A Catechism of the Steam Engine Part 28

550. _Q._--Will you further ill.u.s.trate this doctrine by an example?

_A._--The screw steamer Fairy, if enlarged to three times the size while retaining the same form, would have twenty-seven times the capacity, nine times the sectional area, and nine times the power. The length of such a vessel would be 434 feet; her breadth 63 feet 4-1/2 inches; her draught of water 16-1/2 feet; her area of immersed section 729 square feet; and her nominal power 1080 horses. Now as the lengths of the Fairy and of the new vessel are in the proportion of 1 to 3, the speeds will be in the proportion of the square root of 1 to the square root of 3; or, in other words, the speed of the large vessel will be 1.73 times greater than the speed of the small vessel. If therefore the speed of the Fairy be 13 knots, the speed of the new vessel will be 22.49 knots, although the proportion of power to sectional area, which is supposed to be the measure of the resistance, is in both cases precisely the same. If the speed of the Fairy herself had to be increased to 22.29 knots, the power would have to be increased in the proportion of the cube of 13 to the cube of 22.49, or 5.2 times, which makes the power necessary to propel the Fairy at that speed equal to 624 nominal horses power.

STRUCTURE AND OPERATION OF PADDLE WHEELS.

551. _Q._--Will you describe the configuration and mode of action of the paddle wheels in general use?

_A._--There are two kinds of paddle wheels in extensive use, the one being the ordinary radial wheel, in which the floats are fixed on arms radiating from the centre; and the other the feathering wheel, in which each float is hung upon a centre, and is so governed by suitable mechanism as to be always kept in nearly the vertical position. In the radial wheel there is some loss of power from oblique action, whereas in the feathering wheel there is little or no loss from this cause; but in every kind of paddle there is a loss of power from the recession of the water from the float boards, or the _slip_ as it is commonly called; and this loss is the necessary condition of the resistance for the propulsion of the vessel being created in a fluid. The slip is expressed by the difference between the speed of the wheel and the speed of the vessel, and the larger this difference is the greater the loss of power from slip must be--the consumption of steam in the engine being proportionate to the velocity of the wheel, and the useful effect being proportionate to the speed of the ship.

552. _Q._--The resistance necessary for propulsion will not be situated at the circ.u.mference of the wheel?

_A._--In the feathering wheel, where every part of any one immerged float moves forward with the same horizontal velocity, the pressure or resistance may be supposed to be concentrated in the centre of the float; whereas, in the common radial wheel this cannot be the case, for as the outer edge of the float moves more rapidly than the edge nearest the centre of the wheel, the outer part of the float is the most effectual in propulsion. The point at which the outer and inner portions of the float just balance one another in propelling effect, is called the _centre of pressure_; and if all the resistances were concentrated in this point, they would have the same effect as before in resisting the rotation of the wheel. The resistance upon any one moving float board totally immersed in the water will, when the vessel is at rest, obviously vary as the square of its distance from the centre of motion--the resistance of a fluid varying with the square of the velocity; but, except when the wheel is sunk to the axle or altogether immersed in the water, it is impossible, under ordinary circ.u.mstances, for one float to be totally immersed without others being immersed partially, whereby the arc described by the extremity of the paddle arm will become greater than the arc described by the inner edge of the float; and consequently the resistance upon any part of the float will increase in a higher ratio than the square of its distance from the centre of motion--the position of the centre of pressure being at the same time correspondingly affected. In the feathering wheel the position of the centre of pressure of the entering and emerging floats is continually changing from the lower edge of the float--where it is when the float is entering or leaving the water--to the centre of the float, which is its position when the float is wholly immerged; but in the radial wheel the centre of pressure can never rise so high as the centre of the float.

553. _Q._--All this relates to the action of the paddle when the vessel is at rest: will you explain its action when the vessel is in motion?

