Errors in Linear Measurement | Instrumental Errors in Linear Measurement

Errors in Linear Measurement

What is Linear Measurement?

Linear measurement is the measurement of this linear horizontal distance between two places on the earth’s surface.

Surveying studies assist us in determining the relative position of points, the height of buildings without actually measuring the settlement, and so on. It is usually done prior to the construction of a building.

During an engineering survey, linear and angular measurements are equally significant. Bearing, rotation, and other angular measurements are used, whereas distance is a linear measurement.

Errors in Linear Measurement Categories

There are numerous things that we refer to as errors. We also use a variety of different names to describe this.

The core difficulty is that we can never know the true value of any measured quantity, therefore the value we choose is always subject to some uncertainty.

We can try a variety of strategies to reduce our errors, but we will never be able to eliminate them.

We can categorize errors into three types for the purposes of working with them:

  • Gross
  • Systematic
  • Random

Rather than any other feature of their character, this divide is dependent on what causes the errors and how we deal with them. Other classification techniques exist, but this one is both thorough and useful.

Gross Errors

Gross Errors are also referred to as “blunders.” They can be of any size or shape, and they are usually the result of negligence.

Writing down the incorrect value, reading the instrument improperly, and measuring to the wrong mark are all examples of serious errors.

They can be caused by humans, machines, weather, and a variety of other factors. We deal with major mistakes by following strict protocols and constantly double-checking our work.

Systematic Errors

Systematic errors are those that we can mathematically model and thus correct. They are caused by the mathematical model of the technique we are utilizing not matching what is happening in the real world.

We reduce and calculate with measurements based on models, and there will be inconsistencies if the models are not complete.

For example, if we measure a distance without accounting for the slope of the tape, we will have a systematic mistake that can be minimized if we utilize the proper measurement process model.

We can eliminate, or at least reduce, systematic mistakes through meticulous labor, the use of the proper model for the process at hand, and the application of checks that detect.

Systematic errors in measurements. It is important to note that checks that employ the same measurement methodologies may miss some systematic mistakes, therefore devising methods for detecting systematic errors requires some ingenuity.

Random Errors

Random errors are ones that have no obvious source but are a result of the measurement procedure itself.

All measurements must be performed to some degree of precision, and we cannot anticipate the exact measurement we will acquire.

Random errors, on the other hand, have highly distinct statistical behavior and may thus be dealt with statistically.

Random errors are the minor discrepancies between repeated measurements of the same quantity, which are frequently of the order of the finest division in the measuring scale.

We can eliminate or reduce the consequences of random errors using statistical processes, such as using the mean of a collection of observations as the value to be used in subsequent calculations.

With the understanding that errors are present in all of our measurements and activities, we can now look at one measurement procedure and observe how errors affect it.

We’ll start with linear measurements, such as those made with tapes and other tools like EDM.

Instrumental Errors in Linear Measurement

They include:

Length other than standard

Tape makers do not guarantee that 100 ft. steel tapes are exactly 100.00 ft. in length. Every time the tape is used, an error due to the improper length occurs.

Temperatures that are not typical

Steel tapes are standardized at a temperature of 68° F (20° C).

The length of the tape will alter when the temperature rises or falls. The temperature of the tape can differ significantly from the temperature of the measured air.

This can be verified using;

  • In this case, a = coefficient of thermal expansion
  • Tm stands for mean-field temperature.
  • To = temperature of the calibration
  • L = length as measured
  • Positive adjustment is made if Tm>To.


If the strain is higher than normal, the tape will stretch. When less than standard tension is used, the tape will be shorter than usual.

This can be corrected by:

  • Cp=(P-Po) L/Aε
  • Where P denotes the applied pull
  • Po stands for standard pull.
  • L = length as measured
  • A = cross-sectional area
  • Young’s Modulus = ε
  • Positive correction is used if P>Po.

Incorrect Chain Length

There could be some inconsistency in the production of the chains. The chain’s length is not always accurate. As a result, every time the chain is used, there may be an error owing to the erroneous length.

We can apply correction factors to prevent this type of inaccuracy.

  • Actual length = measured length multiplied by the adjustment factor
  • Actual length = Measured length + Actual chain length/Incorrect chain length

A positive correction is done if the actual chain length is greater than the wrong chain length.


A tape that is not supported all the way along its length will sag. Sag can be reduced by applying the proper tension.

This can be fixed by saying;

  • Cs=L/24(W/T) ²
  • where L denotes the measured length
  • W denotes the chain’s weight.
  • T is an abbreviation for tension/pull.

If the chain is not securely held, it sags. The correction that has been done is negative.

Inadequate alignment

This error occurs when one end of the tape is disconnected or when there is an impediment in the path. The real distance will be shorter than the measured distance.

Inaccurate marking

This issue occurs at random as a result of incorrectly placed chaining pins. Errors can be reduced by carefully placing chaining pins and then double-checking the measurement.

Improper reading or interpolation

When reading or noting the measurement clearly or in a hurry, the inaccuracy occurs. Errors can be reduced by reading carefully and using a tiny scale to obtain the final value.

Corrections of Errors in Linear Measurements

Gross errors are often the easiest to correct. We can mathematically treat them as zero by using the average of several data sets.

