The air that surrounds us weighs about one-thirteenth of a pound per cubic foot and exerts a pressure, at sea level, of nearly fifteen pounds per square inch. Its temperature varies from 30° below to 100° above the Fahrenheit zero. The pressure of the air decreases about one-half pound for each thousand feet of altitude; at the top of Mt. Blanc it would be, therefore, only about six pounds per square inch. The temperature also decreases with the altitude. The weight of a cubic foot, or density, which, as has been stated, is one-thirteenth of a pound ordinarily, varies with the pressure and with the temperature. The variation with pressure may be described by saying that the quotient of the pressure by the density is constant: one varies in the same ratio as the other. Thus, at the top of Mt. Blanc (if the temperature were the same as at sea level), the density of air would be about 6/15 × 1/13 = 2/65: less than half what it is at sea level. As to temperature, if we call our Fahrenheit zero 460°, and correspondingly describe other temperatures—for instance, say that water boils at 672°—then (pressure being unchanged) the product of the density and the temperature is constant. If the density at sea level and zero temperature is one-thirteenth pound, then that at sea level and 460° Fahrenheit would be

(0 + 460) / (460 + 460) × 1/13 = 1/26.

These relations are particularly important in the design of all balloons, and in computations relating to aeroplane flight at high altitudes. We shall be prepared to appreciate some of their applications presently.

Generally speaking, the atmosphere is always in motion, and moving air is called wind. Our meteorologists first studied winds near the surface of the ground: it is only of late years that high altitude measurements have been considered practically desirable. Now, records are obtained by the aid of kites up to a height of nearly four miles: estimates of cloud movements have given data on wind velocities at heights above six miles: and much greater heights have been obtained by free balloons equipped with instruments for recording temperatures, pressures, altitude, time, and other data.

When the Eiffel Tower was completed, it was found that the average wind velocity at its summit was about four times that at the base. Since that time, much attention has been given to the contrasting conditions of surface and upper breezes as to direction and velocity.

Air is easily impeded in its movement, and the well-known uncertainties of the weather are closely related to local variations in atmospheric pressure and temperature. When near the surface of the ground, impingement against irregularities therein—hills, cliffs, and buildings—makes the atmospheric currents turbulent and irregular. Where there are no surface irregularities, as on a smooth plain or over water, the friction of the air particles passing over the surface still results in a stratification of velocities. Even on a mountain top, the direction and speed of the wind are less steady than in the open where measured by a captive balloon. The stronger the wind, the greater, relatively, is the irregularity produced by surface conditions. Further, the earth’s surface and its features form a vast sponge for sun heat, which they transfer in turn to the air in an irregular way, producing those convectional currents peculiar to low altitudes, the upper limit of which is marked by the elevation of the cumulus clouds. Near the surface, therefore, wind velocities are lowest in the early morning, rising to a maximum in the afternoon.

Every locality has its so-called “prevailing winds.” Considering the compass as having eight points, one of those points may describe as many as 40% of all the winds at a given place. The direction of prevalence varies with the season. The range of wind velocities is also a matter of local peculiarity. In Paris, the wind speed exceeds thirty-four miles per hour on only sixty-eight days in the average year, and exceeds fifty-four miles on only fifteen days. Observations at Boston show that the velocity of the wind exceeds twenty miles per hour on half the days in winter and on only one-sixth the days in summer. Our largest present dirigible balloons have independent speeds of about thirty-four miles per hour and are therefore available (at some degree of effectiveness) for nearly ten months of the year, in the vicinity of Paris. In a region of low wind velocities—like western Washington, in this country—they would be available a much greater proportion of the time. To make the dirigible able to at least move nearly every day in the average year—in Paris—it must be given a speed of about fifty-five miles per hour.

Figures as to wind velocity mean little to one unaccustomed to using them. A five-mile breeze is just “pleasant.” Twelve miles means a brisk gale. Thirty miles is a high wind: fifty miles a serious storm (these are the winds the aviator constantly meets): one hundred miles is perhaps about the maximum hurricane velocity.

As we ascend from the surface of the earth, the wind velocity steadily increases; and the excess velocity of winter winds over summer winds is as steadily augmented. Thus, Professor Rotch found the following variations:

These results are shown in a more striking way by the chart. At a five or six mile height, double-barreled hurricanes at speeds exceeding 200 miles per hour are not merely possible; they are part of the regular order of things, during the winter months.

