26. Constraints from dsnap vs. dfrag

Note: These values come fro L8AC.
Note 2: Don't forget the constraint that d_snap > 2.2 in.

For m_head = 5 lb
The only two constraints here are PE < 600 ft-lb and d_snap > 2.2 in.

d_frag, ft ↓ d_snap, in →	*1.4*	*1.6*	*1.8*	*2.0*	*2.2*	*2.4*	*2.6*	*2.8*	*3.0*
2	695	694	694	693	692	691	689	685	680
3	692	691	689	688	685	682	678	671	659
4	687	685	683	680	676	671	663	650	630
5	682	679	675	671	665	656	643	624	592
6	675	671	666	659	650	638	620	592	546
7	666	661	654	645	633	616	592	554	491
8	657	650	641	630	614	592	560	510	428
9	646	638	626	612	592	564	523	460	357
10	635	624	610	592	567	532	482	405	277

d_frag, ft ↓ d_snap, in →	*1.4*	*1.6*	*1.8*	*2.0*	*2.2*	*2.4*	*2.6*	*2.8*	*3.0*
2	-0.48	-0.48	-0.49	-0.49	-0.50	-0.51	-0.52	-0.53	-0.55
3	-0.50	-0.51	-0.52	-0.52	-0.53	-0.55	-0.56	-0.58	-0.61
4	-0.53	-0.53	-0.54	-0.55	-0.57	-0.58	-0.60	-0.63	-0.67
5	-0.55	-0.56	-0.57	-0.58	-0.60	-0.62	-0.64	-0.68	-0.73
6	-0.57	-0.58	-0.60	-0.61	-0.63	-0.66	-0.69	-0.73	-0.79
7	-0.59	-0.61	-0.62	-0.64	-0.66	-0.69	-0.73	-0.78	-0.85
8	-0.62	-0.63	-0.65	-0.67	-0.70	-0.73	-0.77	-0.83	-0.90
9	-0.64	-0.66	-0.68	-0.70	-0.73	-0.77	-0.81	-0.88	-0.96
10	-0.66	-0.68	-0.70	-0.73	-0.76	-0.80	-0.86	-0.92	-1.02

d_frag, ft ↓ d_snap, in →	*1.4*	*1.6*	*1.8*	*2.0*	*2.2*	*2.4*	*2.6*	*2.8*	*3.0*
2	59	64	69	76	85	95	109	127	152
3	88	96	104	115	127	143	164	191	229
4	118	127	139	153	170	191	218	254	305
5	147	159	174	191	212	239	273	318	381
6	176	191	208	229	255	286	327	381	457
7	206	223	243	267	297	334	382	449	533
8	235	255	278	306	340	382	436	508	609
9	265	287	313	344	382	430	491	572	686
10	294	319	347	382	424	477	545	636	762

No constraints of its own (zero of negative velocities, supersonic speeds). Boldface is from PE and d_snap. Allowed range = 380–760 ft s^-1.

For m_head = 6 lb
There are three sets of constraints here, PE, d_snap, and v_frags. The PE is the most extensive, and disallows half the values. The d_snap also eliminates half the value, but largely overlaps the PE. The v_frags eliminates only a few values at the lower right, and duplicates exclusions there from PE. All the exclusions are shown in boldface each of the tables below.

d_frag, ft ↓ d_snap, in →	*1.4*	*1.6*	*1.8*	*2.0*	*2.2*	*2.4*	*2.6*	*2.8*	*3.0*
2	694	693	692	691	688	684	676	656	594
3	690	688	686	682	677	667	648	606	465
4	685	682	677	671	661	644	611	534	285
5	678	673	666	656	640	613	562	443	53
6	669	662	652	638	615	576	502	331	-230
7	659	649	636	616	586	533	432	198	-565
8	647	635	617	592	551	483	351	46	-952
9	634	618	596	564	513	426	259	-127	-1390
10	619	599	572	532	469	362	156	-321	-1879

