INTRODUCTION:
While taking a turn, the centrifugal forces develop so a vehicle
and its contents are immediately subjected to centrifugal forces.
More is the speed of vehicle sharper is the curvature and thus the
greater the influence on vehicles and drivers of the change from
tangent to curve. When transition curves are not provided, drivers
tend to create their own transition curves by moving laterally
within their travel lane and sometimes the adjoining lane, which is
risky not only for them but also for other road users. For faster
roads, spiral transition curves are used to affect a gradual
increase of the lateral acceleration or sideways force felt by the
occupants of a moving vehicle, and the steady application of super
elevation, the tilting of the road surface to help prevent vehicles
running off the curve. These curves, together with parabolic
vertical curves, are dealt with in a later set of notes. This
fieldwork which entitles lying of a simple curve by transit and the
tape by incremental and deflection angle method teaches on how to
use a theodolite on curves and chords. This fieldwork also has
different formulas to memorize in getting the curve. In order to
get the curve we have 5 steps found in the procedures area.
OBJECTIVES:
1. To acquire the knowledge in getting the curve by Different
formulas.
2. To develop the technical know-how to use theodolite.
3. To apply the value of teamwork to simplify the organization
of the jobs/role.
4. To improve analysis of finding the curve.
5. To apply the value of excellence and patience in measuring
the curve.
PROCEDURES: The professor gives the following data:d1=
_______D=_______let I=d1 + 4DLength of Spiral= _________
Compute the elements of the spiral curve given the data above
referring to the computations section.
*NOTE: The radius of the simple curve will be the radius of the
spiral curve and also the same for the value of the angle of
Intersection.
Set the transit at the designated point PI on the site. Level
and orient the transit at the magnetic south while vernier A is at
zero reading.
Sight the location of PC along the given direction of the back
tangent using a range pole. Using the tape, locate the position of
PC. The distance of PC to PI is the length of the tangent line of
the simple curve which is shown in the computations section.
Invert the telescope and rotate it following the measurement of
the computed I to locate the direction of the forward tangent.
Along this forward tangent, locate the position of PT which is
also at a distance of Tangent from PI.
Exactly along the back tangent, also locate the position of TS
which is the point where the tangent line meets the desired
transition spiral curve. The distance from PI to Ts is shown in the
computations section.
Follow the same procedure to locate ST which is the point where
the spiral meets the forward tangent.
Then lay the incremental chord and its corresponding incremental
deflection angle with respect to the Back Tangent.
Do the same on the other side of the simple curve. Due to
symmetry equal, the data used in the first side will be the same on
the other side.
COMPUTATIONS:When dealing with spiral curves, it is important to
always know the description of the simple curve because this two
are inseparable. That is why in the computation section, I will
include the formulas used for the simple curve.
If the azimuth of the backward and the forward tangents are
given, the intersection angle I can be solved using:
The tangent distance must be solved using:
The middle ordinate distance (M) can be computed using:
The length of the curve (Lc) can be computed using:
The station of PC can be computed using:
The station of PT can be found by:
The length of the first sub chord from PC, if PC is not exactly
on a full station (otherwise C1= a full chord length)
The length of the last sub chord from PT, if PT is not exactly
on a full station (otherwise C2= a full chord length)
The value of the first deflection angle d1:
The value of the last deflection angle d2:
Incremental Chord and Tangent Offset Method
The tangent offset distance x1 must be solved using:
The tangent offset distance y1 must be solved using:
The tangent offset distances x2 must be solved using:
The tangent offset distance y2 must be solved using:
The tangent offset distance x3, must be solved using:
The tangent offset distance y3 must be solved using:
The tangent offset distance xn, must be solved using:
The tangent offset distance yn, must be solved using:
The formula of finding the percentage error:
For Spiral Curve:The formula for finding the radius:
The formula for finding :
The formula for finding Xs:
The formula for finding Ys:
The formula for finding the Lc:
The formula for finding the ST:
The formula for finding the LT:
The formula for finding the deflection angle ():
The formula for finding P:
The formula for finding the Ts:
To find the stationing of TS:
To find the stationing of SC:
INTSTURMENTS:
THEDOLITETheodolite is a precision instrument for measuring
angles in the horizontal and vertical planes. A modern theodolite
consists of a movable telescope mounted within two perpendicular
axesthe horizontal axis, and the vertical axis. When the telescope
is pointed at a target object, the angle of each of these axes can
be measured with great precision, typically two seconds of arc.
