W. J. Jurens

October, 1976

(revised and updated, June 2001)

The following tables and charts should be useful to those interested in determining the approximate changes in relative projected areas of warship internals with variations in angle on the bow and angle of fall. Such determinations are useful, for example, in the statistical simulation of naval gunfire actions where the probable effect of individual hits is to be taken into account by a "Monte-Carlo" type random event generator.

The geometry of the vessel used in this study has been specifically selected to be representative of as many typical vessels as possible. The overall dimensions and proportions of the hull -- and to a certain extent of the superstructure as well -- were selected by averaging the actual measurements of approximately forty battleship and battlecruiser designs produced from c. 1920-1945. These dimensions were used to produce a transparent scale model at a scale of 1:1000, which was then photographed with a 35mm camera while the angle on the bow and the angle fall were varied in a consistent manner and at equal increments of 30 degrees horizontally and 20 degrees vertically, with one additional photo being taken from directly overhead. The resulting frames of film were then enlarged and transferred to transparent acetate sheets, which were in turn analysed with the planimetric capabilities of an Apple II+ computer with an attached graphics tablet. The resulting output was subsequently divided into a number of categories and printed out with additional routines used to compute relative percentages of areas from the raw area figures obtained planometrically. The resulting output, allowing for systematic and accidental errors in measurement and computation, is considered to be accurate to within 1-3 percent.

A few cautions and explanations of the methods used in coding the data and its interpretation are probably in order. The areas listed under "Turret(s)" include all projected turret surfaces and associated barbettes. The areas listed are for the entire projected area of the space involved both above and below the waterline, and thus no allowance has been made for the protective effects of the ocean surrounding the hull. In practical terms, especially at low angles of fall, much of the area of the sides of the magazines and engineering spaces would, in fact, be practically inaccessible to shell fire because they are well below the waterline. In addition, the projected areas here obtained take no account of the possible screening or shielding effects of unarmored portions of the ship located in the superstructure or elsewhere. This can sometimes lead to some misleading results. For example, although a small portion of the deck area of the forward magazines is still visible and projected at an angle on the bow of 180 degrees and an angle of fall of 20 degrees, the chances of a projectile actually penetrating almost the entire length of the target's superstructure in order to reach this area are abysmally small. Of course the masking effects of superimposed armored target areas are taken into account in all cases. The rather large proportion of target represented as "miscellaneous" covers projected target area through which an inbound projectile would intercept essentially no armored areas (or vital) at all.

It will be noted from the above that the effects of changes in angle on the bow are at a maximum when the angle of fall is small, decreasing rather rapidly thereafter as the angle of fall increases, and eventually becoming zero when the angle of fall is 90 degrees. Generally speaking, in the model used in this study the effects of screening are essentially absent beyond angles of fall of 45 degrees. The tabulated values for "Total Area" are raw areas and for the vessel in question may be converted to square meters by multiplying by the constant 6.916. The tabulated "Total Area Ratio" is the ratio of the total area at any given angle on the bow and angle of fall combination to that of the entire target at an angle on the bow of 90 degrees and an angle of fall of 0 degrees. Drawing C1569 gives the total projected area of the target at any given angle on the bow and angle of fall combination to that of the rectangular "footprint" of the water plane.

Click on the following to see the drawings:

- Geometry Database
- Angle of Fall 00 Degrees
- Angle of Fall 20 Degrees
- Angle of Fall 40 Degrees
- Angle of Fall 60 Degrees
- Angle of Fall 90 Degrees
- Projected Area Ratio vs Angle on the Bow and Target Area for Standard Warship

The raw data may be downloaded (probably by 'right-clicking'), in two common spreadsheet formats:

Last Updated: 11 August, 2001.

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