elevation of the range-finder was altered. The other scale was set
to the range recorded by the range-finder, and the height of the
target could then be read off.
Long base height-finders usually consist of two instruments at the
ends of a base about a mile in length. Sighting planes in these
instruments are kept laid on the target; the triangle formed by the
intersection of a vertical plane with three planes, one of which is a
horizontal plane passing through the base and the other two are
extensions of the sighting planes, is mechanically solved; and the
height of the point where the two planes of sight intersect (i.e. the
height of the target above the base) is plotted at the same time.
The principle of this method is shown in fig. 3. AX and BY are
two horizontal lines, parallel to each pther. The sighting planes of
RANGE-FINDERS AND POSITION-FINDERS
245
th_> instrument would be attached to axles whose axes were on any
parts of AX and BY. AXQZ and BYQZ represent planes of which
the sighting planes form small parts. It is obvious that QZ is hori-
zontal, and that ZK, PL or any vertical line between QZ and the
horizontal line KL (which is parallel to the axes of the sighting
planes) represents the height of an aircraft in the line ZQ, say at P.
In the simplest form of height-finder, the plotting is done on a board
fixed beneath B, the triangle AZB being reproduced there on a small
scale and upside down. A straight edge is attached to the sighting
frame at B and consequently moved round B in front of the board
as the elevation of the frame is altered. Another straight edge is
pivoted on the right of B at a distance from it which represents AB
to the scale of the instrument. It is kept set to the altitude angle
which is measured at A and telephoned to B. The point where the
two straight edges intersect consequently represents the point Z.
Upon the board below B, a series of horizontal lines are marked,
their distance from a zero line passing through the pivots of the
straight edges representing heights above the ground, to the scale
of the instrument. The height of the target can therefore be ascer-
tained by noting against which of the horizontal lines on the board
the intersection of the two straight edges comes. Such height-
finders have serious disadvantages, the principal one being the
difficulty in getting the two instruments on to the same target.
Height- and Range-finder. Towards the end of the war Messrs.
Barr and Stroud produced a most ingenious instrument which
recorded both the height and range of aircraft, and which was at
once adopted by the British Government.
It is used in a similar manner to an ordinary one-man range-
finder, and the observer has only to keep the aircraft in the field of
view and make coincidences. As will be explained later, if the height
of the aircraft remains constant the coincidence will not alter as the
range alters. The field of view is so arranged that the rays of light
entering by the left window of the instrument form an erect image
over the whole field, with the exception of a narrow central hori-
zontal strip in which an inverted image is formed by the rays enter-
ing by the right window. The lower separating line is the one on
which coincidences are made. The advantage of this " strip "
system is that it is considerably easier to keep the aircraft in the
field of view than if the field were divided into two equal parts, one
of them being inverted. As in field instruments, the inversion of the
image in the field above the separating line is found to facilitate
making accurate coincidences.
The eye-piece of the range-finder is placed at right angles to the
plane of triangulation, so that if the angle of sight to the target is 60
the observer looks down at an angle of 30. It is provided with two
lens combinations on a rotatable cap which give magnifications of
15 and 25 diameters, and also with light filters for varying atmos-
pheric conditions. There is a window above and to the left of the
eye-piece, through which the usual ivory range scale can be seen.
In a small casing on the top of the range-finder there is a most
ingenious mechanism which converts ranges into the heights corre-
sponding to them as the angle of sight varies. The ranges and
heights can be read through two windows in close proximity to one
another. This mechanism actually solves the trigonometrical for-
mula r sin o = h; where r is the range of the target, a the angle of
sight to it, and h its height. This formula may be written as:
log r+log sin a = log h; and it is mechanically solved as follows: a
differential gear is employed, the upper member of which is rotated
in accordance with a logarithmic sine scale of angles of sight, and the
lower member is rotated in accordance with a logarithmic scale of
ranges, the jockey wheel accordingly revolving around the axis of
the differential with a motion corresponding to a logarithmic scale of
heights. It will be noted that the angle of elevation and the range
are known, or rather are determined by the instrument, so that the
duty of the gears is to convert the angle and range scales to logarith-
mic form and then to add them together by means of the differential
gear as explained above. The conversion of the reciprocal range
scale motion of the range-finder deflecting prism gear into logarith-
mic range scale motion, and the angular motion, of the range-finder
in elevation into motion corresponding to a logarithmic scale of sines,
is done in each case by means of toothed spiral gears.
