Long before the advent of GPS (Global Positioning System) I was a navigator of fast jet aircraft in the Royal Air Force. I was a Qualified Navigation Instructor and specialised in the most challenging navigation scenarios - low level, radar navigation day or night. It was more exciting at night. I wonder what would happen now without GPS?

The mathematicians amongst you may get frustrated as you like things very accurate. I am no mathematician, I am a navigator. I round figures up, round them down and think ‘that looks about right’. They always are.

On this page I will guide you through the basics of navigation. First I want you to remember a magic number. **60**. I also want you to remember your 6 times tables … 6, 12, 18, 24, 30, 36, 42, 48, 54 … and wait for it … 60!

Why is the number 60 so magic in navigation?

- How many seconds are there in a minute? … 60
- How many minutes are there in an hour? … 60
- How many hours are there in a day? … 24 Is this divisible by 6 … Yes
- How many degrees subtend the arc of a circle? 360 … Is this divisible by 6 and 60? … Yes
- How many nautical miles are there between each degree of longitude? You catch on quick! … 60

If you can deal with the number 60 and the 6 times table in your head, you can perform some real complicated sums quite easily. We will cover some calculations later but in the meantime, why do you think that fast jets fly at either 420, 450, 480, 510 or 540 knots (nautical miles an hour)? Hopefully you saw a pattern.

Divide the speeds by the magic number 60 and the speeds equal 7, 7.5, 8, 8.5 and 9 nautical miles a minute! These numbers make calculations easier when flying. The quickest I flew was 600 knots which made my calculations really easy (divisible by 60 and by 10). Would you believe that there is also a ‘1 in 60’ rule. I will cover this later.

Fact 1. The Earth rotates around its North-South axis every 24 hours. This rotation creates the phenomenon of sunrise and sunset. Because of the tilt of the Earth winter days are shorter than summer days. Somewhere in the middle there will be a few days when daylight hours equal to nighttime hours.

The images below are based on sunrise and sunset times throughout 2017 for the latitude where I live. The times vary with latitude. The more north you are the longer daylight in the summer and the longer nighttime is in the winter. This is because of the Earth's tilt towards or away from the sun respectively.

Fact 2. The Earth is spherical. It is not a ball but an oblate spheroid (it is fatter toward the bottom). For our simplified navigator’s understanding let us consider the Earth like a ball. Whichever way we look at a ball it looks like a circle. Question. How many degrees subtend the arc of a circle? 360.

Fact 3. Different time zones are used around the world, but how many? If there are 24 hours in a day, how many time zones do you think there are around the world? Answer = 24. Now it gets a bit tricky! How many degrees of longitude are in a timezone? Answer = 360 degrees of the circle divided by 24 = 15 degrees.

Facts 4, 5, 6 and 7. The 0 degree meridian runs through the old Naval College at Greenwich in London. From here lines of longitude are either East or West. It is known as the Greenwich, or Prime, Meridian. This gives purpose to the phrase Greenwich Mean Time, or GMT.

Facts 8 to 12. Timezones are designated a letter code starting at the 0 degree meridian of longitude. East of Greenwich is timezone A, or Alpha, and this increases by 15 degree chunks of longitude in alphabetical order to timezone M, or Mike, in the most eastern parts of Russia. To the west of Greenwich is timezone Z, or Zulu. Timezones to the west do not follow an alphabetical order and I have no clue why this is.

Fact 9. Being in the UK is a bit awkward because the country is divided by timezones. To avoid any confusion ALL Flying Operations are conducted in ZULU. When British Summer Time starts, time is known as ALPHA but Flying Operations are still conducted in ZULU, (ALPHA minus 1 hour).

Answer: The rule of thumb is 30 minutes after sunset to 30 minutes before sunrise.

In the UK it is illegal to fly drones at night without the express permissions for the CAA.

In aviation the standard unit for distance is the nautical mile. It is different to the statute (or road) mile. It equates to 6076 feet but where does this come from? Consider the lines of latitude on our ball-shaped Earth. Starting from the equator heading north there are 90 degrees, or lines, of latitude to the North Pole. Likewise there are 90 to the South pole. Therefore 180 degrees, or lines, of latitude between the Poles.

