CHAPTER XIV

THEORY AND EXPERIMENTAL STUDY OF METHODS OF CAMERA SUSPENSION

=General Theory.=—In addition to the limitation of exposure set by the ground speed of the plane another limitation is set by the _vibration_ of the camera. This may be caused either by the motor, or by the elastic reactions of the plane members to the strains of flight. Unlike the movement of the image due to the simple motion of the plane, movements due to vibration may be eliminated by proper anti-vibrational mounting of the camera.

The effect of vibration may show as an indistinctness of the whole image—this is its only effect with a between-the-lens shutter—or as a band or bands of indistinctness parallel to the curtain opening (Fig. 76). These are due to shocks or short period vibrations during the passage of the focal-plane shutter.

The obvious remedy for vibration troubles is to mount the camera on some elastic, heavily damping support, like sponge rubber or metal springs. Such a mounting should, however, be designed on sound principles derived from a proper analysis of the nature and effect of the possible motions of the camera. Otherwise, the vibrational disturbances may be increased rather than diminished by the camera mount. Such an analysis, based merely on general mechanical principles, shows that all motions of the camera are resolvable into _six_. These are three _translational_ motions, namely, two at right angles in one plane such as the horizontal, and one in the plane at right angles to this (vertical); and three _rotational_ motions, one about each of the above directions of translational motion as an axis (Fig. 77).

Brief consideration will show that only the latter—the rotational motions—are of any importance when the small displacements due to vibration are in question. To illustrate the negligible effect of vibrations which merely move the camera parallel to itself in any direction it is only necessary to imagine the camera moved parallel to the ground through a large distance, such as 10 centimeters. Now 10 centimeters motion of the camera at 3000 meters elevation means, with a 25 centimeter camera lens,

.25 1 ———— × 10 = ———— centimeter 3000 1200

motion on the plate, which would be only a tenth the distance separable by a good lens. If we reduce this motion to the small fraction of a centimeter which vibration would actually produce, it is evident that such vibration is of absolutely no importance. Similarly, if we imagine the camera, under the same conditions, moved vertically with reference to the ground by ten centimeters, the scale of the picture would merely be changed by 1/12000 or by 1/1000 centimeter on a 12 centimeter plate, again quite negligible.

When we consider motions of rotation, however, the case is quite different. If the camera is mounted so that the effect of any vibration is to rotate it around a horizontal axis, this is exactly equivalent to rotating the beam of light from the lens so that it sweeps across the plate. Thus a millimeter displacement of the lens of the camera with the plate remaining fixed gives approximately a millimeter motion of the image. Consequently, a rotation producing only a fraction of a millimeter's relative motion of lens and plate during the period the curtain aperture is over a given point would cause fatal blurring—and the visible vibration of plane longerons and cross members is easily of half millimeter amplitude or more. Reduced to angular units it is easily shown that a rotation of one degree per second—which is quite slow as plane oscillations go—is beyond the limits of toleration. Translational motions of large amplitude may be allowed, but the mounting of the camera must not permit these translations to be at all different for different parts of the camera.

The proper way to eliminate vibrational effects is to devise a mounting that will transmit only the translational shocks or that will transform the rotational ones into translations. Platforms pivoted and cross-linked so as to be free to move only parallel to themselves (described in the next chapter) represent one attempt to reach this result. Quite the simplest and most scientific form of mounting to achieve this end is to support the camera solely _in the plane of the center of gravity_. The principle here involved is easily grasped if we note that when we jar a camera supported above or below its center of gravity, the effect is to start the camera vibrating with the center of gravity oscillating pendulum-like about the point of support. The closer the center of gravity to the center of support, the smaller the moment of the body about the latter point.

=Experimental Study of Methods of Camera Support.=—Conclusive evidence as to the merits of any system of camera mounting can be obtained only under conditions that eliminate the effect of other variables which may be equally efficacious in diminishing the effects of vibration, but which have only limited application. Very brief exposures—1/500 second and less—will, for instance, result in good pictures with almost any condition of vibration. Hence a sharp picture offers no proof of the merits of a camera mounting unless it is known that the exposure was no shorter than the limit set by the ground speed of the plane. In fact it may be said that the chief object of studying methods of camera suspension is to increase the allowable exposure to a maximum, thus lengthening the working hours and multiplying the useful working days for aerial photography.

The most satisfactory method of test yet developed is to fly over a light or a group of lights on the ground with the camera shutter open. In the first use of this method, which originated in the English Service, such flights were made at night, but later it was found that good results could be got by placing the lights in a forest and making the tests when the sun was fairly low. One of the group of lights must be periodically interrupted, at a known rate, to furnish the time intervals.

