‘The stuff the movie-makers dream of.’ In Lake Michigan, a graveyard of long-lost ships captivates historians

After a year of scouring the depths of Lake Michigan with a sonar-equipped fishing boat, Steve Radovan finally got a hit on the gray-scale monitor in the captain’s cabin in May 2016.

The 71-year-old shipwreck enthusiast powered down the Discovery’s engines and dropped a waterproof camera attached to a rope into roughly 300 feet of water. The images revealed a three-masted barquentine, covered in mussels and algae but lying on the bottom still largely intact. After reporting the finding to the state of Wisconsin, he learned the foundered ship was the Mojave…

For the full story click here


Dredging and Dredging Equipment


Dredge in Norfolk Harbour, 2009.  We have a great deal of information on dredges used on the Great Lakes around the turn of the last century on a companion site; click here to see that.

Applications Guide for Statistical Analyses in Dredged Sediment Evaluations

Joan U. Clarke, Dennis L. Brandon
U.S. Army Corps of Engineers Miscellaneous Paper D-96-2
June 1996

Dredged sediment evaluations often require statistical analysis of chemical or biological test results. However, the resulting data are frequently problematic for standard statistical procedures because of improper experimental design, insufficient replication, failure to meet statistical test assumptions, outliers, and missing or below detection limit observations. Such nonideal data can seriously affect the error rates of statistical tests. This in turn increases the likelihood of drawing false inferences concerning the potential of a dredged sediment for adverse biological effects.

Simulations were conducted to investigate the impact of nonideal data on the performance of statistical tests recommended for dredged sediment evaluations.
Statistical test error rates were assessed using data that violated the normality and equality of variances assumptions, as well as data that included outliers or nondetects.

This report includes a brief introduction to statistical aspects of sediment sampling, some basic experimental designs and problems that can arise, errors in statistical testing and the importance of power, testing the normality and equality of variances assumptions and implications of violations, the effect of outliers, methods for analyzing less-than detection limit data and interpreting statistical test results. Program statements are provided for recommended statistical testing procedures using some popular statistical software packages. This report is intended as a companion to the statistics appendix of the Inland Testing Manual.

Dredging and Dredged Material Management

U.S. Army Corps of Engineers EM 1110-2-5025
31 July 2015

This Engineer Manual (EM) presents a comprehensive summary of the dredging equipment and dredged material placement techniques used by the U.S. Army Corps of
Engineers (USACE), and it describes the management and design processes associated with new work and maintenance dredging related to navigation projects. Guidance is provided on the following dredging topics:

  1. Evaluation and selection of dredging equipment for various materials to be dredged.
  2. Planning, designing, constructing, operating, and managing environmentally acceptable open-water and confined dredged material placement areas for both short- and long-term placement (disposal) needs.
  3. Planning, designing, developing, and managing dredged material for beneficial uses while incorporating ecological concepts and engineering designs with environmental, economical, and social feasibility.

Note: In this document, the terms “placement” and “disposal” are used synonymously to describe dredged material deposition after its removal from the dredging prism.

Dredging Equipment

July 1981

This manual contains the following: information on procurement of dredging; types of equipment available, their characteristics and capacities; basic economics of dredging operations; and preparation of plans and specifications for the procurement of dredging for harbours, anchorages, turning basins and ship channels. A catalogue (description and characteristics) of dredges currently in the Navy inventory is included for guidance in the potential procurement of dredging by assignment of Navy equipment.

Testa’s Restaurant: an old Favourite of Chet and Myrtle’s Closes to Rebuild

Testa’s restaurant in Palm Beach, an old hangout of Chet and Myrtle Warrington in their years in Palm Beach, closes 15 July 2017 to rebuild. Testa’s was started in 1921, moved to its current location and building in 1946, a couple of years before Chet’s yacht tied up at the West Palm Beach Municipal Marina shown below.

It remained a favourite of theirs until Chet’s death in 1961 and Myrtle’s in 1976.

Buoyancy and Stability: An Introduction

Ever since people set out to sea in ships, the issues of buoyancy and stability have been of importance. In spite of this, the treatment it receives in textbooks is often lacking. Following is an overview of the subject; basic understanding of the principles is essential in performing the experiment and interpreting the results.



Figure 1

Buoyancy is ultimately what makes things float, such as the buoy in Figure 1. This is true whether the material the boat is made of is lighter than water (like the balsa wood rafts Thor Heyerdahl and his crew crossed the Pacific with in 1947) or heavier than water. The latter would include objects from the buoy shown to the ships of the U.S. Navy.

