Instrument for Determining the Tangential Angles of Circular Curves, such as Railway Curves.
Year: 1890

page_text: Date of Application, 3rd July, 1890
Complete Specification Left, 3rd Apr., 1891-Accepted, 3rd July, 1891
TRUVIDIONAL STUITIVATION.
Instrument for Determining the Tangential Angles of Circular
Curves, such as Railway Curves.
I, JOHN JAMES WESTWOOD CRAUFURD, of Dudley House, Baron's Court
Road, West Kensington, in the County of London, Civil Engineer, do hereby
declare the nature of this invention to be as follows:-
This invention has reference to an instrument for determining the tangential angles
of circular curves such as a railway curve, whereby the tangential angles for a circular
curve of any radius and for any length of chord can be read off at a glance without the
necessity of making any calculation. For this purpose I employ two plates one
mounted to turn upon the other and each furnished with a circular scale, that upon
the one plate, which I will call the base plate, being outside of and concentric with
that on the other plate which I will call the movable plate and which may with
advantage be arranged to work in a recess in the top of the base plate. The scale
on the base plate is divided into any suitable number of equal parts say for example
ten, which are designated degrees, and each of these parts is subdivided into sixty
equal parts to represent minutes.
The scale upon the outer circumference of the movable plate is so divided that
the divisions representing chords or chains and parts thereof of any given length
and for a given radius of curve, shall when read off on the base plate, give the
correct tangential angle for a given length of chord and radius.
To adapt the instrument for determining the tangential angles for curves of
various radii, the movable plate can be provided on one or on both sides with a
number of concentric scales, each scale corresponding to a different radius to that
of the others.
The movable plate is arranged to revolve on a central spindle firmly fixed to the
base plate, and can be clamped down by a screw nut. A slotted plate, hinged to a
movable arm may be provided to facilitate the reading of the angles.
By providing several movable plates each furnished with a number of scales for
different radii, a complete set of scales for curves of all ordinary radii can be
obtained. The divisions on the movable plate can be such as to adapt the instru-
ment for use with different methods of measurements as for examples, the English,
French, or American methods.
By my invention not only can the tangential angle for the whole chord be deter-
mined without any calculations whatever, but also the tangential angles for the
broken chords at each end of the curve, the broken chord at the commencement of
curve being first read off, and then successively the total angle from point of
observation to each succeeding chord until the end of curve is reached when the
necessary angle for the broken chord at that end is read off.
With ordinary care
at starting, no possible mistake can occur.
.

page_text: COMPLETE
SPECIFICATION.
Instrument for Determining the Tangential Angles of Circular
Curves, such as Railway Curves.
I, JOHN JAMES WESTWOOD CRAUFURD, formerly of Dudley House, Baron's
Court Road, West Kensington, in the County of London, but now of the Brazil
Great Southern Railway, Itaqui, Brazil, Civil Engineer, do hereby declare the
nature of this invention and in what manner the same is to be performed to be
particularly described and ascertained in and by the following statement :-
This invention has reference to an instrument for determining the tangential
angles of circular curves such as railway curves, whereby the tangential angles for
a circular curve of any radius, and for any length of chord, can be read off at a
glance without the necessity of making any calculation. For this purpose 1 employ
two plates one mounted to turn upon the other and each furnished with a circular
scale, that upon the one plate, which I will call the base plate, being outside of and
concentric with that on the other plate, which I will call the movable plate, and
which may with advantage be arranged to work in a recess in the top of the base
plate. The scale on the base plate is divided into any suitable number of equal
parts say for example ten, which are designated degrees, and each of these parts is
subdivided say into sixty equal parts to represent minutes. The scale upon the
movable plate is so divided that the divisions, representing chords or chains and
parts thereof of any given length and for a given radius of curve, shall when read
off on the base plate, give the correct tangential angle for a given length of chord
and radius.
To adapt the instrument for determining the tangential angles for curves of
various radii, the movable plate can be provided on one or on both sides with a
number of concentric scales, each scale corresponding to a different radius to that
of each of the others.
In the accompanying drawings,
Fig. 1 is a central section; and
Fig. 2 a plan of an instrument constructed according to this invention for the
purpose mentioned.
Fig. 3 is a diagram illustrating the method of setting out curves with this
instrument.
1 is the base plate of about 5 inches diameter having upon its upper side a
circular scale 2 divided into ten equal parts or degrees each of which is subdivided
into sixty equal parts or minutes. 3 is the movable plate of about 4 inches
diameter and having upon its upper side four concentric circular scales 4
repre-
senting chords or chains and parts thereof of any desired length and for a given
radius of curve. In Fig. 1 two movable plates 3 and 3ª are shown, each of which
may be provided on both sides with a number of concentric but different circular
scales. The movable plate or plates is or are mounted upon a central spindle 5
which may advantageously be carried by a plate 6 capable of rotating in the base
plate 1. For this purpose the plate 6 may be held within a recess in the base
plate by a ring 7, and is provided with a toothed ring 8 with which engages a
pinion 9 carried by a rotary milled finger piece 10. 11 is a nut by which the
movable plate 3 (or plates) can be clamped upon the plate 6 so as to rotate with
this plate when it is rotated by the pinion 9. 12 is a slotted plate provided with
an index or pointer 13 to facilitate the reading of the angles. This slotted plate is
hinged, so as to be able to turn upward, to a ring 14 that is capable of rotary
motion in an annular recess in the periphery of the base plate, and of being fixed in
any desired position by a screw 15.
Each scale on the plate or plates 3 represents a radius of a curve denoted in
chains, and cach concentric scale counting from the circumference towards the
centre, is for a curve of one half the radius of the preceding one, thus the outer

