Measuring Distances
One of the most basic geospatial tasks is to measure distances, from a few feet to thousands of miles. Measuring smaller distances, or lengths, is a task for technicians, engineers, and physicists; measuring longer ones is for astronomers. (Distance is the measure of separation between two points that are not necessarily connected, whereas length implies a physical connection between them. In topographic mapping, the horizontal distance is that between two plumb lines.)
All the methods and techniques used by geospatial professionals to measure distances can be grouped into four categories: direct measurement, dead reckoning, trigonometric calculation, and time of flight.
Direct measurement
For centuries, surveyors measured distances using rods and chains. Commonly used legacy “chains” of 66 feet (approximately 20 meters) were composed of 100 links, which were used to measure and report distances longer or shorter than an exact multiple of chain lengths. The units of measurement for such measurement tools as chains were often a function of their primary uses. For instance, in cadastral surveys of sectionalized land system of the American western states, the basic unit of mile (5,280 feet) was defined by 80 chains. To be accurate, direct measurement tools need to be of a known length and non-elastic. Preferably, they are subdivided, such as with links in a chain or ticks on a ruler.
Another way to measure distances directly is to count the number of repetitions of a given action that advances an object along a path by a known distance. Examples include pedometers, which count steps, and odometers, which measure distance based on the number of revolutions of a wheel of known diameter. For example, the Distance Measuring Indicator (DMI), a standard feature of Applanix’s Position and Orientation Systems for Land Vehicles (POS LV), is a wheel-mounted rotary shaft encoder that measures precise linear distance traveled.
Dead Reckoning
In navigation, dead reckoning is the process of calculating one's current position by using a previously determined position, called a fix, and advancing that position based upon known or estimated course and speed over elapsed time. Inertial navigation systems (INS) use dead reckoning to continuously calculate the position, orientation, and velocity (direction and speed) of a moving object without the need for external references. An INS consists of one or more inertial measurement units (IMU)—which, in turn, are composed of orthogonally mounted accelerometers and gyroscopes—and a computer. INS-based dead reckoning can be used to measure the distance between any two points on a path travelled by a vehicle or a vessel.
Trigonometric measurement
Optical rangefinders (known as stereoscopic, parallax, or split-image rangefinders) were used for many decades for military purposes, such as setting the range on artillery pieces, and by photographers. The user rotated one or both of two lenses or mirrors until the target was in focus or the top and bottom parts were vertically aligned. Then, based on the known distance between the two lenses or mirrors and the angle of the latter with respect to the target, trigonometry provided the distance.
Surveyors’ theodolites, too, are used in conjunction with trigonometry to measure distances. They consist of a telescope mounted movably within two perpendicular axes, such as to enable the measurement of both horizontal and vertical angles with great precision, typically on the scale of arcseconds. Measuring distance with a theodolite consists, essentially, of applying trigonometry to the difference in angle from the theodolite to the bottom and the top of a survey rod of known length held, usually vertically, at the target. Modern theodolites have evolved into total stations, which measure angles and distances electronically and read them directly to computer memory.
Time of Flight
Sonar, radar, and laser-based devices—electronic distance measurement (EDM) instruments and LiDAR—measure distances based on the round-trip time of signals reflected from their targets—whether they be sound waves, microwaves, or laser light pulses—multiplied by the signals’ propagation speed. In surveying and construction, EDM have largely replaced tape measures.
Various schemes using cell towers or other “beacons of opportunity,” such as television towers, also use some variation on this principle. In the case of bathymetric sonar, the propagation speed is that of sound in water, which varies with the water’s density and salinity. In the case of all the radio-frequency devices, the speed is that of light.
GNSS uses time of flight to measure the distances between the receiver and each satellite (called ranges), a procedure known as trilateration, as well as trigonometry to calculate the receiver’s position in 3D based on those of the satellites, which are carefully monitored. GNSS is used to measure distances on the ground by determining the latitude and longitude of two points and then calculating the distance between them using metrics for a spherical Earth based on a great circle.