Launching is the operation by which a ship is transferred from the building ship into the water, and is performed by causing her to rest on a carriage, the cradle, which is allowed to slide along lubricated inclined planes, the ways, that extend from the slip into the water, until she is water-borne. She may enter the water broadside on, bow on, or stern on ; the latter condition only will be investigated. In discussing the statics of launching it is assumed that the ship descends along the ways so slowly that the velocity may be neglected; the effects of the actual velocity will be considered afterwards.
Let the ship be resting on the ways OA (Fig. 1), which are inclined at an angle ?, the forward end of the cradle being at A and the water-level at OP; let the water-line wl be parallel to OP. The ship will move along the ways the distance OZ before entering the water. As she continues to descend, the water-level coincides with water-lines parallel to wl, and when she has moved the distance OZ the water-level will correspond with wl. It is more convenient, however, to assume that the ship is stationary on the ways, and that the water-level has slowly risen until it is at wl and as the inclination of the ways is always known, with every assumed rise of water-level the corresponding descent along the ways, or the horizontal travel will be known.
The ship's weight W will act downwards through the center of gravity G at all times; but if, at any instant, the water-level is at wl there will be an upward pressure and opposite to the weight of the volume of water displaced, and this upward pressure or buoyancy D will act through the center of gravity of the displaced fluid B, the center of buoyancy. The quantity of water thus displaced is termed the ship's displacement, and is usually measured by its weight in tons ; 35 cubic feet of ordinary salt water, or 36 cubic feet of fresh water, weighing one ton. As the water-level rises or falls, the volume displaced changes in shape and in quantity, causing the displacement to change in quantity and the center of buoyancy to change in position. These changes can, however, be represented graphically.
In Fig. 2, let w1l1, w2l2 .... wnln be a series of horizontal water-lines, and AC be a vertical through the foot of the stern-post ; from this vertical set off along the water-lines to and convenient scale, the displacements up to each water-line ; the curve drawn through the points thus plotted will be the curve of displacement. In like manner set off along each water-line the distance the center of buoyancy lies forward of the vertical AC; the curve drawn through these points is called the buoyancy curve. It does not show the actual positions of the centers of buoyancy, but gives the intersections of verticals through these centers with the corresponding water-lines.
Having these curves drawn with the given water-line, the displacement and center of buoyancy are readily found for any other waterline, being its intersections with these curves.
The ship will float when the displacement equals the weight; then if AM represent W, to the scale of curve of displacement and the weight line MP he drawn parallel to AC, its intersection with the curve of displacement at A will be a point on the water-line cutting off a displacement equal to the ship's weight. This water-line WL is called the flotation line.
This is the equation of the Curve of Resultants R V, Fig. 3, which passes through the intersections of the water-lines with the lines of action of the resultants. In this equation x = o when D =0, so that the origin of the curve is at R, the intersection of the water-line passing through the lowest point of the ship, which is in most cases the foot of the stern-post, with the vertical passing through G, the center of gravity. Also when D=W, x = ∞, so that the flotation line is the asymptote of the curve of resultants, and the two will never meet. Knowing these properties, the curve of resultants is constructed in the following manner:
Draw the sheer plan of the ship, the bottom of the keel A S having the inclination of the line of keel-blocks; then the line of ways AT representing the top of the ground- ways in the proposed position both as regards height and inclination. Draw a number of waterlines spaced from 18 inches to two feet apart, and calculate for every water-line the displacement and distance of center of buoyancy forward of vertical through foot of stern-post AC, and from the values thus obtained plot the curves of displacement Aa and buoyancy Ab, and construct the weight MP, flotation WL, and gravity GR lines. The curve of resultants RV has its origin at R, and WL is its asymptote. Any intermediate point N corresponding to a water-line wl is at once found.
For any water-line the resultant W—D is equal to pa, and its line of action is the vertical passing through the intersection of the waterline with the curve of resultants at A, or the value of the resultant can be calculated, so that we can at once determine the actual pressure on the ways and the line of action of this pressure. Conversely, knowing the line of the resultant, its value and the corresponding water-line can be found ; thus if the line of action passes through N, wNl is the corresponding water-line, and pa the value of the resultant, which can also be calculated as before.