The gearing is connected through three couplings to the working
head, the elevation gear and the deflecting prism gear respectively.
By means of suitable gearing the jockey wheel of the differential is
driven from the working head, the upper member by the elevation
gear, and the lower member by the deflecting prism gear. The range
scale is connected to the lower member, and the height scale to a
level wheel carrying the jockey wheel.
The advantage of arranging the working head to operate the
jockey wheel is that in the frequent case of aircraft flying at a con-
stant height the images in the field of view, when once set, can be
kept in coincidence by simply elevating the instrument so as to keep
the target in the centre of the field, without any rotation of the work-
ing head. The movement of the instrument in elevation auto-
matically controls the position of the deflecting prism, the height
scale remaining unaltered so long as the working head is not rotated.
When the target rises or falls, the images will move out of coin-
cidence and must be brought back into alignment by rotating the
working head, thus altering the reading of the height scale by the
appropriate amount. The working head and elevating gear may, of
course, be worked at one time, in which case the combined effect of
the spiral gears and the differential is that the two scales always
read correctly as long as the coincidence is maintained.
The instrument has a base length of two metres, and is carried in
the mounting forks in two eccentric bearing rings, the object of the
eccentricity being to balance the weight of the height-scale gear box
as the instrument is rotated in elevation. The elevating gear with
a handwheel on the left of the observer, is of the worm-wheel type.
The handwheel is provided with a two-speed clutch ; the speed being
changed by merely pressing in or releasing, with the palm of the
hand, a small lever connected with the hand grip.
The azimuth training gear is also of the worm and worm-wheel
type and has a two-speed clutch. Its handwheel is on the right of
the eye-piece, and in a convenient position for the man who, looking
through a small prismatic telescope near the right-hand end of the
instrument, keeps it laid for direction on the target.
The worm wheels for movements in both azimuth and altitude
are mounted on friction slip-bearings, so that the instrument can be
rapidly moved and the target brought into its field of view. An
elevating lever is fitted near the left-hand end of the instrument to
allow of rapid elevation. An adjustable azimuth scale and reader are
provided; and a means of levelling the upper part of the mounting.
Before using the instrument, its correct levelling must be attended
to and checked by means of two bubbles attached to the upper part
of the mounting. The lower part of the mounting is a very rigidly
constructed tripod with pointed feet having discs to prevent their
sinking into soft ground.
Three operators are required for working the instrument, viz. :
(l) The observer who makes " coincidences " by turning the working
head on the top of the instrument with his right hand, and who also
keeps the separating line on the target by turning the elevation
handwheel with his left hand. (2) The operator for line who, looking
through the prismatic sighting telescope, traverses the instrument
with the handwheel and keeps the cross line in his telescope accu-
rately laid for line on the target ; and (3) the scale reader, who, stand-
ing in front of the instrument, reads heights off the height scale; and,
if required, also reads the range and angle of sight scales.
In anti-aircraft gunnery, where the target may move at a
speed of two or more miles a minute, there is great difficulty
in ascertaining what deflections are required to compensate for
the travel of the target during the time of flight of the projectile.
There is not only the lateral deflection to be considered, as with
a ship moving in one plane; but also a vertical one. It is obvious
that if an aircraft is flying at a constant height, the angle of
sight to it from the gun will not remain constant. Vertical
deflection equal to the alteration of the angle of sight during
the time of flight of the projectile must therefore be allowed for.
