I assumed that the object started from rest with zero initial velocity and the shutter opening coinciding with that instant. If you can't manage that you have one equation in two unknowns -- not enough information. Your equation appear to have t^2 in the denominator. If we measure t from the instant the object is released, the distance it falls in an interval t2 - t1 is (x2 - x1) = 0.5*g*(t2^2 - t1^2) = 0.5*g*(t2 + t1)*e. Two measurements with t1 the same for both will give e. Unfortunately, that's hard to do. Knowing the size of the object will remove the uncertainty resulting from an unknown magnification. Roger > > >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 :-) -- _______________________________________ R. Eichhorn Professor of Mechanical Engineering University of Houston Fax: 713-743-4503 Tel: 713-743-4383 email: eichhorn@uh.edu