As the ship descends, the water-line rises, the resultant becomes smaller and its line of action moves forward. Let the forward poppet-lashing pass under the ship below S, then when the waterlevel has risen to w1l1 the line of action will pass through T. If it rises higher the line of action will pass forward of S, and if it sinks lower the line of action will pass aft of S. When aft of 6" the resultant meets the equal and opposite reaction of the ways, and the motion of the ship is not affected by it; but when the line of action is forward the reaction of the ways is not opposite, as it cannot move forward of S; the ship therefore pivots about its forward support at S, the stern lifting. The forward poppet-lashing, when using two lines of ways, or the forefoot, when launching on the keel, is called the pivoting point. While aft of this point, the pressure due to the resultant is distributed over the whole length of the cradle; but when the line of action passes through 6" or is forward of it, the whole pressure due to the resultant is concentrated at 61 Since the value of the resultant decreases as the water-level rises, it follows that when the line of action passes through 6" this concentrated pressure is greatest. The ways, poppet-lashing, and ship must be strong enough to resist this pivot pressure, and its value should always be carefully ascertained.
As a practical example, take a ship whose launching weight is 1500 tons, having ways 18 inches broad and a cradle 200 feet long.
But at the instant after pivoting, when the line of action passes forward of the pivot, and the ship has begun to change trim, the whole resultant pressure will now be concentrated on not more than two poppets on each side, or two feet of the cradle ; and if W—D now equals 594 tons, the pressure per square foot will now be
594/(2 x 1.5 x 2) = 99 tons
In actual practice the pressure will be less than this, as it will be somewhat distributed over the forward pieces of the bilge-ways; but this will suffice to show how great the pressure may become, and how carefully the strength of poppet-lashings and poppets should be proportioned, to avoid all possibility of accident.
As this pivot pressure reacts on the ship, she must be strong enough to resist it, otherwise deformation or crushing may occur. Ships of ordinary form and scantling may be considered safe if the usual precautions are observed, since there have been many successful launches. But with ships of unusual types, especially those of very great tonnage or very light scantlings, a careful investigation should be made, and an ample factor of safety provided for, internal shoring being used when necessary.
Suppose the ship to descend along the ways with inappreciable velocity and gradually enter water having a constant known level. In Fig. 4, let OH be the water-level and R Fthe curve of resultants, and wl be any water-line ; wl will coincide with OH when the ship has moved the distance Oo. If the ship had remained stationary and the water had risen to the level wl, the line of action of the resultant would pass through n, the intersection of the curve with the water-line, at a distance on from the line of ways ; when the ship has descended the ways and occupies the position shown in dotted lines the resultant pressure acts through N, ON being equal to on. The line of action of the resultant pressure will therefore pass at a distance from O, equal to the distance from the intersection of the curve of resultants with the water-line, to the intersection of this water-line with the line of ways. The intersection of the normal or average waterlevel with the line of ways, projected at O, is called the shore line.
For the water-line w1l1 which intersects the curve at the same point where the latter meets the line of ways, the line of action passes through the shore-line at O ; and for any water-line below w1l1 the resultant will pass inside the shore line. It therefore follows that, as the ship descends along the ways and enters the water, the resultant downward pressure acts inside of the shore-line as long as the waterlevel is at a water-line whose intersection with the curve of resultants is below the line of ways, and the resultant acts outside the shoreline when this intersection is above the line of ways.
The actual position of the line of application of the resultant downward pressure during the ship's descent along the ways, when any given water-line coincides with the water-level, is found by drawing the distance line Nn parallel to the line of ways through the intersection of the water-line and the curve at n ; ON is evidently equal to on, and A is therefore the point required.
This resultant pressure must meet an equal and an opposing force in order that the ship may remain in equilibrium. This opposing force is the reaction of the ways ; they must evidently be long enough to produce this reaction for all positions of the ship between the original one of rest and the final one of flotation.