The winds of the upper air, though vastly more powerful, are far less irregular than those near the surface: and the directions of prevailing winds are changed. If 50% of the winds, at a given location on the surface, are from the southwest, then at as moderate an elevation as even 1000 feet, the prevailing direction will cease to be from southwest; it may become from west-southwest; and the proportion of total winds coming from this direction will not be 50%. These factors are represented in meteorological papers by what is known as the wind rose. From the samples shown, we may note that 40% of the surface winds at Mount Weather are from the northwest; while at some elevation not stated the most prevalent of the winds (22% of the total) are westerly. The direction of prevalence has changed through one-eighth of the possible circle, and in a counter-clockwise direction. This is contrary to the usual variation described by the so-called Broun’s Law, which asserts that as we ascend the direction of prevalence rotates around the circle like the hands of a watch; being, say, from northwest at the surface, from north at some elevation, from northeast at a still higher elevation, and so on. At a great height, the change in direction may become total: that is, the high altitude winds blow in the exactly opposite direction to that of the surface winds. In the temperate regions, most of the high altitude winds are from the west: in the tropics, the surface winds blow toward the west and toward the equator; being northeasterly in the northern hemisphere and southeasterly in the southern: and there are undoubtedly equally prevalent high-altitude counter-trades.

The best flying height for an aeroplane over a flat field out in the country is perhaps quite low—200 or 300 feet: but for cross-country trips, where hills, rivers, and buildings disturb the air currents, a much higher elevation is necessary; perhaps 2000 or 3000 feet, but in no case more than a mile. The same altitude is suitable for dirigible balloons. At these elevations we have the conditions of reasonable warmth, dryness, and moderate wind velocities.

Sailing Balloons

In classifying air craft, the sailing balloon was mentioned as a type intermediate between the drifting balloon and the dirigible. No such type has before been recognized: but it may prove to have its field, just as the sailing vessel on the sea has bridged the gap between the raft and the steamship. It is true that tacking is impossible, so that our sailing balloons must always run before the wind: but they possess this great advantage over marine sailing craft, that by varying their altitude they may always be able to find a favorable wind. This implies adequate altitude control, which is one of the problems not yet solved for lighter-than-air flying machines: but when it has been solved we shall go far toward attaining a dirigible balloon without motor or propeller; a true sailing craft.

This means more study and careful utilization of stratified atmospheric currents. Professor Rotch suggests the utilization of the upper westerly wind drift across the American continent and the Atlantic Ocean, which would carry a balloon from San Francisco to southern Europe at a speed of about fifty feet per second—thirty-four miles per hour. Then by transporting the balloon to northern Africa, the northeast surface trade wind would drive it back to the West Indies at twenty-five miles per hour. This without any motive power: and since present day dirigibles are all short of motive power for complete dirigibility, we must either make them much more powerful or else adopt the sailing principle, which will permit of actually decreasing present sizes of motors, or even possibly of omitting them altogether. Our next study is, then, logically, one of altitude control in balloons.

Field and Speed

An aerostat (non-dirigible balloon), unless anchored, drifts at the speed of the wind. To the occupants, it seems to stand still, while the surface of the earth below appears to move in a direction opposite to that of the wind. In the sketch, if the independent velocity of a dirigible balloon be PB, the wind velocity PV, then the actual course pursued is PR, although the balloon always points in the direction PB, as shown at 1 and 2. If the speed of the wind exceed that of the balloon, there will be some directions in which the latter cannot progress. Thus, let PV be the wind velocity and TV the independent speed of the balloon. The tangents PX, PX´, include the whole “field of action” possible. The wind direction may change during flight, so that the initial objective point may become unattainable, or an initially unattainable point may be brought within the field. The present need is to increase independent speeds from thirty or forty to fifty or sixty miles per hour, so that the balloon will be truly dirigible (even if at low effectiveness) during practically the whole year.

Suppose a dirigible to start on a trip from New York to Albany, 150 miles away. Let the wind be a twenty-five mile breeze from the southwest. The wind alone tends to carry the balloon from New York to the point d in four hours. If the balloon meanwhile be headed due west, it would need an independent velocity of its own having the same ratio to that of the wind as that of de to fd, or about seventeen and one-half miles per hour. Suppose its independent speed to be only twelve and one-half miles; then after four hours it will be at the position b, assuming it to have been continually headed due west, as indicated at a. It will have traveled northward the distance fe, apparently about sixty-nine miles.

After this four hours of flight, the wind suddenly changes to south-southwest. It now tends to carry the balloon to g in the next four hours. Meanwhile the balloon, heading west, overcomes the easterly drift, and the balloon actually lands at c. Unless there is some further favorable shift of the wind it cannot reach Albany. If, during the second four hours, its independent speed could have been increased to about fifteen and a half miles it would have just made it. The actual course has been fbc: a drifting balloon would have followed the course fdh, dh being a course parallel to bg.