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A short class with Sarah and her students. The other ways are under More.
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Let's begin our discussion on determining the scale of a photograph. The formula we generally use is Scale = f / (H - h), where 'f' is the focal length of the camera, 'H' is the height of the aircraft, and 'h' is the height of the terrain.
What happens if the terrain elevation changes while keeping the height of the aircraft constant?
Great question! If the terrain elevation changes, the scale of the photograph will also change. A higher terrain elevation—meaning 'h' increases—reduces the denominator, making the scale smaller or numerically larger. Keep this in mind as it directly impacts the image's accuracy.
Can you give us an example to illustrate this?
Sure! If the aircraft is at 1200 m above mean sea level, and the terrain elevation is 80 m, the scale would be calculated as 15/(1200-80), resulting in around 1:7467, meaning 1 cm on the photo equals 7467 cm on the ground. Remember the acronym 'H change, Scale range!' to help you recall how elevation affects scale.
Does this mean lower elevations give us larger scales – more detail?
Exactly! A smaller 'h' means a larger scale or more detail in your photograph.
To summarize, the scale of a photograph is inversely proportional to the difference in altitude; as the terrain elevation rises relative to your flying height, the scale diminishes.
Next, we will look into determining the flying height needed to achieve a given photograph scale. Can anyone tell me what formula we would use?
Is it the same one for scale? Scale = f / (H - h)?
That's correct! But here, we need to rearrange it to find H. For example, if we want a scale of 1:10,000 with a terrain height of 1600 m, and the focal length is 20 cm, we calculate it as H = scale * focal length + terrain height.
Could you demonstrate that calculation?
Certainly! H = (10,000 * 0.20) + 1600 m gives us 3600 m for the required flying height.
So, is flying higher always better for capturing details?
Not necessarily! While a higher flight allows us to cover larger areas, it reduces detail, making strategic altitudes essential.
In summary, to achieve a specific scale, you can rearrange the formula to solve for H, taking both terrain height and scale into account.
Now let’s explore how we calculate ground distances between points A and B using their coordinates. The equation we'll use is X = x * (H - h) / f and Y = y * (H - h) / f.
Could you show us how we can apply this?
Absolutely! For example, if point A has photographic coordinates of (2.75, 1.39) cm, and B is at (-1.80, 3.72) cm, we first convert the coordinates to ground coordinates using the above formulas.
And then we would find the distance using the formula for calculating lengths, right?
Exactly! After obtaining coordinates for both points, we can use the distance formula to find AB = √[(X_A - X_B)² + (Y_A - Y_B)²].
Interesting! I see how each coordinate contributes to the final measurement.
To summarize, using photographic coordinates in conjunction with altitude and focal length allows us to derive exact ground distances.
The ratio of image distance to ground distance, fundamental in photogrammetric calculations.
The height at which an aircraft must fly to achieve the desired scale and detail in aerial photographs.
The actual distance between geographic points derived from photographic measurements.
The coordinates used to determine the location of points on a photograph, essential for distance calculations.
To find the scale, just do not fail, divide focal length by height - prevails!
Imagine flying high like a bird, noticing landscapes below as blurred; but with focus tight, your photos delight, revealing the world in exacting sight.
Remember: Fly high, Focus low, Scale grows. H - h over f is the key, let it flow!
F.H.S.E. - Focal length, Height, Scale, Elevation - key terms to remember.
Term
Scale of Photograph
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Term
Focal Length
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The height of the aircraft above mean sea level.
The distance from the lens to the image sensor in a camera, affecting image scale.
Point with a known location used to help georeference images during mapping.
Points used to establish connections in photogrammetry for better adjustment.
A ratio that expresses the relationship between a distance on a photograph and the corresponding ground distance.
This section outlines a series of solved examples that demonstrate the principles and applications of photogrammetry, particularly focused on calculating scales, flying heights, and lengths of lines on photographs.
In this section, several solved examples provide practical applications of photogrammetric concepts. Key calculations include determining the scale of photographs based on focal length and elevation, flying heights necessary to achieve specified scales, and deriving ground distances from photographic measures. These examples solidify understanding of aerial mapping techniques.
This section encompasses a variety of solved examples that are instrumental in understanding fundamental principles of aerial photogrammetry. The main focus of the examples includes:
Scale Calculation: Examples demonstrate how to determine the scale of photographs at varying altitudes and terrain elevations using the formula Scale = f / (H - h), where f is the focal length, H is the flying height, and h is the terrain height.
Flying Height Determination: Some examples involve calculating the required flying height of an aircraft to achieve photographs at specific scales, involving the same scale formula rearranged to yield H.
Ground Distance Calculation: Example problems help ascertain the length of lines between points on the ground based on their photographic coordinates, utilizing the relationships established through the earlier formulae.
Application of Controlled and Uncontrolled Scales: Several examples highlight how overlap and dimensions can influence the overall mapping scale and operational parameters for aerial photography, underscoring the importance of meticulous planning in photogrammetric surveys.
These examples, rooted in practical computation, serve as essential exercises to reinforce the knowledge of aerial mapping and triangulation methods introduced earlier in the chapter.