d_frag, ft ↓ d_snap, in →	*1.4*	*1.6*	*1.8*	*2.0*	*2.2*	*2.4*	*2.6*	*2.8*	*3.0*
2	-0.49	-0.49	-0.50	-0.51	-0.52	-0.54	-0.57	-0.62	-0.73
3	-0.51	-0.52	-0.53	-0.55	-0.56	-0.59	-0.64	-0.71	-0.87
4	-0.54	-0.55	-0.56	-0.58	-0.61	-0.64	-0.70	-0.80	-1.02
5	-0.56	-0.58	-0.60	-0.62	-0.65	-0.70	-0.77	-0.89	-1.16
6	-0.59	-0.60	-0.63	-0.66	-0.70	-0.75	-0.84	-0.98	-1.31
7	-0.61	-0.63	-0.66	-0.69	-0.74	-0.80	-0.90	-1.08	-1.45
8	-0.64	-0.66	-0.69	-0.73	-0.78	-0.86	-0.97	-1.17	-1.60
9	-0.66	-0.69	-0.72	-0.77	-0.82	-0.91	-1.04	-1.26	-1.74
10	-0.69	-0.72	-0.76	-0.80	-0.87	-0.96	-1.10	-1.35	-1.89

d_frag, ft ↓ d_snap, in →	*1.4*	*1.6*	*1.8*	*2.0*	*2.2*	*2.4*	*2.6*	*2.8*	*3.0*
2	66	73	83	95	112	136	173	237	377
3	99	110	125	143	168	204	260	356	566
4	132	147	166	191	224	272	346	475	755
5	165	184	208	239	281	340	433	593	944
6	198	220	249	286	337	408	519	712	1132
7	231	257	291	334	393	476	606	830	1321
8	264	294	332	382	449	544	692	949	1510
9	297	331	374	430	505	613	779	1068	1699
10	330	367	415	477	561	681	865	1186	1887

m_head, lb	N	PE, ft-lb	v_bodyafter, ft s-1	v_frags, ft s-1	d_frags, ft	d_snap, in
5	18	280–590	-0.7 to -1.0	380–760	5–10	2.4–3.0
6	18	160–590	-0.7 to -1.1	380–860	2–10	2.4–3.0
7
8
9

For m_head = 7 lb

There are three sets of constraints here, PE, d_snap, and v_frags. The PE is the most extensive, and disallows more than half the values. The d_snap also eliminates half the values, but largely overlaps the PE. The v_frags eliminates a third of the values, at the lower right, and duplicates exclusions there from PE. All the exclusions are shown in boldface each of the tables below.

d_frag, ft ↓ d_snap, in →	*1.4*	*1.6*	*1.8*	*2.0*	*2.2*	*2.4*	*2.6*	*2.8*	*3.0*
2	693	698	689	685	677	656	570	-1596	246
3	688	685	680	671	653	606	412	-4463	-319
4	681	675	666	650	618	534	190	-8475	-1109
5	672	663	649	624	573	443	-96	-13,630	-2126
6	661	648	628	592	519	331	-444	-19,940	-3368
7	647	630	603	554	454	198	-856	-	-4836
8	632	610	574	510	380	46	-1332	-	-6531
9	615	587	541	460	296	-127	-1871	-	-8451
10	596	561	505	405	202	-321	-2473	-	-10,600

d_frag, ft ↓ d_snap, in →	*1.4*	*1.6*	*1.8*	*2.0*	*2.2*	*2.4*	*2.6*	*2.8*	*3.0*
2	-0.49	-0.50	-0.12	-0.53	-0.56	-0.62	-0.76	-1.81	0.17
3	-0.52	-0.54	-0.56	-0.58	-0.63	-0.71	-0.92	-2.49	0.48
4	-0.55	-0.57	-0.59	-0.63	-0.69	-0.80	-1.08	-3.18	0.78
5	-0.58	-0.60	-0.63	-0.68	-0.75	-0.89	-1.24	-3.86	1.08
6	-0.61	-0.64	-0.67	-0.73	-0.82	-0.98	-1.40	-4.55	1.39
7	-0.64	-0.67	-0.71	-0.78	-0.88	-1.08	-1.56	-	1.69
8	-0.67	-0.70	-0.75	-0.83	-0.94	-1.17	-1.72	-	2.00
9	-0.70	-0.71	-0.79	-0.88	-1.01	-1.26	-1.88	-	2.30
10	-0.72	-0.77	-0.83	-0.92	-1.07	-1.35	-2.05	-	2.61

