> The starting point is kind of hard to > discern. it appears that they weren't all lined up in a straight > line. Roger The pinheads here indeed not lined up perfectly to start with - that makes the task of deducing the axis of rotation more difficult but not impossible. The axis is not at the centre of the white circle. Actually, that peice of card was there for me to deduce exposure - I took a grey card meter reading for ambient light) which I fixed before taking the shot. I also took other frames without flash to deduce the contribution of flash to the total picture. Curtain movement should place them in a curve, not a sine > wave, shouldn't it? Also, only the final position is fairly well > defined, but not the starting point. On the full res image I was able to sort of deduce the starting point. I ste a "brush" to the same diameter as the head then moved it around till it looked right over the end of the tails. I put all the coordinates in a spreadsheet and set solver to find (by a least squares model) the coordinate which was - on average - equidistant from the pin and tail of all the tracks. Residuals were small - less than 2 pixels af full res. > Even then, the diameter of the > pinhead on one track I measured is about 3 mm (in my roughly 12cm by > 25cm printout), while the track is about 67 mm. This gives a > precision of only about 4 percent. > At an exposure of 1/6s, 33 1/3 rpm gives an angular rotation of 200 > degrees/s. Thus an exposure time of 1/6 s should give an angular > rotation of the pinheads of 33 1/3 degrees. My measurements of the > angle give about 30 degrees, but they are imprecise because I can't > tell the starting point precisely enough. I might even repeat it with 1) black velvet instead of black turntable mat (to minimise blotchyness) 2) longer pins to increase the differential focus effect (making any noise from the background less noticable. > Would a half black - half white disc do a better job? Purely for exposure: maybe. My trial (for testing Karl's patent 2nd curtain trigger) was primarily to demonstrate flash / ambient trails > Do you let > your students come up with their own method to measure the shutter > speed this way? Or do you tell them how to do it? This one would be > useless at a shutter speed of 1/4000s, I think. How do you do that? 1) A faster turntable ;o) 2) The turntable itself is not truly 33 rpm: that's just the maker's speed. Also, unless you use manual exposure, the Canon EOS displays the nearest shtter speed (when set to AV mode) not the precise speed it has decided to use. To test it's shutter I should have used TV mode. Chris was right: the shutter speed (assuming 33 rpm) was longer than the displayed 1/6 second but by my reckoning not as low as 1/8) > I would have required my students (engineers, not > photographers!) to present an error analysis with uncertainty bounds > and a proposal for doing it better the next time and maybe awarded it > a C-, especially if I knew that the shutter speed was 1/6s within a > percent of so. Note comment above on shutter speed. Estimated origin, pixels: 602 1341 RMS error 2.17 pixels from residuals of Least Squares fit. HeadX HeadY TailX TailY 897 1405 897 1262 1107 1532 1140 1260 1392 1591 1419 1179 1681 1696 1723 1128 1969 1794 2017 1061 2237 1877 2293 1006 2497 1981 2565 977 2746 2075 2829 917 2986 2164 3071 875 3209 2225 3298 816 > I've assumed that there was no wobble in the turntable. > > Please know that much of this is tongue in cheek! Yes, right ;i)