The basic concept is very simple: for anything placed in a fluid medium, the upward force the medium exerts on the body is equal to the weight of the fluid the body displaces. This is not only true of bodies placed in water; it is also true of those in air. The difference is that, for those in air, the weight of the air displaced is usually not enough to “float” the aircraft. A notable exception are dirigibles such as the “Goodyear blimp,” which is filled with helium, a gas lighter than air. Another lighter-than-air gas used is hydrogen. This is very combustible, as everyone was reminded of when the Hindenburg caught fire in New Jersey in 1938.

Most buoyancy applications are marine ones, and it is those we will concentrate on in this experiment. We will also concentrate on rectangular forms and flat-bottomed vessels, which simplifies the math somewhat. However, these principles can be extended to just about any floating craft.

Using a flat-bottomed craft also makes it easier to understand why displacing a fluid works. Consider first the following: how the force of the fluid on the flat hull of a craft varies with depth1:


Figure 2: Illustrating Water Pressure Increasing in Proportion to Draught

For a fluid at rest, the hydrostatic pressure increases linearly with depth, thus




Figure 3 Inadequate Freeboard

where p is the hydrostatic pressure, γ is the unit weight of the water, and D is the depth from the water’s surface to the bottommost point of the vessel, usually called the draught. This distance from the water line to the top of the rectangle (the gunwale) is called the freeboard; the results of inadequate freeboard can be seen in Figure 3.

In any case, for a vessel of beam (width) W and a length L the volume it displaces is given by the equation



Combining and rearranging these two equations,



For the boat to float, it has to be in static equilibrium, and so the downward force of the weight of the boat Wboat must equal the upward force Fbuoyant. Therefore,



So we’ve established a relationship between the weight of the boat and the volume of water it displaces. The “far right” hand side only applies to boats with a flat bottom and straight sides.

What this means is that there are three ways we can weigh an existing boat:

  1. We can simply weigh it on a scale. For small boats this isn’t too difficult; larger ones can be tricky.  We can then estimate how far it will sink into the water.

  2. We can measure the freeboard, then obtain D and, knowing L, W and the unit weight of water, we can compute the weight of the boat. This works easily for rectangular boats; for real boats, you have to determine the relationship between the actual waterline and the displacement, then see where the actual waterline ends up.

  3. We can use an overflow method, which is okay for small experiments (like Archimedes used) but not so hot on a larger scale.  But this illustrates our concept.

Procedure for determining volume of water displacement2:


Figure 4 Displacement





Buoyancy is a fairly straightforward concept, although it may be a little hard to grasp up front. Stability—the ability of the ship to resist overturning—is a little more difficult, although it’s obviously important, as the following diagram of a ship with waves coming at the beam shows3.


Figure 5 Showing the Transverse Movements of an Easy-Rolling Vessel Among Waves, and Also of a Raft

Let’s define (or recall) a couple of terms.

Centre of Gravity: this is easy, mathematically this is the centroid of the mass or weight of the ship. An illustration of this is below.


Figure 6: Centre of Gravity of a Ship

Centre of Buoyancy: this is a little trickier, this is the centroid of the cross-sectional area of the ship under the water line, as shown below.


Figure 7 Centre of Buoyancy of Box-Shaped Vessel

As you can see, for a box-shaped vessel which is not listing (i.e., leaning at an angle) or has no squat (i.e., not angled along the length of the boat) the centre of buoyancy is located halfway down the draught of the vessel, halfway across the beam, and dead amidships.

The centre of gravity and the centre of buoyancy are not necessarily at the same place; in fact, they are usually different. That difference determines both the stability of the ship and, literally, how it rolls.

We know that motor vehicles with high centres of gravity (such as off-road vehicles) are more prone to turn over in use than those with lower centres of gravity. Ships are the same; we need to have a way to decide how stable a ship is and whether there is a point that a ship becomes unconditionally stable or unconditionally unstable.

As long as a ship is upright, and both the centre of gravity and the centre of buoyancy are in the centre of the ship in all respects, it is theoretically possible for a ship never to turn over. As a practical matter this is impossible; even very large ships like cruise ships, which use their size to resist roll in most wave situations, are going to roll some. Below is a diagram which shows the centre of gravity and the centre of buoyancy for a ship which is upright and which is inclined 14º.


