A Catechism of the Steam Engine · Chapter 28Influence of the Size of Vessels Upon Their Speed
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549. Q.--Will large vessels attain a greater speed than small, supposing each to be furnished with the same proportionate power?
A.--It is well known that large vessels furnished with the same proportionate power, will attain a greater speed than small vessels, as appears from the rule usual in yacht races of allowing a certain part of the distance to be run to vessels which are of inferior size. The velocity attained by a large vessel will be greater than the velocity attained by a small vessel of the same mould and the same proportionate power, in the proportion of the square roots of the linear dimensions of the vessels. A vessel therefore with four times the sectional area and four times the power of a smaller symmetrical vessel, and consequently of twice the length, will have its speed increased in the proportion of the square root of 1 to the square root of 2, or 1.4 times.
550. Q.--Will you further illustrate 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.