25b--Mhead = 6

For m_head = 6 lb
Increasing the mass of the head to 6 lb increases the number of allowable solutions by shifting the pattern of constraints to the left. The result is a broad zone of disallowed values in the lower left, a narrower zone of allowed values from upper left to lower right, and a small zone of disallowed values in the upper right. The lower boundary of the allowed values is once again defined by PE = 600 ft-lb. the upper boundary, however is defined by two coincident constraints—PE = 0 and v_frags = 1100 ft s^-1. The coincidence of these two constraints shows that there is additional physical meaning to our apparently arbitrary limit for v_frags. To keep things simple, the two masks are here shown as one.

As before, we begin with PE because it offers the most constraints. The allowed values of PE range from 210 to 590 ft-lb. Their greater number (18 of 81 cases) means that a 6-lb head is heavy enough to allow a sizeable range of acceptable solutions.

R_bullet, in ↓ R_head, in →	*3.50*	*3.75*	*4.00*	*4.25*	*4.50*	*4.75*	*5.00*	*5.25*	*5.50*
*4.75*	667	651	628	593	535	431	212	-380	-3153
*5.00*	675	663	647	623	588	531	431	228	-284
*5.25*	681	672	660	643	619	584	528	431	242
*5.50*	686	679	669	657	639	615	580	524	431
*5.75*	690	684	676	666	653	636	611	576	521
*6.00*	693	688	681	673	663	650	632	608	572
*6.25*	695	691	686	679	671	660	647	629	604
*6.50*	697	693	689	683	677	668	658	644	626
*6.75*	699	696	692	687	681	674	666	655	641

The velocity of the fragments is again considered next because it has the potential to provide additional constraints. In this case, three values at the upper right exceeded 1100 ft s^-1 and were disallowed. They coincided with negative values for PE, and so did not add to the constraining process. The mask shown below represents v_frags and PE. The allowed values for v_frags ranged from 430 to 840 ft s^-1.

R_bullet, in ↓ R_head, in →	*3.50*	*3.75*	*4.00*	*4.25*	*4.50*	*4.75*	*5.00*	*5.25*	*5.50*
*4.75*	290	326	372	432	516	641	844	1238	2317
*5.00*	270	299	324	380	439	521	641	831	1183
*5.25*	254	277	306	342	387	446	526	641	820
*5.50*	240	261	285	314	350	394	452	530	641
*5.75*	229	247	268	292	321	357	401	458	534
*6.00*	220	236	254	274	299	328	363	407	464
*6.25*	212	226	242	260	281	305	334	370	413
*6.50*	206	218	232	248	266	287	311	341	376
*6.75*	200	211	224	238	254	272	293	317	347

As for m_head = 5 lb, t_lurch < 25 ms offers milder constraints than PE, and falls within the broader area constrained by PE. It disallows about 15% of the values, again in the lower left. The disallowed values are shown in boldface.

R_bullet, in ↓ R_head, in →	*3.50*	*3.75*	*4.00*	*4.25*	*4.50*	*4.75*	*5.00*	*5.25*	*5.50*
*4.75*	20.7	18.4	16.1	13.9	11.6	9.4	7.1	4.8	2.6
*5.00*	22.2	20.1	17.9	15.8	13.7	11.5	9.4	7.2	5.1
*5.25*	23.7	21.6	19.6	17.5	15.5	13.4	11.4	9.4	7.3
*5.50*	25.0	23.0	21.1	19.1	17.2	15.2	13.3	11.3	9.4
*5.75*	26.2	24.3	22.4	20.6	18.7	16.8	15.0	13.1	11.2
*6.00*	27.2	25.5	23.7	21.9	20.1	18.3	16.5	14.7	12.9
*6.25*	28.2	26.5	24.8	23.1	21.4	19.7	17.9	16.2	14.5
*6.50*	29.2	27.5	25.9	24.2	22.6	20.9	19.3	17.6	16.0
*6.75*	30.0	28.4	26.8	25.3	23.7	22.1	20.5	18.9	17.3

The speed of the lurch ranged from 0.7 to 2.3 ft s^-1, much more here than with the 5-lb head. The acceptable speeds, all rearward, were 0.9–1.2 ft s^-1, close to the observed -0.8 ft s^-1.

R_bullet, in ↓ R_head, in →	*3.50*	*3.75*	*4.00*	*4.25*	*4.50*	*4.75*	*5.00*	*5.25*	*5.50*
*4.75*	-0.78	-0.80	-0.84	-0.89	-0.95	-1.05	-1.20	-1.51	-2.34
*5.00*	-0.76	-0.78	-0.81	-0.85	-0.89	-0.96	-1.05	-1.19	-1.46
*5.25*	-0.75	-0.77	-0.79	-0.82	-0.85	-0.90	-0.96	-1.05	-1.18
*5.50*	-0.74	-0.75	-0.77	-0.80	-0.82	-0.86	-0.90	-0.96	-1.05
*5.75*	-0.73	-0.74	-0.76	-0.78	-0.80	-0.83	-0.86	-0.91	-0.96
*6.00*	-0.72	-0.74	-0.75	-0.76	-0.78	-0.81	-0.83	-0.87	-0.91
*6.25*	-0.72	-0.73	-0.74	-0.75	-0.77	-0.79	-0.81	-0.84	-0.87
*6.50*	-0.71	-0.72	-0.73	-0.74	-0.76	-0.78	-0.79	-0.82	-0.84
*6.75*	-0.71	-0.72	-0.73	-0.74	-0.75	-0.76	-0.78	-0.80	-0.82

These results show that the snap of a 6-lb head is constrained to speeds between 4.1 and 4.8 ft s^-1, a range consistent with the observed v_snap > 3.3 ft s^-1.

R_bullet, in ↓ R_head, in →	*3.50*	*3.75*	*4.00*	*4.25*	*4.50*	*4.75*	*5.00*	*5.25*	*5.50*
*4.75*	5.80	5.41	5.07	4.78	4.51	4.27	4.06	3.87	3.69
*5.00*	6.10	5.70	5.34	5.03	4.75	4.50	4.27	4.07	3.88
*5.25*	6.41	5.98	5.61	5.28	4.98	4.72	4.49	4.27	4.08
*5.50*	6.72	6.27	5.88	5.53	5.22	4.95	4.70	4.48	4.27
*5.75*	7.02	6.55	6.14	5.78	5.46	5.17	4.91	4.68	4.47
*6.00*	7.33	6.84	6.41	6.03	5.70	5.40	5.13	4.88	4.66
*6.25*	7.63	7.12	6.68	6.28	5.94	5.62	5.34	5.09	4.86
*6.50*	7.94	7.41	6.94	6.54	6.17	5.85	5.56	5.29	5.05
*6.75*	8.24	7.69	7.21	6.79	6.41	6.07	5.77	5.49	5.24