Another difficulty arises in connexion with the setting of the
fuze. The fuze will not burn at the same rate if the projectile
is fixed at different angles of sight, owing to the variation of
atmospheric pressures at different heights. To help to overcome
these difficulties a most ingenious apparatus was brought out
during the war by Messrs. Brocq of Paris, and was adopted by
most of the Allied Powers.
The general principle of the instrument is as follows: The height
of the target must first be measured by a height-finder and set on the
instrument. Two operators, who face one another, follow the target,
looking through two telescopes which are rigidly connected. One
keeps a vertical cross line in his telescope in line with the target
by turning a traversing handle; and the other keeps a horizontal
cross line in line, by turning an elevating handle. Connected with
the traversing and elevating handles are the armatures of two
magnetos which, when turned, generate electric currents, the
voltages of the currents depending upon the speed at which they are
turned. These currents are transmitted to two special voltmeters
(attached to the gun mountings near the layers) from which the
lateral and vertical deflections required can be read off, and then
applied to the sights. On their way to the voltmeters the currents
pass through rheostats which modify them in such a way that the
deflections recorded are correct for the time of burning of the fuze.
The exact length of fuze required to burst the shell at the target
can also be read off another part of the instrument.
The general arrangement of the apparatus is shown diagrammati-
cally in fig. 4. It consists of three main parts, viz. :
I. The double telescope, which consists of a metal drum upon
which are mounted, on the same spindle, the two right-angle tele-
scopes referred to above. The traversing and elevation handles are
placed conveniently for the two operators. Each has a quick and
slow motion (four to one), the ajteration from one to the other being
effected by pushing in or putting out the handle. When a quick
release knot at the top of the instrument is pressed down, the gears
are put out of action, and the telescope can be quickly moved until
the target is in their fields of view. Angles of sight and bearings can
be read off conveniently placed scales, if required. When the handles
are turned, the currents generated by the magnetos pass along
246
RANGE-FINDERS AND POSITION-FINDERS
cables to the " fuze indicator and time rheostat " and thence to the
" deflection voltmeters."
As the body of the " double telescope " traverses about a vertical
axis, but laying is dene in the plane of sight, it is necessary to
multiply the angular velocity of the body of the instrument by the
cosine of the angle of sight in order to obtain the angular velocity
of the target. This is effected electrically by passing the current
from the lateral magneto through a rheostat, whose resistance is
varied by a rubbing contact passing along it, as the telescopes are
elevated or depressed.
Another rheostat and an accumulator (connected to the fuze
indicator and time rheostat) cause an angle of sight needle in the
fuze indicating voltmeter to move to the same angle of sight as that
of the telescopes ; this needle is controlled by another circuit.
2. The fuze indicator and time rheostat consist mainly of the time
rheostat, a fuze indicating voltmeter, a microphone and an external
accumulator of three cells.
As explained above, the currents generated by the magnetos pass
through rheostats on their way to the deflection voltmeters. These
rheostats are situated beneath the time adjusting dial, and their
resistance is altered as the dial is turned. The setting of the dial is
dependent upon the height of the aircraft and the setting of the fuze,
and is effected as follows: A graduated height arm is moved by
means of a milled head until it reads the height obtained from a
height-finder. On its right-hand upper edge is a reader for reading
the fuze curves on the time adjusting dial. The latter is turned until
the reader of the height arm is on the fuze curve representing the
length at which the fuzes have been set.
I JAM/ftM
ru INDICATOR AND
TIMC RHEOSTAT
DOUail TELESCOPE
FIG. 4. Arrangement of Brocq apparatus.
The angle of sight needle in the fuze indicating voltmeter is con-
trolled by two circuits, viz,: that referred to in (i) which tends to
set it at the angle of sight of the telescopes, and another in which are
the vertical magneto armature in the double telescope, the rheostat
beneath the time adjusting dial and another rheostat which auto-
matically adds eight seconds to the time of flight. This eight seconds
is an allowance for the time taken to set the fuze, load, lay and fire
the gun. The angle of sight needle therefore makes with its zero or
horizontal line an angle equal to the angle of sight to the predicted
position of the target at which the shell will burst. When the height
arm is moved, a height strip inside the fuze indicating voltmeter is
also moved. Its height above the zero line of the angle-of-sight needle
represents, to the scale of the instrument, the height of the target.
