Set the transit at PC. Level and orient the transit at the magnetic south while fernier A is at zero reading. Sight the location of vertex VI following the given direction of the back tangent TTL and mark the location on the ground at a distance TTL from PC. Set the horizontal fernier to zero again and start locating intermediate points of the curve until your reach PC using incremental chord lengths and their deflection angle from the backward tangent. Upon reaching PC, transfer the instrument at PC.
Again level the instrument and with the telescope inverted position, sight the VI . After locating VI, plunge the telescope into normal position and locate VI which is along the line from VI to PC, and at a computed distance TO from PC. Mark VI with chalk. Once again, set the horizontal fernier A at zero reading while sighting the position of VI. Using the incremental chord lengths and their deflection angles, lay intermediate points of the second curve on the ground until you reach OPT.
Many groups, including transportation agencies, accident investigators and transportation researchers, would find an accurate, quick and safe method to estimate the radius of horizontal curves particularly useful. The radius estimating methods were as follows: Basic ball bank indicator (BIB) Advanced Basic ball bank indicator Chord length Compass Field survey Global Positioning System (GAPS) unit Lateral acceleration Plan sheet Speed advisory plate and Vehicle yaw rate But in this research, you will only have a glimpse of the last three methods.
Plan sheet method: The plan sheet method determines the radius of a curve by using information provided ones-built plan sheets, which are accessible at local transportation offices. Plan sheets contain information such as location of PC and OPT, deflection angle and engage length for all horizontal curves. The information provided on plan sheets is usually the as built information. From this information, each curve radius was calculated. The required information found on the plan sheets was the location of the start of the curve (PC), the end of the curve (OPT) and the degrees of turn of the curve C).
This information was input into the following curve radius-estimation equation and the radius of the curve was calculated as follows (Carlson et al. , 2005): Advisory speed plate method Advisory speeds for curves have been determined in the field by making several trial nuns through the curve at different speeds in a test-vehicle equipped with a ball- bank indicator. The ball-bank reading indicates overturning forces on the vehicle and is a combined measure of the centrifugal force, vehicle roll and super elevation.
The generally accepted criteria for setting advisory speeds are ball-bank readings of 14 deg for speeds below 20 MPH, 12 deg for speeds between 20 and 35 MPH and Diodes for speeds of 35 MPH or greater. 4 These criteria are based on tests conducted in the sass that were intended to represent the 85-90th-percentile curve speed. 5. Another method used to determine the advisory speed is using the monograph in the Traffic Control Devices Handbook (TECH) which utilizes the following standard curve formula: at which discomfort begins for an average rider in a 1930 vintage car.
This factor may not be valid for modern vehicles. The side friction factors recommended in the design criteria of the American Association of State Highway and Transportation Officials (SHASTA) vary from 0. 17 at low speed to 0. 10 at the highest speed. 7 However, these values also are based on tests conducted in the sass and represent he limit at which a rider will notice a “side pitch” and begin to feel some discomfort. The ball-bank readings of 14 deg 12 deg and 10 deg were found in these earlier studies to correspond to side friction values of 0. 1, 0. 18 and 0. 15, respectively. The friction factors used in current criteria do not reflect the maximum safe speed but rather an average comfortable speed. Modern cars on dry pavement are capable of generating friction coefficients of 0. 65 and higher before skidding. 8 Friction coefficients of 0. 40 and higher are typical on wet pavements. Thus, a curve designed or 70 MPH could be driven well over 100 MPH before it skidded out. Modified yaw rate method The modified yaw rate method is a measure of the deflection angle of the curve.
With the same roll rate sensors, only this time mounted in an inverted position, the deflection angle of the curve was measured as the test vehicle traversed the highway. The data acquisition unit (in this case a VICTIM) simultaneously recorded the yaw rate (degrees per second) and the distance traveled along the curve. Essentially, the modified yaw rate method is an automated version of the compass method; however, he compass method required additional time and exposed the field crews to potential hazards and along the road (Carlson et al. 2005). The lateral accelerometer also allowed the researchers to place one of the roll-rate sensors in an inverted position such that it would act as a pseudo yaw rate transducer and record the deflection of the curve while the lateral accelerometer simultaneously measured the distance traveled along the curve. Although the same data can be obtained by walking the curve with a handheld compass and a measuring wheel, the latter approach requires additional time and exposes the field crews to potential hazards on and along the road.
COMPUTATIONS: 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 solve using: The middle ordinate distance (M) can be computed using: The length of the curve (LLC) can be computed using: The station of PC can be computed using: The station of OPT can be found by: (otherwise CLC= a full chord length) The length of the last sub chord from OPT, if OPT is not exactly on a full station (otherwise CA= a full chord length)
The value of the first deflection angle del : The value of the last deflection angle do: Incremental Chord and Tangent Offset Method The tangent offset distance XSL must be solved using: The tangent offset distance yell must be solved using: The tangent offset distances xx must be solved using: The tangent offset distance Y must be solved using: The tangent offset distance xx, must be solved using: The tangent offset distance y must be solved using: The tangent offset distance axon, must be solved using: The tangent offset distance yen, must be solved using: The formula of finding the percentage error:
DISCUSSION Fieldwork no. 5 was all about laying of a compound curve using transit and tape. This using transit effectively, and to learn how to work hand in hand with our group mates but the main objective of this fieldwork is to be able to lay a compound curve by incremental chords and deflection angle method. What we had to do in this fieldwork is to simply lay out a compound curve, which was explained to be a curve made up of two or more circular arcs of successively shorter or longer radii, Joined tangentially without reversal of curvature.
