The Sewerage of Sea Coast Towns
by
Henry C. Adams
Part 2 out of 3
which the storm water has to be held up for tidal reasons. It
is found that on the average the whole of the rain on a rainy
day falls within a period of 2-1/2 hours; therefore, ignoring
the relief which may be afforded by overflows, if the sewers
are tide-locked for a period of 2-1/2 hours or over it would
appear to be necessary to provide storage for the rainfall of a
whole day; but in this case again it is permissible to run a
certain amount of risk, varying with the length of time the
sewers are tide-locked, because, first of all, it only rains on
the average on about 160 days in the year, and, secondly, when
it does rain, it may not be at the time when the sewers are
tide-locked, although it is frequently found that the heaviest
storms occur just at the most inconvenient time, namely, about
high water. Table No. 9 shows the frequency of heavy rain
recorded during a period of ten years at the Birmingham
Observatory, which, being in the centre of England, may be
taken as an approximate average of the country.
TABLE No. 9.
FREQUENCY OF HEAVY RAIN
-------------------------------------------------------
Total Daily Rainfall. Average Frequency of Rainfall
-------------------------------------------------------
0.4 inches and over 155 times each year
0.5 " 93 "
0.6 " 68 "
0.7 " 50 "
0.8 " 33 "
0.9 " 22 "
1.0 " 17 "
1.1 " Once each year
1.2 " Once in 17 months
1.25 " " 2 years
1.3 " " 2-1/2
1.4 " " 3-1/3
1.5 " " 5 years
1.6 " " 5 years
1.7 " " 5 years
1.8 " " 10 years
1.9 " " 10 years
2.0 " " 10 years
--------------------------------------------------
It will be interesting and useful to consider the records for
the year 1903, which was one of the wettest years on record,
and to compare those taken in Birmingham with the mean of those
given in "Symons' Rainfall," taken at thirty-seven different
stations distributed over the rest of the country.
TABLE No. 10.
RAINFALL FOR 1903.
Mean of 37
stations in
Birmingham England and
Wales.
Daily Rainfall of 2 in and over ...... None 1 day
Daily Rainfall of 1 in and over ...... 3 days 6 days
Daily Rainfall of 1/2 in and over .... 17 days 25 days
Number of rainy days.................. 177 days 211 days
Total rainfall ...................... 33.86 in 44.89 in
Amount per rainy day ................ 0.19 in 0.21 in
The year 1903 was an exceptional one, but the difference
existing between the figures in the above table and the average
figures in Table 9 are very marked, and serve to emphasise the
necessity for close investigation in each individual case. It
must be further remembered that the wettest year is not
necessarily the year of the heaviest rainfalls, and it is the
heavy rainfalls only which affect the design of sewerage works.
CHAPTER VIII.
STORM WATER IN SEWERS.
If the whole area of the district is not impermeable the
percentage which is so must be carefully estimated, and will
naturally vary in each case. The means of arriving at an
estimate will also probably vary considerably according to
circumstances, but the following figures, which relate to
investigations recently made by the writer, may be of interest.
In the town, which has a population of 10,000 and an area of
2,037 acres, the total length of roads constructed was 74,550
lineal feet, and their average width was 36 ft, including two
footpaths. The average density of the population was 4.9 people
per acre. Houses were erected adjoining a length of 43,784
lineal feet of roads, leaving 30,766 lineal feet, which for
distinction may be called "undeveloped"--that is, the land
adjoining them was not built over. Dividing the length of road
occupied by houses by the total number of the inhabitants of
the town, the average length of road per head was 4.37 ft, and
assuming five people per house and one house on each side of
the road we get ten people per two houses opposite each other.
Then 10 x 4.37 = 43.7 lineal feet of road frontage to each pair
of opposite houses. After a very careful inspection of the
whole town, the average area of the impermeable surfaces
appertaining to each house was estimated at 675 sq. ft, of
which 300 sq. ft was apportioned to the front roof and garden
paths and 375 sq. ft to the back roof and paved yards. Dividing
these figures by 43.71 in ft of road frontage per house, we
find that the effective width of the impermeable roadway is
increased by 6 ft 10 in for the front portions of each house,
and by a width of 8 ft 7 in, for the back portions, making a
total width of 36 ft + 2(6 ft 10 in) + 2(8 ft 7 in) = 66 ft 10
in, say 67 ft On this basis the impermeable area in the town
therefore equals: 43,7841 in ft x 67 ft =2,933,528; and 30,766
lin ft x 36 ft = 1,107,576.
Total, 4,041,104 sq. ft, or 92.77 acres. As the population is
10,000 the impermeable area equals 404, say, 400 sq. ft per
head, or ~ (92.77 x 100) / 2037 = 4.5 per cent, of the whole
area of the town.
It must be remembered that when rain continues for long
periods, ground which in the ordinary way would generally be
considered permeable becomes soaked and eventually becomes more
or less impermeable. Mr. D. E. Lloyd-Davies, M.Inst.C.E., gives
two very interesting diagrams in the paper previously referred
to, which show the average percentage of effective impermeable
area according to the population per acre. This information,
which is applicable more to large towns, has been embodied in
Fig. 16, from which it will be seen that, for storms of short
duration, the proportion of impervious areas equals 5 per cent.
with a population of 4.9 per acre, which is a very close
approximation to the 4.5 per cent. obtained in the example just
described.
Where the houses are scattered at long intervals along a road
the better way to arrive at an estimate of the quantity of
storm water which may be expected is to ascertain the average
impervious area of, or appertaining to, each house, and divide
it by five, so as to get the area per head. Then the flow off
from any section of road is directly obtained from the sum of
the impervious area due to the length of the road, and that due
to the population distributed along it.
[Illustration: FIG. 16.--VARIATION IN AVERAGE PERCENTAGE OF
EFFECTIVE IMPERMEABLE AREA ACCORDING TO DENSITY OF POPULATION.]
In addition to being undesirable from a sanitary point of view,
it is rarely economical to construct special storm water
drains, but in all cases where they exist, allowance must be
made for any rain that may be intercepted by them. Short branch
sewers constructed for the conveyance of foul water alone are
usually 9in or 12 in in diameter, not because those sizes are
necessary to convey the quantity of liquid which may be
expected, but because it is frequently undesirable to provide
smaller public sewers, and there is generally sufficient room
for the storm water without increasing the size of the sewer.
If this storm water were conveyed in separate sewers the cost
would be double, as two sewers would be required in the place
of one. In the main sewers the difference is not so great, but
generally one large sewer will be more economical than two
smaller ones. Where duplicate sewers are provided and arranged,
so that the storm water sewer takes the rain-water from the
roads, front roofs and gardens of the houses, and the foul
water sewer takes the rain-water from the back roofs and paved
yards,
it was found in the case previously worked out in detail that
in built-up roads a width of 36 ft + 2 (8 ft 7 in) = 53 ft 2
in, or, say, 160 sq. ft per lineal yard of road would drain to
the storm water sewer, and a width of 2 (6 ft 10 in) = 13 ft 8
in, or, say, 41 sq. ft per lineal yard of road to the foul
water sewer. This shows that even if the whole of the rain
which falls on the impervious areas flows off, only just under
80 per cent. of it would be intercepted by the special storm water
sewers. Taking an average annual rainfall of 30 in, of which 75 per
cent. flows off, the quantity reaching the storm water sewer in the
course of a year from each lineal
30 75
yard of road would be --- x 160 x --- = 300 cubic
12 100
feet = 1,875 gallons.
[Illustration: FIG. 17.--SECTION OF "LEAP WEIR" OVERFLOW]
The cost of constructing a separate surface water system will
vary, but may be taken at an average of, approximately, l5s.
0d. per lineal yard of road. To repay this amount in thirty years
at 4 per cent, would require a sum of 10.42d., say 10-1/2d. per annum;
that is to say, the cost of taking the surface water into special
10-1/2 d. x 1000
sewers is ---------------- = 5.6, say 6d. per 1,000
1875
gallons.
If the sewage has to be pumped, the extra cost of pumping by
reason of the increased quantity of surface water can be looked
at from two different points of view:--
1. The net cost of the gas or other fuel or electric current
consumed in lifting the water.
2. The cost of the fuel consumed plus wages, stores, etc., and
a proportion of the sum required to repay the capital cost of
the pumping station and machinery.
The extra cost of the sewers to carry the additional quantity
of storm water might also be taken into account by working out
and preparing estimates for the alternative schemes.
The actual cost of the fuel may be taken at approximately 1/4
d. per 1,000 gallons. The annual works and capital charges,
exclusive of fuel, should be divided by the normal quantity of
sewage pumped per annum, rather than by the maximum quantity
which the pumps would lift if they were able to run
continuously during the whole time. For a town of about 10,000
inhabitants these charges may be taken at 1-1/4 d. per 1,000
gallons, which makes the total cost of pumping, inclusive of
capital charges, 1-1/2 d. per 1,000 gallons. Even if the extra
cost of enlarging the sewers is added to this sum it will still
be considerably below the sum of 6 d., which represents the
cost of providing a separate system for the surface water.
Unless it is permissible for the sewage to have a free outlet
to the sea at all states of the tide, the provision of
effective storm overflows is a matter of supreme importance.
Not only is it necessary for them to be constructed in well-
considered positions, but they must be effective in action. A
weir constructed along one side of a manhole and parallel to
the sewer is rarely efficient, as in times of storm the liquid
in the sewer travels at a considerable velocity, and the
greater portion of it, which should be diverted, rushes past
the weir and continues to flow in the sewer; and if, as is
frequently the case, it is desirable that the overflowing
liquid should be screened, and vertical bars are fixed on the
weir for the purpose, they block the outlet and render the
overflow practically useless.
