Some additional Information from Active Captain
More Anchoring Mathematics >>>
Wow, last week's item about anchor alarm math generated a lot of
comments, arguments, and ideas. It's amazing how anchoring brings this
out in people - and we didn't even say which type of anchor is the best!
Comments from multiple boaters pointed out that our anchor alarm distance
formula needed to take tide swing into consideration in order to add to
the accuracy. Perhaps it doesn't add much when you're in a 1 foot tidal
area but surely when the tide swing is something like 8 feet or more, it
really matters, right?
Well, actually, no. And after many nights at anchor in our home port
on the Penobscot Bay with 10-12 foot tides, trust me, it doesn't matter
at least as far as an anchor alarm goes. Good old Pythagoras and his
a^2 + b^2 = c^2 triangle theorem provides the proof.
Consider the triangle formed by your bow, anchor position, and the
location on the sea floor where your boat is located. That's a right
triangle which makes the math pretty easy. The hypotenuse (c) is the
So let's go back to last week's example - a 42 foot sailboat with a bow
that's 5 feet off the water. We'll add that the anchor is set exactly at
high tide in 15 feet of water with a tide swing of 8 feet and a good
scope of 5:1 let out. This means 5 * (15 + 5) = 100 feet of rode is let
out. Using the Pythagorean theorem, the distance the boat is back along
the sea floor is: sqrt((100 * 100) - ((15 + 5) * (15 + 5))) = 97.98'
Fast forward to low tide and the distance the boat is actually pushed
back is now: sqrt((100 * 100) - ((7 + 5) * (7 + 5))) = 99.27'
Subtracting the two gives the amount the boat moved backwards because
of the tide swing: 99.27 - 97.98 = 1.29 feet or about 15.5 inches.
So that huge tide swing that took more than half the water away from
the anchorage will push the boat back by about a foot. That's something
that would be difficult to detect with today's technology.
Tide doesn't really matter for anchor alarms but tide swing has a huge
effect on scope. Now that's something to sit up and notice when you're
in an area with larger tides. Looking at this same example with our
sailboat anchoring at low tide this time, they'd drop their anchor in
7 feet of water and put out 5 * (7 + 5) = 60 feet of rode to get 5:1
scope. Now switch to high tide with 8 feet more water and their 60 feet
of rode is only giving 60 / (15 + 5) = 3:1 scope. Now that's dramatic
and might very well not be enough. We hear about boats dragging at high
tide in Maine all the time. This is why it happens.
We realize that the old salts among us know this well but recognize that
there are many skippers new to cruising who are part of our community.
It's a valuable lesson to remember to always put out scope for the
water depth at high tide. At anchor, we don't want either our anchor
alarm or yours going off!
One more thing.
Last week we mentioned that there wasn't a manufacturer who used heading
as an input into their anchor alarm along with the GPS location offset to
create a much more accurate anchor alarm. We were wrong. We were contacted
by Vesper who's AIS WatchMate 850 has a heading input capability and does
everything we've been wanting in an anchor alarm. It is an AIS transponder,
feeds back AIS info to other chartplotters or PC's, and has it's own low
power display for showing AIS or anchor alarm data.
Now we can be wrong about many things. But in this case, it is especially
embarrassing. You see, on January 25, 2012, the Vesper 850 was our Defender
1st product of the week. Honest - you can look it up in the newsletter
archive. For that week, the 850 was offered at about $900 which was an
unheard of price. As AIS has continued to get less expensive, prices have
dropped - the normal Defender price is $830 today and dropping it into your
shopping cart saves a few more dollars because of minimum advertised pricing