_A._--When the wheel of a coach rolls along the ground, any point of its periphery describes in the air a curve which is termed a cycloid; any point within the periphery traces a prolate or protracted cycloid, and any point exterior to the periphery traces a curtate or contracted cycloid--the prolate cycloid partaking more of the nature of a straight line, and the curtate cycloid more of the nature of a circle. The action of a paddle wheel in the water resembles in this respect that of the wheel of a carriage running along the ground: that point in the radius of the paddle of which the rotative speed is just equal to the velocity of the vessel will describe a cycloid; points nearer the centre, prolate cycloids, and points further from the centre, curtate cycloids. The circle described by the point whose velocity equals the velocity of the ship, is called the _rolling circle_, and the resistance due to the difference of velocity of the rolling circle and centre of pressure is that which operates in the propulsion of the vessel. The resistance upon any part of the float, therefore, will vary as the square of its distance from the rolling circle, supposing the float to be totally immerged; but, taking into account the greater length of time during which the extremity of the paddle acts, whereby the resistance will be made greater, we shall not err far in estimating the resistance upon any point at the third power of its distance from the rolling circle in the case of light immersions, and the 2.5 power in the case of deep immersions.

554. _Q._--How is the position of the centre of pressure to be determined?

_A._--With the foregoing a.s.sumption, which accords sufficiently with experiment to justify its acceptation, the position of the centre of pressure may be found by the following rule:--from the radius of the wheel substract the radius of the rolling circle; to the remainder add the depth of the paddle board, and divide the fourth power of the sum by four times the depth; from the cube root of the quotient subtract the difference between the radii of the wheel and rolling circle, and the remainder will be the distance of the centre of pressure from the upper edge of the paddle.

555. _Q._--How do you find the diameter of the rolling circle?

_A._--The diameter of the rolling circle is very easily found, for we have only to divide 5,280 times the number of miles per hour, by 60 times the number of strokes per minute, to get an expression for the circ.u.mference of the rolling circle, or the following rule may be adopted:--divide 88 times the speed of the vessel in statute miles per hour, by 3.1416 times the number of strokes per minute; the quotient will be the diameter in feet of the rolling circle. The diameter of the circle in which the centre of pressure moves or the effective diameter of the wheel being known, and also the diameter of the rolling circle, we at once find the excess of the velocity of the wheel over the vessel.

556. _Q._--Will you ill.u.s.trate these rules by an example?

_A._--A steam vessel of moderately good shape, and with engines of 200 horses power, realises, with 22 strokes per minute, a speed of 10.62 miles per hour. To find the diameter of the rolling circle, we have 88 times 10.62, equal to 934.66, and 22 times 3.1416, equal to 69.1152; then 934.66 divided by 69.1152 is equal to 13.52 feet, which is the diameter of the rolling circle. The diameter of the wheel is 19 ft. 4 in., so that the diameter of the rolling circle is about 2/3ds of the diameter of the wheel, and this is a frequent proportion. The depth of the paddle board is 2 feet, and the difference between the diameters of the wheel and rolling circle will be 5.8133, which will make the difference of their radii 2.9067; and adding to this the depth of the paddle board, we have 4.9067, the fourth power of which is 579.64, which, divided by four times the depth of the paddle board, gives us 72.455, the cube root of which is 4.1689, which, diminished by the difference of the radii of the wheel and rolling circle, leaves 1.2622 feet for the distance of the centre of pressure from the upper edge of the paddle board in the case of light immersions. The radius of the wheel being 9.6667, the distance from the centre of the wheel to the upper edge of the float is 7.6667, and adding to this 1.2622, we get 8.9299 feet as the radius, or 17.8598 feet as the diameter of the circle in which the centre of pressure revolves. With 22 strokes per minute, the velocity of the centre of pressure will be 20.573 feet per second, and with 10.62 miles per hour for the speed of the vessel, the velocity of the rolling circle will be 15.576 feet per second. The effective velocity will be the difference between these quant.i.ties, or 4.997 feet per second. Now the height from which a body must fall by gravity, to acquire a velocity of 4.997 feet per second, is about .62 feet; and twice this height, or 1.24 feet, multiplied by 62-1/2, which is the number of Lbs. weight in a cubic foot of water, gives 77-1/2 Lbs. as the pressure on each square foot of the vertical paddle boards. As each board is of 20 square feet of area, and there is a vertical board on each side of the ship, the total pressure on the vertical paddle boards will be 2900 Lbs.

557. _Q._--What pressure is this equivalent to on each square inch of the pistons?

