4. Examples

A= L1 x L2 = 20 km x 16 km = 20000 m x 16000 m, Longitudinal overlap (OL) = 60% = 0.6, Side overlap (OS) =30% = 0.3, Scale 1: 15000, Photograph size = 23 cm x 23 cm = 0.23 m x 0.23 m = (L x L) N1 = Number of photographs per flight line = [L / {(1 – OL ) scale * L}] + 1 = [20000 / {(1 – 0.6) 15000 * 0.23}] + 1 = 14.49 + 1 = 16 (taking round figure to cover entire area) N2 = Number of flight lines = [L / {(1 – OS ) scale * L}] + 1 = [16000 / {(1 – 0.3) 15000 * 0.23}] + 1 = 6.62 + 1 = 8 (Taking whole no of flight lines) Total number of photograph required = N1 x N2 = 15 x 8 = 120 No

This example shows how to calculate the number of aerial photographs required to cover an area effectively. We start with the dimensions of the area, which is 20 km by 16 km, and convert it to meters for easier calculations.

1. First, compute the area as: A = 20 km x 16 km = 20000 m x 16000 m.
2. Determine the longitudinal overlap (OL), which is given as 60%, meaning 0.6 in decimal form. This overlap is crucial as it ensures that adjacent photographs will capture some of the same area, helping in creating seamless maps.
3. For the side overlap (OS), given as 30% or 0.3, which also helps in ensuring good coverage in the sideways direction.
4. We are also given the photographs' scale of 1:15000 and their size of 23 cm by 23 cm, converted to meters for calculations.
5. To find the number of photographs per flight line (N1), we use the formula based on area, overlap, and scale: N1 = L / {(1 – OL) * scale * size}
6. Plugging in our values: N1 = [20000 / {(1 - 0.6) * 15000 * 0.23}] + 1. This computes to approximately 16 photographs.
7. Similarly, compute the number of flight lines (N2) using side overlap: N2 = [16000 / {(1 - 0.3) * 15000 * 0.23}] + 1, yielding approximately 8 flight lines.
8. Finally, multiply the number of photographs per flight line by the number of flight lines to get the total number of photographs required: Total = N1 * N2 = 16 * 8 = 120 photographs.

Imagine you're taking pictures of a large garden to create an aerial map. Each photo captures a section of the garden, but to make sure you don't miss any parts, you intentionally overlap each photo with the next. Just like how you would overlap photos to maintain continuous coverage of your subject, the same principle applies here to ensure the entire area is captured with proper overlaps.

Example 4.11: The distance from the principal point of a photograph to the image of the top of a tower is 6.44 cm and the elevation of the tower above the above datum is 250 m. What is the relief displacement of the tower if the scale is 1:10,000 above datum and the focal length of the camera is 20 cm? Solution: r = 6.44 cm, h = 250 m, scale =1:10000, f = 20 cm d = r h / H and S = f / H or H = f / S So, d = r h S / f d = (6.44 / 100) * 250 / (0.20 * 10000) = 6.44 / 800 = 0.00805 cm

In this example, we are tasked with calculating the relief displacement for a tower from its photograph.

1. Understand the variables: r is the distance from the principal point to the top of the tower image (6.44 cm), h is the elevation of the tower above the datum (250 m), scale is given as 1:10,000, and f is the focal length of the camera (20 cm).
2. Convert values to consistent units: Since we're working with cm for r and f, we need to convert h to cm too. Calculate H which is the height above the datum corresponding to the scale and focal length: H can be derived from the scale by noting that S = f / H, rearranging gives H = f / S where S = 1/10000 when translated into decimal. Calculate H = 20 cm / (1/10000) = 200,000 cm or 2000 m.
3. Next step is to calculate the relief displacement (d) using the formula d = (r * h * S) / f:
   • First calculate r in meters (6.44 cm = 0.0644 m), then apply values:
   • d = (0.0644 m * 250 m * (1/10000)) / 0.20 m = 0.00805 m.
4. The final value of relief displacement is then simply stated in cm for a clear response, thus d = 0.00805 cm.