Leap weir overflows are theoretically most suitable for
separating the excess flow during times of storm, but in
practice they rarely prove satisfactory. This is not the fault
of the system, but is, in the majority of the cases, if not
all, due to defective designing. The general arrangement of a
leap weir overflow is shown in Fig. 17. In normal circumstances
the sewage flowing along the pipe A falls down the ramp, and
thence along the sewer B; when the flow is increased during
storms the sewage from A shoots out from the end of the pipe
into the trough C, and thence along the storm-water sewer D. In
order that it should be effective the first step is to
ascertain accurately the gradient of the sewer above the
proposed overflow, then, the size being known, it is easy to
calculate the velocity of flow for the varying depths of sewage
corresponding with minimum flow, average dry weather flow,
maximum dry weather flow, and six times the dry weather flow.
The natural curve which the sewage would follow in its downward
path as it flowed out from the end of the sewer can then be
drawn out for the various depths, taking into account the fact
that the velocity at the invert and sides of the sewer is less
than the average velocity of flow. The ramp should be built in
accordance with the calculated curves so as to avoid splashing
as far as possible, and the level of the trough C fixed so that
when it is placed sufficiently far from A to allow the dry
weather flow to pass down the ramp it will at the same time
catch the storm water when the required dilution has taken
place. Due regard must be had to the altered circumstances
which will arise when the growth of population occurs, for
which provision is made in the scheme, so that the overflow
will remain efficient. The trough C is movable, so that the
width of the leap weir may be adjusted from time to time as
required. The overflow should be frequently inspected, and the
accumulated rubbish removed from the trough, because sticks and
similar matters brought down by the sewer will probably leap
the weir instead of flowing down the ramp with the sewage. It
is undesirable to fix a screen in conjunction with this
overflow, but if screening is essential the operation should be
carried out in a special manhole built lower down the course of
the storm-water sewer. Considerable wear takes place on the
ramp, which should, therefore, be constructed of blue
Staffordshire or other hard bricks. The ramp should terminate
in a stone block to resist the impact of the falling water, and
the stones which may be brought with it, which would crack
stoneware pipes if such were used.
In cases where it is not convenient to arrange a sudden drop in
the invert of the sewer as is required for a leap weir
overflow, the excess flow of storm-water may be diverted by an
arrangement similar to that shown in Fig. 18. [Footnote: PLATE
IV] In this case calculations must be made to ascertain the
depth at which the sewage will flow in the pipes at the time it
is diluted to the required extent; this gives the level of the
lip of the diverting plate. The ordinary sewage flow will pass
steadily along the invert of the sewer under the plate until it
rises up to that height, when the opening becomes a submerged
orifice, and its discharging capacity becomes less than when
the sewage was flowing freely. This restricts the flow of the
sewage, and causes it to head up on the upper side of the
overflow in an endeavour to force through the orifice the same
quantity as is flowing in the sewer, but as it rises the
velocity carries the upper layer of the water forward up the
diverting plate and thence into the storm overflow drain A deep
channel is desirable, so as to govern the direction of flow at
the time the overflow is in action. The diverting trough is
movable, and its height above the invert can be increased
easily, as may be necessary from time to time. With this
arrangement the storm-water can easily be screened before it is
allowed to pass out by fixing an inclined screen in the
position shown in Fig. 18. [Footnote: PLATE IV] It is loose, as
is the trough, and both can be lifted out when it is desired to
have access to the invert of the sewer. The screen is self-
cleansing, as any floating matter which may be washed against
it does not stop on it and reduce its discharging capacity, but
is gradually drawn down by the flow of the sewage towards the
diverting plate under which it will be carried. The heavier
matter in the sewage which flows along the invert will pass
under the plate and be carried through to the outfall works,
instead of escaping by the overflow, and perhaps creating a
nuisance at that point.
CHAPTER IX.
WIND AND WINDMILLS.
In small sewerage schemes where pumping is necessary the amount
expended in the wages of an attendant who must give his whole
attention to the pumping station is so much in excess of the
cost of power and the sum required for the repayment of the
loan for the plant and buildings that it is desirable for the
economical working of the scheme to curtail the wages bill as
far as possible. If oil or gas engines are employed the man
cannot be absent for many minutes together while the machinery
is running, and when it is not running, as for instance during
the night, he must be prepared to start the pumps at very short
notice, should a heavy rain storm increase the flow in the
sewers to such an extent that the pump well or storage tank
becomes filled up. It is a simple matter to arrange floats
whereby the pump may be connected to or disconnected from a
running engine by means of a friction clutch, so that when the
level of the sewage in the pump well reaches the highest point
desired the pump may be started, and when it is lowered to a
predetermined low water level the pump will stop; but it is
impracticable to control the engine in the same way, so that
although the floats are a useful accessory to the plant during
the temporary absence of the man in charge they will not
obviate his more or less constant attendance. An electric motor
may be controlled by a float, but in many cases trouble is
experienced with the switch gear, probably caused by its
exposure to the damp air. In all cases an alarm float should be
fixed, which would rise as the depth of the sewage in the pump
well increased, until the top water level was reached, when the
float would make an electrical contact and start a continuous
ringing warning bell, which could be placed either at the pumping
station or at the man's residence. On hearing the bell the man would
know the pump well was full, and that he must immediately repair to
the pumping-station and start the pumps, otherwise the building
would be flooded. If compressed air is available a hooter could be
fixed, which would be heard for a considerable distance from the station.
[Illustration: PLATE IV.
"DIVERTING PLATE" OVERFLOW.
To face page 66.]
It is apparent, therefore, that a pumping machine is wanted
which will work continuously without attention, and will not
waste money when there is nothing to pump. There are two
sources of power in nature which might be harnessed to give
this result--water and wind. The use of water on such a small
scale is rarely economically practicable, as even if the water
is available in the vicinity of the pumping-station,
considerable work has generally to be executed at the point of
supply, not only to store the water in sufficient bulk at such
a level that it can be usefully employed, but also to lead it
to the power-house, and then to provide for its escape after it
has done its work. The power-house, with its turbines and other
machinery, involves a comparatively large outlay, but if the
pump can be directly driven from the turbines, so that the cost
of attendance is reduced to a minimum, the system should
certainly receive consideration.
Although the wind is always available in every district, it is
more frequent and powerful on the coast than inland. The
velocity of the wind is ever varying within wide limits, and
although the records usually give the average hourly velocity,
it is not constant even for one minute. Windmills of the modern
type, consisting of a wheel composed of a number of short sails
fixed to a steel framework upon a braced steel tower, have been
used for many years for driving machinery on farms, and less
frequently for pumping water for domestic use. In a very few
cases it has been utilised for pumping sewage, but there is no
reason why, under proper conditions, it should not be employed
to a greater extent. The reliability of the wind for pumping
purposes may be gauged from the figures in the following table,
No. 11, which were observed in Birmingham, and comprise a
period of ten years; they are arranged in order corresponding
with the magnitude of the annual rainfall:--
TABLE No. 11.
MEAN HOURLY VELOCITY OF WIND
Reference | Rainfall |Number of days in year during which the mean |
Number | for |hourly velocity of the wind was below |
| year | 6 m.p.h. | 10 m.p.h. | 15 m.p.h. | 20 m.p.h. |
----------+----------+----------+-----------+-----------+-----------+
1... 33.86 16 88 220 314
2... 29.12 15 120 260 334
3... 28.86 39 133 263 336
4... 26.56 36 126 247 323
5... 26.51 34 149 258 330
6... 26.02 34 132 262 333
7... 25.16 33 151 276 332
8... 22.67 46 155 272 329
9... 22.30 26 130 253 337
10... 21.94 37 133 276 330
----------+----------+----------+-----------+-----------+-----------+
Average 31.4 131.7 250.7 330.8
It may be of interest to examine the monthly figures for the
two years included in the foregoing table, which had the least
and the most wind respectively, such figures being set out in
the following table:
TABLE No. 12
MONTHLY ANALYSIS OF WIND
Number of days in each month during which the mean velocity of
the wind was respectively below the value mentioned hereunder.
Month | Year of least wind (No. 8) | Year of most wind (No. *8*) |
| 5 10 15 20 | 5 10 15 20 |
| m.p.h. m.p.h. m.p.h. m.p.h. | m.p.h. m.p.h. m.p.h. m.p.h. |
------+-------+-----+-------+-------+-------+------+------+-------+
Jan. 5 11 23 27 3 6 15 23
Feb. 5 19 23 28 0 2 8 16
Mar. 5 10 20 23 0 1 11 18
April 6 16 23 28 1 7 16 26
May 1 14 24 30 3 11 24 31
June 1 12 22 26 1 10 21 27
July 8 18 29 31 1 12 25 29
Aug. 2 9 23 30 1 9 18 30
Sept. 1 13 25 30 1 12 24 28
Oct. 5 17 21 26 0 4 16 29
Nov. 6 11 20 26 3 7 19 28
Dec. 1 5 19 24 2 7 23 29
------+-------+-----+-------+-------+-------+------+------+-------+
Total 46 155 272 329 16 88 220 314
During the year of least wind there were only eight separate
occasions upon which the average hourly velocity of the wind
was less than six miles per hour for two consecutive days, and
on two occasions only was it less than six miles per hour on
three consecutive days. It must be remembered, however, that
this does not by any means imply that during such days the wind
did not rise above six miles per hour, and the probability is
that a mill which could be actuated by a six-mile wind would
have been at work during part of the time. It will further be
observed that the greatest differences between these two years
occur in the figures relating to the light winds. The number of
days upon which the mean hourly velocity of the wind exceeds
twenty miles per hour remains fairly constant year after year.
As the greatest difficulty in connection with pumping sewage is
the influx of storm water in times of rain, it will be useful
to notice the rainfall at those times when the wind is at a
minimum. From the following figures (Table No. 13) it will be
seen that, generally speaking, when there is very little wind
there is very little rain Taking the ten years enumerated in
Table No. 11, we find that out of the 314 days on which the
wind averaged less than six miles per hour only forty-eight of
them were wet, and then the rainfall only averaged .l3 in on
those days.
TABLE No. 13.
WIND LESS THAN 6 M.P.H.
-----------+-------------+------------+--------+----------------------------------
Ref. No. | Total No. | Days on | | Rainfall on each
from Table | of days in | which no | Rainy | rainy day in
No. 11. | each year. | rain fell. | days. | inches.
