and the minimum tension on sheerstrake equals

Maximum bending moment × Neutral axis below sheerstrake Total moment of inertia

Tension stress per square inch. The compression on the bottom plating is similarly computed, substituting the distance of neutral axis above keel for "below sheerstrake."

The value of the maximum tensile strength per square inch of section varies of course with the size and proportions of vessels. A suitable value for vessels of wholesome proportions built to any of the great classification societies' rules is about 2 tons per square inch in small vessels to about 9 in the largest liners, taking the comparative method of calculating the bending moment given above.

It will be evident from an examination of the table showing a specimen calculation of the moment of inertia of a ship's cross section, that the further the sectional area of the ship is arranged from the neutral axis, the greater will be the moment of resistance to bending. It is in recognition of this geometrical quality that the upper deck in 3-deck and other ships is made the strength deck, and that the keel plate and garboards are thickened as well as the sheerstrake and stringer being increased at that level, in addition to reinforcing the bilge; for, with a ship rolling and pitching, it must often happen that the greatest bending moments will frequently be exerted at the bilge and upper deck gunwale. By making the shelter deck in 3-deck vessels the strength deck," a great increase in the strength of these ships has been made in recent years, as demonstrated by actual practice, steamers of this class being now practically "4-deckers" from a strength point of view.

CHAPTER VIII.

RESISTANCE OF SHIPS.

The Admiralty Coefficient.

THE amount of power required to propel a vessel at a given speed is generally computed by (1) the Admiralty Coefficient formula, or (2) a formula based on the ship's actual resistance, the former being purely empirical and requiring great judgment and practice in the selection of the coefficient, and the other founded on scientific experimental data and theories which have acquired confirmatory proof amounting to law, since they were first enunciated by William Froude. The following notes on resistance are taken principally from the papers by this eminent investigator, and from the later work of Middendorf, Taylor, and others.

The Admiralty Coefficient (C) is calculated from the results of actual trials, and is based on the false assumptions that the area of wetted surface (S) for similar ships is proportional to the power of the displacement (D3), and that the resistance (R) plus

the propulsive coefficient

E.H.P.

I.H.P.

:)

varies as the cube of the

speed (V). From this we get the well-known formula:

It will be obvious that these coefficients must cover a wide range of values, hence the difficulty of their application by the inexperienced. For this reason we append a table of values in vessels of greatly divergent types. It should, however, be noted that for vessels of similar form but different lengths, the coefficient will show great disparity, and for vessels of similar form and length but different draught, there will likewise be much dissimilarity in the coefficient. In the selection of this coefficient it should also

be remembered that the class of steamer to which it is applied must be similar not only in form, but in type of engine as well, and of corresponding speed. same speed, as will be explained later. This does not necessarily mean the

FROUDE'S LAW OF COMPARISON.

Froude discovered that there was great resemblance between As the result of experiments with models and full sized ships their "curves of resistance," i.e., a curve plotted off with a scale of knots as abscissæ, and the pounds resistance to towing as ordi

nates. See Fig. 51.

To test this, however, it is necessary to apply the Law of Comparison, which he thus states:

"If the ship be D times the dimension of the model and at the speeds V1, V2, V3

the measured resistances of the model

are R1, R2, R3 then for speed VDV1 VDV2 VDV: of the ship, the resistance will be D8R1, D3R2, D2R3.

To the speeds of model and ship thus related, he applied the term "corresponding speeds." This law expresses the resistance due to surface friction, plus wavemaking resistance, the former being commonly referred to as skin resistance and the other as residuary resistance, embracing as it does, the resistance caused

by the motion of the waves and the drag of dead water eddies, such as are formed at abrupt endings to bossings, the siding of stern posts and in the wake of propeller struts. The skin resistance is proportional to the area of wetted surface, and is responsible for almost the total resistance up to about 8 knots speed. Beyond this speed the total resistance increases rapidly, showing the effect of the residuary resistance. This will be more readily understood, when we recollect that the wave undulations progressively increase in height with increases in speed, and that the crests of these waves are accountable for about 95 per cent of the total residuary resistance, the remaining 5 per cent, as already stated, being due to eddies, etc. Referring to the diagram here reproduced, showing curves of residuary and skin resistances, "the graduated undulations in the residuary resistance curve are due to quasihydrostatic pressure against the after-body, corresponding with the variations in its position with reference to the phases of the train of waves comprising the wave line profile, there being a comparative excess of pressure (causing a forward force or diminution

of resistance) when the after-body is opposite a crest, and the reverse when it is opposite a trough. Their spacing is uniform at a uniform speed, because waves of given speed have always the same length; it is more open at the higher speeds, because waves are longer the higher their speed; their amplitude is greater at

RESISTANCE IN TONS.

B

FIG. 52.

the higher speeds, because the waves made by the ship are higher; body, because the wave system by diffusing itself transversely and their amplitude diminishes with increased length of middle

loses its height."