Roger Eichhorn wrote:
>
> In a time t in seconds, a heavy object will fall a distance x (in
> meters) = gt^2/2, where the t^2 is time squared and g is the
> acceleration of gravity, 9.8 m/s^2. Thus, at 1/400 second, the
> object will fall 0.0306 mm, hardly a simple blur to measure on film.
ummm, no
s = 1/2 ge(2t + e)
where s is the distance,
g is acceleration due to gravity
e is the exposure time in seconds
and t is the delay between the object being dropped and the shuter
opening.
so the blur distance actually depends on both the shutter speed and how
long you wait between droping the object and firing the shutter.
And, of course, the actual blur on the film depends on the magnification
factor. the 0.0306mm figure would be rather significant if the object
were being recorded at 10 times actual size, and the 1.2 cm you mention
later would be all but immesurable if the magnification was 1/10000.
> _______________________________________
> R. Eichhorn
> Professor of Mechanical Engineering
Clearly I shouldn't expect you to be unaware of these simple facts :-)
A major problem would be releasing the object and firing the shutter
simultaneously.
If we assume that this is done electrically, then all we need to
consider is the latency the camera exhibits. (remember that a meter
reading may be taken, mirror may need to be lifted and an aperture
stopped down, all before the shutter can be opened).
In any case I've heard of a camera with a claimed 6ms latency (I expect
that this is without the need to lift the mirror, but bear with me)
Let's assume your 1/400th of a second with various latencies:
latency object travel
0 0.0306 mm
6ms 0.1776 mm
10ms 0.2756 mm
100ms 4.961 mm
So the error is certainly larger than what it is we're trying to
measure.
If deliberately delay the fring of the shutter for 1 secons (and
obviously drop the object from around 10 metres above the camera) the
error due to the latency in the camera is less, but errors resulting
from air resistance affecting the velocity of the object may start to
become significant.
We also can't ignore the fact that a focal plane shutter will conspire
to add even more variables.
If the curtain runs in a direction parallel to the falling object, the
actual path recorded on the film will be longer or shorter depening on
whether the curtain moves in the same direction as the image or in the
opposite direction.
Even with the curtain running in a direction 90 degrees from the
direction of the falling object, the curtain will only open and close
incrementally, with the time taken to open being some time a little
shorter than the flash sync speed. so it can take between 2 and 16 ms
for the centre portion of the film to be exposed after the shutter
starts to open. (for sync speeds between 1/250 and 1/60 respectively).
*however* if you measure the start and finish of the blur against a
calibrated background, you could determine the shutter speed bt
calculating the time at which thestart of the exposure of that
particular piece of film started, and when it stopped. Incidentally
this might tell you something about the latency too :-)
Steve
p.s. for the curious...
s = 1/2 ge(2t + e)
= 1/2g (e)(2t + e)
= 1/2g (t - t + e)(t + t + e)
= 1/2g ((t+e) - t)((t+e) + t)
= 1/2g ((t+e)^2 - t^2)
= 1/2g(t+e)^2 - 1/2gt^2
= distance object falls in t+e seconds less
distance object falls in t seconds
= distance object falls in the e seconds after t seconds
n.b. assumes starting from rest, ignoring air resistance, and local
garavitational anomalies :-)