-----------+-------------+------------+--------+----------------------------------
1 | 16 | 14 | 2 | .63 and .245
2 | 15 | 13 | 2 | .02 and .02
3 | 39 | 34 | 5 | .025, .01, .26, .02 and .03
4 | 36 | 29 | 7 | / .02, .08, .135, .10, .345, .18
| | | | \ and .02
5 | 34 | 28 | 6 | .10, .43, .01, .07, .175 and .07
6 | 32 | 27 | 5 | .10, .11, .085, .04 and .135
7 | 33 | 21 | 2 | .415 and .70
8 | 46 | 40 | 6 | .07, .035, .02, .06, .13 and .02
9 | 26 | 20 | 6 | .145, .20, .33, .125, .015 & .075
10 | 37 | 30 | 7 | / .03, .23, .165, .02, .095
| | | | \ .045 and .02
-----------+-------------+------------+--------+----------------------------------
Total | 314 | 266 | 48 | Average rainfall on each of
| | | | the 48 days = .13 in
The greater the height of the tower which carries the mill the
greater will be the amount of effective wind obtained to drive
the mill, but at the same time there are practical
considerations which limit the height. In America many towers
are as much as 100 ft high, but ordinary workmen do not
voluntarily climb to such a height, with the result that the
mill is not properly oiled. About 40 ft is the usual height in
this country, and 60 ft should be used as a maximum.
Mr. George Phelps, in a paper read by him in 1906 before the
Association of Water Engineers, stated that it was safe to
assume that on an average a fifteen miles per hour wind was
available for eight hours per day, and from this he gave the
following figures as representing the approximate average duty
with, a lift of l00 ft, including friction:--
TABLE NO. 14
DUTY OF WINTDMILU
Diameter of Wheel.
10
12
14
16
18
20
25
30
35
40
The following table gives the result of tests carried out by
the United States Department of Agriculture at Cheyenne, Wyo.,
with a l4 ft diameter windmill under differing wind
velocities:--
TABLE No. 15.
POWER or l4-rx WINDMILL IN VARYING WINDS.
Velocity of Wind (miles per hour).
0--5 6-10 11-15 16-20 21-25 26-30 31-35
It will be apparent from the foregoing figures that practically
the whole of the pumping for a small sewerage works may be done
by means of a windmill, but it is undesirable to rely entirely
upon such a system, even if two mills are erected so that the
plant will be in duplicate, because there is always the
possibility, although it may be remote, of a lengthened period
of calm, when the sewage would accumulate; and, further, the
Local Government Board would not approve the scheme unless it
included an engine, driven by gas, oil, or other mechanical
power, for emergencies. In the case of water supply the
difficulty may be overcome by providing large storage capacity,
but this cannot be done for sewage without creating an
intolerable nuisance. In the latter case the storage should not
be less than twelve hours dry weather flow, nor more than
twenty-four. With a well-designed mill, as has already been
indicated, the wind will, for the greater part of the year, be
sufficient to lift the whole of the sewage and storm-water,
but, if it is allowed to do so, the standby engine will
deteriorate for want of use to such an extent that when
urgently needed it will not be effective. It is, therefore,
desirable that the attendant should run the engine at least
once in every three days to keep it in working order. If it can
be conveniently arranged, it is a good plan for the attendant
to run the engine for a few minutes to entirely empty the pump
well about six o'clock each evening. The bulk of the day's
sewage will then have been delivered, and can be disposed of
when it is fresh, while at the same time the whole storage
capacity is available for the night flow, and any rainfall
which may occur, thus reducing the chances of the man being
called up during the night. About 22 per cent, of the total
daily dry weather flow of sewage is delivered between 7 p.m.
and 7 a.m.
The first cost of installing a small windmill is practically
the same as for an equivalent gas or oil engine plant, so that
the only advantage to be looked for will be in the maintenance,
which in the case of a windmill is a very small matter, and the
saving which may be obtained by the reduction of the amount of
attendance necessary. Generally speaking, a mill 20 ft in
diameter is the largest which should be used, as when this size
is exceeded it will be found that the capital cost involved is
incompatible with the value of the work done by the mill, as
compared with that done by a modern internal combustion engine.
Mills smaller than 8 ft in diameter are rarely employed, and
then only for small work, such as a 2 1/2 in pump and a 3-ft
lift The efficiency of a windmill, measured by the number of
square feet of annular sail area, decreases with the size of
the mill, the 8 ft, 10 ft, and l2 ft mills being the most
efficient sizes. When the diameter exceeds l2 ft, the
efficiency rapidly falls off, because the peripheral velocity
remains constant for any particular velocity or pressure of the
wind, and as every foot increase in the diameter of the wheel
makes an increase of over 3 ft in the length of the
circumference, the greater the diameter the less the number of
revolutions in any given time; and consequently the kinetic
flywheel action which is so valuable in the smaller sizes is to
a great extent lost in the larger mills.
Any type of pump can be used, but the greatest efficiency will
be obtained by adopting a single acting pump with a short
stroke, thus avoiding the liability, inherent in a long pump
rod, to buckle under compression, and obviating the use of a
large number of guides which absorb a large part of the power
given out by the mill. Although some of the older mills in this
country are of foreign origin, there are several British
manufacturers turning out well-designed and strongly-built
machines in large numbers. Fig. 19 represents the general
appearance and Fig. 20 the details of the type of mill made by
the well-known firm of Duke and Ockenden, of Ferry Wharf,
Littlehampton, Sussex. This firm has erected over 400
windmills, which, after the test of time, have proved
thoroughly efficient. From Fig. 20 it will be seen that the
power applied by the wheel is transmitted through spur and
pinion gearing of 2 1/2 ratio to a crank shaft, the gear wheel
having internal annular teeth of the involute type, giving a
greater number of teeth always in contact than is the case with
external gears. This minimises wear, which is an important matter,
as it is difficult to properly lubricate these appliances, and they
are exposed to and have to work in all sorts of weather.
[Illustration: Fig. l9.--General View of Modern Windmill.]
[Illustration: Fig. 20.--Details of Windmill Manufactured by Messrs. Duke and
Ockenden, Littlehampton.]
It will be seen that the strain on the crank shaft is taken by
a bent crank which disposes the load centrally on the casting,
and avoids an overhanging crank disc, which has been an
objectionable feature in some other types. The position of the
crank shaft relative to the rocker pin holes is studied to give
a slow upward motion to the rocker with a more rapid downward
stroke, the difference in speed being most marked in the
longest stroke, where it is most required.
In order to transmit the circular internal motion a vertical
connecting rod in compression is used, which permits of a
simple method of changing the length of stroke by merely
altering the pin in the rocking lever, the result being that
the pump rod travels in a vertical line.
The governing is entirely automatic. If the pressure on the
wind wheel, which it will be seen is set off the centre line of
the mill and tower, exceeds that found desirable--and this can
be regulated by means of a spring on the fantail--the windmill
automatically turns on the turn-table and presents an ellipse
to the wind instead of a circular face, thus decreasing the
area exposed to the wind gradually until the wheel reaches its
final position, or is hauled out of gear, when the edges only
are opposed to the full force of the wind. The whole weight of
the mill is taken upon a ball-bearing turn-table to facilitate
instant "hunting" of the mill to the wind to enable it to take
advantage of all changes of direction. The pump rod in the
windmill tower is provided with a swivel coupling, enabling the
mill head to turn completely round without altering the
position of the rod.
CHAPTER X.
THE DESIGN OF SEE OUTFALLS.
The detail design of a sea outfall will depend upon the level
of the conduit with reference to present surface of the shore,
whether the beach is being eroded or made up, and, if any part
of the structure is to be constructed above the level of the
shore, whether it is likely to be subject to serious attack by
waves in times of heavy gales. If there is probability of the
direction of currents being affected by the construction of a
solid structure or of any serious scour being caused, the
design must be prepared accordingly.
While there are examples of outfalls constructed of glazed
stoneware socketed pipes surrounded with concrete, as shown in
Fig. 21, cast iron pipes are used in the majority of cases.
There is considerable variation in the design of the joints for
the latter class of pipes, some of which are shown in Figs. 22,
23, and 24. Spigot and socket joints (Fig. 22), with lead run
in, or even with rod lead or any of the patent forms caulked in
cold, are unsuitable for use below high-water mark on account
of the water which will most probably be found in the trench.
Pipes having plain turned and bored joints are liable to be
displaced if exposed to the action of the waves, but if such
joints are also flanged, as Fig. 24, or provided with lugs, as
Fig. 23, great rigidity is obtained when they are bolted up; in
addition to which the joints are easily made watertight. When a
flange is formed all round the joint, it is necessary, in order
that its thickness may be kept within reasonable limits, to
provide bolts at frequent intervals. A gusset piece to stiffen
the flange should be formed between each hole and the next, and
the bolt holes should be arranged so that when the pipes are
laid there will not be a hole at the bottom on the vertical
axis of the pipe, as when the pipes are laid in a trench below
water level it is not only difficult to insert the bolt, but
almost impracticable to tighten up the nut afterwards. The
pipes should be laid so that the two lowest bolt holes are
placed equidistant on each side of the centre line, as shown in
the end views of Figs. Nos. 23 and 24.
[Illustration: Fig. 2l.-Stoneware Pipe and Concrete Sea Outfall.]
With lug pipes, fewer bolts are used, and the lugs are made
specially strong to withstand the strain put upon them in
bolting up the pipes. These pipes are easier and quicker to
joint under water than are the flanged pipes, so that their use
is a distinct advantage when the hours of working are limited.
In some cases gun-metal bolts are used, as they resist the
action of sea water better than steel, but they add
considerably to the cost of the outfall sewer, and the
principal advantage appears to be that they are possibly easier
to remove than iron or steel ones would be if at any time it
was required to take out any pipe which may have been
accidentally broken. On the other hand, there is a liability of
severe corrosion of the metal taking place by reason of
galvanic action between the gun-metal and the iron, set up by
the sea water in which they are immersed. If the pipes are not
to be covered with concrete, and are thus exposed to the action
of the sea water, particular care should be taken to see that
the coating by Dr. Angus Smith's process is perfectly applied
to them.
