Tower Height

Value to Enter:

Enter the height above the ground at which the antenna for Radio #1 and/or Radio #1 is installed. If no heights are entered, or if only one height is entered, and if the Distance Between Towers is provided, the calculator will attempt to determine the un-entered values for distance and height. If both antenna heights are entered, but no distance is provided, the calculator will present the greatest distance for the given heights.

Significance of This Value:

The tower height is used as input for calculating the distance between towers based on the curvature of the earth. If no tower height is entered then it's assumed that two towers of equal height are used and that they are at the minimum distance apart. If tower height is provided then it's assumed that this is the actual installation height of the antenna, above the ground. Hence, if a value is provided it must take into consideration the required Fresnel Zone clearance and any obstruction height that must be overcome. If only distance between towers is entered than the tower height is calculated based on Radio Line-of-Sight.

Background and Technical Perspective:

Earth Curvature and the Visual Line-of-Sight

Visual line-of-sight extends to the earth's horizon. To calculate the distance to the horizon the assumption is made that the earth's surface is a perfect sphere at which point simply geometry allows calculation. An antenna is some particular height above the ground (the tower height value.) From this height a line is constructed to meet the circle on the horizon and extend to the top of the other tower (a line tangent to the circle that intersects the tops of the two towers). This distance is referred to as the Visual Line-of-Sight (VLOS). Careful study of the geometry reveals that the VLOS distance is very slightly longer than the distance along the ground between two points. The ground distance follows the circumference of the earth and is a measurement of the distance between the bases of the two towers. VLOS is the distance from the top of one tower to the top of the other tower. The towers are perpendicular to the surface of the earth and, hence, tilt "away" from each other slightly (because they are both parallel to radii of the circle). By the Pythagorean Theorem for right triangles it should be evident that the difference between the VLOS and the ground distance is essentially equal to the short leg of the "tilt" triangle (the horizontal, upper-most leg depicted in the diagram to the right.) The distance between the bases of the two towers (along the surface of the earth) can be seen to be slightly shorter than the VLOS distance from tower top to tower top.

The difference between VLOS and ground distance is relatively small in most practical situations. Even a 10-foot (3-meter) tall tower has roughly a 4-mile (6 km) VLOS. That's a difference of much less than 10 feet over 20,000+ feet (3 m over 6 km). Because of this relationship (between tower height and the relatively huge VLOS distances achieved from even a small tower) the ground distance is never considered in field design and measurement. On the other hand, Radio Line-of-Sight differs significantly from VLOS and must be considered.

Radio Line-of-Sight

Radio signals, like all electromagnetic radiation (such as light), diffract (bend) when they pass from a medium of one density into a medium of a different density. This is how a lens bends light rays (light moves from the low-density air into the higher-density glass of the lens.) This is why a person trying to spear a fish under the surface of the water must adjust their aim (because the fish isn't where it appears to be!)

The earth's atmosphere becomes less dense with altitude. The greatest change in density (per foot of increased height) takes place close to the ground. Consider a radio wave propagating from a vertical antenna. It moves perpendicular to the antenna. Consequently (because the earth "curves away from under the ray") the signal will begin to encounter less dense portions of the atmosphere. This change in density tends to curve the ray back towards the earth. As a result, a signal can, to a small degree, "follow" the curve of the earth around and reach a point that is actually beyond the visible horizon. This distance, which is slightly greater than the VLOS, is called the Radio Line-of-Sight (RLOS). A constant of proportionality of 4/3 is used to relate VLOS to RLOS is standard atmospheric conditions. Standard temperature is 59 degrees Fahrenheit (15 degrees Celsius). Standard barometric pressure is 29.92 inches (1013.25 mb) of barometric pressure. Deviations in temperature and pressure that are consistent with those experienced close to the ground will not effect the practical results of calculations for wireless communication networks. Atmospheric conditions do change dramatically as altitude increases, so interpretation of results for heights greater than 2000 feet should be cautious.

The term "Radio Line-of-Sight" is sometimes used to refer to the radius of the Fresnel Zone. The origin of this usage is unclear and using the term in this way seems to be inappropriate.