**The Question: Is this mooring suitable?**

This is an nice physics problem. We need to understand both the steady state behaviour and transient loading due to wind gusts and sudden changes in direction.

**Buoyancy of Ground Tackle**

- Weight of chain
- Let
*w*_{13}, and*m*_{20}be the weight in water per meter of the 13mm and 20mm chain respectively. These values vary slightly by manufacturer, and are specified in air, but conservatively we expect*w*_{13}≈ 2.8kg/m and*m*_{20}≈ 7.5kg/m in air. - Weight of the anchor
- The weight of the anchor in air is
*w*_{a}= 500kg.

The specific gravity of concrete is *S**G*_{s} ≈ 2.5 and of steel is *S**G*_{c} ≈ 7.5. The definition of specific gravity relative to water is,

$$
SG = \frac{\rho}{\rho_\text{water}}
$$

where *ρ*_{water} = 1000kg/m^{3} is the density of the water, and *ρ* is the density of the object. We can use this together with Archimedes principle to correct for the effect of buoyancy on the ground tackle. Archimedes principle, the effective weight of an object immersed in water its true mass less the amount of water displaced,

$$
w^\prime = w(1 - \frac{\rho_\text{water}}{\rho}) = w(1 - \frac{1}{SG})
$$

The effective weight of the anchor in water revised by this calculation is *w*_{a}^{′} = 300kg and the effective weights in water per unit length are *w*_{13}^{′} = 2.4kg/m and *w*_{20}^{′} = 6.4kg/m for the 13mm and 20mm chains respectively.

This results in a total effective weight of ground tackle of **342kg**.

(Strictly speaking we should also correct for the buoyancy of the objects in air, but as the density of air is about 1000 times less than that of water, the difference is only about 0.1% or 3.5kg which we neglect.)

**Sustained Winds**

The main force pulling against the ground tackle derives from wind. So we need to calculate the wind loading of Hale Kai. For high wind velocities, the force of wind is given by the Lord Rayleigh’s drag equation,

$$
F_w = \frac{1}{2}\rho_\text{air} C_D A v^2
$$

where *A* is the area of the cross-section perpendicular to the wind, *C*_{D} is the aerodynamic drag coefficient which depends on the shape of the object and its roughness, and *v* is the wind speed.

Estimating *C*_{D} for the above-water portion of the hull is complex. Without recourse to complex simulations or experiments, we estimate it as somewhere between a sphere (*C*_{D} = 0.5) and a streamlined body (*C*_{D} = 0.04). We will use a value of 0.3. For the mast and rigging, we will use a value of 1.

The beam of Hale Kai is 9’ or 2.75m. Approximating the cross section as a rectangle of height 1m from the waterline to the top of the coachroof, this gives a cross-sectional area of 2.75m^{2}. The mast is about 10m high and about 0.1m thick. We double this to account for the rigging for a cross-sectional area of 2m^{2}.

Combining these, when the vessel is pointed into the wind, as it will be when the wind is sustained and the system is in equilibrium, and using a wind speed of 33m/s, the force applied to the chain is,

$$
F_w = \frac{1}{2}\rho_\text{air}(C_\text{hull}A_\text{hull} + C_\text{rigging}A_\text{rigging})v^2
= \frac{1}{2}\cdot 1.2 (0.4\cdot 2.75 + 1\cdot 2) 33^2 = 1845\text{N} \approx 188 \text{kgf}
$$

In the worst case, if all of that force is pulling directly upwards on the anchor and chain (an implausible steady state water level of 11m) there is still a **safety factor of 1.8** in the static case. Sustained hurricane force winds (Category 1 on the Saffir-Simpson Scale) will not pull the anchor from the bottom. It would take sustained winds of greater than 45m/s (87kt) to do so.

**Wind Gusts**

As we have seen, for static loading, the shape of the vessel is much more important than its displacement. This is not true of scenarios where the mooring system is experiencing sudden changes. Let us suppose that the system is in equilibrium as above and then a powerful gust of wind of 41m/s arrives perpendicular to the main axis of the boat, on its side.

