end of the sliding ways often rises to the surface shortly after the vessel has entered the water. In the diagram a complete set of curves has been given to fully illustrate the matter, but for practical purposes only that part of the diagram where the vessel is represented to be moving from the position where the C.G. is at the way ends, to the end of the second period, is required.

As the minimum moment against tipping is a very important thing, it will be useful to know what variation will be made in its amount by any alteration to the length and form of the standing ways of this vessel :

Lengthening the standing ways 10 feet increases the moment from 9,700 to 13,700 foot-tons.

Shortening the ways 10 feet decreases the moment to 5,300 foot

tons.

Increasing the camber from 12 inches to 18 inches increases the moment to 14,500 foot-tons.

Decreasing the camber to 6 inches decreases the moment to 4,000 foot-tons.

If with a certain declivity of ways for the launching of a vessel, it is found, by calculation, she will tilt, the standing ways must be extended further out into the water, or, if this cannot be done conveniently, their outer ends must be lowered, or ballast put into the fore end of the vessel. The first two increase the buoyancy moment about the end of the standing ways, and the third decreases the weight moment about the same point.

♪ = mean angle of declivity of ways under vessel.
Bangle between ways and dog shores.
fcoefficient of friction (between 1.0 and .7).

The ratio of second period to length of sliding ways cannot be got lower than about 25 per cent without danger of tipping.

RUDDERS.

In determining the most suitable area of rudder it is usual to take the same as a percentage of the immersed longitudinal plane of the ship, which percentage will vary with the degree of fineness of the vessel.

Having fixed upon the area, the diameter of stock may be calculated by various formulæ, some of them, unfortunately, of a very approximate character, and on this account, where high speed will be attained, it is advisable to carefully calculate the required diameter irrespective of the result obtained by the classification societies' formulæ. For this purpose it is necessary to know, (1) the hard over angle of rudder, (2) centre of pressure on rudder blade, (3) maximum pressure exerted at hard over with ship at full speed. The angle of helm being usually 35°, the pressure on blade at this angle at full speed may be found from the formula, -P representing the pressure in lbs.

PAV2X sin axp.

It should be stated that speed of vessel in knots per hour plus 20 per cent to allow for the slip; A=area of rudder in square feet, including emerged surface; and p-pressure in lbs. per sq. foot at 1 knot, 3.19 lbs. per sq. foot.

Before, however, the twisting moment on the stock can be solved, the centre of pressure must be located. This centre being the breadth from the leading edge with the helm amidships, does not arrive at the centre of gravity of rudder until 90° is reached, and as 35° is the usual angle, it will be sufficiently close to take .37 of the breadth of the rectangle equalling the rudder area:

Centre of pressure from centre of stock=1=

Thus from the length, breadth, draught, area of midship section, and displacement, the mean length of entrance and run and the mean angle can be got. There are other methods of working this out, which will occur to any one, but the method given is perhaps the simplest.

In order to get the length and angle of entrance and run separately (instead of the mean as stated), it is necessary to have in addition, the displacement in two portions, one forward of the midship section, and one aft, the distance of the midship section from one end of the ship, and the mean draught of each of these portions; treating them, in fact, as two separate ships, one of which has no run and one no entrance.

In my earlier attempts I retained the actual breadth of the ship as the breadth of the block ship, and varied the depth, but I prefer the plan before given of using for the block ship the mean draught of the actual ship. In ships with extremely raking sterns or stern posts, I take the length at half depth when that can be got (or the mean length) as the length of the block ship. In single screw steamers, I take the length to the forward stern post.

The block ship will often be found of use in forming first or

Fig. 35.

21

N14.8

7.9

3.5

-S-S. NO. 4 DRAUGHT 17.3 FORD. 19'11"

Fig. 34.

approximate designs, and in this view it may be interesting to compare the wetted skin surface of actual ships with that of the equivalent block ships, this being an important element in speed calculations and otherwise.

In the foregoing table I have selected fourteen ships of very diverse types, giving their dimensions, block models, actual wetted surface (exclusive of that of keels or rudder), and wetted surface of block ship, and the ratio of one to the other.

From this it will be seen that in first approximations in comparing one ship with another we shall not commit a grievous error in using the surface of the block ship, and also that a very close approximation indeed may be made to the actual wetted surface by multiplying the surface of the block ship by one of the coefficients in the table, according to the type of the ship. In the second column SS means single screw, TS means twin screw, and P paddle. In No. 10 I ought to explain, that not only was the rudder of exceptional breadth, part of which, to make the comparison with the others more even, has been included, but there was a peculiar overhanging portion under water near the top of the stern post, by which the mean length taken for the block ship exceeds that of the actual ship between perpendiculars.

To show more clearly the relation of the block model to that of the actual ship, I have selected No. 4 in the table, as being a fair example of a merchant mail steamer of considerable speed, and in Fig. 36 I have given the curve of areas of transverse sections; and I have put it in this form that the ordinates are equal to the half areas of the corresponding transverse sections divided by the draught of water (less depth of keel) at the several sections. This is in fact the curve of form, or fineness of model.

Above this I have drawn the half-breadth plan of the block ship, the length, breadth, and area of this being of course equal to those of the curve, and the length and angle of entrance and run a mean of those of the actual curve of form.

2

Where W.S. wetted surface of hull proper in square feet, excluding bossing, rudder, bar keel, etc.

Llength on load water line.

Bextreme breadth.

dr extreme draught in flat plate keel vessels, and

draught corrected to flat plate keel conditions in

bar keel vessels.

c=constant from the following table :