How To Cheat With an Under Water Compass

If you use a compass underwater you'll eventually run into a situation where you'll have to calculate a bearing in your head while under water.  This can be very difficult - especially if you're like me and are reallly bad at mental math.  Luckily there is an easy way to "cheat".  All you have to do is forget all of those numbers on your compass!

The Basic Method:
Basically what we are going to do is replace the numbers on your compass with a simpler system.  Bt don't worry, you won't have to alter your compass, this is all in your head.  If you look at your compass you'll notice that there are "ticks" on the magnetic disk.  Depending on the model of the compass the number of ticks will vary - some will have a tick every 5 or 10 degrees, others only on the 16 points of the compass.  But no matter how many ticks there are this system will work.  To keep things simple we'll pretend our compass has a total of 16 ticks.  Four of these ticks are your cardinal points - going clockwise around the compass they are: North (0 degrees), East (90 degrees), South (180 degrees) and West (270 degrees).  On an compass with 16 points there will be three points between each of the cardinal points.  Now technically these points all have names and bearing between them - for example the three ticks between north and east will be (going clockwise) north-north-east (usually written NNE, or 22.5 degrees), NE (45 degrees), and ENE (67.5 degrees).  But instead we will call them N+1 (north + 1 tick) N+2 and N+3.  Then there is East, E+1, E+2 and E+3.  Then it's South, S+1, S+2 and S+3.  Finally we have West, W+1, W+2 and W+3.  To make things even simpler we'll refer to north, east south and west as N, E, S, and W respectively. 

 

So now our compass which originally had 360 degrees on it has 16 points.  But how does this simplify things?  This simplifies things because 99% of the time all you want to do is make a 90 degree turn or a 180 degree turn, and this system is designed to do just that.  As I mentioned our bearings are now described as a cardinal point plus ticks.  Lets say you are swimming north and want to turn 90 degrees to the right.  That's an easy turn, as 90 degrees of north is east.  But what if you are swimming at N+1 and want to turn 90 degrees right.  Well that is easy - 90 degrees to the right of N+1 is E+1.  Or in other words to make a 90 degree turn to the right you simply move one letter clockwise on the face of your compass, but do not change the number of ticks.  To turn left we simply move counter-clockwise.  So a 90 degree turn left of N+1 is W+1.  To turn 180 degrees we move 2 letters around the compass.  So 180 degrees from N+1 is S+1.  Easy!  For all of your turns all you need to do is move the appropriate number of letters clockwise or counter-clockwise, but keep the same "tick" number.  Just remember - to turn right move clockwise on the dial, to turn left move counter-clockwise on the dial.  Here's an example:

Example:
Let's say you are swimming towards a wreak, which is located at a bearing of 22.5 degrees (in our new system this is N+1).  But along the way we encounter a huge kelp forest we can't go through.  So in order to swim around it without loosing our course we must use a special technique covered in detail in the navigation patterns page.  Basically this pattern consists of 4 90-degree turns.  For this pattern to work we'll have to make one turn to the right (i.e. must add 90 degrees), two turns to the left (during each one we must minus 90 degrees), and then another turn to the right (add 90 degrees).  By using this technique we'll end up on the other side of the kelp forest along our original bearing.  Here's how this works out:

Old System: Our first turn is to the right, meaning we add 90 degrees.  This is 22.5 + 90 = 112.5 degrees.  Not too bad.  Now we enter our second turn, where we have to turn left (subtract) 90 degrees.  That 112.5 - 90 = 22.5.  OK, now we need to turn left again, so we subtract another 90 degrees.  So 22.5-90 = -67.5 degrees.  Of course there isn't a -67.5 on your compass, so now we must subtract 67.5 from 360.  360 - 67.5  = 292.5 degrees.  Wow, this is getting hard.  But luckily there is only one turn left.  This turn is to the right, so we add 90 degrees - that's 292.5 + 90, which is 382.5 degrees.  But wait - there is only 360 degrees in a circle, so we need to subtract 360 from the 382.5 degrees.  When this is done we find our desired bearing is 22.5.  Wow, my head hurts!

