# Relationship between focal length and flying height scale

Calculate the flying height necessary for a given photo scale. Scale: 1" = '. 9" x 9". Photograph. Figure Relation of focal length to area coverage. Map scale is the proportion between a distance on a map and a where f is the focal length of the camera, H is the flying height of the aircraft above mean sea. Scale is the ratio of the size of any object or feature or area within the photo to its If you know the camera focal length and the flying altitude of the aircraft you.

The proportion, or ratio, is also typically expressed in the form 1: The representative fraction 1: If we were to change the scale of the map such that the length of the section of road on the map was reduced to, say, 0.

When we talk about large- and small-scale maps and geographic data, then, we are talking about the relative sizes and levels of detail of the features represented in the data.

In general, the larger the map scale, the more detail is shown. This tendency is illustrated below in Figure 2. Click on the buttons beneath the map to zoom in and out on the town of Gorham. Adapted from Thompson, One of the defining characteristics of topographic maps is that scale is consistent across each map and within each map series.

This isn't true for aerial imagery, however, except for images that have been orthorectified. Overlap and Sidelap While it might be expected that the flight line would coincide with the X-axis of the image, this is rarely the case.

The flight line would only coincide with the X-axis if there was no wind and the plane was able to fly straight along the flight line. Under windy conditions, the pilot must compensate by flying slightly into the wind in order to stay on course. This process is known as crabbing and affects the area of overlap between images.

### Airphoto Geometry

Crabbing The flight line can always be determined by plotting the principal point of one airphoto on the area of overlap with the adjacent image. This point is known as the conjugate principal point. In the example below, the first image has a tree at its principal point and the second image has a building. The location of the same building on the first image identifies the conjugate principal point.

The flight line is given by connecting the principal point and the conjugate principal point with a straight line. Conjugate Principal Point Airphoto Scale On a large scale map, the effect of curvature of the Earth's surface is negligible and the map is planimetrically correct. Map scale can therefore be defined as the ratio of map distance to ground distance, usually expressed as a representative fraction.

On an airphoto, scale can be thought of as the ratio of photo distance to ground distance. We can estimate the scale as the ratio of the photo distance between the principal point and the conjugate principal point to the air base ground distance between exposure stations. However, because the airphoto is a perspective view, this ratio is only approximately correct.

Airphoto scale varies from the centre towards the edges of the image. Airphoto scale can also be determined based on the camera focal length and the altitude of the front nodal point of the camera lens at the instant of exposure. However, an implication of this is that airphoto scale varies with terrain elevation. Higher elevations are closer to the camera lens and are therefore shown on the image at larger scale than areas of lower elevation that are further from the lens.

This is illustrated in the following diagram. Airphoto Scale The scale at point A can be determined as the ratio of the image distance ao in the positive image plane to the ground distance AOA. This relationship proves that airphoto scale is equal to the focal length divided by the height of the lens above the terrain. The airphoto metadata provide values for the focal length f and the height of the lens above sea level H.

To determine the scale at points A and B, we need to know their elevations above mean sea level. This information can be obtained by inspecting a topographic map of the area.

Assume that the ground elevation at A is m, the ground elevation at B isand the height of the lens above mean sea level is m. The elevation of the runway is m ASL.

## Photogrammetry

If the focal length of the camera is mm, what is the altitude of the aircraft? Conversely, a telephoto lens, with its longer focal length, views a smaller area and produces a larger scale image. Flying height also affects photo scale. The higher the altitude of the aircraft or satellitethe smaller the scale of the resulting image. Variations in ground elevation are the main reason for scale distortion in airphotos. Higher elevations are closer to the camera and thus appear at larger scale in the image.

This implies that in Southern Ontario where the maximum relief is unlikely to exceed m, a flying height of m is adequate to minimize scale distortion. However, in the Rockie Mountains where maxmimum relief might be 3, m, a flying height of 30, m would be required.

### 4. Map and Photo Scale | The Nature of Geographic Information

Scale changes are primarily due to changes in terrain elevation but there can also be scale changes between successive images along a flight line due to changes in flying height between prints. This can occur due to turbulence that prevents the pilot from maintaining a constant altitude. Further distortion can occur due to the camera not being level to the ground at the instant of exposure.

This can occur if the nose of the aircraft is slightly up or down pitch or if a wing is tilted up or down roll. Both conditions can be caused by turbulence or by manoeuvering to stay on course. The result is the introduction of distortion due to obliqueness in the image. Obliqueness is measured by the angle between a vertical plumb line through the centre of the lens and the optical axis of the camera lens. The principal point P is always at the intersection of the optical axis of the camera lens and the image plane.

The nadir N is the intersection of the vertical plumb line through the centre of the lens and the image plane. On a true vertical airphoto, the principal point and the nadir are the same point but on an oblique airphoto they are at different positions on the image plane. Obliqueness in Airphotos Because photographs are perspective views, all airphotos are subject to radial or relief displacement which causes objects in the image to be displaced outward from the nadir of the image.

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Displacement increases with the height of the object and distance from the nadir. The following diagram illustrates the radial displacement of a series of hydro poles in a true vertical airphoto. The pole that lies directly below the camera lens is seen in plan view. Poles that lie close to the nadir principal point in a vertical airphoto are only slightly displaced while poles further from the nadir are displaced greater distances on the image. The bottom of the pole is closer to the nadir than the top of the pole.

The same effect can be seen in images of urban areas in which the tops of buildings are displaced outward relative to the base of the buildings. Radial Displacement Radial displacement is a source of distortion and can result in tall objects that are close to the nadir hiding objects that are further away from the nadir. Radial displacement can also make 3-d viewing difficult if objects appear too dissimilar in successive images.

This is especially a problem if the scene contains tall objects. Nevertheless, radial displacement can be useful. Radial displacement of objects results in the sides as well as the tops of objects being visible in the airphoto.

This can facilitate interpretation since objects such as office buildings and apartment buildings that may be difficult to distinguish from a plan view may be distinguished based on the appearance of the sides of the buildings, e. Since radial displacement is always outward from the nadir of the image, we can locate the nadir by finding the intersection of lines showing the direction of object displacement, e.

As will be discussed in the next section, we can also use radial displacement as a means of calculating the heights of objects in the image. Distortion due to scale changes, obliqueness and radial displacement can make it difficult to transfer detail from airphotos to maps. This is most likely to be a problem in mountainous terrain where there is significant loca relief. The effect is to dramatically change the shape of objects as they appear in successive images along a flight line.

Distortion in Airphotos The above diagram illustrates an extreme case in which successive images along a flight line have been taken from opposite sides of a mountain ridge. Left hand image, side A of the mountain occupies most of the image while side B is a narrow sliver. The opposite is true in the right hand image.

• 4. Map and Photo Scale

This problem can be minimized by: The logic of the radial displacement method is illustrated in the following diagram.

The vertical line PQ represents an object, e. On the image, the building is appears as the line aq.