Understanding Block Coefficients

By Stuart Slade
Updated 19 December 1998

Sorry this took so long to get around to but here goes. Block coefficient is determined by taking a notional rectangular block, the length, width and depth of which are those of the ship in question. The volume of this block is then calculated.

The actual volume of the ship hull in question is then assessed and expressed as a proportion of the volume of the block.

Norman Friedman's Battleship Design and Development has a good account of these things (its long out of print unfortunately). DK Brown has also produced a series of books and articles covering the minute details of hull design.

If you look at a hull form profile (the horizontal section through the hull at the waterline), you'll see that the curves are not smooth and continuous from bow to mid section. Normally, the entry is fine, stays that way for a while and then starts to widen quickly. The reason for this is the way water flows past the hull. Hulls work best in smooth water. At the point of entry, the curve of the hull is convex, it bulges towards an observer sitting in the water off the bow. This pushes the water to one side (in three dimensions) and generates a positive pressure sine wave along the hull. The amplitude of this pressure wave is determined by the hull form and some other things.

However, where the hull shifts from a gentle to a rapid increase in beam, the curve is effectively concave (viewed from our observer in the water). This generates a negative pressure sine wave, the amplitude of which is determined by the rate and length of that particular design feature. If the peaks of the two waves coincide (that is the maximum positive pressure coincides with the maximum negative pressure), the two waves cancel each other out and the hull is sailing in smooth water. Sneaky, isn't it?

This is one of the reasons why the Iowa's had problems in heavy weather. The long, fine bow section lacked internal buoyancy so it had tended to dig in. In addition, the form of the bow meant that the first positive pressure wave negative peak was well forward of any cancellation so it sucked the bow downwards. Adding a blister forward, around A and B turrets (as was projected to improve torpedo defense) would have shifted the negative pressure curve aft, increasing the downward pull on the bows. This was not good.

These pressure waves have other, interesting effects. The waterline of a ship is usually drawn as a straight line. However, the combinations of pressure curves means that the real waterline actually varies up and down according to the pressure wave at that point. In some cases, these variations were enough to cover the armor belt of to lift it clear of the water. Either way they mess up freeboard something horrible. One of the reasons the Japanese used that unique wavy sheer line was that it followed the pressure waves around the hull, maintaining freeboard and, thus, seaworthiness. A great example of meticulous attention to detail while completely blowing the important things in life.

There are other applications of this as well. For example, the US WW2 cruisers and the Arleigh Burke class destroyers all have fantails that slope upwards towards the stern. Not at speed they don't - the ships dig their sterns in and that deck becomes horizontal.

These things are why making major changes to hulls is so fraught with danger. We've had a lot of proposed modifications to battleships on these boards, mostly directed to the Iowa's (for example, removing turrets to allow for flight decks or VLS systems).

The most elementary of these are gee-whiz modifications (wouldn't it be great if....) that do not make any allowances for weight and trim changes. Some of these would have changed trim by so much that the bows would have gone right under (I do work these things out you know!!!). As for the topweight......

The next group try to make the weights add up so that the net total comes out the same. These look more convincing but usually fall foul of stability and stress calculations. A large area of weight carried high will not compensate for a small area carried lower even though the totals add up to the same. Stress is a real swine to accommodate, especially with the BBs. The weight of those turrets was so great that the hull was virtually designed around the stress loadings they imposed.

If a conversion system is going to work, not only have the weights got to add up but they have to do so in roughly the same places. If the pressure waves around the hull are distorted, they cease to interact properly and the wave-making resistance shoots up. Suddenly, there is an acute loss of speed.

Another nasty point about gun turrets and their weight. The weight of the turret and its barbette are carried by the ship's keel - its the only thing strong enough to do it. There has to be the correct level of buoyancy at those points to support the turrets. Now, take the turret out, that added buoyancy arches that part of the ship's spine upwards and CRACK - gurgle gurgle.

You can do the same with the ship's engines which is why replacing steam turbines with much lighter gas turbines is problematical.

What about wing turrets??? The problem with them was that they required great reinforcement of the ship's keelson and bottom to support the weight. In the early days, this wasn't so much of a problem and the weight invested in the reinforcement was comparable to that needed for the taller barbettes needed if guns were going to be superimposed. Soon those lighter guns (12 inch etc.) were replaced by much heavier mountings and the structural penalties got nightmarish. Centerlining guns got to be the only viable solution and the weight penalty of the barbette required for superimposition wasn't so bad.

Another minor problem with pressure waves is that they create areas of stagnant water (water that moves at the same speed and direction as the ship) at points along the hull. By and large, these are nothing much to worry about but there have been cases where the outfall from the ship's toilets discharged directly into an area of stagnant water with the result that the poor crew were faithfully followed around the oceans by their own by-products. This was quickly rectified at a refit.


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