Difference Between Horizontal and Vertical

In the field of astronomy, geophysics, and related fields, a path or plane that passes through an astronomical or geographical point is considered to be vertical if it is in the gravity direction of the local area at that particular point. On the other hand, a direction, or plane, is considered to be horizontal when it is parallel to the vertical direction. In general, anything which is vertical may be drawn from the top to the bottom (or from down towards up) like the y-axis within the Cartesian coordinate system. A good example of a horizontal plane can be the flooring of an area. A good illustration of vertical would be the wall of a room.

Historical Definition

The word horizontal comes from the Latin Horizon, which comes directly from the Greek horizon, which means 'separating' or 'marking a boundary'. The word "vertical" comes from the Latin word 'verticalis', which comes from the same root as vertex, which means "highest point" or, more specifically, the point of turning, like in the Whirlpool.

Girard Desargues defined the term "vertical" as perpendicular to the Horizon in his book 'Perspective' in1636.

Geophysical Definition

The plumb line and the spirit level

In engineering, physics as well as construction work, the path referred to as vertical is typically the one along which a plumb-bob hangs. A spirit level that takes advantage of the buoyancy of the air bubble, along with its ability to move upwards vertically, can be utilized to check for horizontality. A water level device can also be utilized to establish horizontality.

Modern lasers with rotary axes that can be levelled automatically are sophisticated instruments and operate on the same basic principle.

The Earth's spherical surface

If the curvature of the Earth is taken into consideration, the notions of horizontal and vertical acquire a different significance. In the case of a homogenous, spherical and non-rotating planet, the plumb bob is able to pick up as vertical direction of the radial. In essence, it's now impossible for the vertical walls to be parallel. This has practical applications in civil and construction engineering. e.g., the tops of towers in suspension bridges are farther from each other than the lower ones.

Additionally, horizontal planes may cross each other when they are tangent planes to separate points on the Earth. Particularly, a plane which is tangent to an area on the Equator can intersect the plane tangent to the North Pole at a right angle. Also, the equatorial line has a parallel plane to that of the tangent at the North Pole and, as such, is believed to be a horizontal plane. It is also an equilateral plane that is used to locate points on the Equator. In this way, it is possible for a plane to be both vertical and horizontal at different places.

Additional Problems

For rotating earth, the plumb line diverges from the direction of the radial axis as a function of the latitude. Only on the Equator and North and South Poles do the plumb line coincides with the local radius. This is more complicated since Earth isn't a homogeneous smooth sphere. The Earth is the non- homogeneous, non-spherical planet that is in motion. The vertical does not have to be located along a radial line. It can also be curved and shift with the passage of time. In a smaller context, an elevation to one side could cause the plumb bob to deflect from its true Zenith.

On a bigger scale, the gravitational field of the Earth, which is about radial near the surface, isn't as radial when it is being affected by the Moon at higher altitudes.

The independence of Vertical and Horizontal motions

By ignoring the curvature of the Earth, the horizontal and vertical movements of a projectile in the direction of gravity are not dependent on one another. The vertical movement of the projectile is not directly affected by horizontal components of velocity at which it launches, while in the opposite way, the horizontal displacement of a projectile is not affected due to the vertical component. The idea dates back at least to Galileo.

If the curvature of the Earth's surface is considered, the independence of the two motions is not true. For instance, even projectiles launched in a horizontal direction (i.e., having a Zero vertical component) might escape from the surface of the Earth and possibly disappear completely.

Mathematical definition

In two dimensions

When it comes to a 1D orthogonal Cartesian coordinate system on a Euclidean plane, to indicate that a line is horizontal or vertical, an initial designation is required to be drawn. The first step is selecting the vertical direction. It is typically known as the "Y" Direction. The horizontal direction, typically called the "X" direction, is then determined automatically. You can also do the opposite, i.e., make the x-axis in which the y-axis gets automatically identified. There is no reason to pick either the horizontal or vertical for the initial designation since both directions are in line in this respect.

The following holds in the case of two dimensions:

For the entire plane, at any location P on the surface, there exists just one vertical line inside the plane and only one horizontal line in the plane. The symmetry breaks down as you move into the three-dimensional space.

The term "vertical line" refers to a line that runs parallel to the vertical direction. Horizontal lines are any line that is normal to the vertical line.