The intersection of the needle and strip therefore represents the
position of the target at the moment of the shell burst. Fuze curves
are marked on the glass cover of the voltmeter, and the curve which
is nearest to the intersection of the needle and strip will indicate the
length at which fuzes are to be set. This fuze length is called down
the microphone to the fuze setters, and is transmitted to the sight
setter by the man taking up the shell.
3. The deflection voltmeters are of the dead-brat type and read
to 10 on either side of zero. Two are provided for each gun ; one for
lateral and the other for vertical deflection. As a rule, two guns can
be worked by one Brocq equipment, four deflection voltmeters
being provided. The required deflection is read by the upper pointer.
Corrections for wind are applied by moving the scale by means of a
knob beneath the voltmeter, the amount of correction being indi-
cated on the scale by the lower pointer.
Stereoscopic range-finders were extensively used by the Cen-
tral Powers for anti-aircraft work. (A. C. W.)
SOUND-RANGING
The method of locating hostile guns by the sound, or sounds,
consequent on their discharge was introduced on the British
front in France during 1916. It had at that time already been
in use in the French army for many months. It speedily proved
its usefulness, especially in circumstances which rendered other
methods of location very difficult or impossible. The system
of concealment known as " camouflage " added considerably
to the difficulty of finding the position of gun-pits on photographs
taken from the air, and, further, these photographs offered no
certain method of deciding whether a gun position, once
identified, were occupied or no. The locations given by sound-
ranging frequently enabled well-concealed positions, which had
previously been missed on air photographs, to be detected, and
offered a sure index as to whether known positions were active
at a given time. Although air photographs always offered
valuable confirmation of the sound-ranging locations, and were,
when available, consulted with this object in view, the method is,
of course, quite independent of such support. It works as well
at night, or when, owing to fog, mist, or smoke, the visibility
is poor, as on clear days; it can detect batteries so well hidden
as to be invisible from the air or on air photographs; it is always
ready when once the apparatus has been installed; and a location
can be obtained, under favourable conditions, within a minute
or two of the arrival of the report of the piece. On the other hand
the instalment of the apparatus necessitates the laying of
several miles of wire, and involves considerable preliminary
labour in other ways; the method will not work during a heavy
bombardment; and certain weather conditions, to be discussed
later, render locations almost impossible. The difficulty first
mentioned will quite possibly be surmounted or diminished;
the other two seem, at present, insuperable.
The method has been elaborated to permit the directing of
fire on a hostile piece by comparing the record of the sound of
discharge of the piece with that of the burst of the shell directed
against it. With iz-in. and o-2-in. howitzers destructive shots
have been directed very successfully by sound-ranging.
Principles. The method generally adopted in the British, French,
and American armies is to record the instant of the arrival of the
sound made by the hostile piece at certain fixed and carefully sur-
veyed posts, spaced at intervals varying from 1,000 to 2,000 yards.
If it be assumed that the sound spreads out from the source with a
known velocity, the same in all directions, then a known interval
between the arrival of the sound at two fixed posts will determine a
curve on which the source must lie. This curve is a hyperbola with
the two posts Pi and Pi as foci, for the determining condition is that
the difference of the radii vectores SPi, SPi be constant. If, in addi-
tion, the time of arrival at a third post be known, then the interval
between this and the time of arrival at either Pi or P 3 will fix a second
hyperbola on which the source must lie, and so determine the posi-
tion of the source. In practice three posts are not sufficient, since
any uncertainty caused by the recording of a spurious sound at a
post would falsify the location. In general six posts are used, which,
taken consecutively in pairs, give five lines which should all inter-
sect. Any accidental selection of the record of a spurious sound at
one or more of the posts is then at once detected by the non-inter-
section of the curves. Records of the sound at five, or indeed four,
of the posts are generally sufficient for the experienced sound-ranger,
even when several guns are being recorded at short intervals, so that
the use of six posts allows for the sound not being successfully re-
corded at one or two of the posts.
