# Boat Tying Quiz Puzzle Answer

Recently one of our crew (see what we did there) went on a boating holiday on the Norfolk Broads. It was a really nice break, albeit a little cold, but that was just the time of year.

You might be aware that many parts of the Broads are tidal, and so care is needed when mooring that there is enough slack in the ropes. Moor up at high tide with ropes like banjo strings and when the water level has dropped a few feet the boat will be at a bit of an angle!

Before taking out the boat he received instructions and got the following advice:

If there is a small tidal range where you are mooring (a foot or so) use the ropes on the side of the boat nearest to the bank. But if the tidal range is bigger (two or three feet) use the ropes on the side of the boat farthest from the bank.

Now, the speed limit on many parts of the Broads is four miles per hour, and it never rises higher than six miles per hour. This meant that he had plenty of time while pootling along to consider why this might be the case. And towards the end of the holiday the penny dropped.

So, can so work out why?

The reason he came up with is all to do with Pythagoras' theory.

If you tie off using the nearside ropes (say two feet of horizontal distance) and the water drops three feet, then the rope needs to be just over three and a half feet long to cover the fall (Root (2 * 2 + 3 * 3)) an extension of about 19 inches.

If you tie off using the farside ropes (say twelve feet of horizontal distance) and the water drops three feet, then the rope needs to be just under twelve and a half feet long to cover the fall (Root (12 * 12 + 3 * 3)) an extension of about five inches.

The more slack in the mooring ropes, the more the boat will move about in the wind and the wash from other boats. So it's better to use the farside ropes.

Of course, there might be other reasons, but it was only a one-week trip.