How do anchors work

An intense squall blew up last night. The wind was around 25 knots, gusting to 30 (a little over 55 kph). Not a biggie as far as these things go but was one of the strongest we've experienced. At this velocity the boat is very actively swinging back and forth on its anchor chain, it's hard to hear someone speak 20 feet away and is strong enough to knock you off your feet if you are unsteady (e.g. due to waves). After our initial surprise at the sudden increase in wind, we quickly took down anything that could blow away then let out more anchor chain and waited for the squall to blow itself out, watching other boats take similar cautionary actions. An hour later and everything was back to normal.

However, one question remained. Why did we let out more anchor chain? The boys were curious, so the next day we had a little discussion of the physics of anchors and a little demonstration.

old style

Anchors use two forces to hold boats in place. Friction and gravity. When most people think of anchors they picture a big metal fish-hook-like object attached to the end of a chain or rope. While those types of anchors are still in use, most these days look like some kind of plough or claw. However, your anchor is actually the secondary thing holding the boat in place. Most of the time (in settled conditions) you arrange things so that there is no or very little stress on the anchor itself. The primary thing holding your boat in place is the chain.  This is achieved through a bit of friction, gravity and angles.

modern plough

A boat at anchor creates a right angle triangle between the anchor on the bottom, the sea floor right under the boat and the boat's bow. Anchors hold best when the chain pulls along the sea floor in a horizontal direction, dragging the anchor and with the best designs, digging them in deeper and deeper. Anchors usually break free with little effort if the pulling force is approaching vertical. This means a smaller angle at the anchor is better. This is the friction part of the equation (anchor is using friction to stick to the bottom and dig in). In addition, the anchor chain is heavy and wants to lie on the bottom. This creates even more friction as the chain drags on the sea floor. Increasing the amount of chain that we had out last night made a smaller (better) angle where the anchor meets the sea floor which increased the amount of force (wind) required to move the anchor or break us free.

However, letting out more chain has another positive effect that isn't always obvious and this is where the demonstration came in. What I wanted to show is that the weight of the anchor chain alone significantly improves the holding and in calmer conditions is almost the only force that is needed to hold our boat in place. The anchor chain makes the top side of the triangle and is quite heavy. As the angle decreases, the force (wind) required to keep the chain (top of the triangle) straight increases (it's a non-linear increase in effort but I don't know what the factor is).

To demonstrate this we took one of our long, heavy dock lines, attached it to a cleat at the bow then ran it back along the boat deck to the cockpit. First I had the boys try to lift the line and hold it straight from 10 feet from the bow. They did this with ease. Then they stepped back 5 feet and tried again. This time it was more difficult. Then they stepped back another 5 feet. At this point Aidan couldn't get the line to stay straight except when he yanked on it (this simulates a boat surging on its anchor in the wind). They stepped back another 5 feet and now Aidan couldn't straighten the line at all and Austin could only do it by yanking. Back another 5 feet and neither of them could straighten it.

We discussed that each time they stepped back they needed to lift and keep raised more line, which increased the total weight they needed to lift. Each time they stepped back they were also making the line more horizontal, which has a similar effect to moving farther from the fulcrum of a lever (only it has the inverse effect of increasing the amount of force required rather than reducing it).

Singing songs

Austin has been learning to sing several Raffi songs from our song book. This was inspired a few days ago while we were sailing from Bequia to Mayreau. To pass the time my mother (who is visiting) and Austin started to sing Baby Beluga. They couldn't remember all the words so Austin pulled out our Raffi song book and they sang the whole album. Austin has been singing several of these songs each day and has learned day-o, Baby Beluga and Kumbaya. He sings other songs from the book to Aaron each night.

Corrosion

At dinner we all chatted about corrosion and two different way corrosion affect boats (my grandfather was a corrosion engineer which is how we got onto the topic).  The first type is your everyday rust. This is where the corrosion happens simply by exposing the metal to moisture in the air. The second type we talked about is galvanic corrosion where a metal higher in the galvanic series steals electrons from a metal lower in the series. The farther apart the metals are the faster the reaction.


We then talked about various ways we could protect against corrosion.


 - paint over metal to reduce the amount of moisture contacting the metal
 - isolating metals that are far apart in the galvanic series 
 - installing sacrificial anodes to prevent important metals like a stainless steel propeller shaft from corroding when in sea water

School for hermit crabs

When we were visiting the little sandy island of Petit Tabac (scenes from Pirates of the Caribbean were filmed here) Austin and several of the other kids at the beach (two families from Norway and one from Australia/England) decided to build a "school" for the hermit crabs that they found crawling through the sand. The school was built of sand with high walls, tunnels and archways. They fortified the outer wall against the surf using large blocks of white sand stone.

There were a couple places where roots from some of the shore plants created a natural bridge from inside the school to the outside. The kids decided that if a crab was good enough to find this escape route and be able to navigate it then they wouldn't be re-captured and put back. Kind of like a graduation!

Austin noticed that most of the crabs preferred a specific, swirly shell type. The crabs didn't fight or eat each other but seemed to be helping each other escape by building pyramids of crabs where the last one would be able to climb high enough to escape over the wall.

Swimming at the Tobago Cays

Austin and I spent about two hours swimming around our boat. We saw a sting ray and several other small fish.

We are anchored over sand so spent some time diving down to see who was living in the sand. We found crab holes (no crabs seen) and a couple queen conch wandering about.