Horizontal lines don't cross one another. They're parallel.

Vertical lines don't cross each other. They're parallel.

Not all of these basic geometrical facts are valid in 3D space.

In three dimensions

In the 3-D case, the situation becomes more complicated because it includes vertical and horizontal planes in addition to vertical and horizontal lines. Take point P and mark a line across P in the vertical direction. A plane that includes P and is in a normal direction to the direction you have chosen can be described as the horizontal plane located at P. A plane passing through P that is normal to the vertical plane is a vertical plane in P. At any point P, there exists only one horizontal plane. However, there can be numerous vertical planes. This is a novel feature that appears when you consider three-dimensional space. The symmetry present in the two-dimensional model is no longer valid.

In the Classroom

In the case of 2 dimensions, as previously mentioned, the standard designation of the vertical is that it coincides with the y-axis when using coordinate geometry. This is a common practice that can cause disorientation in classrooms. For a teacher writing on a whiteboard, the y-axis is actually vertical in terms of plumbline verticality. However, for the student, the axis could be on a table with a horizontal surface.

Discussion

While the term "horizontal" is frequently used in daily life and in language, it is the subject of many misperceptions.

The notion of horizontality is logical only when it is an easily quantifiable gravity field, i.e., in the "neighbourhood" of a star, planet or another object. If the gravity field becomes extremely fragile (the mass is too tiny or far away from the point of significance), the idea of being horizontal is no longer a valid significance.

A plane is only horizontal at the point you choose. Horizontal planes that intersect at two distinct points are not parallel; they are intersecting.

In general, a horizontal plane can only be perpendicular to a vertical line when both are specified with regard to the same point. The horizontal direction can only be vertical when it is located at the same point. Therefore, both horizontality and verticality are strictly local concepts, and it is necessary to specify which location the direction or plane is referring to. It is important to note that (1) exactly the same limitation applies to straight lines within the plane, which is that they are only horizontal when they pass through the reference point, and (2) the straight lines contained in the plane but not passing through the reference point are not always horizontal in any way.

In actuality, the gravity field of a planet that is heterogeneous like Earth is distorted because of the uneven spatial distribution of substances with various densities. The actual horizontal planes are not parallel even if the reference points are along an identical vertical line since a vertical line can be slightly curved.

At any point, the gravitational force does not remain constant in time because the things that cause the force are changing. For example, on Earth, the horizontal plane at a particular place (as determined by the spirit levels) is affected by the direction of the Moon (air, sea, and land tides).

When a planet is rotating, like the Earth, the gravitational force of the Earth (and the other objects of celestial origins, such as the Moon or the S) differs in comparison to the apparent net force (e.g., or on an object that is free-falling) that can be observed in the lab or out in the field. The difference is due to the centrifugal force that is associated with the planet's rotating. It is a fictional force that only occurs when experiments or calculations are carried out in a non-inertial frame of reference, like on the surfaces of Earth.

In general, the things that are horizontal may be drawn from right to left (or the other way around, from right to left) like the x-axis within the Cartesian coordinate system. And the things that are vertical maybe drawn from top to bottom or in the opposite way.

Practical Application in Everyday Life

The idea that a plane is horizontal is far from simple, but, in actual, the majority of these effects and variations are relatively minor as they are easily measured and can be predicted with high precision. However, they might not have a significant impact on our lives.

This chasm between the apparent simplicity of the concept and the actual difficulty of the process of defining (and quantifying) it in terms of science results from the fact that most sizes and scales that are of importance in everyday life are three orders in magnitude (or more) smaller than the size of Earth. Thus, the Earth appears flat locally, and the horizontal planes that are found in close proximity appear to be parallel. However, these statements are only approximate. Their acceptance in any particular situation or use depends on the requirements that apply, particularly in terms of precision. In graphic contexts like drawing, coordinate geometry or drafting on rectangular papers, it is common to link any of its dimensions with the horizontal even when the entire sheet of paper is placed on the flat horizontal (or inclined) table. In this situation, the horizontal direction usually runs from the left side of the paper and then to its right-hand side. This is not a formality (although it's somehow natural in drawing the natural world as perceived in reality). It can cause confusion or misinterpretations, particularly in an educational setting.