Telenary

SOURCES OF ERRORS IN LINEAR MEASUREMENT AND CORRECTIONS There are various sources of errors in making direct linear measurement and those errors must be examined for their cause and effect so that precaution may be taken to guard against unacceptable errors. However , errors are of three kinds. 1. SYSTEMATIC OR CUMULATIVE ERRORS: These errors exist in any survey measurement and each additional measurement increases the effect of the errors such errors which maybe either positive or negative can be an appreciable effect but the effect can be reduced by taking enough precautionary measures or by the application of corrections to the observed measurement. • The six sources of this type of error are as follow: 1. Wrong length of tape 2. Poor ranging 3. Poor straightening/ alignment 4. Slope 5. Sag 6. Temperature 2. COMPENSATION OR ACCIDENTAL ERRORS: Although every precaution maybe taken, certain unavoidable errors always exist in any measurement. Such errors are generally of less importance than systematic errors. As they are sometimes positive and sometimes negative they tend to cancel out in the long run. • There are two sources of this types of errors: i. Holding and marking ii. Variation in tension 3. GROSS ERRORS: These are errors that arise as a result of mistakes, carelessness or lack of experience. They are quite random and allowance cannot be made for them. • The four source of mistake are: i. Displacement of arrows ii. Displacement of station marks iii. Miscounting tape length iv. Misreading the tape • CORRECTIONS TO DISTANCE MEASUREMENT: Different method and formula are adopted in the correction of error in distance measurement according to the source of such error, they are as follows: 1. EFFECT OF WRONG LENGTH OF TAPE This is the most serious of errors, particularly with a chain because of its tendency to stretch. Chain and fiber tapes should be tasted frequently, steel bands need testing less frequently but should always be tested for precise work or after ant repairs. However, measurement made with a tape found to be in error can be corrected using the formula: True Distance = Actual Length of Tape Measurement Distance Nominal Length of Tape Where Area calculations made from measurement which are in error they can be corrected using the formula: True Area = Actual Length of Tape Measured Area Nominal Length of Tape 2. POOR RANGING: This gives rise to a relatively small error, if a whole tape length deviated a distance from the ranged straight line the error in length is d2/2L Where L is the length of tape and d is distance measured. 3. POOR ALIGNMENT: The effect is similar to that of poor ranging but if both ends of the tape are on the correction line and the center is off by a distance, the effect is greater being 2d2/1 or twice the errors arising in each half of the tape . 4. SLOPE; Although the effect of slope is similar to that of poor ranging but the vertical plane it can be the source of large errors. The correction is given by L(1-cos 0). Where 0 is the angle of slope and L is the length of the line. For difference in height between two points, the slope correction is given as. Δh2 2L Where L = Distance between the two points. 5. SAG: When a tape is suspended as in step chaining or when measuring over rough ground the unsupported part will sag given an observed reading which will be great the amount of error caused by sag is proportional to W2L3cos20 24T2 Where: w = weight of the tape per meter length in Newtons or kilogramme force. T = tension applied to the tape in the same unit weight. L = Length of tape between supports 0 = The angle of slope between tape supports. And it increases at the cube of the suspended length. 6. TEMPERATURE VARIATION: The effect of temperature variation is negative in work where a chain is used. For precise measurement a steel band temperature correction must be made. Therefore the error = L×C×T Where L = measured length C = Coefficient of expansion T = temperature difference from standard 7. VARIATION IN TENSION: The tension applied to a tape should be the same as that applied when testing it against a standard variation. Tension are bound to occur even when using a spring balance, but the resulting errors are small and tend to compensate each other, if the tape is consistently pulled too hard or too lightly a cumulative error will arise and this should be guided against particularly when using lines or plastic tapes. The formula is given as: Correction = L ( TF - TS ) AE Where TF = Tension applied to tape(N) TS = Standard Tension (N) L = Tape length under tension in meters. A = Cross-sectional area of the tape (mm2) E = Young modulus of elasticity for the tape material (Nmm2) ( for steel tape is 200,000N mm-2 or 200 KN/mm-2).