Measurement of Distance

Measurement is one of the pillars of science. Whether measuring how far a planet is away or how big your pencil is, understanding how to measure distance accurately is necessary. Distance is an important building block of physics and everyday life, allowing us to comprehend the measure of the space between two points. From old ropes and feet to modern-day laser light and satellites, our techniques in measuring distance have come a long way, which will be our topic of discussion today. So let’s begin! 

1.0What is Distance?

Distance is a derived physical quantity that represents the total length of the path an object travels during its motion. In simple words, it describes how much ground an object has covered. Distance is a scalar quantity, meaning it only has magnitude but not direction. Unlike displacement, which is the shortest path between any two points and in a single direction, distance is the total length of the actual path taken to reach the destination. 

For instance, if you walk along a rectangular field and come back to the original point, your displacement can be zero, but the distance travelled is the total length of the walk.

2.0Units of Measuring Distance

Units of any measurement are essential to standardise values and results, and enable comparison. In the international system, units are of two types: a unit that is internationally accepted and a unit accepted locally, which is valid for a certain region. In this case, the SI unit of distance is the metre (m). Units of distance are classified into various types based on the use and extent of distance measured: 

3.0Tools for Measuring Distance

There are different types of tools which are used to directly measure the distance between any two points, classified according to the extent of distance to be measured: 

A. Basic Measuring Instruments (Short Distances)

• Ruler/Scale: School, lab, and architectural usage for straight short measurements.
• Measuring Tape: Flexible, suitable for furniture, rooms, and clothes.
• Vernier Callipers: An accurate instrument in engineering for items of small sizes.
• Screw Gauge (Micrometer): For extremely small distances (e.g., wire size).

B. Intermediate Tools (Medium Distances)

• Odometer: Built into vehicles to monitor journey distance.
• Measuring Wheel: Rolled across the ground to gauge big flat surface distances.
• Surveying Chains: Used in measuring land.

C. Advanced Devices (Long/Astronomical Distances)

• Ultrasonic Sensors: Distance measurement with sound waves, commonly employed in robotics.
• Laser Rangefinder: A precise device employing laser beams that is utilised in defence and sports.
• Radar/Sonar: Echo-based distance measuring devices for air and underwater distances.
• Parallax Method: Astronomical technique employing star position changes for stellar distances.

4.0Formulas for Measuring Distances

Not every distance can be calculated using the specialised measuring tools mentioned above. There are some special formulas for measuring distances that make this calculation a bit easier task, which include: 

Constant Speed Formula (Uniform Motion)

$Distance=Speed\times Time$

This formula is specifically used when an object moves with a constant speed in uniform motion. 

Equations of Motion (For Accelerated Motion)

The second and third equations of kinematics also give the equation for calculating speed when the object is in accelerated motion: 

• Second Equation of Motion

$s=ut+\frac{1}{2}a{t}^2$

• Third Equation of Motion:

$v^2=u^2+2as\Rightarrow s=\frac{v^2-u^2}{2a}$

In both equations: 

• s: Distance covered
• v: final velocity 
• u: initial velocity
• t: time taken 

Echo/SONAR Method (Sound-based Measurement)

In practical applications, such as on ships or in tunnels, where there is an echo of sound, this method is used, which uses the speed and time of sound to measure a certain distance: 

$Distance=\frac{\text{Speed of Sound}\times Time}{2}$

5.0How to Measure Distance 

Based on the requirement and accuracy, distance can be measured using either direct methods with tools or indirect calculations using the distance formulas discussed earlier. Follow these steps for accurately measuring distances: 

• Select the correct tool depending on the required scale and accuracy.
• Align the starting point (zero mark) properly.
• Prevent parallax error in reading values.
• Take repeated measurements for accuracy.
• Make proper unit conversions if necessary.

6.0Importance of Measuring Distance

Knowledge of distance and how to measure it is crucial for various fields, including theoretical studies and practical use, such as:

• Science and Engineering: Assists in calculating motion, force, and energy. The examples of distance measurement, in this case, include using vernier callipers in the laboratory or sonar in oceanic exploration.
• Transportation and Navigation: Distance is used to calculate time, fuel consumption, and best routes. Examples here are odometers in automobiles and surveyors' measuring wheels.
• Experiments: Valid scientific measurements are ensured through precise distance measurement. For example, the length of an inclined plane or the object's fall height in motion experiments.
• Astronomy: Parallax, light-year, and radar methods measure distances of celestial objects. One usual example of distance measurement is light years to express the distance between stars.
• Daily Life: Applied in sports (race tracks), construction (sizes of plots), fitness (steps to distance), and even in cooking (distance on measuring cups).