[Illustration: Fig. 22.--Spigot and Socket Joint for Cast Iron Pipes.]
[Illustration: Fig. 23.--Lug Joint for Cast Iron Pipes.]
[Illustration: Fig. 24.--Turned, Board, and Flanged Joint for Cast Iron Pipes.]
Steel pipes are, on the whole, not so suitable as cast iron.
They are, of course, obtainable in long lengths and are easily
jointed, but their lightness compared with cast iron pipes,
which is their great advantage in transport, is a disadvantage
in a sea outfall, where the weight of the structure adds to its
stability. The extra length of steel pipes necessitates a
greater extent of trench being excavated at one time, which
must be well timbered to prevent the sides falling in On the
other hand, cast iron pipes are more liable to fracture by
heavy stones being thrown upon them by the waves, but this is a
contingency which does not frequently occur in practice.
According to Trautwine, the cast iron for pipes to resist sea
water should be close-grained, hard, white metal. In such metal
the small quantity of contained carbon is chemically combined
with the iron, but in the darker or mottled metals it is
mechanically combined, and such iron soon becomes soft, like
plumbago, under the influence of sea water. Hard white iron has
been proved to resist sea water for forty years without
deterioration, whether it is continually under water or
alternately wet and dry.
Several types of sea outfalls are shown in Figs. 25 to 31.[1]
In the example shown in Fig. 25 a solid rock bed occurred a
short distance below the sand, which was excavated so as to
allow the outfall to be constructed on the rock. Anchor bolts
with clevis heads were fixed into the rock, and then, after a
portion of the concrete was laid, iron bands, passing around
the cast iron pipes, were fastened to the anchors. This
construction would not be suitable below low-water mark. Fig.
26 represents the Aberdeen sea outfall, consisting of cast iron
pipes 7 ft in diameter, which are embedded in a heavy concrete
breakwater 24 ft in width, except at the extreme end, where it
is 30 ft wide. The 4 in wrought iron rods are only used to the
last few pipes, which were in 6 ft lengths instead of 9 ft, as
were the remainder. Fig. 27 shows an inexpensive method of
carrying small pipes, the slotted holes in the head of the pile
allowing the pipes to be laid in a straight line, even if the
pile is not driven quite true, and if the level of the latter
is not correct it can be adjusted by inserting a packing piece
between the cradle and the head.
Great Crosby outfall sewer into the Mersey is illustrated in
Fig. 28. The piles are of greenheart, and were driven to a
solid foundation. The 1 3/4 in sheeting was driven to support
the sides of the excavation, and was left in when the concrete
was laid. Light steel rails were laid under the sewer, in
continuous lengths, on steel sleepers and to 2 ft gauge. The
invert blocks were of concrete, and the pipes were made of the
same material, but were reinforced with steel ribs. The Waterloo
(near Liverpool) sea outfall is shown in Fig. 31.
[Footnote 1: Plate V.]
Piling may be necessary either to support the pipes or to keep
them secure in their proper position, but where there is a
substratum of rock the pipes may be anchored, as shown in Figs.
25 and 26. The nature of the piling to be adopted will vary
according to the character of the beach. Figs. 27, 29, 30, and
31 show various types. With steel piling and bearers, as shown
in Fig. 29, it is generally difficult to drive the piles with
such accuracy that the bearers may be easily bolted up through
the holes provided in the piles, and, if the holes are not
drilled in the piles until after they are driven to their final
position, considerable time is occupied, and perhaps a tide
lost in the attempt to drill them below water. There is also
the difficulty of tightening up the bolts when the sewer is
partly below the surface of the shore, as shown. In both the
types shown in Figs. 29 and 30 it is essential that the piles
and the bearers should abut closely against the pipes;
otherwise the shock of the waves will cause the pipes to move
and hammer against the framing, and thus lead to failure of the
structure.
Piles similar to Fig. 31 can only be fixed in sand, as was the
case at Waterloo, because they must be absolutely true to line
and level, otherwise the pipes cannot be laid in the cradles.
The method of fixing these piles is described by Mr. Ben
Howarth (Minutes of Proceedings of Inst.C.E., Vol. CLXXV.) as
follows:--"The pile was slung vertically into position from a
four-legged derrick, two legs of which were on each side of the
trench; a small winch attached to one pair of the legs lifted
and lowered the pile, through a block and tackle. When the pile
was ready to be sunk, a 2 in iron pipe was let down the centre,
and coupled to a force-pump by means of a hose; a jet of water
was then forced down this pipe, driving the sand and silt away
from below the pile. The pile was then rotated backwards and
forwards about a quarter of a turn, by men pulling on the arms;
the pile, of course, sank by its own weight, the water-jet
driving the sand up through the hollow centre and into the
trench, and it was always kept vertical by the sling from the
derrick. As soon as the pile was down to its final level the ground
was filled in round the arms, and in this running sand the pile
became perfectly fast and immovable a few minutes after the
sinking was completed. The whole process, from the first
slinging of the pile to the final setting, did not take more
than 20 or 25 minutes."
[Illustration: PLATE V.
ROCK BED. Fig. 26--ABERDEEN SEA OUTFALL. Fig. 27--SMALL GREAT
CROSBY SEA OUTFALL. Fig. 29--CAST IRON PIPE ON STEEL CAST AND
BEARERS. Fig. 31--WATERLOO (LIVERPOOL) SEA OUTFALL.]
(_To face page 80_.)
Screw piles may be used if the ground is suitable, but, if it
is boulder clay or similar material, the best results will
probably be obtained by employing rolled steel joists as piles.
CHAPTER XI.
THE ACTION OF SEA WATER ON CEMENT.
Questions are frequently raised in connection with sea-coast
works as to whether any deleterious effect will result from
using sea-water for mixing the concrete or from using sand and
shingle off the beach; and, further, whether the concrete,
after it is mixed, will withstand the action of the elements,
exposed, as it will be, to air and sea-water, rain, hot sun,
and frosts.
Some concrete structures have failed by decay of the material,
principally between high and low water mark, and in order to
ascertain the probable causes and to learn the precautions
which it is necessary to take, some elaborate experiments have
been carried out.
To appreciate the chemical actions which may occur, it will be
as well to examine analyses of sea-water and cement. The water
of the Irish Channel is composed of
Sodium chloride.................... 2.6439 per cent.
Magnesium chloride................. 0.3150 " "
Magnesium sulphate................. 0.2066 " "
Calcium sulphate................... 0.1331 " "
Potassium chloride................. 0.0746 " "
Magnesium bromide.................. 0.0070 " "
Calcium carbonate.................. 0.0047 " "
Iron carbonate..................... 0.0005 " "
Magnesium nitrate.................. 0.0002 " "
Lithium chloride................... Traces.
Ammonium chloride.................. Traces.
Silica chloride.................... Traces.
Water.............................. 96.6144
--------
100.0000
An average analysis of a Thames cement may be taken to be as
follows:--
Silica................................ 23.54 per cent.
Insoluble residue (sand, clay,
etc.)............................ 0.40 "
Alumina and ferric oxide............... 9.86 "
Lime.................................. 62.08 "
Magnesia............................... 1.20 "
Sulphuric anhydride.................... 1.08 "
Carbonic anhydride and water........... 1.34 "
Alkalies and loss on analysis.......... 0.50 "
-----
100.00
The following figures give the analysis of a sample of cement
expressed in terms of the complex compounds that are found:--
Sodium silicate (Na2SiO3)........ 3.43 per cent.
Calcium sulphate (CaSO4)......... 2.45 "
Dicalcium silicate (Ca2SiO4).... 61.89 "
Dicalcium aluminate (Ca2Al2O5).. 12.14 "
Dicalcium ferrate (Ca2Fe2O5)..... 4.35 "
Magnesium oxide (MgO)............ 0.97 "
Calcium oxide (CaO)............. 14.22 "
Loss on analysis, &c............. 0.55 "
-----
100.00
Dr. W. Michaelis, the German cement specialist, gave much
consideration to this matter in 1906, and formed the opinion
that the free lime in the Portland cement, or the lime freed in
hardening, combines with the sulphuric acid of the sea-water,
which causes the mortar or cement to expand, resulting in its
destruction. He proposed to neutralise this action by adding to
the mortar materials rich in silica, such as trass, which would
combine with the lime.
Mr. J. M. O'Hara, of the Southern Pacific Laboratory, San
Francisco, Cal., made a series of tests with sets of pats 4 in
diameter and 1/2 in thick at the centre, tapering to a thin
edge on the circumference, and also with briquettes for
ascertaining the tensile strength, all of which were placed
in water twenty-four hours after mixing. At first some of the
pats were immersed in a "five-strength solution" of sea-water
having a chemical analysis as follows:--
Sodium chloride.................... 11.5 per cent.
Magnesium chloride................. 1.4 " "
Magnesium sulphate................. 0.9 " "
Calcium sulphate................... 0.6 " "
Water.............................. 85.6 " "
100.0
This strong solution was employed in order that the probable
effect of immersing the cement in sea-water might be
ascertained very much quicker than could be done by observing
samples actually placed in ordinary sea-water, and it is worthy
of note that the various mixtures which failed in this
accelerated test also subsequently failed in ordinary sea-water
within a period of twelve months.
