'It’s easy for any sailor to remember how to draw tidal vectors with a handy little aide-mémoire!' Says Dick Everitt.
In the last Nav in a nutshell we saw how each hour’s tidal strength and direction is tabulated in a tidal atlas, chart or computer program.
Even with GPS navigation, we still need to be aware of how these tidal streams will influence our passage through the water.
For instance, if we need to get to a harbour at a certain time to enter, say, a locked marina we need to estimate how long it’ll take us to get there, then work backwards to get an approximate departure time.
The simplest plan is to always go with the tidal stream and let it help us along.
So, if we reckon our boat will do about 5 knots through the water, and the water itself is moving with us at 2 knots, our combined speed over the ground is 7 knots – just like walking along a moving walkway at the airport.
Conversely, if we went directly against the tidal stream our speed over the ground would be 3 knots, ie 5 knots minus 2 knots.
It’s also worth noting that GPS only measures this combined speed, SOG (speed over the ground) or how fast the shadow of our boat is moving over the seabed.
However, when the tidal stream isn’t flowing parallel with us we need to construct a vector triangle.
I know this strikes dread into some navigation students, so I’ll keep it really simple. Old salts might have already decided to stop reading by now, but even they might find this little aide-mémoire useful for remembering the convention for how many arrowheads you put on each leg of the vector triangle.
Boats have one bow wave, so the water track has one arrowhead; we walk on the ground with two feet so the ground track has two arrowheads; and the tidal stream arrow is the third one and has three arrowheads – just like the ripples on the water!
A vector triangle is just a scale drawing of the forces acting on our boat, so if we rowed across a river aiming in a straight line from A to B (see diagram) the current would sweep us sideways so we’d end up at C.
The same thing happens at sea (see illustrations, below).
Our boat will head north (000°) at 5 knots and the tidal stream will push us east (090°) at 2 knots. So, for an hour’s worth of time we draw a line 5 miles long – the water track – representing how far the boat will have travelled and, from that point, a line representing the tidal stream heading east for 2 miles – the tidal stream arrow.
Draw a line completing the triangle – the ground track – and this shows, despite keeping the boat heading north, that we would be crabbing sideways at 020° along this line at about 5.4 knots.
We must also allow for a small amount for leeway, or how much the wind will push us sideways.
This depends on the boat, the wind and the waves, say 5° normally to 20° if it’s rough and the waves are moving us sideways.
To keep things simple in the diagram we’ve made the wind push us in the same direction as the tide: but it might be coming from the other side of the boat, so we’d have to subtract 5°.
The good thing about GPS is it will look down from on high and show us how much the combined wind and tide is pushing us sideways and tell us the COG (course over the ground) which is the same as ground track.
Once we have drawn all the lines on the chart we have an EP (estimated position), and the symbol we draw is a triangle with a dot in. However, it’s a mistake to think we’re exactly on that dot because it’s only estimated, and the boat speed, heading, tide and wind rate and direction could all have varied over our hour of travel.
To allow for all of those possible errors, prudent navigators draw a rough ‘circle of uncertainty’ around the EP with a radius of up to 10% of the distance travelled. In our simple case, we therefore draw a circle of about 1 mile in diameter.
Projecting an EP forward is also a good way of seeing where our ground track will take us, and in the diagram (above, right) the circle of uncertainty reminds us that we could get too close to those shallow patches.
With an independent log we can also plot an occasional EP while under way as a rough check on the GPS.
Hopefully this simple explanation might encourage reluctant navigators to have a go at traditional navigation – just in case the chart plotter breaks down – or at least have a better understanding of what SOG and COG means.
This Nav in a Nutshell was published in the January 2012 issue of PBO. For more useful archive articles explore the PBO copy shop.