Part 3

This particular difficulty has considerably delayed the development of the aeroplane. It may, however, be overcome by very simple methods--simple, at least as far as their mechanical features are concerned. If the outer limb of the plane is tilted upward, it is because the wind pressure is greater there. The wind pressure is greater because the velocity is greater. We have only to increase the wind pressure at the inner limb, in order to restore equilibrium. This cannot be done by adjusting the velocity, because the velocity is fixed by the curvature of path required: but the total wind pressure depends upon the _sail area_ as well as the velocity; so that by increasing the surface at the inner limb we may equalize the value of _L_, the lifting force, at the two ends of the plane. This increase of surface must be a temporary affair, to be discontinued when moving along a straight course.

Let us stand in the rear of an aeroplane, the main wing of which is represented by _ab_. Let the small fan-shaped wings _c_ and _d_ be attached near the ends, and let the control wires, _e_, _f_, passing to the operator at _g_, be employed to close and unclasp the fans. If these fans are given a forward inclination at the top, as indicated in the end view, they will when spread out exert an extra lifting force. A fan will be placed at each end. They will be ordinarily folded up: but when rounding a curve the aviator will open the fan on the inner or more slowly moving limb of the main plane. This represents one of the first forms of the _aileron_ or wing-tip for lateral control.

The more common present form of aileron is that shown in the lower sketch, at _s_ and _t_. The method of control is the same.

The cellular Voisin biplanes illustrate an attempt at self-sufficing control, without the interposition of the aviator. Between the upper and lower sails of the machine there were fore and aft vertical partitions. The idea was that when the machine started to revolve, the velocity of rotation would produce a pressure against these partitions which would obstruct the tipping. But rotation may take place slowly, so as to produce an insufficient pressure for control, and yet be amply sufficient to wreck the apparatus. The use of extra vertical rudder planes, hinged on a horizontal longitudinal axis, is open to the same objection.

Wing Warping

In some monoplanes with the inverted _V_ wing arrangement, a dipping of one wing answers, so to speak, to increase its concavity and thus to augment the lifting force on that side. The sketch shows the normal and distorted arrangement of wings: the inner limb being the one bent down in rounding a curve. An equivalent plan was to change the angle of inclination of one-half the sail by swinging it about a horizontal pivot at the center or at the rear edge: some machines have been built with sails divided in the center. The obvious objection to both of these plans is that too much mechanism is necessary in order to distort what amounts to nearly half the whole machine. They remind one of Charles Lamb's story of the discovery of roast pig.

The distinctive feature of the Wright machines lies in the warping or distorting of the _ends only_ of the main planes. This is made possible, not by hinging the wings in halves, but by the flexibility of the framework, which is sufficiently pliable to permit of a considerable bending without danger. The operator, by pulling on a stout wire linkage, may tip up (or down) the corners _cc´_ of the sails at one limb, thus decreasing or increasing the effective surface acted on by the wind, as the case may require. The only objection is that the scheme provides one more thing for the aviator to think about and manipulate.

Automatic Control

Let us consider again the condition of things when rounding a curve, as in the sketch on page 32. As long as the machine is moving forward in a straight line, the operator sits upright. When it begins to tip, he will unconsciously tip himself the other way, as represented by the line _xy_ in the rear view. Any bicyclist will recognize this as plausible. Why not take advantage of this involuntary movement to provide a stabilizing force? If operating wires are attached to the aviator's belt and from thence connected with ailerons or wing-warping devices, then by a proper proportioning of levers and surfaces to the probable swaying of the man, the control may become automatic. The idea is not new; it has even been made the subject of a patent.