"Cheater" System: Now lets use our new system, which is conveniently set up to do 90 degree turns.  For example 90 degrees to the right of north is east, or in our new numbering system is E.  Or in other words to turn 90 degrees to the right we move one letter clockwise on our compass (from N to E).  90 degrees right of N+1 is E+1.  90 degrees right of E+3 is S+3.  Even if we pass north (which is where the math gets real hard) things are simple.  For example 90 degrees left of N+2 is W+2.  Want to do a 180-degree turn (i.e. go back the way you came?)  No problem - just move two letters around the compass - so to go 180 from S+2 you simply turn until your compass reads N+2.  Nothing could be easier.

So to follow the example we would start swimming along our first bearing of N+1 until we hit the kelp.  Now a 90 degree turn to the right is equivalent to moving to one letter clockwise, which gives us E+1.  So we turn until we face E+1 and start to swim.  We reach the end of the kelp, and now need to turn 90 degrees to the left.  Rather then subtracting 90 we simply move one letter counter-clockwise, which brings us to N+1.  The third turn (where things got messy using the old technique) is simply another letter counter-clockwise - W+1.  Finally we do our last right hand turn (one letter clockwise) back to N+1.  Couldn't be easier!

 

But What if There Are More than 16 Ticks?
Most compasses have more then 16 ticks - the average underwater compass has one tick for every 10 degrees.  This equals a total of 36 ticks, or 8 ticks between each of the cardinal points.  But never fear, our tick system still works.  But instead of only having N, N+1, N+2, N+3, E, E+1,  ... we now have N, N+1, N+2, N+..., N+8, E, E+1... and so on.  A 90 degree turn still is nothing more then moving one letter clockwise or counter-clockwise, while keeping the same number of ticks.  So if you are swimming at a bearing of E+5 (140 degrees) a 90 degree turn to the right will put you on a bearing of S+5.  A 90 degree turn to the left puts you on a bearing of N+5.  A 180 degree turn from E+5 is W+5.  Much simpler then adding/subtracting 90 or 180 degrees!
 

Turns That Aren't 90 or 180 Degrees:
This system also simplifies turns which aren't multiples of 90 degrees.  Lets say we are using a compass with ticks every ten degrees.  This means we can easily turn in units of ten degrees.  If you want to turn right by 10 degrees you move one "tick" clockwise.  To move 10 degrees west you turn one "tick" counter-clockwise.  So if you are swimming at E+4 and you want to change you bearing by 10 degrees to the east you at one tick, giving you E+5.

Even if you pass one of the cardinal points things stay simple.  For example, lets say you are swimming at N+3 and want to move 50 degrees (5 ticks) west.  This is a bearing of W+6, but it is also "N-2" or in other words two ticks left of N!  About as hard as things can get is turns greater then 90 degrees.  Lets say you are swimming at S+4 and want to turn 110 degrees to the right.  That's 11 ticks clockwise, which is a bearing of W+6.  This may be hard to count, but it's easy to calculate what the bearing would be.  There is 9 ticks for every 90 degrees, so if we move our dial to W+4 we have moved those 9 ticks (and turned 90 degrees).  11-9 is 2, meaning we have to move 2 more ticks in the same direction to get our full 110 degree turn.  W+4 plus 2 ticks is W+6, our desired bearing.  Easy!


How Accurate is this System?
The obvious downside of this method is that it is not as accurate as using degrees.  Since most compasses only have ticks for every 10 or 15 degrees your accuracy is limited to the angle between ticks, which means that if you round off your bearing correctly you can be out by as much as 5 degrees for a compass with ticks every 10 degrees, or off by upto 7 degrees for a compass with markings every 15 degrees.  But how bad is this?  If we were navigating on land this would be a real problem - over long distances being off by 5-7 degrees can result in you ending up a long ways away from your target.  But underwater this is less of a problem for several reasons:
 

1. We travel shorter distances underwater.  Most diver will swim less then 100m (330') on any one bearing.  It is almost unheard of for a diver to travel much more then 500m (1650') underwater, even with a diver propulsion vehicle.  The following table describes how far off you would be if you were off by the maximum possible angles (5 & 7 degrees).  As you can see you don't end that far off - on average less than 10% of the distance you're swimming.  Although these errors seem large remember that these are worst-case scenarios, and since it's rare to travel over 100m (330') along one bearing it is highly unlikely that you'll ever be off by more then 8 or 9 meters.  Or in other words it will be rare to end up out of visual range of your target.