h a l f b a k e r y
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Before getting to the Idea, here is the problem it hopes
I live in a place where jets fly above, and make a lot of
noise. Some years ago I discovered that there was a
to the effect that the jets were supposed to fly at least
1000 feet (about 305 meters) above the ground,
actually often fly only a little higher than the tree-tops.
Now, consider the Inverse Square Law. If a noise is
generated 1000 feet off the ground, and an equal noise
generated at half that altitude, the noise-energy
at the ground is 4 times higher for the lower-altitude
If the plane flies at 333 feet (1/3 of 1000), the noise-
energy will be 9
times higher than from a plane at 1000 feet.
Trees generally don't grow as high as 100 feet around
so planes can fly fairly safely at 100 feet (1/10 of 1000)
and thus the ground receives 100 times the sound-
as from a plane flying at 1000 feet.
To be fair, there is another factor, in that human
is "logarithmic", not "scalar". Encountering 100 times
noise energy is not the same as experiencing a 100-
louder sound. Nevertheless, the lower-flying planes are
The military presence in this town extends into its
life; there are a lot of retired people here who don't mind
the jets making all that noise. So, there is no easy way
enforce the 1000-foot flying Rule. That's where this Idea
One well-known way to measure the distance to
involves its "angular diameter". Consider a TV --if you
far from it, it appears smaller than if you sit close to it -
but you know it is the same size. Your overall "field of
view" has less of it occupied by the distant TV than is
occupied by the near TV. You can imagine an angle from
your eyes to the left and right edges of the TV; that
is smaller for the distant TV.
Now imagine a camera lens engraved with angular
markings, rather like the circles of a bulls-eye. Any
you make will include those markings in the finished
photograph, and no matter if the finished photo is
enlarged or shrunk, the markings will accurately indicate
the degree to which something in the photograph
the field of view.
So, take a picture of a jet flying by, at some modest
distance, maybe a half-kilometer. The physical
dimensions of the jet are public knowledge, and your
picture now includes its angular diameter. You can use
those two data items to compute exactly how far the jet
is, away from the camera.
More, there is another angular measurement in the
picture, the height of the jet off the ground. When you
know the exact distance of the jet, that height can be
computed easily. So now you have evidence you can
to the Legal System, to make the case that the pilots
don't fly at least 1000 feet can be caught and punished.
(Lenses marked as described here almost certainly exist.
I'm asking that ordinary/common cameras, like on cell
phones, be given an easy way to attach such a lens.)
Jeffrey's Exif viewer
Highly recommended, you probably already have all the info you need [mitxela, Mar 30 2014]
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||So, what happened when you phoned the airbase,
without photographic evidence?
||Also, what's to stop you from using a lens with
different angular measurements?
||I'm not sure how accurate this will be. If you take a photo exactly perpendicular to the longitudinal axis of the jet, then it will be accurate. However, if you are at an angle to the jet your calculations will underestimate the distance.
||Have you tried to do a measurement with commercially available range finders?
||If your camera doesn't have an optical zoom then, given the models of both phone and airplane, the height is a matter of pretty basic math.
||Or just paintball the plane - that should settle any
||Or just hold your thumb up at arms length as you
snap the plane. If your thumb looks smaller than
the plane, the plane is probably too close.
||Even the cheapest digital cameras include lens focal length in the exif data, which when coupled with sensor size (also usually in the exif) gives you all the information you would get from physically marking the lens. My camera also records the phase detection's guess at pupil-to-object distance, but naturally this becomes less and less accurate as the object is moved further away.
||To calculate distance from angular size, you will of course need to take distortion into account - angular size is very rarely uniform across the frame. I suppose it depends on how much accuracy you need, longer focal lengths generally will be more accurate.
||[xaviergisz], you can take multiple photographs.
The planes tend to fly in curved paths (pilots are
practicing for landings on the short deck of an
aircraft carrier), and you can almost always get a
good full-side-view of the plane.
||As for range-finders, these are MILITARY jets. The
pilots won't appreciate being "targeted" by a
||[FlyingToaster], I will assume the Legal System will
want more evidence, or better evidence. We
want to get past the "reasonable doubt" issue.
||[MaxwellBuchanan], if such lens-attachments as
I've described in the main text were common, lots
of people could independently provide data for
the Legal System. It would not be reasonable to
think that ALL of them were using "rigged"
||[mitxela], it is possible, based on your remark and
that of [FlyingToaster], that the angular-diameter
markings don't have to be part of the lens, and can
be added by the image-processing software of the
camera. On the other hand, this is more
susceptible to "rigging"....
||Depth of field will defeat this. The markings in or
near the lens will be far enough out of focus to be
||Nobody appreciates being "painted" by a laser, but there are passive systems: artillery binoculars, etc.
||But a bit of digging in your cellphone manual might turn up something useful as towards angular whatsis.
||Louder, but for a shorter period....
||I don't think any simple passive marking system on
the lens will be in focus.
||Another way to prove you haven't used falsified markings is for someone to go stand where you stood when
took the picture, which is provable by the angular relationships of near and far objects on the ground, and
that the angular sizes of objects on the ground match your lens's markings.
||// Depth of field will defeat this. The markings in or near the lens will be far enough out of focus to be
||// I don't think any simple passive marking system on the lens will be in focus. //
||True, but a problem well solved in gun sights. IIRC, some of them use some sort of hologram to make it
appear that the red dot is infinitely far away, while others achieve the same with a relatively simple lens arrangement
(probably just a collimator, come to think of it). (In that application, the main goal is to make the dot appear to lie on the
line in space along which the bullet will travel, even when you move your eye off-axis, which a simple red dot in the
middle of the eyepiece would not do.) The same might be doable with this. It would likely need
some off-axis optics, and a beamsplitter to superimpose the artificially infinitely far away image on top of the real
scene. That would add a bit to cost, but this is going to be a specialty item anyway. Most people who want to know
the AGL altitudes of planes are going to check an ADS-B website, and most people who want to measure the
sizes of or distances to things with a camera are going to use a fixed-focal length lens and a camera