d_frag, ft ↓ d_snap, in →	*1.4*	*1.6*	*1.8*	*2.0*	*2.2*	*2.4*	*2.6*	*2.8*	*3.0*
2	75	87	103	127	166	237	419	1781	-791
3	112	130	155	191	248	356	628	2671	-1186
4	150	174	206	254	331	474	837	3562	-1581
5	187	217	258	318	414	593	1047	4452	-1976
6	225	260	309	381	497	712	1256	5342	-2372
7	262	304	361	445	579	830	1466	6233	-2767
8	300	347	413	508	662	949	1675	-	-3162
9	337	391	464	572	745	1068	1884	-	-3557
10	375	434	516	636	828	1186	2094	-	-3953

m_head, lb	N	PE, ft-lb	v_bodyafter, ft s-1	v_frags, ft s-1	d_frags, ft	d_snap, in
5	18	280–590	-0.7 to -1.0	380–760	5–10	2.4–3.0
6	18	160–590	-0.7 to -1.1	380–860	2–10	2.4–3.0
7	7	190–570	-0.8 to -1.1	420–840	2–7	2.4–2.6
8
9

For m_head = 8 lb

There are three sets of constraints here, PE, d_snap, and v_frags. The PE is the most extensive, and disallows more than half the values. The d_snap also eliminates half the values, but largely overlaps the PE. The v_frags eliminates a third of the values, at the lower right, and duplicates exclusions there from PE. All the exclusions are shown in boldface each of the tables below.

d_frag, ft ↓ d_snap, in →	*1.4*	*1.6*	*1.8*	*2.0*	*2.2*	*2.4*	*2.6*	*2.8*	*3.0*
2	692	689	684	671	625	81	-19	621	670
3	685	679	667	638	535	-689	-916	527	637
4	675	665	644	592	409	-1767	-2171	395	590
5	663	646	613	534	247	-3153	-3784	225	529
6	648	624	576	462	50	-4847	-5756	17	455
7	630	598	533	377	-184	-6849	-8087	-229	367
8	610	567	483	279	-454	-915	-10,780	-513	266
9	587	533	426	167	-759	-11,780	-13,820	-834	152
10	561	494	362	43	-1101	-14,700	-17,230	-1193	24

d_frag, ft ↓ d_snap, in →	*1.4*	*1.6*	*1.8*	*2.0*	*2.2*	*2.4*	*2.6*	*2.8*	*3.0*
2	87	106	136	190	315	923	-996	-323	-193
3	130	159	204	285	473	1384	-1494	-485	-290
4	174	212	272	380	631	1846	-1992	-647	-386
5	217	265	340	475	788	2307	-2490	-807	-483
6	260	318	408	571	946	2769	-2988	-970	-579
7	304	371	476	666	1104	3230	-3486	-1132	-676
8	347	424	544	761	1261	3692	-3984	-1294	-772
9	391	477	613	856	1419	4153	-4482	-1456	-869
10	434	530	681	951	1577	4615	-4980	-1617	-965

No values allowed. Left half eliminated by d_snap. All but one on right half eliminated because of negative or supersonic values. That one (923) eliminated by PE. Weights of head greater than 7 lb don't work well for any solutions.

m_head, lb	N	PE, ft-lb	v_bodyafter, ft s-1	v_frags, ft s-1	d_frags, ft	d_snap, in
5	18	280–590	-0.7 to -1.0	380–760	5–10	2.4–3.0
6	18	160–590	-0.7 to -1.1	380–860	2–10	2.4–3.0
7	7	190–570	-0.8 to -1.1	420–840	2–7	2.4–2.6
8	0	-	-	-	-	-
9