Some characteristic “trails” obtained by this method of test are shown in Fig. 78. The first trail is that given by a camera rigidly fastened to the fuselage. The second and third show hand camera trails, made by an inexperienced and by an experienced observer, respectively. They show by comparison with the other figures that the human body is an excellent block to vibration, but in unskilled hands a poor check to rapid erratic (probably rotational) motions of the camera. The fourth is the trail given by a camera supported by gimbals bedded in sponge rubber accurately in the plane of the camera's center of gravity. Other trails are shown in the next chapter in connection with the description of practical camera mountings. Clearly the best suspension is that giving the smallest amplitude of displacement during the interval of time covered by an average exposure. It is, in fact, possible to determine from these trails the permissible exposure for any assumed permissible blurring of the image. The rigid mounting trail indicates very bad conditions, calling for literally instantaneous exposures. The center of gravity trail, at the other extreme, shows practically no limitation of exposure in so far as vibration is concerned, thus bearing out the theoretical conditions above discussed. An interesting conclusion from these experiments is that a rapidly running motor gives less harmful vibration than a slow one, although in the war it was a common practice to throttle the motor before exposing. As might be expected, the greater the number of cylinders, the shorter the period and the smaller the amplitude of the vibration.

=Pendular Camera Supports.=—The design of the camera support may be approached from a different standpoint, namely, with the aim of carrying the camera so that it will tend to hang always vertical. In mapping this is of fundamental importance. It is, indeed, a question whether aerial mapping will ever be worthy of ranking as a precision method unless the camera can be mounted so that its pictures are taken in the horizontal, undistorted position.

The simplest way to hold the camera vertical is to mount it on gimbals, with its center of gravity below the point of support. When so mounted the camera swings as a pendulum. Delicacy of response to variation of level is obtained by leaving a considerable distance between the center of gravity and the center of support. Oscillation about the vertical position is to be prevented by some system of dash pots or other damping. A suspension of this kind is furnished with the Brock film camera (Fig. 60).

It will be seen at once that the relation of center of gravity to center of support called for here is in direct contradiction to the requirements for eliminating vibration. Either one requirement or the other must be sacrificed, or else a compromise made in which neither delicate response to inclination of the plane nor fully satisfactory freedom from vibration is attained. This is a very serious objection to the pendular support. But the really vital objection to the pendular support is that it performs its function only very partially. It is entirely satisfactory only under conditions of steady flying, as in a uniform climb or glide, with the plane tail or nose heavy, or in flying with one wing down. As soon as we introduce any acceleration, as in making a turn, the camera follows the plane and not the earth.

It is true that mapping photography is done from a plane flying as level as possible, and that except under bad air conditions it holds its course with very little turning, if handled by a skilled pilot. Nevertheless, a surprisingly small deviation from straight flying causes quite serious variations from the vertical. It is of interest to calculate how large may be the horizontal accelerations that accompany swervings from a straight course which one might think insignificant. For instance, consider the horizontal acceleration due to a turn having a radius of a kilometer when the plane is moving at 100 kilometers per hour. If _a_ is the acceleration, _v_ the velocity of the plane, and _r_ the radius, we have from elementary dynamics that

_v_^2 _a_ = ————— _r_

Substituting the values chosen, we have—

100,000^2 meters _a_ = ————————————— = .77 —————— 3600^2 × 1000 sec^2

The acceleration of gravity being 9.80 meters/sec^2 we have that the ratio of the horizontal acceleration to the vertical is

.77 ———— = .078 9.80

This is the tangent of the angle of deviation from the vertical, from which the angle turns out to be about 4½ degrees, a very considerable error, rapidly multiplied as the speed of the plane is increased. It is, indeed, open to question whether the average deviations from the vertical are not apt to be less with the camera rigidly fixed to the plane, if guided by a skilled pilot who will hold the ship level at the expense of “skidding” the slight turns he must make to hold his direction.

=Gyroscopic Mountings.=—The ideal support for the aerial camera will undoubtedly be one embodying gyroscopic control of the camera's direction. By proper utilization of the principles of the gyroscope it is to be expected that not only can the camera be maintained vertical, but it may be supported anti-vibrationally as well. At the present time the problem of gyroscopic control is in the experimental stage, so that only the elements of the problem and the possible modes of solution can be laid out.

The gyroscope consists essentially of a heavy ring or disc rotating at a high speed on an axis free to point in any direction (Fig. 79). If mounted so that the axes of the supporting gimbals pass through the center of gravity of the rotating disc, the result is a _neutral_ gyroscope. Its characteristic is that its axis maintains its _direction fixed_, but this fixity is with respect to space and not with respect to the gravitational vertical. Consequently, as the earth revolves the inclination of the gyroscopic axis changes with respect to the earth. In latitude 45° this change is approximately a degree in five minutes. Furthermore, the action of friction in the supports, which can never be entirely eliminated, also acts to slowly alter the direction of the gyroscopic axis. Therefore, unless some _erector_ is applied even the gyroscope will not perform the task required of it.

