posted on Jan, 3 2010 @ 02:46 PM
We have experienced a regularly occurring problem when reviewing video footage of flying objects. The problem is that conventional monoscopic
videography does not provide a means to determine the size, distance or velocity of an object. Because of this it is easily argued that the same
object could be small, close to the camera, and slow (such as a bird or model), large, fast, and far away (such as a fighter jet), or even larger and
traveling at unconventional velocities. I have witnessed this debate go back and forth tirelessly on many threads and I believe that many of these
debates have been unnecessary.
I propose that there is a multi-step mathematical way to eliminate or qualify known objects based on size, distance and velocity. This is possible so
long as within the frame, at some point, there is a known star constellation or other object of known size.
This method is based on the acquisition and conversion of the angular size of objects in the video. For the example provided here we will presume
that the time, location, and direction of the observation has been acquired from the observer so that we are dealing with a known star field.
In the image below we have a hypothetical constellation of which the observed object in the video has passed near by.
Because the star field is known, so is the angular distance between any 2 stars. For the sake of illustration we will use 2 stars that span the
majority of the frame for our measurements.
Stars A and B are known to have an angular separation of 16.47 degrees.
We will first test for the possibility that the objects are Canada geese flying in formation. We know that Canada geese have a wingspan of
approximately 2 meters. The objects according to our star field reference are about 0.38 of a degree across.
This would put geese about 302 meters away from the camera. Observing the video we find that the object covers the distance between stars A and B in
0.6 seconds. Again the angular distance between those 2 stars is known to be 16.47 degrees. At 302 meters from the camera this translates to 87
meters. 87 meters in 0.6 seconds is 522 kilometers per hour. This velocity eliminates Canada geese (which have a maximum speed of about 90
kilometers per hour) as a possible solution for these objects.
Using the above information lets test for F-18 Hornet fighter Jets flying in formation. F-18s have a wingspan of 12.3 meters. Given the angular size
in the image, this would put the aircraft at 1.85 kilometers from the camera. At this distance the angular distance between star A and star B would
equal 536 meters. 536 meters in .6 seconds is equivalent to 3216 kilometers per hour. The maximum speed of an F-18 is 1915 kilometers per hour and
that is at an altitude of 12 000 meters. This eliminates the F-18 as a possible solution for these objects.
One more example. We will theorize that the objects are the navigation lights of an aircraft approximately the size of an F-117 Night Hawk stealth
fighter which has a length of 20.9 meters.
Using our reference stars as a ruler again the total angular size of the formation of objects is 1.84 degrees. This would put such an aircraft at a
distance of 651 meters from the camera. At 651 meters 16.47 degrees is equivalent to 188 meters. 188 meters in 0.6 seconds is equivalent to 0.95
Mach. This velocity is well within the performance capabilities of some conventional jet aircraft and thus qualifies as a possible solution.
It should be added that other performance characteristics can be gauged from this method such as g-loading during turns, and whether or not a
conventional craft would be close enough to be heard, etc.
This is a simplified example of this method and further enhancements to accuracy can be implemented such a accounting for light source blooming and
calibration of the cameras frame rate, etc.
I would be happy to hear from those of you who have corrections, criticisms and possible additions.