In her descent along the ways and before pivoting begins, let the ship occupy the position shown in full lines in Fig. 5, the downward resultant pressure acting through N, OH being the water-level, S being the pivoting point, and P the outer end of the ways. There being no equal and opposing force, the resultant causes the ship's stern to descend, taking the position shown in dotted lines. As she continues to move onward she scrapes against the end of the ways, until the displacement of the after-body increases so that she begins to raise her stern, and finally her fore-body strikes on the ways again. This stumbling occurs often; it is dangerous and frequently results in serious damage to the ship ; in shallow water the stern may strike the bottom and the launch be a vexatious and costly failure.
With a ship whose pivoting point S, Fig. 6, is some distance aft of the forefoot another danger may be feared if the ways are so short that the resultant passing through N acts beyond P before the ship has floated. The ship then takes the position shown by the dotted lines, the forefoot falls, striking or scraping the foot of the ways. Although dangerous, this tripping seldom occurs.
These phenomena, although they are modified by the effects of the ship's velocity, show the absolute necessity of having the ways of such ample length that the line of action of the resultant downward pressure shall always be inside the end of the ways, and that the pivot shall always be supported until the ship floats. When the curve of resultants is below the line of ways, it has been shown that the line of action of the resultant lies inside the shore-line and there is no danger when the ways extend into the water ; but when the curve is above the line of ways the resultant moves outside the shore-line, and stumbling or tripping will occur if sufficient length be not provided of underwater ways, the length of ways extending from the normal shore-line measured along the line of the waterlevel.
Let RV be a curve of resultants in Fig. 7, OH the water-level, PS the line of ways and S the pivoting point. For any water-line such as w1l1, the resultant acts through A; as the ship descends the resultant recedes from the shore-line until a water-line wl is reached, such that the corresponding distance-line is tangent to the curve. As the ship continues to descend the resultant now advances towards the shore-line, passing a water-line such as w1l1 whose distance-line corresponds with that of w1l1 until water-line w1l1 is reached and the ship begins to pivot, the resultant then acting inside of N, and it continues to advance towards the shore-line until the ship floats. If the underwater ways extend as far as P, the resultant downward pressure meets the equal and opposite reaction of the ways and the ship is always in equilibrium from start to flotation. But if the underwater ways extend only to P the ship would stumble as soon as water-line w1l1 was passed, and would strike the ways again when wl was reached. Tripping, however, would never occur.
Let the pivoting point be at S, Fig. 7 ; the resultant recedes from the shore-line until wl is reached and then returns towards it. Pivoting begins when water-line w1l1 is reached, and if the underwater ways extend only to P the ship will begin to trip as soon as she descends deeper into the water and will so continue until flotation, as the resultant rapidly moves forward and the pivoting point is unsupported thereafter. If the underwater ways did not extend to P, stumbling would first occur and then tripping.
In general, when the distance-line corresponding to a given length of ways is above a tangent to the curve of resultants of a given ship, neither stumbling nor tripping will occur, and the ship will be well supported from start to flotation ; but when the distance line intersects the curve, stumbling occurs when the pivoting point is forward of the second intersection; tripping occurs when the pivoting point is at the first intersection; stumbling and tripping both occur when the pivoting point is forward of the first intersection, but between it and the second.
To prevent stumbling or tripping and to have the ship well supported from start to finish, the length of underwater ways must not be less than that given by the distance-line tangent to the curve of resultants.
The depth of water above the end of the underwater ways is known as:
Depth of water on end of ways = length under waterways X tangent of angle of inclination of ways.
Or, depth of water on end of ways = length of under waterways X descent per foot X 1/12.
Thus with underwater ways extending 48 feet beyond the shoreline and having an inclination of ¾ inch per foot, depth of water (48 x ¾)/12 = 3 feet.
