Math Geniuses?

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Does anyone know how to calculate the amount of land, in sq ft, you could cover with a photo looking straight down, from a pre-defined altitude. I know that the two main variables would be focal length and altitude (and the MP of the photo), but I do not know the equation (or the focal length for that matter).

For example, if I wanted to recreate Google Earth for my town, by taking photos in a systematic way, all from the same altitude, and then stitch them together, how could I calculate how many shots would be needed to cover a known area?
 
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Take a pic from 100 ft up, print it out and then measure it and then as Meta says think about an overlap
 
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Field of view on the p3 is 94 degs. So that's a triangle with a 94 deg top angle spreading down to the ground. Split that triangle in half down a vertical line that starts at the camera and you get 2 triangles with 47 degrees at the top and a right angle at the bottom. So that tan(47)= x/ h where h is your height and x is half the image width. So your image width is: 2h×tan(47). Mind you I'm not sure about the crop factor on the sensor so things might be a little different.
The empirical way to do this is to stick a ruler on a wall then get a tapemeasure out. Take a shot of the ruler at 3 or 4 distances, go into Photoshop and count the number of pixels that constitutes the ruler in each image and convert that in pixels per inch or cm, then multiply that by 4000 to get the width of the image. Finally go into excell and plot the width of the image versus the distance and that will let you regress a predictive relationship that will give you the image width for any flying height.

Bit convoluted but should be accurate.
 
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Field of view on the p3 is 94 degs. So that's a triangle with a 94 deg top angle spreading down to the ground. Split that triangle in half down a vertical line that starts at the camera and you get 2 triangles with 47 degrees at the top and a right angle at the bottom. So that tan(47)= x/ h where h is your height and x is half the image width. So your image width is: 2h×tan(47).
That's what I'm talking about. Math! (Used to be good at it.)

So plugging in 100 M... 2(100)*tan(47) should give me image width (in M), right?

(Still need to work on it, because when I plug that in to my calculator, I get a neg. number.)
 
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I used the link above and found this triangle calculator.

http://www.calculator.net/triangle-calculator.html

My logic was if we have a FOV of 94 degrees and we drew 2 lines starting at the camera representing the 94 degrees, when they hit a flat surface the 2 angles would be both 43 degrees. If we half the triangle to represent the height from the ground we now create a 90 degree angle with the ground, from the camera the new angle is 47 degrees and the final angle remains 43 degrees.
Using the link above if we input 47 degrees as angle A(position of phantom), 90 degrees as angle B and the height of the phantom as side Z, then press calculate the results will give you a length for side 2, which represents the ground in my calculation, double this and it should give you an approximate distance left to right of the FOV.

So at a height of 400ft the distance covered left to right should be approximately 858ft

Based on a 4:3 image size I calculate it should cover an area 858ft x 643ft (551,694 Sqft)

of course there's every chance I've got it wrapped around my neck.....:confused:

PS make sure you only have the 3 values input above, if there are any other values still in the boxes it will not work.
 
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Based on a 4:3 image size I calculate it should cover an area 858ft x 643ft (551,694 Sqft)

of course there's every chance I've got it wrapped around my neck.....:confused:

Thanks for putting your neck out there!

That number is enough to help me decide upfront whether the idea I have is doable.
 
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You want the horizontal and vertical FOV angles and subject distance. Just google FOV calculators. It will tell you everything
 
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This one will work. http://www.scantips.com/lights/fieldofview.html
You will need to know the mm focal distance equivalent of a full frame sensor for our lens. This would be 16.8mm or 20.2mm depending on if the 94° is a horizontal or diagonal FOV measurement. Choose option 1 and leave it at 36 and 24. This represents a full frame sensor size. Put in your flying height at the subject distance. Hit compute. Multiply horizontal dimension by vertical dimension to get your area in sq ft/meters depending on what units you use for subject distance. You may also want to google photogrammetry calculators
 
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You'll want about a 60% overlap in both horizontal and vertical directions. But using pix4d would be easier as soon as they have it ready for P3 which they are doing
 
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OK. So I'd need to take 2,400 exposures to get a planar panorama of the island I live on.

I wonder how long it would take Photoshop to stitch that?

Ugh. ;)
 

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