"We now learn that the War Office is soon to produce another airship similar to the 'Nulli Secundus,' but with a much greater capacity and a stronger engine. In the newspaper accounts it is said that the gas-bag of this new balloon would be sausage-shaped and 42 feet in diameter, that it is to be provided with an engine of 100 horse-power, which it is claimed will give to this new production a speed of 40 miles an hour through the air, so that, with a wind of 20 miles an hour, it will still be able to travel by land 20 miles an hour against the wind. Probably the writer of the article did not consider the subject from a mathematical point of view. As the mathematical equation is an extremely simple one, it is easily presented so as to be understood by any one having the least smattering of mathematical or engineering knowledge. The cylindrical portion of the gas-bag is to be 42 feet in diameter; the area of the cross-section would therefore be 1,385 feet. If we take a disc 42 feet in diameter and erect it high in the air above a level plain, and allow a wind of 40 miles an hour, which is the proposed speed of the balloon, to blow against it, we should find that the air pressure would be 11,083 lbs.--that is, a wind blowing at a velocity of 40 miles an hour would produce a pressure of 8 lbs. to every square foot of the disc.[3] Conversely, if the air were stationary, it would require a push of 11,083 lbs. to drive this disc through the air at the rate of 40 miles an hour.
[3] Haswell gives the pressure of the wind at 40 miles an hour as 8 lbs. per square foot, and this is said to have been verified by the United States Coast Survey. Molesworth makes it slightly less; but the new formula, according to most recent experiments (Dr. Stanton's experiments at the National Physical Laboratory and M. Eiffel's at Eiffel Tower), is P = 0·003 V², which would make the pressure only 4·8 lbs. per square foot, and which would reduce the total H.P. required from 472 to 283, where P represents pounds per square foot and V miles per hour.
"A speed of 40 miles an hour is at the rate of 3,520 feet in a minute of time. We therefore have two factors--the pounds of resistance encountered, and the distance through which the disc travels in one minute of time. By multiplying the total pounds of pressure on the complete disc by the number of feet it has to travel in one minute of time, we have the total number of foot-pounds required in a minute of time to drive a disc 42 feet in diameter through the air at a speed of 40 miles an hour. Dividing the product by the conventional horse-power 33,000, we shall have 1,181 horse-power as the energy required to propel the disc through the air. However, the end of the gas-bag is not a flat disc, but a hemisphere, and the resistance to drive a hemisphere through the air is much less than it would be with a normal plane or flat disc. In the 'Nulli Secundus' we may take the coefficient of resistance of the machine, considered as a whole, as 0·20--that is, that the resistance will be one-fifth as much as that of a flat disc. This, of course, includes not only the resistance of the balloon itself, but also that of the cordage, the car, the engine, and the men.