Strong solutions were next made of the individual salts
contained in sea-water, and pats were immersed as before, when
it was found that the magnesium sulphate present in the water
acted upon the calcium hydrate in the cement, forming calcium
sulphate, and leaving the magnesium hydrate free. The calcium
sulphate combines with the alumina of the cement, forming
calcium sulpho-aluminate, which causes swelling and cracking of
the concrete, and in cements containing a high proportion of
alumina, leads to total destruction of all cohesion. The
magnesium hydrate has a tendency to fill the pores of the
concrete so as to make it more impervious to the destructive
action of the sea-water, and disintegration may be retarded or
checked. A high proportion of magnesia has been found in
samples of cement which have failed under the action of sea
water, but the disastrous result cannot be attributed to this
substance having been in excess in the original cement, as it
was probably due to the deposition of the magnesia salts from
the sea-water; although, if magnesia were present in the cement
in large quantities, it would cause it to expand and crack,
still with the small proportion in which it occurs in ordinary
cements it is probably inert. The setting of cement under the
action of water always frees a portion of the lime which was
combined, but over twice as much is freed when the cement sets
in sea-water as in fresh water. The setting qualities of cement
are due to the iron and alumina combined with calcium, so that
for sea-coast work it is desirable for the alumina to be
replaced by iron as far as possible. The final hardening and
strength of cement is due in a great degree to the tri-calcium
silicate (3CaO, SiO2) which is soluble by the sodium chloride
found in sea-water, so that the resultant effect of the action
of these two compounds is to enable the sea-water to gradually
penetrate the mortar and rot the concrete. The concrete is
softened, when there is an abnormal amount of sulphuric acid
present, as a result of the reaction of the sulphuric acid of
the salt dissolved by the water upon a part of the lime in the
cement. The ferric oxide of the cement is unaffected by sea-
water.
The neat cement briquette tests showed that those immersed in
sea-water attained a high degree of strength at a much quicker
rate than those immersed in fresh water, but the 1 to 3 cement
and sand briquette tests gave an opposite result. At the end of
twelve months, however, practically all the cements set in
fresh water showed greater strength than those set in sea-
water. When briquettes which have been immersed in fresh water
and have thoroughly hardened are broken, the cores are found to
be quite dry, and if briquettes immersed in sea-water show a
similar dryness there need be no hesitation in using the
cement; but if, on the other hand, the briquette shows that the
sea-water has permeated to the interior, the cement will lose
strength by rotting until it has no cohesion at all. It must be
remembered that it is only necessary for the water to penetrate
to a depth of 1/2 in on each side of a briquette to render it
damp all through, whereas in practical work, if the water only
penetrated to the same depth, very little ill-effect would be
experienced, although by successive removals of a skin 1/2 in
deep the structure might in time be imperilled.
The average strength in pounds per square inch of six different
well-known brands of cement tested by Mr. O'Hara was as
follows:--
TABLE No. 16.
EFFECT OF SEA WATER ON STRENGTH OF CEMENT.
Neat cement 1 cement to 3 sand
set in set in
Sea Water Fresh Water Sea Water Fresh Water
7 days 682 548 214 224
28 days 836 643 293 319
2 months 913 668 313 359
3 months 861 667 301 387
6 months 634 654 309 428
9 months 542 687 317 417
12 months 372 706 325 432
Some tests were also made by Messrs. Westinghouse, Church,
Kerr, and Co., of New York, to ascertain the effect of sea-
water on the tensile strength of cement mortar. Three sets of
briquettes were made, having a minimum section of one square
inch. The first were mixed with fresh water and kept in fresh
water; the second were mixed with fresh water, but kept
immersed in pans containing salt water; while the third were
mixed with sea-water and kept in sea-water. In the experiments
the proportion of cement and sand varied from 1 to 1 to 1 to 6.
The results of the tests on the stronger mixtures are shown in
Fig. 32.
The Scandinavian Portland cement manufacturers have in hand
tests on cubes of cement mortar and cement concrete, which were
started in 1896, and are to extend over a period of twenty
years. A report upon the tests of the first ten years was
submitted at the end of 1909 to the International Association
of Testing Materials at Copenhagen, and particulars of them are
published in "Cement and Sea-Water," by A. Poulsen (chairman of
the committee), J. Jorsen and Co., Copenhagen, 1909, price 3s.
[Illustration: FIG. 32.--Tests of the Tensile Strength of
Cement and Sand Briquettes, Showing the Effect of Sea Water.]
Cements from representative firms in different countries were
obtained for use in making the blocks, which had coloured glass
beads and coloured crushed glass incorporated to facilitate
identification. Each block of concrete was provided with a
number plate and a lifting bolt, and was kept moist for one
month before being placed in position. The sand and gravel were
obtained from the beach on the west coast of Jutland. The
mortar blocks were mixed in the proportion of 1 to 1, 1 to 2,
and 1 to 3, and were placed in various positions, some between
high and low water, so as to be exposed twice in every twenty-
four hours, and others below low water, so as to be always
submerged. The blocks were also deposited under these
conditions in various localities, the mortar ones being placed
at Esbjerb at the south of Denmark, at Vardo in the Arctic
Ocean, and at Degerhamm on the Baltic, where the water is only
one-seventh as salt as the North Sea, while the concrete blocks
were built up in the form of a breakwater or groyne at Thyboron
on the west coast of Jutland. At intervals of three, six, and
twelve months, and two, four, six, ten, and twenty years, some
of the blocks have, or will be, taken up and subjected to
chemical tests, the material being also examined to ascertain
the effect of exposure upon them. The blocks tested at
intervals of less than one year after being placed in position
gave very variable results, and the tests were not of much
value.
The mortar blocks between high and low water mark of the Arctic
Ocean at Vardo suffered the worst, and only those made with the
strongest mixture of cement, 1 to 1, withstood the severe frost
experienced. The best results were obtained when the mortar was
made compact, as such a mixture only allowed diffusion to take
place so slowly that its effect was negligible; but when, on
the other hand, the mortar was loose, the salts rapidly
penetrated to the interior of the mass, where chemical changes
took place, and caused it to disintegrate. The concrete blocks
made with 1 to 3 mortar disintegrated in nearly every case,
while the stronger ones remained in fairly good condition. The
best results were given by concrete containing an excess of
very fine sand. Mixing very finely-ground silica, or trass,
with the cement proved an advantage where a weak mixture was
employed, but in the other cases no benefit was observed.
The Association of German Portland Cement Manufacturers carried
out a series of tests, extending over ten years, at their
testing station at Gross Lichterfeld, near Berlin, the results
of which were tabulated by Mr. C. Schneider and Professor Gary.
In these tests the mortar blocks were made 3 in cube and the
concrete blocks l2 in cube; they were deposited in two tanks,
one containing fresh water and the other sea-water, so that the
effect under both conditions might be noted. In addition,
concrete blocks were made, allowed to remain in moist sand for
three months, and were then placed in the form of a groyne in
the sea between high and low-water mark. Some of the blocks
were allowed to harden for twelve months in sand before being
placed, and these gave better results than the others. Two
brands of German Portland cement were used in these tests, one,
from which the best results were obtained, containing 65.9 per
cent. of lime, and the other 62.0 per cent. of lime, together
with a high percentage of alumina. In this case, also, the
addition of finely-ground silica, or trass, improved the
resisting power of blocks made with poor mortars, but did not
have any appreciable effect on the stronger mixtures.
Professor M. Moller, of Brunswick, Germany, reported to the
International Association for Testing Materials, at the
Copenhagen Congress previously referred to, the result of his
tests on a small hollow, trapezium shape, reinforced concrete
structure, which was erected in the North Sea, the interior
being filled with sandy mud, which would be easily removable by
flowing water. The sides were 7 cm. thick, formed of cement
concrete 1:2 1/2:2, moulded elsewhere, and placed in the
structure forty days after they were made, while the top and
bottom were 5 cm. thick, and consisted of concrete 1:3:3,
moulded _in situ_ and covered by the tide within twenty-four
hours of being laid. The concrete moulded _in situ_ hardened a
little at first, and then became soft when damp, and friable
when dry, and white efflorescence appeared on the surface. In a
short time the waves broke this concrete away, and exposed the
reinforcement, which rusted and disappeared, with the result
that in less than four years holes were made right through the
concrete. The sides, which were formed of slabs allowed to
harden before being placed in the structure, were unaffected
except for a slight roughening of the surface after being
exposed alternately to the sea and air for a period, of
thirteen years. Professor Moller referred also to several cases
which had come under his notice where cement mortar or concrete
became soft and showed white efflorescence when it had been
brought into contact with sea-water shortly after being made.
In experiments in Atlantic City samples of dry cement in powder
form were put with sea-water in a vessel which was rapidly
rotated for a short time, after which the cement and the sea-
water were analysed, and it was found that the sea-water had
taken up the lime from the cement, and the cement had absorbed
the magnesia salts from the sea-water.
Some tests were carried out in 1908-9 at the Navy Yard,
Charlestown, Mass., by the Aberthaw Construction Company of
Boston, in conjunction with the Navy Department. The cement
concrete was placed so that the lower portions of the surfaces
of the specimens were always below water, the upper portions
were always exposed to the air, and the middle portions were
alternately exposed to each. Although the specimens were
exposed to several months of winter frost as well as to the
heat of the summer, no change was visible in any part of the
concrete at the end of six months.
Mons. R. Feret, Chief of the Laboratory of Bridges and Roads,
Boulogne-sur-Mer, France, has given expression to the following
opinions:--
1. No cement or other hydraulic product has yet been found
which presents absolute security against the decomposing action
of sea-water.
2. The most injurious compound of sea-water is the acid of the
dissolved sulphates, sulphuric acid being the principal agent
in the decomposition of cement.
3. Portland cement for sea-water should be low in aluminium and
as low as possible in lime.
4. Puzzolanic material is a valuable addition to cement for
sea-water construction,
5. As little gypsum as possible should be added for regulating
the time of setting to cements which are to be used in sea-
water.
6. Sand containing a large proportion of fine grains must never
be used in concrete or mortar for sea-water construction.
7. The proportions of the cement and aggregate for sea-water
construction must be such as will produce a dense and
impervious concrete.
On the whole, sea-water has very little chemical effect on good
Portland cements, such as are now easily obtainable, and,
provided the proportion of aluminates is not too high, the
varying composition of the several well-known commercial
cements is of little moment. For this reason tests on blocks
immersed in still salt water are of very little use in
determining the probable behaviour of concrete when exposed to
damage by physical and mechanical means, such as occurs in
practical work.
The destruction of concrete works on the sea coast is due to
the alternate exposure to air and water, frost, and heat, and
takes the form of cracking or scaling, the latter being the
most usual when severe frosts are experienced. When concrete
blocks are employed in the construction of works, they should
be made as long as possible before they are required to be
built in the structure, and allowed to harden in moist sand,
or, if this is impracticable, the blocks should be kept in the
air and thoroughly wetted each day. On placing cement or
concrete blocks in sea water a white precipitate is formed on
their surfaces, which shows that there is some slight chemical
action, but if the mixture is dense this action is restricted
to the outside, and does not harm the block.
