Calculating ground footprint from any altitude...

[Mabou2]

Hi all,

I have an interesting math problem (that I am too dang dumb to figure out myself).
I need to shoot a construction zone that is 2700' wide. The Field of View on the P4P is 84 degrees. So if I am shooting straight down, what altitude would I need to get the bird up to in order to cover the entire width of the location?

I have googled and tried several related calculators, but none of them are driven by the FOV and they often give answers that relate to the diagonal... or they just don't have the right specs for a drone camera.

This seems like it shouldn't be that difficult to calculate, but maybe I am THAT much of an idiot where I don't realize how complicated this is. I'm just asking how high I need to fly to capture a 2,700 foot wide location, with a camera that has an 84 degree field of view.

Thanks!
Matt

 

[sar104]

The FOV value of 84° is diagonal. If you are shooting with an aspect ratio of 3:2, which maximizes the use of the sensor, then the horizontal FOV is 73.7°, given by

ø = 2.arctan(tan(84/2).3/sqr(13)) = 73.7°
​

With that value the calculation of height, h, for a given width of image, w, on the ground, is simply given by

h = w/(2.tan(73.7/2))
​

If w is 2700 ft then we get h = 1800 ft.

So, unfortunately, that's probably not going to be possible with the Phantom firmware height restriction of 1640 ft unless you can launch from somewhere a couple of hundred feet above the construction zone, and equally certainly not going to be a legal non-recreational operation in any country with sUAS laws.

 

[Mabou2]

Wow... thanks Sar! To me, there is nothing "simple" about what you wrote. I guess I'm learning that Math is not going to be at the core any career changes.

I also guess I need to let my client know that I cannot get the shot they want. :-(

Thanks SO MUCH for the info.
Take care,
Matt.

 

[sar104]

Wow... thanks Sar! To me, there is nothing "simple" about what you wrote. I guess I'm learning that Math is not going to be at the core any career changes.

I also guess I need to let my client know that I cannot get the shot they want. :-(

Thanks SO MUCH for the info.
Take care,
Matt.

It would have looked much simpler if I had included a diagram, but I'm not in a position to do that right now.

 

[Meta4]

I have googled and tried several related calculators, but none of them are driven by the FOV and they often give answers that relate to the diagonal... or they just don't have the right specs for a drone camera.

It would have looked much simpler if I had included a diagram, but I'm not in a position to do that right now.

SAR gets an A for geometry
His working is confirmed by this calculator: Camera Field of View Calculator (FOV)
If you put the right numbers in the right places it gives you this:

The solution for projects like this is to shoot many overlapping images to create something like this:
This example is a 50 acre site about 1800 ft on the long side.
370 photos (big overlaps) shot using Dronedeploy at 250 feet
The resulting orthophoto is huge (26000 x 27000 pixels) and has incredible detail.

 

[BigAl07]

I also guess I need to let my client know that I cannot get the shot they want. :-(

Matt this is an excellent time/opportunity to start your new quest in UAS Mapping. This size (and larger) can be done utilizing methods that Meta4 touched on above.