In this case, the above water profile is more like a rectangle with a drag coefficient *C*_{D} = 2 and a cross sectional area of 9.45m^{2}, the length of the vessel and the height of the coachhouse roof above the water. This gives, hurricane force wind of 33m/s,

$$
F_w = \frac{1}{2} \cdot 1.2 ( 2\cdot 9.45 + 1\cdot 2) 41^2 = 21180\text{N}
\approx 2159 \text{kgf}
$$

This force is resisted by the underwater drag, again modelled as a rectangle of size 8 ⋅ 1.2, the length at the waterline and the draught,

$$
F_D = \frac{1}{2} \cdot 1000 \cdot 2\cdot 9.6 u^2
$$

where *u* is the speed of the boat in the water. We can immediately work out the terminal speed, the maximum possible value for *u*, when these forces are equal. This turns out to be *u*_{max} ≈ 1.5m/s.

We can proceed numerically to find out how long it takes to reach this terminal velocity. If the gust lasts for some time, *t*, and the wind remains on the beam, the final speed of the vessel will be, from Newton’s Second Law,

$$
a = \frac{F_w - F_D}{m}
$$

where *m* is the mass of the vessel which we will take equal to the displacement, or 6600kg.

```
f_w :: Double -> Double
f_w w = 0.5 * 1.2 * ( 2.0*9.45 + 2.0) * w^2
f_d :: Double -> Double
f_d u = 1000.0 * 9.6 * u^2
accel :: Double -> Double -> Double
accel w u = (f_w w - f_d u) / 6600.0
integrate :: Double -> Double -> Double -> Double -> (Double, Double)
integrate dt w u t
-- stop when we are within 5% of the wind force
| abs (f_w w - f_d u) < 0.05 * f_w w = (u, t)
| otherwise = integrate dt w (u + dt * accel w u) (t + dt)
main :: IO ()
main = do
print (integrate 0.001 41.0 0.0 0.0)
```

`(1.4444449805914912, 1.0099999999999996)`

Running this program computes the speed that we reach by the time the drag force is within 5% of the wind force and how long this takes. We see that it will take just over a second to reach the terminal velocity. This is essentially instantaneous. This is indeed a powerful gust of wind.

What is the effect of this on the anchor system? By assumption, the system began at equilibrium, with the vessel tethered to the anchor and the gust arrived tangent to the swinging circle imparting a speed of *u*_{max} = 1.5m/s nearly instantaneously. The boat will swing around the circle to face into the wind, and as it does so, the force of the wind will lessen, reducing to tolerable levels as shown in the static analysis. The greatest load on the anchor system will therefore be at the beginning of the swing with the anchor providing the centrepetal force to keep it on the circle. The magnitude of this force is,

$$
F_c = \frac{mu^2_\text{max}}{r}
$$

where *r* is the horizontal distance from the anchor.

If *r* is 8m, corresponding to a water depth of about 8m, we get a value of *F*_{c} = 1856N ≈ 189kgf.

To add this force to the sustained wind force from the 33m/s at equilibrium, we recognise that they are acting at right angles to each other, therefore,

$$
F_\text{total} = \sqrt{F_w^2 + F_c^2} = 267\text{kgf}
$$

The total wind speed is is, analogously, 51m/s or about 100kt in a direction about 40 degrees ahead of the beam..

So with sustained winds of 64kt and short gusts of 100ts on the quarter, with a water depth of 8m, we can conclude that the system will hold with a **safety factor of 1.3**.

**Effect of Water Depth**

Throughout, we have made the assumption that all of the forces involved are directly transmitted to the anchor, pulling on it in an upwards direction. We can see that this is true for a water depth of 8m, where we can expect an angle of about 45^{∘} between the chain and the bottom (presuming that it is stretched taut because of wind at the surface).

The magnitude horizontal force as calculated above is related to the tension in the line, *F*_{horiz} = *T* cos *θ*. The magnitude of the vertical force on the anchor is then,

$$
F_\text{vert}
= T\,\sin\theta
= F_\text{horiz}\frac{\sin\theta}{\cos\theta}
= F_\text{horiz}\,\tan\theta
$$

For *θ* = 45^{∘}, the vertical and horizontal forces are equal. When $\theta = 64^\degrees$, the vertical force is about double. As *θ* approaches 90^{∘}, however, the vertical force grows without limit. Actually the limit is the buoyancy of the boat, or 6600kgf, more than enough to lift the anchor.

If the mooring is situated so as to just dry out at extreme low spring tides, then a storm surge of 2m on top of a high spring tide can bring the rode angle to 45^{∘}. This corresponds (because tan (45^{∘}) = 1) exactly to the circumstances analysed above.

