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.

Pressure on dog shores =

W = weight of vessel.

W sin d-fW cos d

cos B

d = mean angle of declivity of ways under vessel.
Bangle between ways and dog shores.

f

=

coefficient 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 a× p.

It should be stated that V-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=

The twisting moment T would then be

T AV2X sin 35° × 3.19 × 7 = inch-pounds,

and equivalent diameter of stock "d" in inches with a fibre stress k of 5,000 lbs.,

The subjoined table gives torsional moments with their equivalent diameters calculated as above, with * 5,000 lbs. per square inch, being a sufficiently high fibre stress to allow for a twisting stress, alternating between right and left, for wrought iron.

In a rudder of rectangular form the centre of pressure from the leading edge is equal to

b (.195 +.305 sin a) = bc,

where b is the mean breadth of rudder, and c a coefficient, as under.

Rudder Stocks per Lloyd's Rule.

The following is the formula prescribed by Lloyd's Register for estimating diameters of rudder stocks, but in no case must the result be less than the tabulated rule size, which see. It should not, however, be used unless the ship is intended for classification in that society's register, as for very high speed vessels the results obtained would be too weak. One of the factors is draught of water, which has little or no value in computing the strength of rudder stock for a rudder of ordinary type hung on a post. Of course, in a rudder with no bottom bearing, as in destroyers and such craft, the case would be entirely different, as then the stock would be figured for bending, the moment for such being much in excess of the torsional one.

* Take 7,000 lbs for steel.