page_text: scale may be graduated for a curve having a radius of say 120 chains, the second
for a curve of 60 chains, the third for a curve of 30 chains and the 4th for a curve
of 15 chains etc. The divisions on the scales represent primarily, single chains, and
are spaced in such a manner as to be equal to the tangential angle of one chain for
a curve of that radius for which the scale is formed, read off in degrees and
minutes on the degree scale of the base plate. Thus let the curve radius be
120 chains; the tangential angle for 1 chain of such a curve is 14 minutes; the
division on the card from 120 (or zero) to 1 is equal to 14 minutes on the degree
scale of the base plate, and all the other divisions on the 120 scale, 1 to 2, 2 to 3,
3 to 4 and so on are each equal to one another, and to 14 or summed up 141, 28
43, 57 etc., minutes respectively.
The first chain of each scale is further subdivided into decimal parts, for the
purpose of obtaining the tangential angle of any decimal parts of a chain that may
be required.
As the radius of the curve to which each concentric scale corresponds is half
that of the preceding outer one, the tangential angle becomes twice as much,
therefore a division of four chains on the 1st scale, equals a division of 2 chains on
the second scale, on the 3rd and on the 4th, the decimal parts proceeding in the
same proportion. A set of these movable plates, with scales on both sides, can be
provided for each instrument in sufficient number, and with radii so arranged as to
enable all the curves most universally used in railway work, to be set out without
any calculations.
The method of using the calculator is as follows:-
The diagram Fig. 3 represents a curve of 6 chain radius, to be set out between
the points A and B, at the commencement and end of the curve; these points
having been previously found out and marked in the ground by the usual methods
known to engineers, and the chainage taken in this case to be continuous, (as in
general on railways), commencing from 0, a point on the straight part of the line,
and ending at 18 another point on the straight part of the line, the points A and B
falling respectively at 2-6 chains and 16.1 chains from the point 0. Supposing the
theodolite to have been properly set up at A, the various tangential angles to
the successive chains 3, 4, 5, .
16.1 have to be calculated and set off on the
ground from the point A. To do this with the calculator hereinabove described,
select the card containing the 6 chain radius, remove the nut 11 from the spindle 5
and placing the card or plate 3 on the revolving plate 6 with zero coinciding more
or less with 10 on the base plate 1, clamp it down tightly by means of the nut 11,
then with the slow motion pinion 9 cause the zeros of the two plates to exactly
coincide. Now the first chord to be set out is 4 of a chain to complete the
3rd chain, therefore opposite 4 in the ring containing the 6 chord scale will be read
on the base plate scale, 1° 54' which is the tangential angle for 4 of a chain, and
which has to be set out by the theodolite to peg 3. Now by the finger piece 10
and pinion
bring forward the zero of upper plate to coincide with 1º 54', on
the base plate, and proceed to read off the full chain tangential angles for
pegs 4, 5, 6
16 or 6° 40%, 11° 27', 16° 13'
63° 58. Then again
making the zero of the plate 3 coincide with this last number, the decimal parts
are thus again brought into play for determining the angle for the remaining parts
of the curve, or 1 of a chain, which will be read off in front of 1 in the 6 chain scale
as before, or 64° 26' (28 minutes added to the last whole chain angle).
This example is necessarily exaggerated, it being seldom that so great an angle
is used, or that the curve is set out entirely from one end only. When it is
required to read a greater angle than 10 degrees, then the zero of the plate 3 is
made to coincide with the last angle which it is possible to read immediately before
the 10, and the full chain angles continued, going round the scale 2 again,
calling 1°
11°, 2° 12°, and so on and for each successive turn making 10° = 20°,
30°, 40°, or 50° according to the number of degrees it is required to read. When it
is necessary to shift on the theodolite on account of obstruction to the sight, this
need not affect the calculator as it is left clamped to the last peg set out, and gives
-