Each degree of latitude is divided into units called minutes. Can you guess how many minutes make a degree? Each minute represents 1 Nautical Mile. Did you guess 60? You are getting good at this! There are 60 nautical miles, or nm, between each degree of latitude. If you wanted to you can now calculate the distance between the Poles: 180 x 60 = 10800 nm.

Like any navigator I am obsessed by time and timing. I do not like being early or late. I like to be 'on time'.

FAQ - Are we nearly there yet?

Answer - it depends on the distance to go and the speed of travel. So how do we calculate this? Consider the standard unit of measurement for speed. On the roads in the UK 'miles per hour' is used. This suggests that speed equates to the distance travelled divided by a time period.

Example Question. You are in a car travelling at 60 mph and your destination is 100 miles away. How long, in minutes, will it take to reach the destination?

Answer. From a navigator's perspective 60 mph is 1 mile per minute so it will take a hundred minutes to reach the destination.

Example Question. You are in a jet travelling at 420 knots and your destination is 56 nautical miles away. How long, in minutes, will it take to reach the destination?

Answer. From a navigator's perspective 420 nautical miles an hour is 7 nautical miles per minute. Divide 56 by 7 to calculate that it will take a eight minutes to reach the destination.

Example question. You are flying at 360 nautical miles an hour. How far will you travel in 7 minutes?

Answer: From a navigator's perspective 360 nautical miles an hour is 6 nautical miles per minute. Therefore 7 times 6 gives us the answer of forty two nautical miles.

To this point we have focused on time, distance and speed. For us to know how to get to where we want to, we need to know where are now. We need to pinpoint and measure the position on the map. So, let us return to latitude and longitude.

Answer: In still air the Phantom 4 drone's speed in GPS mode is 18.5 mph.

In the UK, 500 m line-of-sight is the legal flying limit. At 18.5 mph it will take the drone 60 seconds to cover this distance.

Further Note: In 'Sports mode' the speed is 45 mph. 500 m would be covered in just 24 seconds!

In the diagram provided the horizontal lines represent degrees of latitude and the vertical lines are degrees of longitude. You will see that each are sub divided by 60 minutes. Pinpoint where you are on the map, and starting from the line of latitude immediately to the south (assuming you are in the northern hemisphere) measure the minutes of latitude up to your position. Then you need to ascertain whether you are east or west of the Greenwich/Prime meridian. If you are to the east, measure minutes of longitude from left to right; if you are to the west, measure minutes of longitude from right to left. Your position can be described as 'xx degrees yy minutes North, xxx degrees yy minutes East or West.

It is important to be able how to plot Latitude and Longitude because NOTAM information is described this way.

Knowing your position and your destination you can measure the track between the two points. Draw a line between the points and measure the track as close to the mid-point as possible. Align your protractor to true north and note the angle of the track. In this case the track from the green to blue cross is 304 degree True. If measuring the track from blue to green with track would be 124 degrees True.

For drone operations it likely that Ordnance Survey maps are used for planning purposes. For example measuring distances to no fly areas and so on. Such maps use the conformal Transverse Mercator projection for position plotting.

Countries will have their own national mapping systems. In the UK the National Grid from Ordnance Survey is the standard. For completely mind-blowing detail on the subject you could read the OS 'guide to coordinate systems in Great Britain'. But let us keep it simple.

The clue is in the title National *Grid*. It comprises a series of squares across the national territories and is broken down like so:

- The bottom left corner of the grid is to the West of the Scilly Islands.
- 500km squares are given a letter code H, N, S or T.
- Each contains 25x 100km squares, lettered A to Z excluding I, staring from the top left to the bottom right.
- These contain 10 x 10km squares and so on.

Plotting your position, or the position of a point of interest, starts at the bottom left of the any of these squares. The handy phrase to remember is *Along the corridor and up the stairs* ! These means that you define the eastings first before the northings.

A position can be described numerically to varying degrees of accuracy. A 2 figure, 4 figure or 6 figure grid references. The latter is the usual and describes the position to a 100m square on the map. Let us look at the position of Uffington Castle, Oxfordshire.

Uffington Castle can be found in the 100km grid square SU. The bottom left corner of SU is **4**00km east and **1**00 km north of the grid datum that is west of the Scilly Isles. From the bottom left corner of the SU square the Castle is 29km east and 86 km north ~ described as SU 29 86. But this is not accurate as it describes the bottom left hand corner of a 1 km square. On the image below the red X is the position of the Castle.