RANGE POLESA range pole, which may also be called a lining pole,
is a pole painted with alternating stripes of different colors in
consistent widths used often to site measurements. The tool may be
a common one for surveyors, where the colors for the stripes are
usually red and white or red and yellow.
CHALKA chalk is a soft, white, porous sedimentary rock, a form
of limestone composed of the mineral calcite. This is used in
marking measurements on ground.
A tape measure or measuring tape is a flexible form of ruler. It
consists of a ribbon of cloth, plastic, fiber glass, or metal strip
with linear-measurement markings. It is a common measuring
tool.
TAPE MEASURE
SKETCH:
FINAL DATA SHEETFIELD WORK 7LAYING OF A SPIRAL EASEMENT CURVE
USING TRANSIT AND TAPEDATE: February 26, 2013GROUP NO. 10TIME:
12:00 pm 4:30 pmLOCATION: MIT Parking SpaceWEATHER: SunnyPROFESSOR:
Engr. Cervantes
DATA GATHERED:I= 50Length of Spiral Curve: 500 ftD= 5
STATIONINCREMENTAL CHORDINCREMENTAL DEFECTION ANGLE
BASISOBSERVED
TS7 + 13.825 5004 10
7 + 00486.1753 56 21.97
6 + 50436.1753 10 14.92
6 + 00386.1752 29 7387
5 + 50336.1751 53 0.83
5 + 00286.1751 21 53.77
4 + 50236.1750 55 46.72
4 + 00186.1750 34 39.67
3 + 50136.1750 18 32.62
3 + 0086.1750 7 25.57
2 + 5036.1750 1 18.52
2 + 13.82500
DISCUSSION:
In this fieldwork, we are tasked to lay a spiral easement curve
with the use of the transit and tape using the method that we
always used since the laying of our field work number one which is
all about the simple curve. The method that I was talking about is
the Deflection angle Method. The difference that this fieldwork has
compared to the other fieldwork is that, the spiral curve is a
curve to be layout in an existing curve; the existing curve could
be a simple, compound, or reverse. After we had layout this so
called spiral curve, I have now appreciated why some curving roads
are sometimes sharp and hard to maneuver it. It is because of the
characteristic of the spiral curve base on the computed values and
the design made by the engineer. Since the simple curve is
inter-related to the spiral curve, our professor gives us the
following data that describes the simple curve.
Based on the description of the simple curve, we layout a spiral
curve that fits the simple curve. Of course, before going to the
field and as a lesson learned from our previous fieldworks, we
computed first for the needed values in order to layout the spiral
curve. Since we are very conversant with the application of the
deflection angle method, the fieldwork becomes bread and butter to
our group. It is also an advantage wherein all of the members of
the group know how to manipulate each instrument that is used when
laying a curve especially the theodolite which is needed always
when using the deflection angle method. In here, the possible
source of error is the correctness of the angle measured in the
theodolite because once the user divert the measurement into
minutes or even in seconds, it will have great effect on the
measured description of the whole curve. Since we did the fieldwork
correctly, we only have an error of less than one meter on each of
the two chords. It is because we made sure that every measurement
that we made is accurate.
