Clinometer

What is a clinometer?

A clinometer is an instrument used to measure the angles of slope, elevation, or depression of an object or surface relative to the direction of gravity (i.e., the horizontal plane).

Basic principle of a clinometer

A clinometer works on the simple idea of using gravity as a constant reference point. Imagine holding a string with a weight on the end; it always points straight down. A clinometer uses this same principle: it has a part that always aligns with gravity (like a swinging weight or a bubble in liquid) and a scale. When you tilt the clinometer to look at something, the gravity-aligned part shows you how much the instrument has tilted relative to a perfectly flat, horizontal line. By reading the angle indicated on the scale, you can measure the slope or elevation of what you’re looking at.

How to find out height using a clinometer?

The image above demonstrates how a clinometer, along with basic trigonometry, can be used to calculate the height of a distant object (in this case, a flag pole) without physically measuring it directly.

1. Forming a Right-Angled Triangle:
   • The Observer’s Eye: This is one vertex of the triangle.
   • The Base (Distance): This is the horizontal distance from the observer’s eye (or the point directly below the clinometer) to the base of the object (the flag pole). This forms one leg of the right-angled triangle.
   • The Height (Opposite Side): This is the vertical height of the object from the observer’s eye level to the top of the object. This forms the other leg of the right-angled triangle.
   • The Line of Sight (Hypotenuse): This is the imaginary line from the observer’s eye to the top of the object.
2. Measuring the Angle of Elevation (θ):
   • The image shows a simple clinometer. The observer looks through the clinometer towards the top of the flag pole.
   • The clinometer has a weighted pendulum (represented by the string with the stone at the bottom). When the clinometer is aimed at the top of the pole, the pendulum hangs vertically due to gravity.
   • The angle that the pendulum’s string makes with the clinometer’s horizontal scale is used to determine the angle of elevation.
   • In the image, the clinometer reads 125 degrees from a particular reference point. To find the angle of elevation (θ) from the horizontal, you subtract 90 degrees (because the pendulum is perpendicular to the horizontal when measuring). So, θ=125^∘−90^∘=35^∘. This angle is crucial as it represents the angle between the horizontal line of sight from the observer and the line of sight to the top of the object.
3. The Role of Trigonometry (Tangent Function):
   • In a right-angled triangle, the tangent (tan) of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
   • In our triangle:
     • The side opposite the angle θ is the Height (from eye level to the top of the pole).
     • The side adjacent to the angle θ is the Distance (from the observer to the base of the pole).
   • Therefore, the trigonometric relationship is: tan(θ)= Distance/Height​
4. Calculating the Height:
   • To find the “Height” (from eye level), you can rearrange the formula: Height (from eye level)=tan(θ)×Distance
   • The image directly shows this formula: “Height = tan θ X Distance”.
5. Final Height Calculation (Total Height):
   • It’s important to remember that the “Height” calculated using the formula is only the height from the observer’s eye level to the top of the object.
   • To get the total height of the flag pole, you would need to add the observer’s eye height (or the height of the clinometer from the ground) to the calculated height. Total Height of Object=Height (from eye level)+Observer’s Eye Height

The clinometer allows us to accurately measure the angle of elevation (θ), and by knowing the horizontal distance to the object, we can use the tangent function to solve for the unknown height, leveraging the principles of right-angled triangles.

Clinometer, Inclinometer and Declinometer

The terms “clinometer,” “inclinometer,” and “declinometer” are closely related and often used interchangeably to describe devices that measure angles of slope or tilt. Their names derive from their Greek and Latin roots, reflecting the nature of the measurement.

1. Clinometer:

• Etymology: The word “clinometer” comes from two Greek roots:
  • “klinein” (κλίνειν): meaning “to lean,” “to slope,” or “to incline.”
  • “-meter” (μέτρον): meaning “measure.”
• Meaning: So, a clinometer literally means a “slope measure” or an “incline measure.” It’s a general term for any instrument that measures how much something deviates from the horizontal. It can measure both upward slopes (inclinations) and downward slopes (declinations).

2. Inclinometer:

• Etymology: This term comes from the Latin root:
  • “inclinare”: meaning “to lean towards,” “to bend,” or “to incline.” This itself comes from “in-” (into, towards) and “clinare” (to lean, slope).
  • “-meter”: (from Greek “metron,” as above).
• Meaning: An inclinometer specifically refers to an instrument that measures “inclination,” which is the upward or downward angle relative to the horizontal. While “incline” often implies an upward slope in common usage, in a scientific or engineering context, it broadly refers to any deviation from the horizontal, whether up or down. Therefore, an inclinometer effectively measures both positive (upward) and negative (downward) angles of tilt.

3. Declinometer:

• Etymology: This term also has Latin roots:
  • “declinare”: meaning “to bend down,” “to turn away,” or “to decline.” This comes from “de-” (down, away) and “clinare” (to lean, slope).
  • “-meter”: (from Greek “metron”).
• Meaning: A declinometer, therefore, literally means a “decline measure.” While it could theoretically refer to a general slope measurement, in common usage, particularly in older contexts or specific fields like magnetism, “declinometer” often has a more specialised meaning. For example, a magnetic declinometer is used to measure magnetic declination, which is the angle between magnetic north and true north. In this context, it’s measuring a specific type of “declination” or deviation.

Why the interchangeability?

Because all three terms ultimately refer to measuring some form of “leaning” or “sloping” from a reference plane (usually horizontal), their meanings overlap significantly. “Clinometer” and “inclinometer” are largely synonymous in general use because an instrument that measures an “incline” inherently measures a “cline” (slope). “Declinometer” is less common as a general term for measuring any slope and is more often associated with specific types of angular measurements, such as magnetic declination, where the “decline” refers to a specific deviation.

In most modern contexts, clinometer and inclinometer are the most widely used terms for a device that measures angles of slope or tilt.