Working from the bottom left corner (again) we can visualise that the position is > 900 m east and > 300 m north. Our positon can now be decribed as SU 299 863. This now describes a square 100 m square. We may need a ruler or roma for the next bit. We could measure how far east and north the positon is from the bottom left corner. The positon SU 2992 8634 gives an accuracy of a 10 m square. (Note: yes, you can add another digit to describe a 1 m square.)

Knowing how to plot accurate coordinates will be helpful to describe operations to Air Traffic Control, for your log book and general flight planning.

The rule is written in a quaint way, so I shall simplify it. Say you intend to fly the 304 degree track towards the blue X but actually fly in error by 1 degree, after 60 miles you will be 1 mile off track! If you fly 2 degrees in error, after 60 miles you will be 2 miles off track. Of course these figures are approximate but good enough as a rule of thumb.

Example Question. Your track is 270 but you travelled 120 miles on 269 degrees. How far to the left or right of track will you be?

Answer. From a navigator's perspective you were one degree in error so would be 1 mile off track at the 60 mile point. You will be double that, 2 miles off track, after 120 miles. Your error was to the left, so in this case you could expect to be 2 miles south of your destination!

Example Question. Your track is 180 but you travelled 90 miles on 182 degrees. How far to the left or right of track will you be?

Answer. From a navigator's perspective you were two degrees in error so would be 2 miles off track at the 60 mile point. You will be 1.5 times that, 3 miles off track, after 90 miles. Your error was to the right, so in this case you could expect to be 3 miles west of your destination!

The bottom line is that it pays to be meticulous in planning and accurate when travelling, or you soon get lost.

Wind can give you all sorts of problems if you ignore it or get the calculations wrong. The worst case scenario for fliers is running out of fuel and crashing!

Wind will affect your speed across the ground and can make you drift off course. If you have bicycled on a windy day you would have experienced a wind in your face slowing down your progress. It is best on a bicycle to have a tailwind when the wind is blowing you along making pedalling easier. Winds from the side can make cycling in a straight line tricky. The same goes for aircraft, boats, ships and so on.

First we will look at how to calculate the drift caused by winds from the side. First look at the clock face in image provided. There are fractions at the 15, 20, 30, 40 and the 45 minute marks that will help you in your calculations. Don't forget the magic number 60. At the 30 minute mark the fraction is 1/2 (half of 60), at the 20 minute mark the fraction is 1/3 (third of 60) and so on.

The maximum drift will be experienced when the wind angle (the difference in wind direction and your heading) is 60 degrees or more. The maximum drift can be calculated by dividing the wind speed by your speed in miles per minute.

Example: The wind speed is 20 knots, your speed is 300 knots (or 5 miles per minute). 20 divided by 5 equals 4 degrees maximum drift.

If the wind angle is less than 60 degrees you can use the clock analogy to simplify the calculation. Using the same figures from the example, calculate the drift if the wind angle is 30.

Example: The wind speed is 20 knots, your speed is 300 knots (or 5 miles per minute). 20 divided by 5 equals 4 degrees maximum drift. BUT wind angle is 30 degrees therefore apply 1/2 of the maximum drift. The answer is 2 degrees of drift.

From our bicycle experience we know that the full effect of the wind is when it is front or behind us. For our calculations we now subtract the wind angle from 90, apply the clock analogy to the wind speed and apply the answer to your speed. Let's look at an example:

Example: You are travelling at 360 knots, the wind is 40 knots with a wind angle of 60 degrees in relation to your heading.

Answer: 90 minus the wind angle of 60 equals 30. Apply the clock analogy and the effect wind will be half of 40, equalling 20 knots. If it is a headwind your speed over the ground will be 340 knots. If it is a tailwind your groundspeed will be 380 knots.

Example: You are travelling at 420 knots, the wind is 60 knots with a wind angle of 45 degrees in relation to your heading.

Answer: 90 minus the wind angle of 45 equals 45. Apply the clock analogy and the effect wind will be three quarters of 60, equalling 45 knots. If it is a headwind your speed over the ground will be 375 knots. If it is a tailwind your groundspeed will be 465 knots.

Consult your manufactuer's aircraft limitations section. For example the Phantom series has a wind limit of 15 mph for good reason.

Plan to fly out against the wind. You will have a tail wind on return.

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