Before discussing possible forms of erectors it may be noted in general, first, that these must depend upon gravity; second, that such being the case, they must respond to the resultant of gravity and any acceleration, that is, to the _apparent_ or _pseudo-gravity_. As already seen, this pseudo-gravity, during a turn, is exactly what limits the usefulness of the pendular support, and necessitates recourse to the gyroscope. The problem thus becomes one of making an erector-gyroscope combination which will respond to true gravity and not to pseudo-gravity.

In general this problem would be insoluble, since there is no difference in the nature of the acceleration of gravity and that due to centrifugal force. A way out is offered, however, by the fact that true gravity acts continuously and at a small angle to the axis of the gyro, while the components which cause the pseudo-gravity are of short duration, liable to rapid changes of direction, and, on a turn, act at a large angle. What we require, therefore, is an erector which will respond slowly but surely to the _average_ acceleration, which is downward, but too sluggishly to be affected by the shorter period accelerations due to turns or rolls. Slowness of response is a matter of the erecting forces being small and of the mass and angular velocity of the gyro disc being large. The success of the compromise called for depends on the relative times taken for the gyroscope to tilt seriously from the true vertical, due to the causes above mentioned, and for the average turn or roll. Fortunately the former is a matter of minutes, the latter of seconds or at the worst of fractions of a minute. More than this, since the roll or turn is apt to be of much greater angle than any normal deviation of the gyroscopic axis from the vertical in the same time, we are offered the possibility of some device for filtering out the deviations which alone are to effect the erector. For instance, by shunting the restoring force whenever it is called upon to act through more than a predetermined small angle.

As to the method of erecting the gyroscope, its characteristic property must be kept in mind. This is that the axis does not tilt under an applied force in the direction it would if the gyro were not rotating, but around an axis at right angles to that of the applied couple. Thus in Fig. 79, if a weight is attached as shown, the disc does not incline downward toward the weight, around the axis _Y_, _Y´_, but _precesses_ about the vertical axis Z, Z´. Some means is therefore needed to translate the pull which any gravitational control, such as a freely swinging pendulum, would give, into a pull with _at least a component_ at a finite angle to this.

In the Gray stabilizer several metal balls are slowly rotated in a tray above the center of gravity of the gyroscope. Specially shaped grooves or compartments limit the freedom of motion of these balls so that when the gyro is inclined the balls travel at different distances from the center on the ascending and descending sides. By this scheme a couple is produced about the axis through the center and the low point of the disc, which tilts the apparatus to the gravitational vertical. In an alternative form the balls are carried past the low point by their momentum and are prevented from returning by the walls of the containing compartment, which have meanwhile been advanced by the rotation of the erector as a whole. The net result is to shift the center of gravity of the system of balls in the proper direction to erect the gyro. The rectifying action is purposely made quite slow so that the displacements of the balls due to pseudo-gravity will be averaged out.

In a design due to Lucian, small pendulums work through electric contacts to actuate solenoids which in turn move small weights in the appropriate directions to give the desired tilt. Response is made fairly quick and delicate, and pseudo-gravity, due to turns and rolls, is rendered inoperative by the contacts breaking whenever the pendulums swing more than three or four degrees. This can only happen if they move too quickly for the erecting forces to act, reliance being here placed on the characteristic differences of action in respect to time of real and pseudo-gravitational forces.

Besides the neutral gyroscope as just considered there is the pendular or top type, in which the center of gravity is not in the plane of the supports. In general this type depends on a couple resulting from the gravitational pull and the inevitable friction of the supports to slowly tilt the axis to the gravitational vertical. This type is slower to respond than the designs in which a definite couple in the proper direction is provided and it reaches the true vertical only through a circuitous path.

Three methods of controlling a camera by a gyroscope are suggested. One is to fasten the gyroscope rigidly to the camera and mount the whole system on gimbals. A second is to mount both camera and gyro side by side on gimbals, linking the two so that the camera is moved parallel to the gyro (Fig. 80). A third method is to utilize the gyro to make electric contacts to operate motors which in turn move the camera.

Considerable weight and space are required for a gyroscope capable of stabilizing a camera. The rotating disc should be about half the weight of the camera, and with its mounting may be expected to double the room required for the camera alone. Motive power for maintaining the gyro in continuous rotation may be supplied by an air blast, or the gyro may be made up as an induction motor—the latter necessitating an alternating current supply.

In view of the space and weight limitations in a plane it is a question still to be decided whether it is more economical to stabilize the camera or to stabilize an inclinometer and photograph its indications simultaneously with the release of the shutter which takes the aerial picture.