| 150 × 100 × 1200 | = | 150 × V2 × 1800, | |
| Or, | 120,000 | = | 1800V2, |
| Reduced, | 1200/18 | = | V2, |
| And | V | = | √66.66 = 8.15 knots. |
From the foregoing easily intelligible formulæ we can ascertain with approximate certainty the large quantity of coal necessary to increase speed, the large saving of coal in reducing speed, as well as the means of accommodating the fuel to the voyage, or the voyage to the fuel. It is not necessary here to study very closely the economy of fuel, as this is a question affecting the transport of freight alone. When the mails are to be transported, economy of fuel is not the object desired, but speed; and, consequently, we must submit to extravagance of fuel. This large expenditure of coal is not necessary in the case of freights, as they may be transported slowly, and, consequently, cheaply. But one of the principal reasons for rapid transport of the mails is that they may largely anticipate freights in their time of arrival, and consequently control their movements.
I recently had an excellent opportunity of testing the large quantity of fuel saved on a slight reduction of the speed, and give it as illustrative of the law advanced. We were on the United States Mail steamer "Fulton," Captain Wotton, and running at 13 miles per hour. Some of the tubes became unfit for use in one of the boilers, and the fires were extinguished and the steam and water drawn off from this boiler, leaving the other one, of the same size, to propel the ship. An intelligent gentleman who happened to know that we were using only one boiler, and consequently, but half the power, remarked to me that it was very strange that the ship was still going about eleven miles per hour, without any sail. He said: "It is strange, sir; two boilers of equal size drove us thirteen miles per hour; and here now but one boiler drives us nearly eleven miles, or nearly as fast; when common-sense teaches that the one boiler would drive us only six and a half miles per hour. How is that?" I then explained to him very clearly the natural law relative to power and speed, (See [Rule II.], page 68,) which he at once comprehended and admitted, but with the remark: "Indeed, sir, I would have testified that she ought with one boiler to have gone at only half the speed; or that going at six miles with one boiler, she would go twelve with two."
As it will be interesting to the general reader to examine the details of the increased consumption of fuel at increased rates of speed, I present the following elaborate table recently prepared by Mr. Atherton for his new edition of "Steamship Capability," according to the formula above noticed, and the performance of the best type of vessel in the Royal Navy, the steamer "Rattler." Mr. A. found a higher efficiency in this vessel per horse power than any other in the Navy, and consequently based the consumption of coal in the table on the assumption that the mail and passenger vessels generally should be of as good contractive type as "Rattler." I shall present also another table showing a much larger consumption of fuel by an inferior type of vessel. I use these tables because they are thoroughly correct, and quite as perfect as any that I could construct on the same formula; and because they carry with them the weight of probably the highest authority in Great Britain.
COAL TABLE: No. I.
Displacement,[B] Speed, and Fuel consumed per Day, for Mail, Passenger, and Freight Steamers, whose locomotive performance is equal to that of the best class of ocean steam vessels; assuming the consumption of fuel to be 41/2 lbs. per indicated horse power per hour, equal to 33,000 lbs. raised one foot in one minute. The quantity consumed is expressed in tons per day of 24 hours.
[B] Displacement refers to the number of cubic feet of water displaced by the hull; allowing thirty-five cubic feet to the ton.
| SHIP'S DISPLACEMENT. | SPEED PER HOUR.—NAUTICAL MILES. | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
| TONS. | TONS | TONS | TONS | TONS | TONS | TONS | TONS | TONS | TONS | TONS | TONS | TONS | TONS | TONS | TONS |
| 100 | 1.04 | 1.65 | 2.47 | 3.51 | 4.82 | 6.41 | 8.32 | 10.6 | 13.2 | 16.3 | 19.7 | 23.7 | 28.1 | 33.0 | 38.5 |