Cement mixed with sea water takes longer to harden than if
mixed with fresh water, the time varying in proportion to the
amount of salinity in the water. Sand and gravel from the
beach, even though dry, have their surfaces covered with saline
matters, which retard the setting of the cement, even when
fresh water is used, as they become mixed with such water, and
thus permeate the whole mass. If sea water and aggregate from
the shore are used, care must be taken to see that no decaying
seaweed or other organic matter is mixed with it, as every such
piece will cause a weak place in the concrete. If loam, clay,
or other earthy matters from the cliffs have fallen down on to
the beach, the shingle must be washed before it is used in
concrete.
Exposure to damp air, such as is unavoidable on the coast,
considerably retards the setting of cement, so that it is
desirable that it should not be further retarded by the
addition of gypsum, or calcium sulphate, especially if it is to
be used with sea water or sea-washed sand and gravel. The
percentage of gypsum found in cement is, however, generally
considerably below the maximum allowed by the British Standard
Specification, viz., 2 per cent., and is so small that, for
practical purposes, it makes very little difference in sea
coast work, although of course, within reasonable limits, the
quicker the cement sets the better. When cement is used to
joint stoneware pipe sewers near the coast, allowance must be
made for this retardation of the setting, and any internal
water tests which may be specified to be applied must not be
made until a longer period has elapsed after the laying of the
pipes than would otherwise be necessary. A high proportion of
aluminates tends to cause disintegration when exposed to sea
water. The most appreciable change which takes place in a good
sound cement after exposure to the sea is an increase in the
chlorides, while a slight increase in the magnesia and the
sulphates also takes place, so that the proportion of sulphates
and magnesia in the cement should be kept fairly low. Hydraulic
lime exposed to the sea rapidly loses the lime and takes up
magnesia and sulphates.
To summarise the information upon this point, it appears that
it is better to use fresh water for all purposes, but if, for
the sake of economy, saline matters are introduced into the
concrete, either by using sea water for mixing or by using sand
and shingle from the beach, the principal effect will be to
delay the time of setting to some extent, but the ultimate
strength of the concrete will probably not be seriously
affected. When the concrete is placed in position the portion
most liable to be destroyed is that between high and low water
mark, which is alternately exposed to the action of the sea and
the air, but if the concrete has a well-graded aggregate, is
densely mixed, and contains not more than two parts of sand to
one part of cement, no ill-effect need be anticipated.
CHAPTER XII
DIVING.
The engineer is not directly concerned with the various methods
employed in constructing a sea outfall, such matters being left
to the discretion of the contractor. It may, however, be
briefly stated that the work frequently involves the erection
of temporary steel gantries, which must be very carefully
designed and solidly built if they are to escape destruction by
the heavy seas. It is amazing to observe the ease with which a
rough sea will twist into most fantastic shapes steel joists 10
in by 8in, or even larger in size. Any extra cost incurred in
strengthening the gantries is well repaid if it avoids damage,
because otherwise there is not only the expense of rebuilding
the structure to be faced, but the construction of the work
will be delayed possibly into another season.
In order to ensure that the works below water are constructed
in a substantial manner, it is absolutely necessary that the
resident engineer, at least, should be able to don a diving
dress and inspect the work personally. The particular points to
which attention must be given include the proper laying of the
pipes, so that the spigot of one is forced home into the socket
of the other, the provision and tightening up of all the bolts
required to be fixed, the proper driving of the piles and
fixing the bracing, the dredging of a clear space in the bed of
the sea in front of the outlet pipe, and other matters
dependent upon the special form of construction adopted. If a
plug is inserted in the open end of the pipes as laid, the
rising of the tide will press on the plugged end and be of
considerable assistance in pushing the pipes home; it will
therefore be necessary to re-examine the joints to see if the
bolts can be tightened up any more.
Messrs. Siebe, Gorman, and Co., the well-known makers of
submarine appliances, have fitted up at their works at
Westminster Bridge-road, London, S.E., an experimental tank, in
which engineers may make a few preliminary descents and be
instructed in the art of diving; and it is distinctly more
advantageous to acquire the knowledge in this way from experts
than to depend solely upon the guidance of the divers engaged
upon the work which the engineer desires to inspect. Only a
nominal charge of one guinea for two descents is made, which
sum, less out-of-pocket expenses, is remitted to the Benevolent
Fund of the Institution of Civil Engineers. It is generally
desirable that a complete outfit, including the air pump,
should be provided for the sole use of the resident engineer,
and special men should be told off to assist him in dressing
and to attend to his wants while he is below water. He is then
able to inspect the work while it is actually in progress, and
he will not hinder or delay the divers.
It is a wise precaution to be medically examined before
undertaking diving work, although, with the short time which
will generally be spent below water, and the shallow depths
usual in this class of work, there is practically no danger;
but, generally speaking, a diver should be of good physique,
not unduly stout, free from heart or lung trouble and varicose
veins, and should not drink or smoke to excess. It is
necessary, however, to have acquaintance with the physical
principles involved, and to know what to do in emergencies. A
considerable amount of useful information is given by Mr. R. H.
Davis in his "Diving Manual" (Siebe, Gorman, and Co., 5s.),
from which many of the following notes are taken.
A diving dress and equipment weighs about l75 lb, including a
40 lb lead weight carried by the diver on his chest, a similar
weight on his back, and l6lb of lead on each boot. Upon
entering the water the superfluous air in the dress is driven
out through the outlet valve in the helmet by the pressure of
the water on the legs and body, and by the time the top of the
diver's head reaches the surface his breathing becomes
laboured, because the pressure of air in his lungs equals the
atmospheric pressure, while the pressure upon his chest and
abdomen is greater by the weight of the water thereon.
He is thus breathing against a pressure, and if he has to
breathe deeply, as during exertion, the effect becomes serious;
so that the first thing he has to learn is to adjust the
pressure of the spring on the outlet valve, so that the amount
of air pumped in under pressure and retained in the diving
dress counterbalances the pressure of the water outside, which
is equal to a little under 1/2lb per square inch for every foot
in depth. If the diver be 6 ft tall, and stands in an upright
position, the pressure on his helmet will be about 3lb per
square inch less than on his boots. The breathing is easier if
the dress is kept inflated down to the abdomen, but in this
case there is danger of the diver being capsized and floating
feet upwards, in which position he is helpless, and the air
cannot escape by the outlet valve. Air is supplied to the diver
under pressure by an air pump through a flexible tube called
the air pipe; and a light rope called a life line, which is
used for signalling, connects the man with the surface. The
descent is made by a 3 in "shot-rope," which has a heavy sinker
weighing about 50 lb attached, and is previously lowered to the
bottom. A 1-1/4 in rope about 15 ft long, called a "distance-
line," is attached to the shot-rope about 3 ft above the
sinker, and on reaching the bottom the diver takes this line
with him to enable him to find his way back to the shot-rope,
and thus reach the surface comfortably, instead of being hauled
up by his life line. The diver must be careful in his movements
that he does not fall so as suddenly to increase the depth of
water in which he is immersed, because at the normal higher
level the air pressure in the dress will be properly balanced
against the water pressure; but if he falls, say 30 ft, the
pressure of the water on his body will be increased by about 15
lb per square inch, and as the air pump cannot immediately
increase the pressure in the dress to a corresponding extent,
the man's body in the unresisting dress will be forced into the
rigid helmet, and he will certainly be severely injured, and
perhaps even killed.
When descending under water the air pressure in the dress is
increased, and acts upon the outside of the drum of the ear,
causing pain, until the air passing through the nose and up the
Eustachian tube inside the head reaches the back of the drum
and balances the pressure. This may be delayed, or prevented,
if the tube is partially stopped up by reason of a cold or
other cause, but the balance can generally be brought about if
the diver pauses in his descent and swallows his saliva; or
blocks up his nose as much as possible by pressing it against
the front of the helmet, closing the mouth and then making a
strong effort at expiration so as to produce temporarily an
extra pressure inside the throat, and so blow open the tubes;
or by yawning or going through the motions thereof. If this
does not act he must come up again Provided his ears are
"open," and the air pumps can keep the pressure of air equal to
that of the depth of the water in which the diver may be, there
is nothing to limit the rate of his descent.
Now in breathing, carbonic acid gas is exhaled, the quality
varying in accordance with the amount of work done, from .014
cubic feet per minute when at rest to a maximum of about .045,
and this gas must be removed by dilution with fresh air so as
not to inconvenience the diver. This is not a matter of much
difficulty as the proportion in fresh air is about .03 per
cent., and no effect is felt until the proportion is increased
to about 0.3 per cent., which causes one to breathe twice as
deeply as usual; at 0.6 per cent. there is severe panting; and
at a little over 1.0 per cent. unconsciousness occurs. The
effect of the carbonic acid on the diver, however, increases
the deeper he descends; and at a depth of 33 ft 1 per cent. of
carbonic acid will have the same effect as 2 per cent. at the
surface. If the diver feels bad while under water he should
signal for more air, stop moving about, and rest quietly for a
minute or two, when the fresh air will revive him. The volume
of air required by the diver for respiration is about 1.5 cubic
feet per minute, and there is a non-return valve on the air
inlet, so that in the event of the air pipe being broken, or
the pump failing, the air would not escape backwards, but by
closing the outlet valve the diver could retain sufficient air
to enable him to reach the surface.
During the time that a diver is under pressure nitrogen gas
from the air is absorbed by his blood and the tissues of his
body. This does not inconvenience him at the time, but when he
rises the gas is given off, so that if he has been at a great
depth for some considerable time, and comes up quickly, bubbles
form in the blood and fill the right side of the heart with
air, causing death in a few minutes. In less sudden cases the
bubbles form in the brain or spinal cord, causing paralysis of
the legs, which is called divers' palsy, or the only trouble
which is experienced may be severe pains in the joints and
muscles. It is necessary, therefore, that he shall come up by
stages so as to decompress himself gradually and avoid danger.
