Principle of the Fire Balloon
The general principle of the equilibrium of a fire-balloon is, of course, identical with that of a gas-balloon, but the motion is different, as the degree of buoyancy at each moment varies with the temperature of the air within the balloon, and therefore with the heat of the furnace by which the air is warmed. Dry air expands FORMULA part of its volume for every increase of temperature of 1o centigrade, or FORMULA of its volume for very increase of temperature of 1° Fahr. More than the surrounding air, the air within the bag will expand FORMULA of its volume, and this air must therefore escape. The air within the bag weighs less, therefore, than the air it displaces by the FORMULA part of the latter; and if the weight of this de greater than the weight of the bag and appurtenances, the latter will ascend. It is, therefore, always easy to calculate approximately the ascensional power of a fire-balloon if the temperature of the surrounding air be known, and also the mean temperature of the air within the balloon. Thus, let the balloon contain V cubic feet of hot air at the temperature t (fahr.), and let the temperature of the surrounding air be t (Fahr.) Also suppose the weight of the balloon, can, &c., is W lb, and let the barometer reading be h inches, then the ascensional power is equal to the weight of the air displace-weight of the air displaced -- weight of the heated air -- W lb, viz.,
080728 lb being the weight of a cubic foot of air at temperature 32°, under the pressure of one atmosphere, viz., when the reading of the barometer is 29.922 in. Of course, the motion depends upon the temperature of the air in the balloon as due to the furnace, if the latter is taken up with the balloon; but if the air in the balloon is merely warmed, and the balloon then set by itself, the problem is an easy one, as the rate of cooling can be determined approximately; but it is destitute of interest. We have said that dry air increase its volume by FORMULA part for every increase of 1° (Fahr.), but the air is generally more or less saturated with moisture. This second atmosphere, formed of the vapour of water, is superposed over that of the air, as it were, and, in a very careful consideration of the question, should be taken into account. Even, however, when the air is completely saturated with moisture but little difference is produced; so that for all practical purposes the presence of the vapour of water in the air may be ignored. Of course the amount of vapour depends on the dew-points, and tables of he pressure of the vapour of water at different temperatures are given in most modern works on heat; but, as has been stated, the matter, in an aeronautical point of view, is of very little importance. At first it was supposed that the cause of the ascent of the balloon of the Montgolfiers was traceable to the generation of gas and smoke from the damp straw which was set light to; but the advance of science showed that the fire-balloon owed its levity merely to the rearefaction of the air produced by the heat generated.
Read the rest of this article:
Aeronautics - Table of Contents