4.8.27. Scale

The scale is a ratio of the distance between two objects on the photograph to the distance between the same points on the ground.

Scale helps us understand the relationship between distances measured in a photograph and their actual corresponding distances on the ground. If you take a photograph of a building, the distance between two corners of the building in the image might measure a certain amount of centimeters. The scale tells us how far apart those corners are in real life. For example, if the scale is 1:1000, this means that 1 centimeter on the photograph equals 1000 centimeters (or 10 meters) in real life.

Imagine playing a board game where the board represents a map of a city. Each square on the board is 1 square meter, but when you look at the board, it seems much smaller. In this game, if you were measuring distances from point A to point B on the board, you would use the game's scale to figure out the actual distance in the city - just like using scale in a photograph to find real distances in the field.

The scale S of the vertical photograph is computed using the relationship:

Scale S = f / (H - h)

where 'f' is the focal length and 'H' is the flying height above ground.

To calculate the scale of a photograph taken vertically, you need two key pieces of information: the focal length of the camera and the flying height of the aircraft at the time the photograph was taken. 'Focal length' refers to how strong the camera's lens is; a longer focal length means a closer view. 'Flying height' is how high the aircraft was above the ground when the photo was taken. The formula helps find out how much the photograph has reduced the actual size: Scale S = f (focal length) divided by (H - h) where 'h' is the height of the ground at the specific location. This means the closer you are (lower H), the more accurate your scale will be.

Think of the camera as a telescope looking at a distant object. The higher you go in the sky (like being on a mountain), the smaller the object looks through the telescope. If you were looking only at a flat field with no bumps (the same elevation), the calculations would be straightforward. But if the land has hills, valleys, and uneven terrain, you must adjust calculations. Just like how hiking up a mountain makes things appear smaller!

The scale of a vertical photograph varies at different points depending on their elevations.

In practice, the scale of a photograph won't be uniform across the entire image, especially in regions with varying elevations. If one point is at sea level and another point is on a hill, the camera views them from the same height, but the distances will differ. To account for these variations, photograph scales are adjusted based on the average elevation of the terrain in the photo. This means that understanding the terrain's height is crucial for accurate measurements.

Imagine you are flying over a roller coaster. While you are high up, the various hills (like the elevations in your photograph) make parts of the roller coaster look larger or smaller based on your angle. When you’re measuring how far apart the loops are, you'll find that measuring from above gives a different result than measuring from the ground below. Keeping track of where you're looking from is like adjusting really for elevation on a photograph!

When a camera with larger focal length is used, a larger scale is obtained, and vice versa.

Changing the focal length affects the scale directly. A longer focal length means you're zooming in more on a particular area, making the objects appear larger. This creates a larger scale, allowing for more detailed measurements but covering less area. Conversely, a shorter focal length captures a wider area but at a smaller scale of detail. This principle is crucial when deciding how to capture specific land features, whether for surveying or mapping purposes.

Think of using a magnifying glass to look at a map. If you bring it close (longer focal length), you can see the details of the streets much better, like what stores are there. But you can only see a small section of the map at a time. If you pull the glass away (shorter focal length), you can see a much larger section of the map, but the details aren’t as clear - just like adjusting scale in photographs!

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