The blood can hold about twice as much gas in solution as an
equal quantity of water, and when the diver is working in
shallow depths, up to, say, 30 ft, the amount of nitrogen
absorbed is so small that he can stop down as long as is
necessary for the purposes of the work, and can come up to the
surface as quickly as he likes without any danger. At greater
depths approximately the first half of the upward journey may
be done in one stage, and the remainder done by degrees, the
longest rest being made at a few feet below the surface.
The following table shows the time limits in accordance with
the latest British Admiralty practice; the time under the water
being that from leaving the surface to the beginning of the
ascent:--
TABLE No. l7.--DIVING DATA.
Stoppages in Total time
minutes at for ascent
Depth in feet. Time under water. different depths in minutes.
at 20 ft 10 ft
Up to 36 No limit - - 0 to 1
36 to 42 Up to 3 hours - - 1 to 1-1/2
Over 3 hours - 5 6
42 to 48 Up to 1 hour - - 1-1/2
1 to 3 hours - 5 6-1/2
Over 3 hours - 10 11-1/2
48 to 54 Up to 1/2 hour - - 2
1/2 to 1-1/2 hour - 5 7
1-1/2 to 3 hours - 10 12
Over 3 hours - 20 22
54 to 60 Up to 20 minutes - - 2
20 to 45 minutes - 5 7
3/4 to 1-1/2 hour - 10 12
1-1/2 to 3 hours 5 15 22
Over 3 hours 10 20 32
When preparing to ascend the diver must tighten the air valve
in his helmet to increase his buoyancy; if the valve is closed
too much to allow the excess air to escape, his ascent will at
first be gradual, but the pressure of the water reduces, the
air in the dress expands, making it so stiff that he cannot
move his arms to reach the valve, and he is blown up, with
ever-increasing velocity, to the surface. While ascending he
should exercise his muscles freely during the period of waiting
at each stopping place, so as to increase the circulation, and
consequently the rate of deceleration.
During the progress of the works the location of the sea
outfall will be clearly indicated by temporary features visible
by day and lighted by night; but when completed its position
must be marked in a permanent manner. The extreme end of the
outfall should be indicated by a can buoy similar to that shown
in Fig. 33, made by Messrs. Brown, Lenox, and Co. (Limited),
Milwall, London, E., which costs about L75, including a 20 cwt.
sinker and 10 fathoms of chain, and is approved for the purpose
by the Board of Trade.
[Illustration: FIG 33 CAN BUOY FOR MARKING OUTFALL SEWER.]
It is not desirable to fasten the chain to any part of the
outfall instead of using a sinker, because at low water the
slack of the chain may become entangled, which by preventing
the buoy from rising with the tide, will lead to damage; but a
special pile may be driven for the purpose of securing the
buoy, at such a distance from the outlet that the chain will
not foul it. The buoy should be painted with alternate vertical
stripes of yellow and green, and lettered "Sewer Outfall" in
white letters 12 in deep.
It must be remembered that it is necessary for the plans and
sections of outfall sewers and other obstructions proposed to
be placed in tidal waters to be submitted to the Harbour and
Fisheries Department of the Board of Trade for their approval,
and no subsequent alteration in the works may be made without
their consent being first obtained.
CHAPTER XIII.
THE DISCHARGE OF SEA OUTFALL SEWERS.
The head which governs the discharge of a sea outfall pipe is
measured from the surface of the sewage in the tank, sewer, or
reservoir at the head of the outfall to the level of the sea.
As the sewage is run off the level of its surface is lowered,
and at the same time the level of the sea is constantly varying
as the tide rises and falls, so that the head is a variable
factor, and consequently the rate of discharge varies. A curve
of discharge may be plotted from calculations according to
these varying conditions, but it is not necessary; and all
requirements will be met if the discharges under certain stated
conditions are ascertained. The most important condition,
because it is the worst, is that when the level of the sea is
at high water of equinoctial spring tides and the reservoir is
practically empty.
Sea water has a specific gravity of 1.027, and is usually taken
as weighing 64.14 lb per cubic foot, while sewage may be taken
as weighing 62.45 lb per cubic foot, which is the weight of
fresh water at its maximum density. Now the ratio of weight
between sewage and sea water is as 1 to 1.027, so that a column
of sea water l2 inches in height requires a column of fresh
water 12.324, or say 12-1/3 in, to balance it; therefore, in
order to ascertain the effective head producing discharge it
will be necessary to add on 1/3 in for every foot in depth of
the sea water over the centre of the outlet.
The sea outfall should be of such diameter that the contents of
the reservoir can be emptied in the specified time--say, three
hours--while the pumps are working to their greatest power in
pouring sewage into the reservoir during the whole of the
period; so that when the valves are closed the reservoir will
be empty, and its entire capacity available for storage until
the valves are again opened.
To take a concrete example, assume that the reservoir and
outfall are constructed as shown in Fig. 34, and that it is
required to know the diameter of outfall pipe when the
reservoir holds 1,000,000 gallons and the whole of the pumps
together, including any that may be laid down to cope with any
increase of the population in the future, can deliver 600,000
gallons per hour. When the reservoir is full the top water
level will be 43.00 O.D., but in order to have a margin for
contingencies and to allow for the loss in head due to entry of
sewage into the pipe, for friction in passing around bends, and
for a slight reduction in discharging capacity of the pipe by
reason of incrustation, it will be desirable to take the
reservoir as full, but assume that the sewage is at the level
31.00. The head of water in the sea measured above the centre
of the pipe will be 21 ft, so that
[*Math: $21 \times 1/3$],
or 7 in--say, 0.58 ft--must be added to the height of high
water, thus reducing the effective head from 31.00 - 10.00 =
21.00 to 20.42 ft The quantity to be discharged will be
[*Math: $\frac{1,000,000 + (3 * 600,000)}{3}$]
= 933,333 gallons per hour = 15,555 gallons per minute, or,
taking 6.23 gallons equal to 1 cubic foot, the quantity equals
2,497 cubic feet per min Assume the required diameter to be 30
in, then, by Hawksley's formula, the head necessary to produce
velocity =
[*Math: $\frac{Gals. per min^2}{215 \times diameter in
inches^4} = \frac{15,555^2}{215 * 30^4}$]
= 1.389 ft, and the head to overcome friction =
[*Math: $\frac{Gals. per min^2 \times Length in yards}{240 *
diameter in inches^5} = \frac{15,555^2 * 2042}{240 * 30^5}]
= 84.719. Then 1.389 + 84.719 = 86.108--say, 86.11 ft; but the
acutal head is 20.42 ft, and the flow varies approximately as
the square root of the head, so that the true flow will be
about
[*Math: $15,555 * \sqrt{\frac{20.42}{86.11} = 7574.8$]
[Illustration: FIG 34 DIAGRAM ILLUSTRATING CALCULATIONS FOR THE
DISCHARGE OF SEA OUTFALLS]
--say 7,575 gallons. But a flow of 15,555 gallons per minute is
required, as it varies approximately as the fifth power of the
diameter, the requisite diameter will be about
[*Math: \sqrt[5]{\frac{30^5 \times 15,555}{7575}] = 34.64
inches.
Now assume a diameter of 40 in, and repeat the calculations.
Then head necessary to produce velocity
[*Math: = \frac{15,555^2}{215 \times 40^4}] = 0.044 ft, and
head to overcome friction =
[*Math: \frac{15,555^2 \times 2042}{240 \times 40^5}]
= 20.104 ft Then 0.044 + 20.104 = 20.148, say 20.15 ft, and the
true flow will therefore be about
[*Math: 15,555 * \sqrt{\frac{20.42}{20.15}}]
= 15,659 gallons, and the requisite diameter about
[*Math: \sqrt[5]{\frac{40^5 * 15,555}{15,659}}]
= 39.94 inches.
When, therefore, a 30 in diameter pipe is assumed, a diameter
of 34.64 in is shown to be required, and when 40 in is assumed
39.94 in is indicated.
Let _a_ = difference between the two assumed diameters. _b_ =
increase found over lower diameter. _c_ = decrease found under
greater diameter. _d_ = lower assumed diameter.
Then true diameter =
[*Math: d + \frac{ab}{b+c} = 30 + \frac{10 \times
4.64}{4.64+0.06} = 30 + \frac{46.4}{4.7} = 39.872],
or, say, 40 in, which equals the required diameter.
A simpler way of arriving at the size would be to calculate it
by Santo Crimp's formula for sewer discharge, namely, velocity
in feet per second =
[*Math: 124 \sqrt[3]{R^2} \sqrt{S}],
where R equals hydraulic mean depth in feet, and S = the ratio
of fall to length; the fall being taken as the difference in
level between the sewage and the sea after allowance has been
made for the differing densities. In this case the fall is
20.42 ft in a length of 6,126 ft, which gives a gradient of 1
in 300. The hydraulic mean depth equals
[*Math: \frac{d}{4}];
the required discharge, 2,497 cubic feet per min, equals the
area,
[*Math: (\frac{\pi d^2}{4})]
multiplied by the velocity, therefore the velocity in feet per
second = 4/(pi d^2) x 2497/60 = 2497/(15 pi d^2) and the
formula then becomes
2497/(15 pi d^2) = 124 x * 3rd_root(d^2)/3rd_root(4^3*) x
sqrt(1)/sqrt(300)
or d^2 x 3rd_root(d^2) = 3rd_root(d^6) = (2497 x 3rd_root(16) x
sqrt(300)) / (124 x 15 x 3.14159*)
or (8 x log d)/3 = log 2497 + (1/3 x log 16) + (* x log 300) -
log 124 - log 15 - log 3.14159;
or log d = 3/8 (3.397419 + 0.401373 + 1.238561 - 2.093422 -
1.176091 - 0.497150) = 3/8 (1.270690) = 0.476509.
* d = 2.9958* feet = 35.9496, say 36 inches.
As it happens, this could have been obtained direct from the
tables where the discharge of a 36 in pipe at a gradient of 1
in 300 = 2,506 cubic feet per minute, as against 2,497 cubic
feet required, but the above shows the method of working when
the figures in the tables do not agree with those relating to
the particular case in hand.