_A._--A vessel of 200 horses power will have two cylinders, each 50 inches diameter, and 5 feet stroke, or thereabout. The area of a piston of 50 inches diameter is 1963.5 square inches, so that the area of the two pistons is 3927 square inches, and the piston will move through 10 feet every revolution; and with 22 strokes per minute this will be 220 feet per minute, or 3.66 feet per second. Now, if the effective velocity of the centre of pressure and the velocity of the pistons had been the same, then a pressure of 2900 Lbs. upon the vertical paddles would have been balanced by an equal pressure on the pistons, which would have been in this case about .75 Lbs. per square inch; but as the effective velocity of the centre of pressure is 4.997 feet per second, while that of the pistons is only 3.66 feet per second, the pressure must be increased in the proportion of 4.997 to 3.66 to establish an equilibrium of pressure, or, in other words, it must be 1.02 Lbs. per square inch. It follows from this investigation, that, in radial wheels, the greater part of the engine power is distributed among the oblique floats.

558. _Q._--How comes this to be the case?

_A._--To understand how it happens that more power is expended upon the oblique than upon the vertical floats, it is necessary to remember that the only resistance upon the vertical paddle is that due to the difference of velocity of the wheel and the ship; but if the wheel be supposed to be immersed to its axle, so that the entering float strikes the water horizontally, it is clear that the resistance on such float is that due to the whole velocity of rotation; and that the resistance to the entering float will be the same whether the vessel is in motion or not. The resistance opposed to the rotation of any float increases from the position of the vertical float-where the resistance is that due to the difference of velocity of the wheel and vessel--until it reaches the plane of the axis, supposing the wheel to be immersed so far, where the resistance is that due to the whole velocity of rotation; and although in any oblique float the total resistance cannot be considered operative in a horizontal direction, yet the total resistance increases so rapidly on each side of the vertical float, that the portion of it which is operative in the horizontal direction, is in all ordinary cases of immersion very considerable. In the feathering wheel, where there is little of this oblique action, the resistance will be in the proportion of the square of the horizontal velocities of the several floats, which may be represented by the horizontal distances between them; and in the feathering wheel, the vertical float having the greatest horizontal velocity will have the greatest propelling effect.

559. _Q._--Should the floats in feathering wheels enter and leave the water vertically?

_A._--The floats should be so governed by the central crank or eccentric, that the entering and emerging floats have a direction intermediate between a radius and a vertical line.

560. _Q._--Can you give any practical rules for proportioning paddle wheels?

_A._--A common rule for the pitch of the floats is to allow one float for every foot of diameter of the wheel; but in the case of fast vessels a pitch of 2-1/2 feet, or even less, appears preferable, as a close pitch occasions less vibration. If the floats be put too close, however, the water will not escape freely from between them, and if set too far apart the stroke of the entering paddle will occasion an inconvenient amount of vibratory motion, and there will also be some loss of power. To find the proper area of a single float:--divide the number of actual horses power of both engines by the diameter of the wheel in feet; the quotient is the area of one paddle board in square feet proper for sea going vessels, and the area multiplied by 0.6 will give the length of the float in feet. In very sharp vessels, which offer less resistance in pa.s.sing through the water, the area of paddle board is usually one-fourth less than the above proportion, and the proper length of the float may in such case be found by multiplying the area by 0.7. In sea going vessels about four floats are usually immersed, and in river steamers only one or two floats. There is more slip in the latter case, but there is also more engine power exerted in the propulsion of the ship, from the greater speed of engine thus rendered possible.

561. _Q._--Then is it beneficial to use small floats?

_A._--Quite the contrary. If to permit a greater speed of the engine the floats be diminished in area instead of being raised out of the water, no appreciable accession to the speed of the vessel will be obtained; whereas there will be an increased speed of vessel if the accelerated speed of the engine be caused by diminishing the diameter of the wheels. In vessels intended to be fast, therefore, it is expedient to make the wheels small, so as to enable the engine to work with a high velocity; and it is expedient to make such wheels of the feathering kind, to obviate loss of power from oblique action. In no wheel must the rolling circle fall below the water line, else the entering and emerging floats will carry ma.s.ses of water before them. The slip is usually equal to about one-fourth of the velocity of the centre of pressure in well proportioned wheels; but it is desirable to have the slip as small as is possible consistently with the observance of other necessary conditions. The speed of the engine and also the speed of the vessel being fixed, the diameter of the rolling circle becomes at once ascertainable, and adding to this the slip, we have the diameter of the wheel.

CONFIGURATION AND ACTION OF THE SCREW.

562. _Q._--Will you describe more in detail than you have yet done, the configuration and mode of action of the screw propeller?

