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How much ground can I see?

Discussion in 'Pro/Adv Discussion' started by Tenly, Jun 15, 2016.

  1. Tenly

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    With a Phantom 3 Professional camera pointing straight down at the ground, what are the dimensions of the area on the ground that I can see at various altitudes and at 4K and 1080p for videos and for still photos at 16:9 and at 4:3 aspect ratios respectively?

    Is there a formula that can be used - or a chart that can be referred to?

    I want to plot a search grid with little to no overlap and obviously, the higher up you are, the more ground you can see but I'm curious what the actual numbers are.

    I do know that there are several ways I could determine this via taking pictures from the various altitudes and then measuring the visible areas - I was hoping there might be an existing chart or formula that would save me the trouble.
     
  2. GadgetGuy

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    Use the 94° FOV of the lens, and some basic trigonometry. The 16:9 frame is just an in-camera crop of the full 4:3 sensor frame, and throws away those pixels that you could otherwise use for overlap, to reduce the number of images needed.
     
    #2 GadgetGuy, Jun 15, 2016
    Last edited: Jun 15, 2016
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  3. Wolfiesden

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    Field of View Calculator
    It says 123x91 @400'
    (20mm lens, option 4 1/2.3" CCD)

    The Photo Tools app I have on my phone says:
    128'x96' @400'
    96x72 @300'

    But it only has 1/2" sensor not 1/2.3" so those numbers may be a little on the high side maning the website is probably correct..

    I would make the plots for 120x90 to allow minor overlap and the nice round zeros make the math easy.
     
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  4. Meta4

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    Almost there but you got confused by the lens and sensor size.
    The actual focal length of the P3 lens is 3.61mm and it has a tiny sensor but I'm not sure of the size.
    The correct answer is a considerably bigger area but I can't get the FOV calculator.

    If the P3 shot 3:2 like an SLR the area covered would be 720 x 480
    For the P3 shooting 4:3 the area would be something like 720 x 540

    There's no point using 16:9 as that is just the same 4000 x 3000 image with a bit cut off the top and bottom.
     
  5. Wolfiesden

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    Well according to the DJI site:
    Sony EXMOR 1/2.3”
    FOV 94° 20 mm (35 mm format equivalent) f/2.8, focus at

    The 20mm equivalent is what I used in the calculators.
     
  6. Wolfiesden

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    Width=6.25 mm, Height=4.69 mm, Diagonal=7.81 mm, Aspect 4:3, Crop=5.54x

    Those specs match the Exmor sensor specs I could find online.
    Diagonal 7.81 mm (Type 1/2.3) aspect ratio 4:3
     
  7. GadgetGuy

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    The 20mm equivalent can't be used, unless you also use equivalent calculations for all the other variables. If the actual focal length is 3.61mm, then 3.61mm is the correct focal length value to use in the calculations, and not the 20mm equivalent, which only exists to provide a full frame camera lens focal length comparison. The P3 and P4 cameras have the equivalent focal length of a 20mm lens on a full frame DSLR.
     
    #7 GadgetGuy, Jun 16, 2016
    Last edited: Jun 16, 2016
  8. Tenly

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    I appreciate all of the answers - but I'm not 100% sure how to use the information that's been provided - or if you guys have reached a consensus yet...

    If I'm flying 10m above the ground, what are the dimensions of the ground that I'll be able to see in a photo? Once I know that - if i then rise to 20m, 40m or 100m - how do the length and width change? Linearly? By a common factor? Or is it something I have to calculate independently for each altitude?

    (I realized after I posted my original question that I should not have asked about 4K vs 1080p. That will just control the number of pixels contained within the same area.)
     
  9. Wolfiesden

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    Its not 4k vs 1080p and the number of pixels that matters. Its the format. Meaning 4:3 or 16:9. They have different shapes. For stills, the native shape is 4:3. If you set the photos to be 16:9, the sensor is still shaped 4:3 and the software simply chops of the top top and bottom to form a 16:9 chunk taken from the center of the pixel area.
     
  10. Meta4

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    Without knowing the sensor dimensions, it's difficult to give an accurate answer.
    There are many different Sony Exmor sensors and I've not seen anywhere that DJI have stated which one they use.
    Exmor - Wikipedia, the free encyclopedia
     
  11. GadgetGuy

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    Forgive me, but it's been a while since my last trig class....;)

    Base Coverage is 2.144 times the Elevation Height

    Here is how I arrived at that:

    Tangent Z°= Opposite/Adjacent
    Tangent 47°= y/x

    Use the FOV of 94° and create two mirrored 47° isosceles triangles out of it.
    "x" is the drone elevation above the ground.
    2y is the coverage area on the ground seen by the camera

    Tangent of 47° x Adjacent(X) = Opposite (Y)
    So at a height of X, 2(Y) is the coverage FOV, where
    image.jpeg


    2(Y) = 2 (Tangent of 47° x Adjacent(X))
    Or coverage (2Y) is 2 (Tangent of 47°) (Height)

    Siri tells me that 1.072 is the tangent of 47° :cool:

    So, 2.144 times the Height is the full Base coverage

    If the angle were 45°, or 90° FOV, for a right angle, it would be exactly 2 times the height for mirrored equilateral triangles (1:1:√2)

    You'll need to massage the numbers for the dimensions of the frame, which is rectangular and not circular.
     
