Our analysis consists of the interpretation of the photo series we took with the green "Goooz" ball. Because the ball did not fall onto precisely the same spot in each frame, it is slightly closer or further away from the camera and therefore slightly larger or smaller in each frame. This would make analysis of the height or width of the ball difficult. Therefore, we took the visible width and visible height of the ball and found the compression ratio of the ball, which we defined to the the ratio between the width and the height of the ball (r = y/x). This data is presented in Fig 1.
 

Exposure	Delay (ms)	Width (px)	Height (px)	Compression (y/x)		Exposure	Delay (ms)	Width (px)	Height (px)	Compression (y/x)
9	0.0016	570	567	0.994737		35	15.9985	689	230	0.333817
10	0.0016	503	504	1.001988		36	15.9985	605	228	0.37686
11	0.0016	518	510	0.984556		37	17.9998	648	246	0.37963
12	1.9996	539	440	0.816327		38	17.9998	686	258	0.376093
13	1.9996	504	428	0.849206		39	17.9998	644	234	0.363354
14	1.9996	536	435	0.811567		40	19.9994	749	309	0.41255
15	3.9992	614	420	0.684039		41	19.9994	719	339	0.471488
16	3.9992	569	453	0.796134		42	19.9994	665	264	0.396992
17	3.9992	590	417	0.70678		43	21.999	698	351	0.502865
18	5.9989	647	387	0.598145		44	21.999	689	318	0.461538
19	5.9989	725	378	0.521379		45	21.999	605	288	0.476033
20	5.9989	716	411	0.574022		46	23.9986	626	351	0.560703
21	7.9985	839	327	0.38975		47	23.9986	605	339	0.560331
22	7.9985	838	348	0.415274		48	23.9986	620	378	0.609677
23	7.9985	755	357	0.472848		49	25.9998	581	402	0.69191
24	9.9997	779	288	0.369705		50	25.9998	479	477	0.995825
25	9.9997	719	279	0.388039		51	25.9998	579	429	0.740933
26	9.9997	770	297	0.385714		52	27.9994	446	345	0.773543
27	11.9993	830	291	0.350602		53	27.9994	638	639	1.001567
28	11.9993	818	297	0.363081		54	27.9994	527	438	0.83112
29	11.9993	632	202	0.31962		55	29.9991	572	495	0.865385
30	11.9993	665	216	0.324812		56	29.9991	617	543	0.880065
31	13.9989	779	222	0.284981		57	29.9991	605	459	0.758678
32	13.9989	845	261	0.308876		58	31.9987	467	420	0.899358
33	13.9989	758	207	0.273087		59	31.9987	527	522	0.990512
34	15.9985	650	192	0.295385		60	31.9987	479	519	1.083507

Figure 1: Raw data from stepped-delay photographs.

We didn't have enough time to take enough photographs to produce statistically significant data, but we did take at least three photos at each delay. We averaged the compression ratio of each frame at a given delay to get one value. This helped to reduce inaccuracy caused by the human error and variation inherent in the process of dropping the ball, photographing it, and then measuring the size of the ball in the resulting photograph.

We proceeded to examine how the ball's compression ratio changed during the course of the collision (Fig 2). When the ball initially collides, the compression ratio drops in an approximately linear fashion until it reaches a minimum 14 milliseconds after impact. Then, it increases in a similar linear manner until it reaches a peak 28 milliseconds after impact. It temporarily declines again at the 30 millisecond mark before resuming its climb by the 32 millisecond mark. This odd peak could be explained by experimental error, but, examining the photographs, it seems to be indicative of the ripple-like distortions in the ball after its impact.

It is also possible that the ball's compression ratio changed in a parabolic fashion during the course of the collision; the vertex of the parabola is a bit too sharp, but this could be explained by experimental error.  Also, the second part of the curve, where the compression ratio increases again, is a bit shallower than the first part of the curve.  This could be because energy was lost in the collision (the ball is particularly elastic), or it could also be experimental error.


Fig. 2: Graph of compression ratio versus delay time.

Without more data - i.e., more other balls to compare this one to - we are unable to make any exceptionally exciting conclusions. However, this ball was in contact with the surface we dropped it onto for approximately 32 milliseconds. About 14 milliseconds into the collision, it was over three times as wide as it was high. Such significant compression was expected, given that the green "Goooz" ball is very malleable. This can be compared to the hard rubber ball which we initially attempted to use; that ball's entire collision took place between two flashes separated by a half-millisecond interval, and the ball's distortion was so small as to be almost unnoticeable. That hard rubber ball, in contrast to the soft "Goooz" ball, is so tough that it is almost impossible to squeeze at all with one hand.