If, however, the mooring is situated in 1m of water at low tide then such a surge has the following effect. The total depth of the water is now 9m, and with a taut chain, the horizontal distance between the boat and the anchor is 6m. This increases the centripetal force to 232kgf and the angle with the bottom rises to 56^{∘}. The total vertical force on the anchor now becomes,

(188 + 232) ⋅ tan (56^{∘}) = **623kgf**

which is unacceptably high.

**To be continued**

This static analysis is good as far as it goes. However the anchor rode does not normally form a straight line from the boat and the anchor and this has several consequences. Firstly, the angle between the rode and the sea floor will be as near to horizontal as possible. Secondly, as transient forces cause it to lift, it will resist and pull back, somewhat like a damped spring. The dynamic analysis follows in the next post.

Thanks to Costa and MP4Man for discussing the first draft of this post and spotting embarassing critical errors.

]]>In the box is a Vertex Standard VX-1700. These radios are sold mainly as land mobile transceivers to be installed in government and NGO vehicles, similar to the Codan radios that we used when I worked with the UN. They support fancy features like automatic link establishment (ALE) and encryption, but at their core, they are simply robust HF transceivers. Vertex Standard is the same company that makes Yaesu radios: Yaesu is their amateur radio division.

Together with the radio came an antenna coupler, an SG-230 made by SGC suitable for matching the radio to a long-wire antenna (e.g. a backstay antenna). It also came with a conspicuous whip antenna designed to be mounted on a Humvee or Land Cruiser or some such. I don’t have one of those so it may not be of much use.

The VX-1700 is normally set up to be used by people trained to use radios, not by engineers or radioamateurs. This means that it’s normally set up with a bunch of standard channels, much like a marine radio, and it isn’t permitted to choose frequencies and modes directly. When set up this way, the radio is much less flexible. There are a number of ways to enable variable frequency oscillator (VFO) mode to get around this. One is by shorting two pins on the data connector on the back of the radio. Another is by simply enabling VFO mode using some difficult to obtain “CE-77” software that needs an obsolete version of Windows.

Alfie MM0AAL and I found a third way. Actually, the radio arrived in something called “dealer mode” which seems to have all of these features enabled. But we discovered how to program the radio, including setting “dealer mode”, without needing to run dodgy software.

What happened was this. After making up a power cable, the first thing that we did with the radio was, obviously, hook it to a computer to see if digital transmissions would be possible. In doing this, somehow, the radio became locked. It had a little padlock displaying on the screen and nothing that we could do would unlock it again. It is possible to program one of the four “soft-keys” on the front to lock and unlock it, but they didn’t work, and we didn’t have the dodgy software that would do this.

After some experimentation, we found some undocumented button combinations. When the radio is powered on while holding certain buttons, things happen:

**F + ENT**: displays*RL CLEANING*and the relays click a bunch.**F + 1**or**F + 4**: all symbols on the display illuminate. This is probably a diagnostic for checking the display for faults.**F + 0**: asks for a password.

The last one was definitely intriguing. We found that, pressing **F** would provide access to a limited number of settings. Pressing **ENT** would start entering a four digit passphrase. The default passphrase, or at least the one on this radio, found after a bit of trial and error, is *0123*. Press **ENT** again and apparently the full range of settings is available. No need for special software at all.

The fix, of course, four the problem of the locked radio was to go through the settings and assign the *LOCK* feature to one of the soft-keys (I chose *P2*). It is also very useful to put transmit power selection on another of the soft-keys as the radio arrived only able to transmit at 100W and no lower. This can damage some antenna couplersthat want not more than 10W during tuning as well as radios that would otherwise have to deal with large amounts of reflected power during tuning.

groovy.net started life as the Internet domain for the Groovy Variety Store in Toronto in 1996. This was a space where the arts collective called Idiosyntactix met and worked on experimental projects to make the nascent Internet accessible to people who would not normally have access to it, mainly artists and musicians, and explored the intersection of art and technology. We put on events, published zines, pioneered live streaming (audio, of course, at the time, as live video streaming was a long way off), installed interactive art pieces (such as a public access terminal outside a psychiatric hospital to enable outpatients to access USENET), performed cyborg art (such as at meetings of NATO - uninvited, of course), and were generally fixtures of the vibrant art and technology community in Toronto in the late 1990s.