CONCLUSION:
In this fieldwork, we are tasked to layout a spiral easement
curve on an existing reverse curve. Since the curves are different
in usage and in design, it has the same characteristic since the
two are inter-related. It is important to remember each and
everything about the simple curve because practically, it is always
the start of a more complex curve. We still apply the theory and
procedures that we used when we are laying out a simple curve using
the deflection angle method. We just computed the data that will be
needed to describe and layout the spiral curve and then proceed to
the field to do what we do best. We are aware that the possible
errors that we might encounter are from accurate measurement of the
instruments so we are resilient on that especially on the tape and
the theodolite which serves as the primary instruments in the said
method. We met all the objectives that the manual is requiring us
because of our team effort and for our hunger of excellence. We are
able to master the use of the instruments needed in laying out a
curve specifically the theodolite and the tape. We are also able to
improve and practice more the procedures and knowledge about the
deflection angle method which is for me, the basic and the easiest
method of all. Each time we layout a curve, it gets tougher and
tougher in the sense that we are introduced to a new kind of curve.
But basically, the concept and theories are still the same so the
matter of execution stands out. As long as you know the process and
the variation of a simple curve, there will be no problem on the
complex type of curve such as this reverse curve.
RELATED RESEARCH:Spirals are used to overcome the abrupt change
in curvature and super elevation that occurs between tangent and
circular curve. The spiral curve is used to gradually change the
curvature and super elevation of the road, thus called transition
curve.
Elements of Spiral Curve TS = Tangent to spiral SC = Spiral to
curve CS = Curve to spiral ST = Spiral to tangent LT = Long tangent
ST = Short tangent R = Radius of simple curve Ts = Spiral tangent
distance Tc = Circular curve tangent L = Length of spiral from TS
to any point along the spiral Ls = Length of spiral PI = Point of
intersection I = Angle of intersection Ic = Angle of intersection
of the simple curve p = Length of throw or the distance from
tangent that the circular curve has been offset X = Offset distance
(right angle distance) from tangent to any point on the spiral Xc =
Offset distance (right angle distance) from tangent to SC Y =
Distance along tangent to any point on the spiral Yc = Distance
along tangent from TS to point at right angle to SC Es = External
distance of the simple curve = Spiral angle from tangent to any
point on the spiral s = Spiral angle from tangent to SC i =
Deflection angle from TS to any point on the spiral, it is
proportional to the square of its distance is = Deflection angle
from TS to SC D = Degree of spiral curve at any point Dc = Degree
of simple curve
The introduction of the circular curve at the PC takes place at
a point but drivers and vehicles do not make directional changes
instantaneously.It is also common practice in constructing curves
on highways to tip or super elevate the pavement downward toward
the inside of the curve to aid in the riding quality and safety for
vehicles navigating the curve. Again it is not practicable or
advisable to introduce the super elevation instantaneously. If
introduced on the tangent where it is not needed, the driver must
steer into it slightly with a negative steering angle. If
introduced all on the curve some area of negative super elevation
will generally result or the introduction will be done so quickly
that both the riding quality and the visual attractiveness of the
highway suffer.A solution is to introduce both the curvature and
super elevation at a gradual rate using an easement curve that
gradually changes in radius from infinity to some finite value
where the associated circular curve begins. In short, a spiral
curve is required. There are a number of identifiable curves that
spiral, but their mathematical differences do not affect their
usefulness on highways.The geometry of the spiral curve is more
rigorous that that of the circular curve and handbook tables are
the usual way of working out the deflection angles needed to lay
out a spiral curve in the field. The discussion has been worked out
with reference to Route Location and Design, 5th ed., Hickerson,
Thomas F., New York: McGraw-Hill, 1964, for the appropriate
tables.The spiral curve element generally selected by the designer
is the length of the spiral "ls". The choice is usually made to
introduce super elevation slowly enough so as not to exceed certain
relative slopes between pavement edge and centerline grades. As a
minimum, spiral curve lengths should not be shorter than the
distance covered in two seconds at highway design speed.
REFERENCES:
http://surveying.askdefine.com/(www.surveying.askdefine.com)
http://en.wikipedia.org/wiki/Surveying\(www.wikipedia.com)
http://lecture.civilengineeringx.com/surveying/total-station/(www.cilivilengineeringx.com)
http://blog.enggroupe.com/modern-surveying-equipment/
http://cereview.info/book/surveying/formulas-circular-curves
CE121F | FIELD WORK NO. 72