We also inspected our anchor holding. I showed him how our plow-shaped anchor was well dug into the sand. He joined me on this inspection yesterday too (at Salt Whistle Bay) and saw that in soft sand it can dig in deep enough to be completely buried.

Austin then went snorkeling with my mother for about 45 min. The water was too murky from the day's wave action so they were not able to see much.

Calculating the angle of roll in a rolly anchorage

We've been parked in a very rolly anchorage for the past day. Some anchorages, like this one, are fairly open to the ocean swells and if you're there at the wrong time can be so rolly as to be dangerous. While it's not quite that bad here right now, it is pretty uncomfortable.  This started a discussion around the breakfast table of estimating the angle of roll. The boys started out with pretty unrealistic ideas like 90 or 100 degrees. So then we talked about ways to estimate the roll angle to give a close approximation. Austin's final estimate was that our larger rolls were about 12 degrees. We finished with a little measuring experiment where we used the mast post, the floor and a weighted string to measure how far the boat was healing on some of the larger rolls.

To do this we made the assumption that the weighted string, taped to the top of the mast post (inside the boat) would approximate vertical. We also assumed that the mast post and floor were perpendicular. We then measured how far the weighted string moved from the mast post on a large roll. With these three pieces of information (length of side A, top of mast post to floor, length of side b, mast post to mark on floor and the 90 degree angle between sides A and B) we set out to draw a scale model of our triangle.

Side A: 183.63cm
Side B: 30.05.cm
Angle x: 90deg

We decided that reducing the scale by a ratio of 10:1 would allow us to draw the triangle on Austin's drawing paper. This was also an easy calculation as we just needed to move the decimal one point to the left. This gave us new dimensions for the scale triangle of:

Side A: 18.363cm
Side B: 3.05cm
Angle x: 90deg

We drew these two sides on the paper then added side C by joining points y and x and used a charting compass (same as a compass in a geometry kit with extra features to aid in charting bearings and courses on navigational charts) to measure the angle at point y. The result was 13 degrees. Since we felt that there were probably a few extreme rolls that were a bit larger than the ones we measured we estimate that, in the extreme cases, we are experiencing rolls of up to 15 degrees to a side (Austin worked out that it would be 26 to 30 degrees through the whole arc).

Now imagine cooking breakfast and dinner and pouring drinks while your kitchen floor (walls, table & counters) were all rolling around 30 degrees side to side. Not easy! No messes so far.

Math tools

Jump Math:

Austin has been working with his Jump Math workbook for Grade 6.

He prefers not to go through the workbook in page order, so he randomly flips to a page that looks interesting. In each session, he completes 2-3 pages.

Today, Austin learned about Prime and Composite numbers. He found the grid and instructions (Eratosthenes' Sieve) very helpful, and was able to correctly identify most of the prime numbers from 1-100. He learned that 1 is not a prime number, and we referred to this URL for further clarification and explanation.

I taught Austin how to determine if a number is divisible by 3 (a multiple of 3). If you add the digits together, and the total is a multiple of 3, then the number, itself, is a multiple of 3 (ie. Austin had identified 93 as a prime number, but I showed him that if you add 9+3 = 12, 12 is a multiple of 3 (3x4 = 12)).

Life of Fred:

We have completed the first Bridge quiz in the Life of Fred Fractions book. The Life of Fred series is an entertaining way to deliver math facts. Fred is a 5-year-old professor at Kittens University. He earns $500 per month and he sleeps under his desk. He really, really wants a bicycle.

In Chapter 1, Austin learned about the greater-than and less-than symbols, and was introduced to the saying, "the pen is mightier than the sword," expressed as Pen > Sword. Austin was easily able to relate to this, and remembered where it would have applied in some events in ancient history that he learned about at Academie Duello last year.

In Chapter 2, we were introduced to the concept of a billion (a thousand million), and onomatopoeia (these books are so much more than strictly math). Examples illustrated that it would take Fred over 31 years to list a billion reasons why he should own a bike, if he worked at it day and night.

In Chapter 3, Austin learned about cardinal and ordinal numbers. This concept has really stuck with him, as he continues to use it in his daily life - pointing out when he recognizes an ordinal number (ie. 1st, 2nd, 3rd ...) The Life of Fred books use imperial measures, so there are many opportunities for Austin to work with multiples of 12. One of the questions in this chapter was, "How many feet are in 48 inches?"

In Chapter 4, the book covered diameter and radius. Austin was already familiar with diameter, but hadn't learned about radius yet.

In Chapter 5, "Fred's Budget," Austin was introduced to financial budgeting and hyperbole. I've heard him use the word, "hyperbole," on a number of occasions since he learned its meaning. Fred is using a budget to find out if he can afford to buy a bike. Austin has learned the important distinction between how much Fred earns and how much he can save (because he has monthly expenses).

About every 5 chapters in the Life of Fred books, there is a Bridge quiz. Readers are given five attempts to get 9/10 or more on a 10-question quiz. Since Austin achieved a score of 9/10 on the first quiz, he is ready to proceed to chapter 6.

Math-U-See:

Austin has completed the first section of his Math-U-See textbook. Math-U-See uses manipulatives to teach math concepts. Austin is working on Epsilon (Fractions). The first section uses the green unit blocks to teach the concept of numerators and denominators. For instance, one question requires 10 unit blocks.

The student is instructed to divide the 10 units into 5 equal sets, then to count up two of the sets. Therefore, 2/5 of 10 = 4. These manipulatives help to illustrate the concepts of numerators and denominators.