_A._--The ordinary form of screw propeller is represented in figs. 46 and 47; fig. 46 being a perspective view, and fig. 47 an end view, or view such as is seen when looking upon the end of the shaft. The screw here represented is one with two arms or blades. Some screws have three arms, some four and some six; but the screw with two arms is the most usual, and screws with more than three arms are not now much employed in this country.

The screw on being put into revolution by the engine, preserves a spiral path in the water, in which it draws itself forward in the same way as a screw nail does when turned round in a piece of wood, whereas the paddle wheel more resembles the action of a cog wheel working in a rack.

[Ill.u.s.tration: Fig. 46. Fig. 47. ORDINARY FORM OF SCREW PROPELLER.]

563. _Q._--But the screw of a steam vessel has no resemblance to a screw nail?

_A._--It has in fact a very close resemblance if you suppose only a very short piece of the screw nail to be employed, and if you suppose, moreover, the thread of the screw to be cut nearly into the centre to prevent the wood from stripping. The original screw propellers were made with several convolutions of screw, but it was found advantageous to shorten them, until they are now only made one-sixth of a convolution in length.

564. _Q._--And the pitch you have already explained to be the distance in the line of the shaft from one convolution to the next, supposing the screw to consist of two or more convolutions?

_A._--Yes, that is what is meant by the pitch. If a thread be wound upon a cylinder with an equal distance between the convolutions, it will trace a screw of a uniform pitch; and if the thread be wound upon the cylinder with an increasing distance between each convolution, it will trace a screw of an increasing pitch. But two or more threads may be wound upon the cylinder at the same time, instead of a single thread. If two threads be wound upon it they will trace a double-threaded screw; if three threads be wound upon it they will trace a treble-threaded screw; and so of any other number. Now if the thread be supposed to be raised up into a very deep and thin spiral feather, and the cylinder be supposed to become very small, like the newel of a spiral stair, then a screw will be obtained of the kind proper for propelling vessels, except that only a very short piece of such screw must be employed. Whatever be the number of threads wound upon a cylinder, if the cylinder be cut across all the threads will be cut. A slice cut out of the cylinder will therefore contain a piece of each thread. But the threads, in the case of a screw propeller, answer to the arms, so that in every screw propeller the number of threads entering into the composition of the screw will be the same as the number of arms. An ordinary screw with two blades is a short piece of a screw of two threads.

565. _Q._--In what part of the ship is the screw usually placed?

[Ill.u.s.tration: Fig. 48]

_A._--In that part of the run of the ship called the dead wood, which is a thin and unused part of the vessel just in advance of the rudder. The usual arrangement is shown in fig. 48, which represents the application to a vessel of a species of screw which has the arms bent backwards, to counteract the centrifugal motion given to the water when there is a considerable amount of slip.

566. _Q._--How is the slip in a screw vessel determined?

_A._--By comparing the actual speed of the vessel with the speed due to the pitch and number of revolutions of the screw, or, what is the same thing, the speed which the vessel would attain if the screw worked in a solid nut.

The difference between the actual speed and this hypothetical speed, is the slip.

567. _Q._--In well formed screw propellers what is the amount of slip found to be?

_A._--If the screw be properly proportioned to the resistance that the vessel has to overcome, the slip will not be more than 10 per cent., but in some cases it amounts to 30 per cent., or even more than this. In other cases, however, the slip is nothing at all, and even less than nothing; or, in other words the vessel pa.s.ses through the water with a greater velocity than if the screw were working in a solid nut.

568. _Q._--Then it must be by the aid of the wind or some other extraneous force?

_A._--No; by the action of the screw alone.

569. _Q._--But how is such a result possible?

_A._--It appears to be mainly owing to the centrifugal action of the screw, which interposes a film or wedge of water between the screw itself and the water on which the screw reacts. This negative slip, as it is called, chiefly occurs when the pitch of the screw is less than its diameter, and when, consequently, the velocity of rotation is greater than if a coa.r.s.er pitch had been employed. There is, moreover, in all vessels pa.s.sing through the water with any considerable velocity, a current of water following the vessel, in which current, in the case of a screw vessel, the screw will revolve; and in certain cases the phenomenon of negative slip may be imputable in part to the existence of this current.

570. _Q._--Is the screw propeller as effectual an instrument of propulsion as the radial or feathering paddle?

_A._--In all cases of deep immersion it appears to be quite as effectual as the radial paddle, indeed, more so; but it is scarcely as effectual as the feathering paddle, with any amount of immersion, and scarcely as effectual as the common paddle in the case of light immersions.