| 125 | 1.20 | 1.92 | 2.86 | 4.07 | 5.59 | 7.44 | 9.66 | 12.3 | 15.3 | 18.9 | 22.9 | 27.5 | 32.6 | 38.3 | 44.7 |
| 150 | 1.36 | 2.16 | 3.23 | 4.60 | 6.31 | 8.40 | 10.9 | 13.9 | 17.3 | 21.3 | 25.9 | 31.0 | 36.8 | 43.3 | 50.5 |
| 175 | 1.51 | 2.40 | 3.58 | 5.10 | 7.00 | 9.31 | 12.1 | 15.4 | 19.2 | 23.6 | 28.7 | 34.4 | 40.8 | 48.0 | 56.0 |
| 200 | 1.65 | 2.62 | 3.91 | 5.57 | 7.65 | 10.2 | 13.2 | 16.8 | 21.0 | 25.8 | 31.3 | 37.6 | 44.6 | 52.4 | 61.2 |
| 250 | 1.92 | 3.04 | 4.54 | 6.47 | 8.87 | 11.8 | 15.3 | 19.5 | 24.3 | 29.9 | 36.3 | 43.6 | 51.7 | 60.9 | 71.0 |
| 300 | 2.25 | 3.44 | 5.13 | 7.30 | 10.0 | 13.3 | 17.3 | 22.0 | 27.5 | 33.8 | 41.0 | 49.2 | 58.4 | 68.7 | 80.1 |
| 350 | 2.40 | 3.81 | 5.68 | 8.09 | 11.1 | 14.8 | 19.2 | 24.4 | 30.5 | 37.5 | 45.5 | 54.5 | 64.7 | 76.2 | 88.8 |
| 400 | 2.62 | 4.16 | 6.21 | 8.85 | 12.1 | 16.2 | 21.0 | 26.7 | 33.3 | 41.0 | 49.7 | 59.6 | 70.8 | 83.3 | 97.1 |
| 450 | 2.84 | 4.50 | 6.72 | 9.57 | 13.1 | 17.5 | 22.7 | 28.8 | 36.0 | 44.3 | 53.8 | 64.5 | 76.6 | 90.1 | 105 |
| 500 | 3.04 | 4.83 | 7.21 | 10.3 | 14.1 | 18.7 | 24.3 | 30.9 | 38.6 | 47.5 | 57.7 | 69.2 | 82.1 | 96.6 | 113 |
| 600 | 3.43 | 5.46 | 8.14 | 11.6 | 15.9 | 21.2 | 27.5 | 34.9 | 43.6 | 53.7 | 65.1 | 78.1 | 92.8 | 109 | 127 |
| 700 | 3.81 | 6.05 | 9.02 | 12.8 | 17.6 | 23.5 | 30.4 | 38.7 | 48.4 | 59.5 | 72.2 | 86.6 | 103 | 121 | 141 |
| 800 | 4.16 | 6.61 | 9.87 | 14.0 | 19.3 | 25.6 | 33.3 | 42.3 | 52.9 | 65.0 | 78.9 | 94.6 | 112 | 132 | 154 |
| 900 | 4.50 | 7.15 | 10.7 | 15.2 | 20.8 | 27.7 | 36.0 | 45.8 | 57.2 | 70.4 | 85.4 | 102 | 122 | 143 | 167 |
| 1000 | 4.83 | 7.67 | 11.4 | 16.3 | 22.4 | 29.8 | 38.6 | 49.1 | 61.3 | 75.5 | 91.6 | 110 | 130 | 153 | 179 |
| 1250 | 5.60 | 8.90 | 13.3 | 18.9 | 26.0 | 34.5 | 44.8 | 57.0 | 71.2 | 87.6 | 106 | 127 | 151 | 178 | 208 |
| 1500 | 6.33 | 10.0 | 15.0 | 21.4 | 29.3 | 39.0 | 50.6 | 64.4 | 80.4 | 98.9 | 120 | 144 | 171 | 201 | 234 |
| 1750 | 7.01 | 11.1 | 16.6 | 23.7 | 32.5 | 43.2 | 56.1 | 71.3 | 89.1 | 110 | 133 | 159 | 189 | 223 | 260 |
| 2000 | 7.66 | 12.2 | 18.2 | 25.9 | 35.5 | 47.3 | 61.3 | 77.9 | 97.4 | 120 | 145 | 174 | 207 | 243 | 284 |
| 2500 | 8.89 | 14.1 | 21.1 | 30.0 | 41.2 | 54.8 | 71.2 | 90.5 | 113 | 139 | 169 | 202 | 240 | 283 | 329 |
| 3000 | 10.0 | 16.0 | 23.8 | 33.9 | 46.5 | 61.9 | 80.4 | 102 | 128 | 157 | 191 | 228 | 271 | 319 | 372 |
| 3500 | 11.1 | 17.7 | 26.1 | 37.6 | 51.5 | 68.6 | 89.0 | 113 | 141 | 174 | 211 | 253 | 301 | 354 | 412 |
| 4000 | 12.2 | 19.3 | 28.8 | 41.1 | 56.3 | 75.0 | 97.3 | 124 | 155 | 190 | 231 | 277 | 329 | 386 | 451 |
| 5000 | 14.1 | 22.4 | 33.5 | 47.7 | 65.4 | 87.0 | 113 | 144 | 179 | 221 | 268 | 321 | 381 | 448 | 523 |
| 6000 | 15.9 | 25.3 | 37.8 | 53.8 | 73.8 | 98.3 | 128 | 162 | 203 | 249 | 302 | 363 | 431 | 506 | 591 |
| 7000 | 17.7 | 28.1 | 41.9 | 59.6 | 81.8 | 109 | 141 | 180 | 224 | 276 | 335 | 402 | 477 | 501 | 654 |
| 8000 | 19.3 | 30.7 | 45.8 | 65.2 | 89.4 | 119 | 155 | 196 | 245 | 302 | 366 | 439 | 522 | 613 | 715 |
| 9000 | 20.9 | 33.2 | 49.5 | 70.5 | 96.7 | 129 | 167 | 215 | 265 | 327 | 396 | 475 | 564 | 663 | 774 |
| 10000 | 22.4 | 35.6 | 53.1 | 75.6 | 104 | 138 | 179 | 228 | 285 | 350 | 425 | 510 | 605 | 712 | 830 |
| 12500 | 26.0 | 41.3 | 61.7 | 87.8 | 120 | 160 | 208 | 265 | 330 | 406 | 493 | 592 | 702 | 826 | 963 |
| 15000 | 29.4 | 46.6 | 69.6 | 99.1 | 136 | 181 | 235 | 299 | 373 | 459 | 557 | 668 | 793 | 933 | 1088 |
| 20000 | 35.6 | 56.5 | 84.4 | 120 | 165 | 219 | 285 | 362 | 452 | 556 | 675 | 809 | 961 | 1130 | 1318 |
| 25000 | 41.3 | 65.6 | 97.9 | 139 | 191 | 254 | 330 | 420 | 525 | 645 | 783 | 939 | 1115 | 1311 | 1529 |
| 30000 | 46.6 | 74.0 | 111 | 157 | 216 | 287 | 373 | 474 | 592 | 728 | 884 | 1060 | 1258 | 1480 | 1727 |
By the inspection of this table we can see in condensed form the coal-cost of any speed as high as twenty miles per hour, and for any size of vessel from one hundred tons to thirty thousand tons. Let us find in the left hand column a vessel of 2,500 tons displacement. Pursuing the line along to the right we find in the second column 8.89 tons of coal, which a steamer of this displacement would burn in 24 hours, if running, as indicated at the head of the column, 6 Nautical miles per hour.