The Gyroscope

This device for automatic control is being steadily developed and may ultimately supersede all others. It uses the inertia of a fast-moving fly wheel for control, in a manner not unlike that contemplated in proposed methods of automatic balancing by the action of a suspended pendulum. Every one has seen the toy gyroscope and perhaps has wondered at its mysterious ways. The mathematical analysis of its action fills volumes: but some idea of what it does, and why, may perhaps be gathered at the expense of a very small amount of careful attention. The wheel _acbd_, a thin disc, is spinning rapidly about the axle _o_. In the side view, _ab_ shows the edge of the wheel, and _oo´_ the axle. This axle is not fixed, but may be conceived as held in some one's fingers. Now suppose the right-hand end of the axle (_o´_) to be suddenly moved toward us (away from the paper) and the left-hand (_o_) to be moved away. The wheel will now appear in both views as an ellipse, and it has been so represented, as _afbe_. Now, any particle, like _x_, on the rim of the wheel, will have been regularly moving in the circular orbit _cb_. The tendency of any body in motion is to move indefinitely in a straight line. The cohesion of the metal of the disc prevents the particle _x_ from flying off at a straight line tangent, _xy_, and it is constrained, therefore, to move in a circular orbit. Unless some additional constraint is imposed, it will at least remain in this orbit and will try to remain in its plane of rotation. When the disc is tipped, the plane of rotation is changed, and the particle is required, instead of (so to speak) remaining in the plane of the paper--in the side view--to approach and pass through that plane at _b_ and afterward to continue receding from us. Under ordinary circumstances, this is just what it would do: but if, as in the gyroscope, the axle _oo´_ is perfectly free to move in any direction, the particle _x_ will refuse to change its direction of rotation. Its position has been shifted: it no longer lies in the plane of the paper: but it will at least persist in rotating in a parallel plane: and this persistence forces the revolving disc to swing into the new position indicated by the curve _hg_, the axis being tipped into the position _pq_. The whole effect of all particles like _x_ in the entire wheel will be found to produce precisely this condition of things: if we undertake to change the plane of rotation by shifting the axle in a horizontal plane, the device itself will (if not prevented) make a further change in the plane of rotation by shifting the axle in a vertical plane.

A revolving disc mounted on the gyroscopic framework therefore resists influences tending to change its plane of rotation. If the device is placed on a steamship, so that when the vessel rolls a change of rotative plane is produced, the action of the gyroscope will resist the rolling tendency of the vessel. All that is necessary is to have the wheel revolving in a fore and aft plane on the center line of the vessel, the axle being transverse and firmly attached to the vessel itself. A small amount of power (consumed in revolving the wheel) gives a marked steadying effect. The same location and arrangement on an aeroplane will suffice to overcome tendencies to transverse rotation when rounding curves. The device itself is automatic, and requires no attention, but it does unfortunately require power to drive it and it adds some weight.

The gyroscope is being tested at the present time on some of the aeroplanes at the temporary army camps near San Antonio, Texas.

Wind Gusts

This feature of aeronautics is particularly important, because any device which will give automatic stability when turning corners will go far toward making aviation a safe amusement. Inequalities of velocity exist not only on curves, but also when the wind is blowing at anything but uniform velocity across the whole front of the machine. The slightest "flaw" in the wind means an at least temporary variation in lifting force of the two arms. Here is a pregnant source of danger, and one which cannot be left for the aviator to meet by conscious thought and action. It is this, then, that blindfolds him: he cannot see the wind conditions in advance. The conditions are upon him, and may have done their destructive work, before he can prepare to control them. We must now study what these conditions are and what their influence may be on various forms of aerial navigation: after which, a return to our present subject will be possible.

AIR AND THE WIND

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:

Altitude in Feet Annual Average Wind Velocity, Feet per Second 656 23.15 1,800 32.10 3,280 35. 8,190 41. 11,440 50.8 17,680 81.7 20,970 89. 31,100 117.5

Average Wind Velocities, Altitude in Feet Feet per Second Summer Winter 656 to 3,280 24.55 28.80 3,280 to 9,810 26.85 48.17 9,810 to 16,400 34.65 71.00 16,400 to 22,950 62.60 161.5 22,950 to 29,500 77.00 177.0

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_.

GAS AND BALLAST

A cubical block of wood measuring twelve inches on a side floats on water because it is lighter than water; it weighs, if yellow pine, thirty-eight pounds, whereas the same volume of water weighs about sixty-two pounds. Any substance weighing more than sixty-two pounds to the cubic foot would sink in water.

If our block of wood be drilled, and _lead_ poured in the hole, the total size of wood-and-lead block being kept constantly at one cubic foot, the block will sink as soon as its whole weight exceeds sixty-two pounds. Ignoring the wood removed by boring (as, compared with the lead which replaces it, an insignificant amount), the weight of lead plugged in may reach twenty-four pounds before the block will sink.

This figure, twenty-four pounds, the difference between sixty-two and thirty-eight pounds, then represents the maximum buoyant power of a cubic foot of wood in water. It is the difference between the weight of the wood block and the weight of the water it displaces. If any weight less than this is added to that of the wood, the block will float, projecting above the water's surface more or less, according to the amount of weight buoyed up. It will not rise entirely from the water, because to do this it would need to be lighter, not only than water, but than air.

Buoyancy in Air