And by the use of the data given to us by our professor, e computed for the other elements of the curve before going to the field area. We followed the procedure properly and carefully so we could commit lesser error, but the weather, intense heat, gave us a hard time performing the experiment. We have conducted our experiment at Intramural walls around 9 a. M. Onwards. Discrepancies were found after we have gathered all the necessary data and some factors like the orientation of the transit, mistake in measuring and so forth can be considered as reasons as to why there were minimal errors in the results.
Our group made sure hat we make our measurements as accurate as possible, we worked hand in hand to be able to finish the activity properly and correctly. By laying out the first curve After laying out the from the point of curvature to the point of tangency of the first curve we connect the point of curvature of the second curve on the point of tangency of the second curve and calling it point of compound curve. For us to lay out the curve quickly we think of the most convenient scale. We chose the 1:20 scale.
The idea of scaling would diminish our effort in measuring as well as reducing the errors that ay occur because measuring lengths or distances using the tape create potential errors. CONCLUSION: After performing this particular field work, I can say that we were able to achieve the objectives or goals as to why we performed the said experiment. We were able to use our knowledge from our previous surveying fieldwork like laying out simple curves, they are actually the same, the only difference is that we have 2 radii in compound curves.
I therefore conclude that this fieldwork was successfully and properly accomplished because our group was able to develop cooperation and how to work and in hand. Our chief of party made sure that we all did something to contribute in this particular fieldwork. I commend our leader for showing great attitude in handling us, we had a healthy and light environment despite of the very hot weather.
We were also able to master our skills in using the transit, as we continuously use the transit, we understand better how it works that made our activity less complicated because we were already familiar with it. Lastly, we have successfully laid out a compound curve using the incremental and deflection method. Errors were experienced such as error due to sag of the tape, and as measuring beyond, the direction of the curve becomes confusing that’s an additional grounds of error.
In the midst of this inspection, we could utter that this technique is prone to mistakes and errors. We had to take extra care in order to lessen the errors but at the end of the fieldwork, after computing all the data needed, we have obtained 0. 09%, 0. 09% and 0. 14% for chord 1, chord 2 and the length of the curve respectively. Overall, I say that we have surpassed this fieldwork properly and correctly considering our very minimal errors. The incremental chord and deflection angle use of this method we can properly lay out curves without getting large amount of errors.
The concept of this fieldwork is easy to understand only if you follow the procedure correctly and properly. RELATED RESEARCH A compound curve consists of two (or more) circular curves between two main tangents Joined at point of compound curve (PC). Curve at PC is designated as 1 (RI, L 1, T 1, etc) and curve at higher station is designated as 2 (RE, LA, TO, etc). 0 Elements of compound curve PC = point of curvature OPT = point of tangency PI = point of intersection
PC = point of compound curve TTL = length of tangent of the first curve TO = length of tangent of the second curve VI = vertex of the first curve VI = vertex of the second curve II = central angle of the first curve 12 = central angle of the second curve I = angle of intersection = II + 12 LLC = length of first curve LLC = length of second curve Al = length of first chord LA = length of second chord L = length of long chord from PC to OPT TTL + TO = length of common tangent measured from VI to VI 1800-1 x and y can be found from triangle VI-VI-Pl.
L can be found from triangle PC-PC-OPT Finding the stationing of OPT Given the stationing of PC Given the stationing of PI In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar too line but which is not required to be straight. This entails that a line is a special case of curve, namely a curve with null curvature. Often in two dimensional (plane curves), or three-dimensional (space curves), Euclidean different meanings depending on the area of study, so the precise meaning depends on context.
However many of these meanings are special instances of the definition which follows. A curve is a topological space which is locally homeomorphism to a line. In every day language, this meaner that a curve is a set of points which, near each of its points, looks like a line, up to a deformation. A simple example of a curve is the parabola, shown to the right. A large number of other curves have been studied in multiple mathematical fields.
The term curve has several meanings in non- mathematical language as well. For example, it can be almost synonymous with mathematical function (as in learning curve), or graph of a function (as in Phillips curve). An arc or segment of a curve is a part of a curve that is bounded by woo distinct end points and contains every point on the curve between its end points. Depending on how the arc is defined, either of the two end points may or may not be part of it.
When the arc is straight, it is typically called a line segment. The distinction between a curve and its image is important. Two distinct curves may have the same image. For example, a line segment can be traced out at different speeds, or a circle can be traversed a different number of times. Many times, however, we are Just interested in the image of the curve. It is important to pay attention to context and convention in reading.