Think of a photograph of a building taken from your drone. If the camera isn't perfectly straight, the taller parts of the building might appear displaced from where they actually are in relation to the rest of the image. This phenomenon is called relief displacement. In our tower's case, we measured how far off the tower's top appears due to this displacement and used our calculations to find out exactly how much it's off.

Example 4.12: The vertical photograph of a flat area having an average elevation of 250 m above datum was taken with a camera of 20 cm focal length. A line PQ, 250 m long, measures 8.50 cm on the photograph. A tower TQ appears on the photograph, and the distance between the images of top and bottom of the tower TQ measures 0.46 cm on the photograph. If the distance of the image of the top of the tower from principal point of the photograph is 6.46 cm, determine the height of tower TQ above datum. Solution: Ground distance = 250 m, map distance = 8.50 cm, f = 20 cm, r = 6.46 cm, d = 0.46 cm S = f / H = 0.20 / H [(8.50 / 100) / 250] = 0.20 / H So, H = 0.20 * 25000 / 0.085 H = 588.24 m d = r h / H (0.46 / 100) = (6.46 / 100) * h / 588.24 h = 0.46 * 588.24 / 6.46 h = 41.90 m

This example demonstrates how to calculate the height of the tower from an aerial photograph.

1. Identify the variables: Ground distance (PQ) is 250 m, measured length on the photograph is 8.50 cm, focal length is f = 20 cm, distance r from the principal point of the image to the tower's image top is 6.46 cm, and the parallax difference d = 0.46 cm.
2. Calculate the scale S: The scale can be calculated from the focal length and height (H). Scale S = f / H.
3. We set up the proportions based on the ground to map distances: (Map distance / Ground distance = Scale) that gives us ground height H:
   • (8.50 cm / 250 m) = (0.20 cm) / H. Rearranging gives us H = (0.20 * 25000) / 0.085 = 588.24 m approximately.
4. Next, calculate the height of tower TQ above datum: rearranging d = (r * h) / H leads us to calculate height: Set d = 0.46 cm to find h using our known values: h = (0.46 * 588.24) / 6.46, yielding h = 41.90 m.
5. Therefore, the height of the tower TQ above the datum is approximately 41.90 m.

Imagine taking a picture of a tall tree with a ruler placed next to it. Just like measuring the tree's height using the image while considering where the ruler sits in relation to the camera, we use the principles from this calculation to find out how tall our tower is by analyzing its image on the photo.

Example 4.13: The tower AB 50 m high above the ground, appears in a vertical photograph, was taken at a flying height of 2500 m above msl. The distance of the image of the top of the tower from principal point of the photograph is 6.35 cm. Determine the displacement of the image of the top of the tower with respect to the image of its bottom. The elevation of the bottom of the tower is 1250 m above msl. Solution: r = 6.35 cm= 0.0635 m, h = 50 m H = Flying height above the bottom of tower = 2500 – 1250 = 1250 m The displacement of the image of the top of the tower with respect to the image of its bottom = d = r h / H d = 0.0635 * 50 / 1250 d = 0.254 cm = 2.54 mm

In this example, we calculate the displacement of a tower's image as seen in a vertical photograph.

1. Understand the variables: The tower has a height (h) of 50 m, and its base is at an elevation of 1250 m, with the photograph taken from a flying height of 2500 m above mean sea level (msl).
2. Convert variables: We note the distance of the image of the tower's top from the principal point is r = 6.35 cm, converted to meters as r = 0.0635 m.
3. Calculate effective flying height: The effective height above the tower's bottom is computed as: H = 2500 m - 1250 m = 1250 m, which takes into account the elevation of the bottom of the tower.
4. Calculate displacement: Use the formula d = (r * h) / H. Plugging the values gives: d = (0.0635 m * 50 m) / 1250 m = 0.254 cm or 2.54 mm.
5. This calculation finds the displacement of the top of the tower image consequently providing insight into how high the tower appears relative to its base in the photograph.

Think about how tall buildings can appear shorter or taller based on your viewpoint. If you take a photo of a building standing at an angle, the top may appear shifted compared to the bottom based on the shot. The same measurement concept applies when we look at how the tower appears in the image – the closer it is to the camera, the less displacement we’ll see.

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