WHY AUTO WHEELS LOOK EGG SHAPED 



C. H. Claudy has a very interesting paper 

 in a recent number of the Motor Car 

 which we believe to be of interest to all 

 photographers who make pictures of mov- 

 ing automobiles. 



The author, in undertaking an analysis 

 of the conditions under which the distor- 

 tion of motor car wheels takes place when 

 they are photographed at a high speed, as- 

 sumes a very narrow slit — of one-eighth 

 of ?a\ inch — and a rate of movement of the 

 shatter equal to a passage over a 5-inch 

 plate in i-30th of a second. On this basis 

 the local or relative speed becomes 1-1, 200th 

 of a second, and this figure is one which Mr. 

 Claudy assumes to be attained in practical 

 work. 



EXPOSURE CONDITIONS. 



The next factor to consider is the rela- 

 tion between the distance between auto- 

 mobile and lens, and lens and plate, for, 

 this known, and the speed of the automobile 

 known, a simple calculation in proportion 

 gives the speed of the image of the moving 

 automobile across the sensitive plate. 



SHUTTER SPEEDS. 



I am sure to be questioned here by those 

 not familiar with focal-plane shutters as 

 to the correctness of my statements regard- 

 ing the speed at which they work. It is 

 perfectly true that the picture as a whole 

 receives an. exposure which amounts to only 

 i-i,2ooth of a second, but it is equally 

 true that the small aperture in the curtain 

 seldom, if ever, passes across the 5 inches 

 .of the plate in faster time than i-5oth of 

 a second, about fifteen miles an hour. And 

 this, when you come to think of it, is a re- 

 markable thing in itself — that any, mechan- 

 ism, small and light enough to be carried 

 in the hand, can jerk, from a state of rest, 

 a curtain, rush it suddenly at fifteen miles 

 per hour for 5 inches, and then as suddenly 

 check its . motion, and all without breaking 

 a spring or injuring the mechanism! If 

 the matter is still not quite clear, re-read 

 what I have said above regarding the size 

 of the aperture of curtain and the speed of 

 the slit. ' 



Another factor in this matter is that, by 

 a law of optics, the image on the senstive 

 surface is upside down. By a law of the 

 camera maker, curtain shutters operate from 

 top to bottom. It is plainly to be seen, there- 

 fore, that the bottom of the wheels and the 

 bottom of the automobiles get their pictures 

 taken last, then the middle, which in the 

 meantime has moved, and finally the top, 

 which has moved still more. 



WHEEL MOVEMENT. 



J now come to the last factor in this mat- 

 ter, and one which is really most important, 

 as it is most interesting and seemingly 

 paradoxical. The distortion is always great- 



er in the wheels than anywhere else, and 

 also always greater at the tops of the wheels. 

 This would seem but natural according to 

 the foregoing explanation, were the dis- 

 tortion equal all over the car, but, on the 

 other hand, that of the tops of the wheels 

 far exceeds that anywhere else. This is 

 because the upper parts of the wheels travel 

 several hundreds per cent, faster than the 

 lower parts, while all the rest of the auto- 

 mobile moves at a uniform speed. 



Obviously, the upper spokes of a wheel 

 revolving on the ground travel, with ref- 

 erence to any fixed point, at a much great- 

 er rate than those near the ground. Of 

 course, were the wheel revolving in the 

 air, or considered with reference to its 

 hub only, all parts would have to be con- 

 sidered as moving at the same speed. 



However, we have to do with a fixed 

 point, the lens of the camera. The slit of 

 the shutter secures the impression of the 

 lower part of the wheel first. As it slides 

 across the plate and the upper part is taken, 

 the speed of the image rapidly increases 

 as it approaches the top of the wheel. The 

 motion is thus shown more plainly at the 

 top of the wheel than anywhere else, and 

 any given point has a chance to slide a 

 little further on the plate than those be- 

 low it, which gives to the top of the wheel 

 a blurred look as well as a distinct forward 

 inclination. 



AN EXAMPLE. 



It may be interesting to state that when 

 the upper spoke is absolutely perpendicular 

 its extremity is going at double the speed 

 of the car — 120 miles per hour, if the car 

 be making sixty ; 200 feet per second if the 

 car be making one hundred. This also is 

 a very simple calculation. The spoke from 

 the free end to the ground end is to be 

 considered as a lever. The ground end is 

 the fulcrum, the hub the point of power 

 application. As the upper point of the spoke 

 is twice the distance from the fulcrum that 

 the hub is, the movement of the hub must 

 be twice amplified at the upper part of the 

 spoke. Consequently, if the hub (the car) 

 be making sixty miles per hour, the upper 

 point of the spoke must be making double 

 that, 120 miles per hour. Of course, this 

 condition of affairs obtains for only a theo- 

 retical instant. The fulcrum is not fixed, 

 but moving, and the upright spoke of one 

 instant becomes the horizontal spoke of 

 the next. 



Still, in dealing with pictures, we have 

 to do with minute fractions of a second, 

 and the doubled speed of the top of the 

 periphery of the wheel is an important fac- 

 tor in the egg-shaped distortion which I 

 have tried to explain in as simple a way as 

 possible. 



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