Nature of Sounds from High- Velocity Guns. In the preceding
argument it has been assumed that the sound spreads out with
uniform velocity in all directions from the source. There is little
doubt that this is true, in a still atmosphere of uniform temperature,
of the sound of the discharge of the piece. With the modern high-
velocity gun, however, a second sound, originating in the motion
of the shell through the air, always accompanies the sound of dis-
charge. This second sound is due to a pulse of compression ^set up
by the shell, known as the " shell-wave," or " onde de choc." It is
perceived by an observer in front of the gun as a sharp crack, which
is followed after an interval depending on the type of gun, the
elevation of the gun, and other factors, by the duller, heavier sound
of the discharge, or gun-wave. To examine the formation of the
shell-wave by the passage of the projectile, consider the resultant
disturbance produced by the pulses of compression travelling out
with the velocity of sound from every point of the path of the shell.
For simplicity take in the first case a projectile travelling horizon-
tally with a uniform velocity greater than that of sound; let G be
the position of the gun, Si, Si, . . . SH> be the positions of the
projectile at the end of the 1st, 2nd, . . . loth second (fig. 5).
When the shell is at Sio the compression originating at G has travelled
out as a spherical shell with G as centre for 10 seconds, that originat-
ing at Si has travelled out as a spherical shell with Si as centre for o
seconds, and so on. The envelope of all these spheres is a cone with
its apex at Sio ; if the shell be travelling close to the surface of the
earth the trace of this cone on the surface is ASuC, which represents
the pulse of compression under discussion. If the velocity of the shell
be considered to decrease with time, as in any actual case, the
RANGE-FINDERS AND POSITION-FINDERS
247
interval of space between centres of successive generating spheres
will decrease as the shell travels, and the enveloping cone will be
modified (fig. 6). The form of the shell-wave will resemble roughly
a paraboloid of revolution, the vertex being at the shell as long as the
latter has a velocity exceeding that of sound, and consequently
travelling with a velocity greater than that of sound. After the
velocity of the shell has dropped below that of sound the shell-wave
travels out in all directions with the velocity of sound normal to the
surface.
FIG. 5.
The exact form of the shell-wave will depend upon the range table
of the gun and the interval since the shell left the gun, and cannot
be specified as being any familiar surface. The trace of the wave on
the plane of the earth's surface, with which the observer is in general
concerned, depends further upon the elevation at which the gun is
firing. Since the sphere representing the position of the gun-wave is
one of the generating spheres the shell-wave will touch this sphere.
In fig. 6 where G is the gun, ABC the trace of the gun-wave on the
horizontal plane, ASC the trace of the shell-wave, within the cone
represented by AGC both sounds will be heard, outside the cone
only the sound of discharge. The interval between the two sounds is
FIG. 6
clearly greatest on the line of fire, decreasing as the observer moves
to a flank. As the gun is elevated the interval detected by a listener
in a fixed position decreases, the trace of the shell-wave approaching
that of the gun-wave. This is illustrated in fig. 7. If the gun be
sufficiently elevated no shell-wave is heard by a listener at any
position on the ground, though it may be heard in an observation
balloon. Thus the double sound has been heard by an observer so
situated in the case of a g-2-in. howitzer, firing with full charge
(M.V. 1,500 f.s.), while observers on the ground heard only the
single sound.
Owing firstly to the selective sensitiveness of the human ear, and
secondly to the fact that the shell-wave is generated well above the
surface of the earth, and travels down to the ear without meeting
obstacles and without being hindered by refraction effects, the shell-
wave alone is usually heard when the hostile piece is distant, and is
spoken of as the sound of the piece by the casual listener. Any
attempt to take rough bearings on a gun by estimating the direction
from which the sound appears to be coming then leads to a very
erroneous result, since it is the normal to the shell-wave that is
selected. Unless the listener is on the line of fire such a bearing will