Detailed Explanation

In this example, we are asked to find the scale of a photograph taken from a height of 1200 meters above mean sea level (msl). The scale formula in photogrammetry relates the focal length of the camera to the difference in altitude between the camera and the terrain.

1. Explore the Variables: We identify the altitude of the photograph (H = 1200 m), the focal length of the camera (f = 15 cm), and the terrain elevations (h = 80 m and h = 300 m).
2. Apply the Formula: The scale of the photograph can be calculated using the formula: \(Scale = \frac{f}{(H - h)}\). This equation calculates how the image size relates to its real-world size based on elevation.
3. Calculate the Scale:
4. For h = 80 m: \(Scale = \frac{15 cm}{(1200 m - 80 m)} = \frac{15 cm}{1120 m} \approx 1 : 7467\) which tells us that 1 cm on the photo represents 7467 cm on the ground.
5. For h = 300 m: \(Scale = \frac{15 cm}{(1200 m - 300 m)} = \frac{15 cm}{900 m} \approx 1 : 6000\). This means 1 cm on the photo corresponds to 6000 cm on the ground.

Thus, the calculation for elevation variations demonstrates how scale changes with differences in height.

Detailed Explanation

In this example, we're tasked with determining the scale of a photograph taken from a high altitude over flat terrain.

1. Identify Given Values: We know the focal length (f = 152 mm), the flying height (H = 2780 m), and the elevation of the flat terrain (h = 500 m).
2. Use the Scale Formula: The scale is derived from the same formula: \(S = \frac{f}{(H - h)}\).
3. Convert Units: Ensure the focal length is in the same unit as the flying height, so we convert 152 mm into meters, which equals 0.152 m.
4. Calculate the Scale: Plugging the numbers in:
   \[S = \frac{0.152}{(2780 - 500)} = \frac{0.152}{2280} \approx 1 : 15000\]. Here, the scale signifies that 1 cm in the photograph depicts 15000 cm on the ground.

Detailed Explanation

This example revolves around finding the necessary height for an aircraft to achieve a specific photographic scale.

1. Given Data: We acknowledge the focal length (f = 20 cm), average elevation of terrain (h = 1600 m), and the desired scale (1:10,000).
2. Understanding Scale Requirement: The scale indicates how much ground is represented in the photograph compared to its actual size. In this case, a scale of 1:10,000 means that 1 cm on the photograph corresponds to 10,000 cm on the actual ground.
3. Convert Scale to Fraction: Convert the scale into a formula: \(S = \frac{20/100}{(H - 1600)}\).
4. Rearranging: Rearranging gives us the height we need: \(H = Sf + h\). Plugging in the numbers:
   \[H = (0.2) (10000) + 1600 = 3600 m\]. Thus, to achieve the desired photographic scale, the aircraft must fly at an altitude of 3600 m.

Detailed Explanation

In this scenario, we examine how to establish the scale of a photograph based on specific measurements provided.

1. Analyze the Inputs: We have a line of known ground distance (300 m) that appears as 9 cm on an aerial photograph, with a camera focal length of 30 cm and an elevation of 600 m.
2. Formula Utilization: First, we set up the relationships to find flying height (H). We'll rearrange the relationship: \(\frac{0.09}{300} = \frac{0.30}{(H - 600)}\).
3. Solve for H: By multiplying both sides, we find that: \(H - 600 = \frac{0.30 * 300}{0.09}\) yields \(H = 1600 m\).
4. Calculate Scale: Finally, with determined height, the average scale is found using \(S = \frac{f}{(H - h)}\): \(S = \frac{0.30}{(1600 - 700)} = 1 : 3000\).

Detailed Explanation

This example calculates how high an airplane must fly to capture an aerial photograph with specific measurements adjusted for terrain elevation.

1. Interpret Given Quantities: The measurements established reveal a 12.70 cm line on the photo correlating to a 2.54 cm length on a map whose scale is given as 1/50,000 with an average elevation of 200 m.
2. Set Up Ratios: The relationship between photograph distance, map distance, and scales provides a means to determine the photo scale. Setting equalities shows us the photo scale: \(5.0 = 50000 * Photo scale\) which simplifies to \(Photo scale = 1/10,000\).
3. Final Step - Height Determination: By substituting the values back into the scale equation: \(S = \frac{f}{(H - h)}\), the needed height H can be evaluated leading to the conclusion \(H = 1800 m\).