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).
[Illustration:
FIG. 76.—Captured German photograph, showing zones of poor definition
due to vibration during passage of focal plane shutter aperture.]
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.
[Illustration:
FIG. 77.—Diagram showing possible motions of the airplane camera:
three of translation and three of rotation, and their combinations.]
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.
[Illustration:
FIG. 78.—Tests of camera mounting, made by flying over a bright light
against a dark background. (_a_) Rigid fastening on side of plane;
(_b_) held in the hand, inexperienced observer; (_c_) held in the
hand, experienced observer; (_d_) camera mounted at center of
gravity on gimbals bedded in sponge rubber.]
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.
[Illustration:
FIG. 79.—Diagram of simple gyroscope.]
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.
[Illustration:
FIG. 80.—Diagram of camera linked to gyroscopic stabilizer.]
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.