This result differs somewhat from the one previously obtained,
but there remains a third method, which we can now make trial
of--namely, Saph and Schoder's formula for the discharge of
water mains, V = 174 3rd_root(R^2) x S^.51*. Substituting
values similar to those taken previously, this formula can be
written
2497/(15 pi d^2) = 174 x 3rd_root(d_2)/3rd_root(4^2) x
1^.51/300^.51
or d^2 x 3rd_root(d^2) = 3rd_root(d^6) = (2497 x 3rd_root(16) x
300^.51) / (174 x 15 x 3.14159)
or* log d = 3/8 (3.397419 + 0.401373 + (54 x 2.477121) -
2.240549 - 1.176091 - 0.497150) = 3/8 (1.222647) = 0.458493
* d = 2.874* feet = 34.388 say 34 1/2 inches.
By Neville's general formula the velocity in feet per second =
140 SQRT(RS)-11(RS)^(1/3) or, assuming a diameter of 37 inches,
V = 140 X SQRT(37/(12 x 4) x 1/300) - 11 (37/(12x4x300))^(1/3)
= 140 x SQRT(37/14400) - 11 (37/1440)^(1/3)
= 7.09660 - 1.50656 = 5.59 feet per second.
Discharge = area x velocity; therefore, the discharge in cubic
feet per minute
= 5.59 x 60 x (3.14159 x 37^2)/(4*12^2) = 2504 compared with
2,497 c.f.m, required, showing that if this formula is used the
pipe should be 37 in diameter.
The four formula, therefore, give different results, as
follows:--
Hawksley = 40 in
Neville = 37 in
Santo Crimp = 36 in
Saph and Schoder = 34-1/2 in
The circumstances of the case would probably be met by
constructing the outfall 36 in in diameter.
It is very rarely desirable to fix a flap-valve at the end of a
sea outfall pipe, as it forms a serious obstruction to the flow
of the sewage, amounting, in one case the writer investigated,
to a loss of eight-ninths of the available head; the head was
exceptionally small, and the flap valve practically absorbed it
all. The only advantage in using a flap valve occurs when the
pipe is directly connected with a tank sewer below the level of
high water, in which case, if the sea water were allowed to
enter, it would not only occupy space required for storing
sewage, but it would act on the sewage and speedily start
decomposition, with the consequent emission of objectionable
odours. If there is any probability of sand drifting over the
mouth of the outfall pipe, the latter will keep free much
better if there is no valve. Schemes have been suggested in
which it was proposed to utilise a flap valve on the outlet so
as to render the discharge of the sewage automatic. That is to
say, the sewage was proposed to be collected in a reservoir at
the head of, and directly connected to, the outfall pipe, at
the outlet end of which a flap valve was to be fixed. During
high water the mouth of the outfall would be closed, so that
sewage would collect in the pipes, and in the reservoir beyond;
then when the tide had fallen such a distance that its level
was below the level of the sewage, the flap valve would open,
and the sewage flow out until the tide rose and closed the
valve. There are several objections to this arrangement. First
of all, a flap valve under such conditions would not remain
watertight, unless it were attended to almost every day, which
is, of course, impracticable when the outlet is below water. As
the valve would open when the sea fell to a certain level and
remain open during the time it was below that level, the period
of discharge would vary from, say, two hours at neap tides to
about four hours at springs; and if the two hours were
sufficient, the four hours would be unnecessary. Then the
sewage would not only be running out and hanging about during
dead water at low tide, but before that time it would be
carried in one direction, and after that time in the other
direction; so that it would be spread out in all quarters
around the outfall, instead of being carried direct out to sea
beyond chance of return, as would be the case in a well-
designed scheme.
When opening the valve in the reservoir, or other chamber, to
allow the sewage to flow through the outfall pipe, care should
be taken to open it at a slow rate so as to prevent damage by
concussion when the escaping sewage meets the sea water
standing in the lower portion of the pipes. When there is
considerable difference of level between the reservoir and the
sea, and the valve is opened somewhat quickly, the sewage as it
enters the sea will create a "water-spout," which may reach to
a considerable height, and which draws undesirable attention to
the fact that the sewage is then being turned into the sea.
Chapter XIV
TRIGONOMETRICAL SURVEYING.
In the surveying work necessary to fix the positions of the
various stations, and of the float, a few elementary
trigonometrical problems are involved which can be
advantageously explained by taking practical examples.
Having selected the main station A, as shown in Fig. 35, and
measured the length of any line A B on a convenient piece of
level ground, the next step will be to fix its position upon
the plan. Two prominent landmarks, C and D, such as church
steeples, flag-staffs, etc., the positions of which are shown
upon the ordnance map, are selected and the angles read from
each of the stations A and B. Assume the line A B measures ll7
ft, and the angular measurements reading from zero on that line
are, from A to point C, 29 23' and to point D 88 43', and
from B to point C 212 43', and to point D 272 18' 30". The
actual readings can be noted, and then the arrangement of the
lines and angles sketched out as shown in Fig. 35, from which
it will be necessary to find the lengths AC and AD. As the
three angles of a triangle equal 180 , the angle B C A = 180 -
147 17'-29 23'= 3 20', the angle B D A = 180 -87 41' 30"-
88 43'= 3 35' 30". In any triangle the sides are
proportionate to the sines of the opposite angles, and vice
versa; therefore,
A B : A C :: sin B C A : sin A B C, or sin B C A : A B :: sin
ABC : A C, nr A C = (A B sin A B C) / (sin B C A) = (117 x sin
147 17') / (sin 3 20')
or log A C = log 117 + L sin 147 17' - L sin 3 20'.
The sine of an angle is equal to the sine of its supplement, so
that sin 147 17' = sin 32 43', whence log A C = 2.0681859 +
9.7327837-8.7645111 = 3.0364585
Therefore A C = 1087.6 feet.
Similarly sin B D A: A B :: sin A B D: A D
A B sin A B D 117 x sin 87 41' 30"
therefore A D = --------------- = -----------------------
sin B D A sin 3 35' 30"
whence log A D = log ll7 + L sin 87 41' 30" - L sin 3 35' 30"
= 2.0681859 + 9.99964745 - 8.79688775
= 3.2709456
Therefore AD = 1866.15 feet.
The length of two of the sides and all three angles of each of
the two triangles A C B and A D B are now known, so that the
triangles can be drawn upon the base A B by setting off the
sides at the known angles, and the draughtsmanship can be
checked by measuring the other known side of each triangle. The
points C and D will then represent the positions of the two
landmarks to which the observations were taken, and if the
triangles are drawn upon a piece of tracing paper, and then
superimposed upon the ordnance map so that the points C and D
correspond with the landmarks, the points A and B can be
pricked through on to the map, and the base line A B drawn in
its correct position.
If it is desired to draw the base line on the map direct from
the two known points, it will be necessary to ascertain the
magnitude of the angle A D C. Now, in any triangle the tangent
of half the difference of two angles is to the tangent of half
their sum as the difference of the two opposite sides is to
their sum; that is:--
Tan 1/2 (ACD - ADC): tan 1/2 (ACD + ADC)::
AD - AC : AD + AC,
but ACD + ADC = l80 - CAD = 120 40',
therefore, tan 1/2 (ACD - ADC): tan 1/2 (120 40')::
(1866.15 - 1087.6): (1866.15 + 1087.6),
778.55 tan 60 20'
therefore, tan 1/2 (ACD - ADC) = --------------------
2953.75
or L tan 1/2 (ACD - ADC) = log 778.55 + L tan 60 20'
- log 2953.75 .
= 2.8912865 + 10.2444l54 - 3.4703738
= 9.6653281 .•. 1/2 (ACD - ADC) = 24 49' 53"
.•. ACD - ADC = 49 39' 46". Then algebraically
(ACD + ADC) - (ACD - ADC)
ADC = ---------------------------
2
120 40' - 49 39' 46" 71 0' 14"
.•. ADC = ------------------------- = ------------ = 35 30' 7",
2 2
ACD = 180 - 35 30' 7" - 59 20' = 85 9' 53".
[Illustration: Fig. 35.--Arrangement of lines and Angles
Showing Theodolite Readings and Dimensions.]
Now join up points C and D on the plan, and from point D set
off the line D A, making an angle of 35 30' 7" with C D, and
having a length of l866.15 ft, and from point C set off the
angle A C D equal to 85 9' 53". Then the line A C should
measure l087.6 ft long, and meet the line A D at the point A,
making an angle of 59 20'. From point A draw a line A B, ll7
ft long, making an angle of 29 23' with the line A C; join B
C, then the angle ABC should measure 147 17', and the angle B
C A 3 20'. If the lines and angles are accurately drawn, which
can be proved by checking as indicated, the line A B will
represent the base line in its correct position on the plan.
The positions of the other stations can be calculated from the
readings of the angles taken from such stations. Take stations
E, F, G, and H as shown in Fig. 36*, the angles which are
observed being marked with an arc.
It will be observed that two of the angles of each triangle are
recorded, so that the third is always known. The full lines
represent those sides, the lengths of which are calculated, so
that the dimensions of two sides and the three angles of each
triangle are known. Starting with station E,
Sin A E D: A D:: sin D A E: D E
A D sin D A E
D E = --------------
sin A E D
or log D E = log A D + L sin D A E-L sin A E D.
From station F, E and G are visible, but the landmark D cannot
be seen; therefore, as the latter can be seen from G, it will
be necessary to fix the position of G first. Then,
sin E G D: D E :: sin E D G : E G,
D E sin E D G
or EG= ---------------
sin E G D
Now, sin E F G: E G :: sin F E G : F G
E G sin F E G
F G = -------------
sin E F G
thus allowing the position of F to be fixed, and then
sin F H G : F G :: sin F G H : F H
F G sin F G H
F H= -------------
sin F H G
[Illustration: FIG 36.--DIAGRAM ILLUSTRATING TRIGONOMETRICAL
SURVEY OF OBSERVATION STATIONS.]
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