The curve of resultants can be accurately drawn, and the pivot pressure and length of ways required can be accurately determined when the following are accurately known:
1. The ship's displacement curve.
2. The ship's buoyancy curve.
3. The angle of inclination of the ways.
4. The position of the ship on the ways.
5. The position of the pivot.
6. The weight of the ship.
7. The position of the center of gravity.
8. The water-level at the moment of launching.
The first and second can at once be determined from the ship's lines and the known inclination of the keel-blocks ; the third will be decided by the depth and extent of water available and other practical considerations; the fourth is known ; and the fifth decided by the ship's form ; all being accurately known months before the ship is launched.
But with the remaining three there is more or less uncertainty at the time the launching calculations are made. The ship's weight is only known approximately, even where an accurate record is kept of all the weights placed on board, as the amount added between the time of the calculation and the time of launching cannot usually be accurately foreseen, since circumstances frequently arise necessitating the launch being advanced or postponed from the time originally set. Still less is it possible to foresee the exact position of the ship's center of gravity.
Nor can the water-level at the moment of launching be accurately known, especially in tidal waters. Though the height and time of mean high water are known, during the time lost by unforeseen delays the water-level will change ; and in all waters, freshets and strong winds may change the level.
The variation of these three conditions modifies the curve of resultants, since it is plotted from the equation,
x = Dy/(W – D’)
in which W varies with the weight and y with the position of the center of gravity. The pivot pressure and the length of ways outside the shore-line vary with the curve; and the total length of ways required will vary with the water-level although the curve remain unchanged, as the length of the underwater ways must remain constant with a given curve. All probable variations of these three conditions should therefore be considered in making the launching calculations.
From knowledge of the design and type of ship, the probable receipt of materials and rate of progress of the work, W1 and W2, the respective maximum and minimum values of the ship's weight, may be assumed. Similarly assume that a and b are the respective distances abaft the midship section, of the ship's center of gravity, giving them negative values when the center of gravity is forward.
The curve of displacement Ad and the buoyancy Ad, Fig. 9, remain unchanged, but W1L1 and W2L2 will be the two flotation-lines corresponding to W1 and W2 respectively. Let G1 and G2 be the two limiting positions of the center of gravity at a distance c apart, and G1R1, G2R2 the two verticals, and suppose each weight to be concentrated first at G1 and then at G2.
The distance of the line of ways above or below any given point on the ship, such as the foot of the sternpost, is determined by practical considerations. In Fig. 12, let the water-level be at OH, the line of ways assumed for calculation at Oo, with the shore-line at O, and let o1O1 be any other possible position of the line of ways. If Nn be the tangent distance line, the end of ways is determined by the vertical through N, and its position depends only on the curve and water-level.
The length of underwater ways is therefore entirely independent of the position of the ways, which may be adjusted as is found to be most advantageous.
Cost, convenience, and obstruction of the water-front must often be considered in determining the most advantageous length of underwater ways ; and when possible, ways already constructed should be used. It has been shown that the length of underwater ways necessary to ensure safe launching varies with the ship's weight, the position of her center of gravity and the change of water-level. With any given limit of length of ways, the first and second of these varying conditions should be so controlled that there will be perfect security even though the water be at its lowest probable level. The applications of the four curves of resultants can be arranged graphically so as to readily supply this information.
Hence with the sheer plan of the ship, the positions of G, B, and S" being plotted, and the values being known of W, Gm, and the inclination of the keel-blocks, the amount of pivot pressure is found by direct calculation.
This will be especially useful when it is desired to ascertain whether a slip has sufficient strength to permit the launching of a large and heavy ship; and whether the ship is of such scantlings as will prevent deformation due to the excessive concentrated stresses during the pivoting period of the launch.
It will be observed that the pivot pressure increases as sin p increases ; the greater the difference between the inclination of the keel-blocks and the inclination of the keel after launching, the greater is the pressure. It is therefore advisable to have this difference as small as practical, considerations will permit.
A ship with any drag launched bow on will have a much greater difference than when launched stern on, the pivot pressure will therefore be greater in the former case, and for this reason ships are usually launched stern on.