Forums / The Science / Photometry / Determine Height above ground of Aircraft given some known measurements
Determine Height above ground of Aircraft given some known measurements
Hi!
I am trying to find out if it is possible to determine the height above ground of an aircraft given the following information:
Detailed knowledge of the aircraft's wingspan in feet and inches.
Photo taken of the aircraft directly beneath it as it flies overhead.
Known technical information of camera taking picture, i.e., focal length, etc.
Photo snap shot of the aircraft.
Is this possbile?
Thanks.
Hi DocArne and thank you for getting back to me. I wouldn't be able to use two cameras. So, given that I know the focal length and pixel scale of my camera, and given that I know the wingspan in feet and inches of the aircraft, what would the formula be.On my digital camera it says: 1:2.8-5.6/4.6-16.4 ASPH. I assume I can find out the pixels when I actually do the shooting.Is there a common formula for this? It doesn't have to be accurate to the inch in height above ground, just an approximation would be fine.Thanks.
Hi Bulgin,This is a direct application of trigonometry:tangent (angle_subtended_by_wingspan) = wingspan/distanceso distance = wingspan / tan(angle)the angle_subtended_by_wingspan = pixel_scale * number_of_pixels_across_wingspanpixel scale is usually given in arcsec/pixel, and most calculators require the angle tobe in degrees, so you would need to divide the calculated angle above in arcsec by 3600to convert to degrees.The 2.8-5.6 is the f/stop of the camera lens; I think the 4.6-16.4 gives the focal lengthin mm. This means that you are using a zoom lens, so getting the pixel scale correct willbe your first challenge. If you fix your lens to a specific zoom setting (I'd suggest thebiggest "zoom" or longest focal length), you can determine pixel scale during the daytimeby placing a ruler at some known distance, measure the number of pixels across the rulerin your image, and then use the tangent formula above in reverse:tan(angle) = ruler_length(inches) / distance_to_ruler(inches)once you have the angle, you can determine the pixel scale bypixel_scale = angle / number_of_pixelsGood luck!Arne
Wow! Okay! That is quite a mouthful for a technically savvy but not astronomically so person.Perhaps you could just give me a simple example that I could then use as a template to figure this out.I will be taking the photograph of the aircraft when it is directly overhead so I'm assuming the tangent(angle_subtended_by_wingspan) is 90 degrees? I'm not an astrophysicist or astronomer so much of this is a little stretch for me to comprehend, and trigonometry was not my strong suite in secondary school.It seems like what you are saying is that the number of pixels I can count across the wingspan * pixels_scale will equal the angel_subtended_by_wingspan, and then dividing the wingspan by that number will equal the distance???I'm probably way off here.thanks for your assistance.


Hi Bulgin,It is certainly possible to do this. The accuracy depends on many things, including the pixel scale of your camera and the exposure time/blurring of the object. It is basic trigonometry: the distance is the wingspan divided by the tangent of its angular size. If you have two cameras with an accurate knowledge of the spacing between them, you can even eliminate the requirement to know the wingspan in feet/inches, as you can use parallax to determine the distance.Arne