    #11 GadgetGuy, Jun 16, 2016
    Last edited: Jun 16, 2016
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  12. Tenly

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    Right. I get all that - but thanks for elaborating. When I originally posted my question, it was just a brain fart which made me ask for 4K and 1080p separately.

    The 16:9 vs 4:3 question was legit because if I decide to go the video route, I want to view the captured video on a 16:9 monitor. If I record at 4:3, I'll have letterboxing so I thought I might as well just allow the camera to do the cropping and then use all the pixels in the monitor for review.
     
  13. Tenly

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    I think I follow most of this - except it would have been a bit easier if you used y as the height and x as the ground distance to match the conventions I learned in school.... But that's just being picky.... :)

    Where you lose me is towards the end of the calculation where you state that 2.144*height is the "coverage". If I am following correctly, wouldn't that just be the length of 1 dimension of the coverage area? In a 4:3 ratio area, that would be the length of the width (the 4 dimension) and then the other dimension (the 3 dimension) would be ((2.144*height)/4) * 3 or (6.342*height)/4 ?

    So - if height is 10m, we'd have dimensions of:
    21.44m by 15.855m

    ...or where did I go wrong...???
     
  14. With The Birds

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    The maths appear sound however there might be a potential spanner in the works... DJI state 94deg FOV and suggest 20mm 35mm full frame SLR lens equivalent.

    Issue 1. Lens FOV as usually advertised depicts the viewing angle relating to the diagonally oposing corner to corner frame coverage (as illuminated by the lens).

    Issue 2. Anyone with a passing or more dedicated interest in photography will recall the aspect ratio of a 35mm frame is 3:2. We are informed by dji the phantom camera has a 4:3 frame.

    We need to determine if the 94deg fov is corner to corner at 3:2 or if we need to derive the 3:2 actual from 94 deg at 4:3.

    My suspicion is it will be 94deg diagonally accross a 3:2 frame so more number crunching required.

    I would be tempted to plant the phantom 10m from a wall and measure actuals. You can then easily derive the change for any altitude with confidence.
     
    #14 With The Birds, Jun 16, 2016
    Last edited: Jun 16, 2016
  15. Rastus

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    Great thread.
    I often wonder this type of thing when I setup waypoints on the Litchi Hub web application. I find myself questioning am I'm back far enough to capture the coverage/fov that I need at a particular height with the gimbal at a particular angle...


    Sent from my iPad using PhantomPilots mobile app
     
  16. GadgetGuy

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    Good point about the x and y axes. :cool: It's been a few decades!

    Your extrapolations using the ratio areas make sense to me, as the rectangle of the proportions has to fit within the circumference of the circle of the FOV. Now go out and fly, to confirm it! :)
     
    #16 GadgetGuy, Jun 17, 2016
    Last edited: Jun 17, 2016
  17. GadgetGuy

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    I believe the 94 FOV is based upon the 4:3 apect ratio, and welcome any information that might confirm or refute that belief. :cool:
     
  18. GadgetGuy

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    These questions have also come up in creating spherical panoramas, where it was initially assumed that one needed a final row at the bottom with the camera oriented at each of the 60° of the 360° circle. However, it turns out that not even a single down facing image is necessary, because the 60° up elevation images at 60° intervals fully cover the bottom of the sphere. The DronePan app has sought to minimize the number of images necessary for full overlap coverage, without risking missing a necessary image. It's been a work in progress for almost a year to get it right, allowing for time to stabilize in between yaws, and deciding to shoot row by row, or each segment from top to bottom, yawing only between segments. The latter seems to be faster.
     
  19. With The Birds

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    You may well be right. My suspicion was based on the fact that a 20mm focal length lens mounted on a traditional full frame camera (3:2 aspect ratio) produces a field of view of just over 94deg (longest corner to corner dimension).
     
  20. matti

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    I really must read this thread with more time later: Just a few weeks ago I used Litchi to orbit a 65m church tower from a 100m radius and from 50m altitude. I wanted to get the whole tower in the video plus some of the buildings below it and a small amount of sky above it. I aimed Litchi center POI at 35m and the whole tower very well happened to fit into the frame from that distance but there could have been just a bit more radius because some of the buildings were cropped off from some angles.
     
    #20 matti, Jun 17, 2016
    Last edited: Jun 18, 2016