In a voyage this year by German officers from Berlin, the exact number of bags of ballast they took up led me to guess the capacity of the balloon, allowing for the number of passengers, and the supposed weight of the whole; I found that I was pretty near the mark, and that the expenditure of sand was about in proportion to my own when I took Mr. Walter Powell a journey of 250 miles.
The balloon itself is no bad indicator of what can be achieved, especially in vertical motion, that is by showing the extent of expansion when the silk is throughout fully distended, and if it be so, by the force with which the gas rushes out of the safety valve; it in this way helps and checks barometrical readings, and may at times approximately take the place of that instrument for a rough-and-ready intimation of the height. For example, if a balloon mounts up when only half full at starting, and afterwards rises so high that gas escapes from the neck, then it must be between three and four miles high, roughly speaking.
It is of no use for a novice or an unscientific aëronaut to tell a fanciful tale about his lofty flights to fabulous elevations, when he is known to have taken only a moderate amount of ballast, and only one person besides himself in the car.
If one hears a story that a small aërial affair has been up miles high, or hundreds of miles horizontally, even at a low altitude, do not take it for granted that you have been told the truth, you can easily try and prove it for yourself. Just ask a few questions as to its size, next get at its displacement of air, as you would judge in like manner of a ship’s displacement of water when it has to carry so many thousand tons of cargo.
If you hear that a balloon of thirty or even forty feet in diameter has been 20,000 feet high when filled with coal gas, shake your head and fly to figures, remembering that the following simple calculations will enable you to judge for yourself. Make, in fact, yourself a balloon of tissue or Chinese paper, and bear in mind at the outset the proportion that the diameter bears to the circumference of a circle.
Say you make it of three feet diameter, or thirty-six inches.
In order to find the circumference, which is three times and one-seventh the diameter, multiply the diameter thirty-six by 3·1416—
| Then 3·1416 | |
| 36 | inches. |
| ——— | |
| 188496 | |
| 94248 | |
| ———— | |
| 113·0976 | |
| ======= |
Secondly.—By multiplying this circumference 113, by the diameter 36, it gives the superficial surface.
| 113 | |
| 36 | |
| —— | |
| 678 | |
| 339 | |
| —— | |
| Number of superficial inches on the surface | 4068 |
| === | |