting number of steps he or she has walked in a particular direction.
In the time of sail ships they would throw an object over board and measure with an hourglass how long time it took for the object to pass say the length of the ship or some other predefined distance along the ship. This would allow them to calculate speed by dividing distance by time.
In a spacecraft , you can’t do this because any object dropped off would continue with the same velocity as the spacecraft, as there is no medium like the water to cause friction and slow down the object. However that is also an advantage. Unless you turn on the engines, the spacecraft will move at a constant speed. There are no complicating factors like winds, air resistance, ocean currents etc, affecting it.
Using and accelerometer, the spacecraft can measure how much and for how long it is being accelerated when burning its engines. This allows it to calculate its speed and hence distance covered.
Angles and Triangulation
Almost all sorts of navigation involves finding angles to other objects. These objects could be almost anything:
- light house
- feature in the landscape, like a mountain top or water tower
- celestial body such as the moon, the sun or a star. Most commonly the north star.
An angle requires two lines. There is a line between our measured object and ourselves, but that alone doesn’t form an angle. We need some sort of reference.
This depends entirely on what sort of angle we are measuring:
- Dip or inclination, which says something about high or low an object is. Alternatively the angle in a vertical plane.
- Azimuth or bearing, which gives us an angle in a horizontal plane.
I will refer to these angles as azimuth or dip, although within each profession or field, people use their own established conventions. Dip e.g. could be called inclination or angle of elevation depending on who you talk to. However I don’t intend to teach you the correct terminology used by a given society, but rather the principles at work.
If we want to find e.g. our bearing, then we are interested in the angle an object makes relative to a line going north-south.
Then we will typically use a compass, to find bearing relative to north. While the essential operation is the same, the design will differ depending on how it is used and required accuracy.
For instance on a ship, due to waves, the compass is usually attached to multiple gimbals to keep it steady.
If we want to calculate say, the distance to a lighthouse or mountain top, then we need to know how tall each is, and find the angle of elevation, between our horizon and the top of the lighthouse or mountain top. I’ll refer to this as dip.
To find these angles there are a lot of different instruments which can be used which essentially do the same thing, but which are fine tuned for particular use cases. A confusing thing is that while they are similar their name is completely different.
The simplest of these is the clinometer or inclinometer, which measures angles relative to the nadir. The nadir is a line going through the center of the earth. So essentially the direction which gravity pulls. Hence we can this reference line by simply handing something heavy in thread or use a spirit level. A spirit level is usually used by carpenters. In contains a bubble which must be centered for something to be level.
This is such a simple thing that even some handheld compasses has a primitive clinometer.
The next step up is a sextant. The best know ones are the ones you see used on sail ships, but they are also used in airplanes and spacecraft.
A sextant is basically an instrument which lets you look at two different objects at the same time, and read off the angle between these two objects. A sextant shows each object right next to each other through a combination of mirrors and lenses. So typically to look through a telescope which is split in two, and where each half shows a different object.
When on a ship you use the ocean horizon as the reference line. Then you typically try to look at the sun in the other half, so that the sun and horizon align next to each other in your telescope. This gives the angle of elevation for the sun.
But the sun is just one option, and one you have to be careful with, since you can’t look straight at the sun without colored glasses. At night time one might want to look at say the north star instead, or the moon.
In an airplane you don’t have the luxury of being able to look at the ocean horizon. You might e.g. be above the clouds or flying at night. Hence an airplane or bubble sextant works more like a clinometer. You try to align the bubble in a spirit level, with the celestial body you are looking at through your telescope.
Of course if you are in outer space a spirit level won’t work as there will not be any gravity. Instead you’ll typically look at two different known stars, and find the angle between them.
A theodolite is kind of like a really fancy clinometer. You are not limited to finding dip, but can also find azimuth. And when using a theodolite we don’t assume that we are trying to find our own position, but rather the position of the objects we are looking at through it. That is because theodolites aren’t used for navigation but for surveying.
With a theodolite we are not finding our position. That is already assumed to be known. Instead we are trying to determine position of many different features in the landscape to perform a survey.
One way to do this is to use two theodolites or simply move the same theodolite to, two different positions. The line between these two points is called the baseline and muse be measure accurately in some way. Lets call these points A and B. We could use steel tape to measure the distance between A and B. Then from A and B we measure angles to the same points in the landscape, both the dip and azimuth to the points. Then we can use triangulation to find the distance to each measured point.
Star Camera or Tracker
In modern day spacecraft, whether manned or not, one does not use sextants. Sextants were useful when one did not have advance image processing software and computers. In the Apollo days astronauts would have to identify star constellations manually and then use the sextant to measure the angle between two known stars.