We realised early on that to support these activities, we needed an Internet Service Provider, and that the usual commercial suspects wouldn’t do. So we created Groovy Network Services. We made websites for ourselves and others, and hosted email until well after Web 2.0 concentrated that sort of thing in the hands of a few large providers (actually, we still do, a case in point being this very web site). We also participated in pushing the boundaries of the technical underpinnings of the Internet itself, and any geeks reading this will recognise shibboleths such as the 6bone, SDSL and VoIP. We are still pushing the boundaries of art and technology now scattered across North America and Europe, but no longer as a cohesive arts collective with a definite spatial locus.

One branch of the historical group ended up in Scotland. For a time, focus turned to organising communities in remote places to create Internet infrastructure. This built on the Berlin branch’s observation about the importance of the economics of land and infrastructure and the legal object Groovy Network Services Ltd was created to facilitate this project. It worked well. Particularly well in those places where the community had organised to buy the land on which they lived, generate their own electricity, and establish their own communications networks. Still, the object was to enable connecting *to* the Internet rather than *creating* the Internet. Attempts to build a meaningful, local, on-line community, independent of the behemoths of Silicon Valley, fell flat.

The Internet has changed. The Web is dominated by gigantic social media services, and no longer has the decentralised anarchistic flavour that fuelled hopes that it would upset the global order and empower the marginalised. There has been change and upset, and powerful organisations, large companies and governments, slowly and ponderously figured out how they could use the amplificatory character of the Internet to solidify their position. Capital got there in the end, and in retrospect there was little that we could have done about it for all our cleverness and agility. The front line of societal change is no longer the Internet as it was in the 1990s.

There is good reason to believe that the current front line is in the effort to survive the incipient climate catastrophy. To a great extent, this is playing out in the world’s oceans. The challenge for us, the local “us” who come from that small arts collective in Toronto in the 1990s, is to figure out how to apply everything that we have learned about economics and telecommunications, everything that we know about using art and the media to shape discourse, and to apply it to this problem. Just as our tools two decades ago were a Sparc 1+ and an SGI Indy an essential requirement to get out on the ocean, to understand, measure, communicate and encourage others to do likewise, is a boat.

And now we have one, the Cutter Hale Kai, to be developed into a platform for the next phase of our art.

]]>]]>I and my wife, Kitty, were the original owners of Hale Kai. I ordered it built in late 1977. I told Terry Erskine that I had another year’s service in the US Air Force before I retired, so to take his time. The boat was shown in the London Boat Show in January 1979 by Terry. I retired and went to Plymouth, liked it because I could hand start it when the batteries were low. We sailed around the British Isles and across the English Channel several times to Europe in order to learn to compute and navigate the tidal currents, and then left England in August 1979 just in time to be caught 20 miles west of Ushant, France in the infamous Fastnet Storm. We secured for the approaching apparent storm winds and seas, and we sailed with a reefed storm staysail until the seas got too high, then finally removed storm staysail, lashed the tiller and laid ahull. We got knocked down several times with the mast tip hitting the water in 60+ ft. seas, but ended up with no damage other than a bent wind vane on the masthead. This tells one just how well designed and well built a Golden Hind 31 is for ocean sailing.

We crossed the Atlantic twice, circumnavigated the Mediterranean twice, and cruised North Africa, South America, Bahamas, and the East Coast of USA over the next 8 years, putting over 50,000 miles on Hale Kai. Because of severe illness in our parent’s, we reluctantly gave up sailing to take care of them and sold the boat to a retiring US Navy officer and his wife who wanted to cruise the Northern British Isles. I still have both my navigation and social logs of all our travels, ports, and rivers we cruised during those years. I was a fan of Joshua Slocum, so for navigation I used solely my sextant, American Practical Navigator, H.O.229, Nautical Almanac, stopwatch, depth sounder, a trailing log, and two digital watches. I had no other navigation equipment. Being an amateur radio operator, I used my HAM radio to get the exact time for my digital watches. I also used the HAM radio for checing into the maritime mobile channels, and the SSB frequencies of the HAM radio for weather reports. We took the mast off, lashed it to the bow railing and boom cradle, and cruised the major canals of France. We had no troubles during the 8 years after the Fastnet Storm, and we greatly missed her for a number of years after we sold her.

I am now 86 years old, and can no longer sail. Thank you again for the memories. If you wish any further history of Hale Kai (Polynesian for “Home on the Sea”, and pronounced: ’hahley cahee;), please let me know.

Jim Haynes

Richmond, TX

It is a triple-keel, cutter-rigged, Golden Hind 31 called