Understanding Measurement: Magnitudes, Units, and Errors

Magnitudes and Metrology

5 Magnitudes: Length, mass, time, volume, luminous intensity.

Metrology: The science that studies everything concerning measurement.

  • Dimensional: From the measurements.
  • Ponderal: Attempts to measure weights.
  • Study: Quantities, unit systems, measurement instruments, norms, standards, and instructions.

Systems of Units

International System, CGS system, metric system…

Measurement Instruments

Rule, calipers, angle gauge, scale, protractor, Palmer, stopwatch, and micrometer.

Metrotechnics

Establishes and regulates the use of a set of techniques, skills, methods, and processes on which we rely to apply technical metrology.

Measurement and Measure

  • Measurement: When we determine numerically the value of a length, mass, time, etc.
  • Measure: Results obtained from the measurement.

Developing Measurement

Tools, precision and appreciation, skill of operator, and environmental conditions.

Environmental Conditions

Temperature, humidity, lighting.

Direct and Indirect Measurement

  • Direct Measurement: When the value of the quantity is obtained immediately by reading on the scale of the instrument.
  • Indirect Measurement: When the value of the quantity is not obtained directly with the measuring instrument, but requires a previous calculation.

Table Measurements

Length, volume, capacity, mass, intensity, power…

Components

Dial gauge, dial, needle, needle probe, small field, and indexes.

Verification

Verify that items meet certain characteristics: dimensions, shape, material…

Fundamentals of Measurement

Magnitude

Anything that can be measured.

Fundamental Magnitude

One that can be fully defined without resorting to any other.

Derived Magnitude

One that is defined by a combination of one or more fundamental quantities.

Measure

To compare quantities of the same nature.

Unit of Measure

The amount taken as reference to compare magnitudes of the same species.

Measuring Standard

The realization of a unit of measure so that its value is unchanged.

Meter

The length equal to 1,650,763.73 times the wavelength in a vacuum, corresponding radiation.

System of Units

An ordered set of fundamental and derived units that are each defined and have simple relationships.

Length

The magnitude that indicates the distance or separation between bodies.

Plane Angle

The magnitude that indicates the opening between two concurrent lines belonging to the same plane.

Radian

The angle corresponding to an arc that has the same length as the radius of the circle that contains it.

Accuracy and Error in Measurement

Objective Measurement

To obtain a piece’s dimensions as accurately as possible.

Reading vs. Measured Value

This expression indicates that the reading done on the scale of the measuring instrument does not necessarily coincide with the actual value of the dimension of the piece.

Accuracy

The greater or lesser extent to the approximation of the actual value of the magnitude.

Precision

The ability of a measuring instrument to provide results with a minimum error.

Estimation

A slight variation of the magnitude that we can read on its scale.

Measurement Error

The difference between the reading obtained on measurement and the actual value of the magnitude.

True Value

The measure asymmetric.

Systematic Errors

Those that occur consistently in all actions.

Parallax Error

Occurs when the scale and pointer are not coplanar and the visual is not perpendicular to them.

Absolute Error

The difference between the value of the measure and the value of the magnitude.

Relative Error

The ratio of the absolute error and the actual measurement of the quantity.

Nominal Measure

The value of the size indicated on the map.