However today we can simple use a camera to take pictures of the sky and use image processing to identify constellations and find two or more known stars to use for triangulation. One can use off the shelf scientific cameras for this purpose.
But often because of the higher strains space puts on equipment one might need to built unique versions, or harden existing technology in some ways.
Usually the number of megapixels on such cameras will be much smaller than for commercial cameras as megapixels is pretty irrelevant for astronomy. One can simply take multiple pictures and string them together if you want larger pictures. What does matter however is light sensitivity and that tends to diminish when adding more mega pixels on a sensor.
Gyroscopes are such a big topic, that it really needs its own article, so I’ll just cover a minimum, here to get more in depth in my next article.
A gyroscope is essentially the combination a regular spinning top and multiple gimbals.
Gimbals are used in a lot of different products. They are separate movable joints. For instance they are used to hold cameras so that no matter how you move your arm, the camera stays steady.
If we take 3 gimbal rings and place the equivalent of a spinning top inside it, then we get a gyroscope.
If you consider a spinning top, you’ve probably noticed how it doesn’t tip over, despite the fact that gravity would pull one side down if it was not perfectly aligned. We see the same thing with a bike. If the wheels spin fast enough, you don’t tip over. If you spin an object attached to a string around yourself you would also notice how it doesn’t fall down despite gravity but appears to be levitating. So without getting into the details here, you can see that things that rotate don’t easily change orientation. The faster the object spins, the harder it is to change its orientation.
This is utilized in a gyroscope, where you point it in one direction and it keeps that direction, even if the airplane, ship or spacecraft containing it changes orientation. By attaching sensors on the joints of the gimbals one can measure how much a vehicle turns relative to the stable spinning disc of the gyroscope.
This is useful in almost any kind of navigation, perhaps most obvious in airplanes. While a ship can compare its heading with magnetic north, an airplane needs something to tell it whether its nose is pointing towards the ground, the sky or is flying straight (pitch). You also want to know how much you are rotated (roll).
Likewise in a spacecraft it is even more crucial, as many planets have no magnetic field.
Inertial Navigation Systems
What we can construct is a kind of advance dead reckoning system, where we use accelerometers to figure out acceleration and hence velocity and distance traveled over time. Add gyroscopes to this mix and we keep track of orientation as well, which is important to know if you want to determine your position. You can’t know your position if you only know distance traveled but not which direction you took. All of this combined is called an Inertial Navigation System (INS). Inertial Navigation Systems are widely used in missiles, aircraft, spacecrafts and even ships.
Of course with any system based on dead reckoning, inaccuracies will build up over time. INS systems are no exception.
That is why you still need a Star Tracker to correct your position occasionally. Or if you were more primitive you’d use a sextant.
Navigation Using Electronic Sensors
The instruments I’ve shown thus far are mainly large scale mechanical and optical devices, where you can clearly see what is going on. Of course this isn’t how navigation is done in modern equipment. Back in the 60s and 70s these devices were still rather large and clunky electromechanical devices.
Today however these instruments have been replaced by tiny electronic sensors, which can easily fit into a modern smartphone. Here are examples of some breakout boards from Sparkfun, which contains tiny sensors containing magnetometers, accelerometers and gyroscopes.
A magnetometer is basically a sensor which can sense a magnetic field. Together with a 3 axis accelerometers it can be used to create an electronic compass. This is one of the reasons why today it makes more sense to talk about sensors rather than specifically about particular instruments. As we tend to just read raw data and feed it to a micro-controller (small computer). It is the software running on the micro-controller which really decides what kind of instrument we have.
Micro-controllers have become so small and cheap that, one doesn’t built special purpose devices to the same degree. E.g. two decades ago I might have built an electronic circuit made up of transistors and capacitors to make a light emitting diode pulse or blink. Today I might instead just attach the diode to a tiny micro-controller which I program to make the light emitting diode pulse or blink. One could thus say that software is in many ways replacing purpose built electro-mechanical instruments of the past.
While we have lots of different of very looking equipment, used to look at different kinds of objects, they are all based on the same principles. Almost all navigation or position finding is based on finding angles, as we can more easily measure those than actual distances. By knowing either multiple angles or an angle and a distance, we can find a third unknown distance.
Whenever we find an angle we need to have some kind of reference to find it, which could be based on gravity, aligning with the horizon, magnetic north or simply finding angles between two arbitrary known objects.
These angle measurements are not always easy to perform continuously, so we supplement our navigation and position finding with various forms of dead reckoning. That is keeping track of our current direction and speed to calculate and estimate of current location.