Figure 8 Vessel Floating Upright (left,) and Inclined 14 Degrees (right)

We need to look at this carefully and note the following:

  • The point G is the centre of gravity of the ship.

  • The point B or B’ is the centre of buoyancy of the ship. In the course of inclination the centre of buoyancy will change because the shape of the cross-section under the waterline changes; this is fairly simple to calculate for rectangular ships and more complicated for curved hull shapes.

  • The point M is the metastatic point of the ship. The distance GM is called the metastatic height of the ship.

  • If point G is below point B or B’, the ship is unconditionally stable; it will not turn over unless G and B’ is changed by taking on water, shifting cargo in the ship, etc.

  • If point G is below point M, the ship is conditionally stable, and if point G is above point M, the ship is unconditionally unstable.

The reason for this last point is simple: the ship above is rolling in a clockwise direction. The resisting moment of the buoyancy, calculated by (GZ)(Wbuoyant) is counter-clockwise, as the buoyant force is upward. This is true as long as G is below M. If G moves upward above M, then the now driving moment (GZ)(Wbuoyant) turns clockwise, the same direction as the rolling of the ship, and the ship will generally turn over4.

Thus the location of M, abstract as it may seem, becomes a critical part of the design of a ship. But how is it done? There are two methods we will discuss here of determining the metastatic height of a ship.

Determining Metastatic Height

Theoretical Method

This method uses the following formula to determine the location of the metacentre:



For a rectangular vessel, the moment of inertia is the same as we used in mechanics of materials, i.e., LW3/12, and is applied as follows:


The displacement volume was given earlier. We then compute the distance between the metacentre M and the centre of buoyancy B as follows:


Note carefully that this is NOT the metacentric height GM; it is then necessary to subtract the distance from the centre of buoyancy to the centre of gravity from this result to obtain GM. This is done as follows:


Figure 9: Computing GM From the Height of the Metacentre Above the Centre of Buoyancy

It’s worth noting here that the location of point M is independent of the centre of gravity and dependent upon the geometry of the ship and its volume under the water line (or total weight.)

Timing the Roll

This method is sort of an “old salt’s” rule of thumb method. First, let’s define the roll time. The roll time is the time it takes for a ship to start from rest at an angle of roll (port or starboard,) roll to the opposite side, and return to the original orientation. This can be approximated by the equation5




  • tr = roll time of ship, seconds
  • GM = metastatic height of ship, meters or feet
  • W = beam of ship, meters or feet
  • C = constant based on units of GM and B
    = 0.44 for units of feet
    = 0.80 for units of meters

Solving for metastatic height,



This is significant for another reason: another rule of thumb used in yacht design is that the roll time is seconds should be between 1 and 1.1 times the beam W of the boat in meters6. Yachts with shorter roll times tend to “check” or quickly come back to centre when in rough seas; this can be a hard experience for passengers and make a complete mess of stowed cargo. Yachts with longer roll times will come over like they’re about to capsize, and then slowly roll back around. The usual result of this is seasickness and a miserable ride.

1Walton, T. (1899) Know Your Own Ship. Charles Griffin and Company, London, England. Much of the material that follows on buoyancy and stability comes from this work.

2Keep in mind that the unit weight of sea water is greater than fresh. Why is this so?

3Seamanship pointer: if you’re in a boat and are facing high waves, wake, etc., best way to take them is to point the blow into the direction the waves are coming from, not take the waves on the beam.

4Whether it actually does gets into issues of freeboard, rate of roll, etc., which are beyond this presentation or experiment.

5Nudelman, N. (1992) Yacht Design Course. Lesson 6: Stability. Westlawn Institute of Marine Technology, Stamford, CT.

6Gerr, D. (1992) The Nature of Boats. International Marine Publishing, Camden, ME. Much of the material on this method of determining GM is taken from this source.

Chicago Yacht Club Regatta, Late 1940’s

Following are some photographs from a Chicago Yacht Club regatta on Lake Michigan in the late 1940’s.

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I can’t be more specific about the date; however, one of Chet’s signature achievements at the Club took place in June 1946 when he, as Chairman of the Power Yacht Committee, helped to instigate the Commodore Fleet Review.  That helped launch his bid to become Commodore of the Club in 1950, fifty years after his father had held the post.  Given the large number of sail boats shown, it’s probably another event, but I’m pretty sure it’s in that era.