Systematic errors can be corrected by modifying the mathematical model and properly applying valid checks.

Random errors are also reduced by carefully collecting a series of data and performing a statistical analysis on the mean value.


When you make a measurement, it is important to understand that there are several errors that can occur, and even if you understand the methodologies used to reduce them, you cannot anticipate the errors that will be present.

When a measurement process is followed correctly, we can minimize systematic and random errors.

Even if we have done so properly, however, it is important to recognize that there are still some sources of errors in the measurement process.

We must continually be conscious of the limitations and possible sources of error in our measurements as we use them to better understand their context.


How can errors in linear measurement be reduced?

Errors can be reduced by carefully placing chaining pins and then double-checking the measurement.

When reading or noting the measurement clearly or in a hurry, inaccuracy occurs. Errors can be reduced by reading carefully and using a tiny scale to obtain the final value.

What are the four types of measurement error?

Instrumental error, excessive error, error due to external reasons, and error owing to flaws are the four sources or forms of systematic error.

What are the four sources of measurement error?

Errors that cannot be eliminated through the mathematical treatment of data are known as residual errors. Residual errors can only be reduced by improving the instrumentation used for measurements and by improving in the methodology.

How can systematic errors be reduced or minimized?

Errors that occur from one source to another as a result of improper measurement procedures can be reduced through careful attention to detail, proper monitoring, and increased discipline.

How can random errors be reduced or minimized?

Errors that occur from natural causes are known as random errors. Random errors can be reduced by carefully collecting the data and applying statistical analysis.

How is an instrument error corrected?

By using a ratio of values, an instrument error can be corrected. If the ratio between two sets of data differs from the true ratio by a certain amount, the same correction factor that is applied to one set should also be applied to the other set.

What are numerical data and graphic data?

Numerical data is the raw data obtained by counting the number of units in a set. Graphic data is the mathematical representation of numerical data in the form of charts or graphs.

How can you ensure that a survey measurement is free of mistakes?

Follow the fundamental administrative principles.

  • Clarify the “key players” in the region and nationally, and be sure to seek methods to collaborate with them to avoid the possibility of “spoilers.”
  • Perform pre-testing on all questionnaires.
  • Understand the data collection process fully, from beginning to end.
  • Understand the region’s climate and geography.
  • Perform pilot tests in rural areas.
  • Clarify the purpose of data collection and its uses among relevant agencies and organizations.

Why are measurement errors important?

When a measurement has an error, it can greatly affect the quality of the information collected. When a measurement is incorrect, it can give rise to many issues that influence the quality of decision-making.

When a measurement is inaccurate, it will not result in a much higher value than other measurements that are flawed.

What is the difference between error and mistake in survey?

Mistakes are frequently referred to as big errors, yet they should not be considered errors at all. They are errors, frequently caused by exhaustion or an untrained surveyor.

The fact that these inaccuracies may be calculated allows the surveyor to compute and then apply a correction to the measurement to decrease its influence.

Can errors be prevented?

The errors that can be prevented most easily are those that arise in the process of measurement. By using high-quality equipment, by paying careful attention to the instructions, and by following proper procedure, it is possible to prevent these types of errors.

What is the difference between measurement error and statistical error?

Measurement error occurs as a result of an incorrect reading; this can be attributed to a mistake made by an individual in data collection or the method used for measurement.

The statistical error occurs as a result of the difference between the actual population value and the one predicted by a mathematical model. This difference can be caused by any number of causes, such as errors in algorithms and data collection.

What is the arithmetic mean?

An arithmetic mean is the average of all values in a set divided by their sum.

What is the median?

The median is one value in a set that divides it into two equal halves: half values below it and half values above it.

What is linear measurement?

Linear measurement is the process of collecting information about two-dimensional items, like the height and width of an object.

What is round-off error?

Round-off error occurs as a result of inaccurately reducing measurements to whole numbers by ignoring the decimal points.

What are the 3 sources of survey error?

The decomposition entails dividing the overall difference into four components, three of which are well-known flaws in survey-based estimates: coverage error, sampling error, and nonresponse error.

What is true error in surveying?

A genuine mistake is the discrepancy between a quantity’s real value and its observed value.

What is sampling error?

Sampling error occurs as a result of the differences between the characteristics of the individuals in a population and those in the sample.

This discrepancy can be assessed by comparing results with those found by other surveys or administrative data. In case there is no comparison, researchers often use statistical models to predict how much sampling errors might differ from what they actually are.

What is an accidental error in the survey?

Accidental errors are those that persist after mistakes and systematic errors have been eliminated and are caused by a mix of factors outside the observer’s control.

What is a measurement error in statistics?

When the response supplied differs from the true value, measurement mistakes arise; such inaccuracies can be attributed to the respondent, the interviewer, the questionnaire, the collection method, or the respondent’s record-keeping system.

What are the sources of error that occur most in taping and how can they be avoided?

Errors due by the tape not being horizontal are systematic, and recorded lengths are always longer than genuine lengths.

Errors from the tape being off ‐ line are also systematic, and they cause recorded lengths to be longer than genuine lengths. Careful alignment can eliminate this type of mistake.

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