page_text: The method of chains can be used for any system; English of 66 feet to the
chain, American of 100 feet to the chain, or for the metrical system.
Thus suppose it is required.to set out a curve of 1122 feet radius by the English
1122
system, then
66
= 17 chains radius, the card or plate 3 to be used: to set out
4500
100
4500 feet radius by the American system, then = 45 chains radius. In the
metrical system, railway curves are generally set out with 20 metre, 25 metre,
or 50 metre chains, therefore if a curve of say 1500 metres radius has to be set out
with 20 chains, then = 75 chain radius, or with 25 chains then
1500
20
1500
60
25
chains radius, or with 50m chains, then
1500
50
30 chains radius.
Thus it will be seen that the principle of the calculator depends on the relation
between the length of chord, and the radius, so that any length of chord may be
taken arbitrarily, and the tangential angle at once found, provided the radius is
divided by that length of chord and the resulting chain radius found amongst the
movable cards or plates.
Some of the movable cards or plates 3 arc or may be moreover prepared for
the American degree system, and are calculated in exactly the same way as the
chain curves, each successive concentric scale radius, diminishing by one half the
preceding one, thus if the outside scale is 20°, the 2nd will be 10°, the 3rd 5° and
the next 2, 1 and so on, but this does not preclude the degree cards or plates from
being used as chain cards, and rice versa, as they can be reduced to their relative
values in the other system. A list of these values is included in the instructions
provided for the use of the calculator, as also a comparative list of the value in
decimal parts of a chain of every foot up to 66 feet, and for every metre in the
various systems of metre chains. For the American system this is not necessary,
as the chain being of a 100 feet length, it can be easily seen at a glance what
decimal part any length may be of the whole chain.
The hinged index 13 is designed to be clamped in front of a number whilst
shifting round the card, or to keep it in front of a number marking the tangential
angle of one peg till such a time as the angle for the next peg is required.
The advantage resulting from the use of this instrument is that no calculation is
required, and that not only can the tangential angle be read off at sight for the
whole chord or chain, but also for any decimal parts of the same, both at the com-
mencement and at the end of a curve, the part of a chain at commencement being
read off first, then each successive full chain, and lastly the part of a chain at the
end of a curve. This is an advantage which it is believed no other instrument
or tables possess, as although many useful sets of tables have been invented and
calculated for setting out curves, yet they all necessitate a calculation to find the
tangential angle for parts of chains at the commencement and end of a curve which
calculations are the most frequent and the most troublesome to make.
ordinary care at starting, no possible mistake can occur.
With
Having now particularly described and ascertained the nature of the said inven-
tion and in what manner the same is to be performed 1 declare that what I
claim is :-
1. An instrument for determining the tangential angles of circular curves such as
railway curves, comprising two plates, namely a base plate having a circular scale

page_text: divided into a suitable number of equal parts or degrees each of which is subdivided
say into sixty equal parts or minutes, and a movable plate mounted to rotate upon
the base plate and having thereon one or more circular scales arranged within and
concentric with that on the base plate and representing chords or chains or parts
thereof for a given radius of curve substantially as hereinbefore described.
2. The construction of apparatus for determining the tangential angles of
circular curves substantially as hereinbefore described and shown in the drawings
annexed:
..
W. LLOYD WISE,
Per F. J. Brougham,
46, Lincoln's Inn Fields, London, W.C., Agent for the Applicant.