29c. Constraints with 105 deg

The results are again presented sequentially for weights of 5, 6, 7, and 8 lb, with a summary at the end. The very wide angle, which includes rearward motion of some of the cloud, provides some positive (forward) lurches, particularly with very low masses of head and cloud. Nonetheless, all the ranges include the observed lurch of -0.8 ft s^-1.
The allowed PEs are shown in bold green, the disallowed values in red. The masking is developed for PE and then applied to v_lurch.

For m_head = 5 lb
The allowed PEs are 110–540 ft-lb. Note the familiar inverse pattern for m_cloud and v_cloud.

v_cloud, ft s^-1 ↓ m_cloud, lb →	*0.1*	*0.2*	*0.3*	*0.4*	*0.5*	*0.6*	*0.7*	*0.8*	*0.9*	*1.0*
0	1105	1105	1105	1105	1105	1105	1105	1105	1105	1105
50	1102	1098	1094	1090	1086	1082	1078	1074	1071	1067
*100*	1090	1074	1059	1043	1028	1012	996	981	965	950
*150*	1070	1035	1000	965	930	895	860	825	789	754
*200*	1043	981	918	856	793	731	668	606	543	480
*250*	1008	910	813	715	618	520	422	324	226	128
*300*	965	825	684	543	403	262	121	-20	-161	-302
*350*	914	723	532	340	149	-43	-235	-427	-619	-811
*400*	856	606	356	106	-144	-395	-645	-896	-1147	-1398
*450*	789	473	157	-160	-477	-794	-1111	-1428	-1746	-2064
*500*	715	325	-66	-457	-848	-1240	-1631	-2033	-2415	-2808
*550*	633	161	-312	-785	-1259	-1732	-2206	-2680	-3155	-3630
*600*	543	-19	-582	-1145	-1708	-2272	-2836	-3401	-3965	-4530

The allowed values for v_lurch are +0.4 to -1.3 ft s^-1. They are less negative than with Θ_cl = 70°, but still include the observed value of -0.8 ft s^-1.

v_cloud, ft s^-1 ↓ m_cloud, lb →	*0.1*	*0.2*	*0.3*	*0.4*	*0.5*	*0.6*	*0.7*	*0.8*	*0.9*	*1.0*
0	0.95	0.96	0.96	0.96	0.96	0.96	0.96	0.96	0.96	0.96
50	0.91	0.87	0.82	0.78	0.74	0.69	0.65	0.60	0.56	0.52
*100*	0.86	0.78	0.69	0.60	0.51	0.42	0.34	0.25	0.16	0.07
*150*	0.82	0.69	0.56	0.42	0.29	0.16	0.02	-0.11	-0.24	-0.38
*200*	0.78	0.60	0.42	0.25	0.07	-0.11	-0.29	-0.47	-0.64	-0.82
*250*	0.73	0.51	0.29	0.07	-0.15	-0.38	-0.60	-0.82	-1.05	-1.27
*300*	0.69	0.42	0.16	-0.11	-0.38	-0.64	-0.91	-1.18	-1.45	-1.72
*350*	0.64	0.34	0.02	-0.29	-0.60	-0.91	-1.22	-1.54	-1.85	-2.17
*400*	0.60	0.25	-0.11	-0.46	-0.82	-1.18	-1.54	-1.89	-2.25	-2.61
*450*	0.56	0.16	-0.24	-0.64	-1.04	-1.44	-1.85	-2.25	-2.66	-3.06
*500*	0.51	0.07	-0.38	-0.82	-1.26	-1.71	-2.16	-2.61	-3.06	-3.51
*550*	0.47	-0.02	-0.51	-1.00	-1.49	-1.98	-2.47	-2.96	-3.46	-3.96
*600*	0.42	-0.11	-0.64	-1.17	-1.71	-2.24	-2.78	-3.32	-3.86	-4.40

For m_head = 6 lb
The same inverse property of m_cloud and v_cloud is seen here. PE ranges between 130 and 590 ft-lb, like before. As before, v_cloud is not less than 200 ft s^-1.

v_cloud, ft s^-1 ↓ m_cloud, lb →	*0.1*	*0.2*	*0.3*	*0.4*	*0.5*	*0.6*	*0.7*	*0.8*	*0.9*	*1.0*
0	1075	1075	1075	1075	1075	1075	1075	1075	1075	1075
50	1071	1067	1063	1060	1056	1052	1048	1044	1040	1036
*100*	1060	1044	1028	1013	997	982	966	951	935	919
*150*	1040	1005	970	935	890	865	829	794	759	724
*200*	1013	950	888	826	763	701	638	575	513	450
*250*	978	880	783	685	587	489	392	294	196	98
*300*	935	794	654	513	372	231	91	-50	-191	-333
*350*	884	693	501	310	118	-73	-265	-457	-649	-841
*400*	825	576	326	75	-175	-425	-676	-927	-1178	-1429
*450*	759	443	126	-190	-507	-824	-1141	-1459	-1776	-2094
*500*	685	294	-96	-487	-879	-1270	-1662	-2054	-2446	-2838
*550*	603	130	-343	-816	-1289	-1763	-2237	-2711	-3186	-3660
*600*	513	-49	-612	-1175	-1739	-2303	-2867	-3431	-3996	-4561

The allowed values for v_lurch are +0.4 to -1.1 ft s^-1, very similar to the 5-lb results. They include the observed -0.8 ft s^-1.

v_cloud, ft s^-1 ↓ m_cloud, lb →	*0.1*	*0.2*	*0.3*	*0.4*	*0.5*	*0.6*	*0.7*	*0.8*	*0.9*	*1.0*
0	0.90	0.90	0.90	0.90	0.90	0.90	0.90	0.90	0.90	0.91
50	0.85	0.81	0.77	0.72	0.68	0.64	0.59	0.55	0.50	0.46
*100*	0.81	0.72	0.63	0.54	0.46	0.37	0.28	0.19	0.10	0.01
*150*	0.76	0.63	0.50	0.37	0.23	0.10	-0.03	-0.17	-0.30	-0.44
*200*	0.72	0.54	0.37	0.19	0.01	-0.17	-0.34	-0.52	-0.70	-0.88
*250*	0.68	0.46	0.23	0.01	-0.21	-0.43	-0.66	-0.88	-1.10	-1.33
*300*	0.63	0.37	0.10	-0.17	-0.43	-0.70	-0.97	-1.24	-1.51	-1.78
*350*	0.59	0.28	-0.03	-0.34	-0.66	-0.97	-1.28	-1.59	-1.91	-2.22
*400*	0.54	0.19	-0.16	-0.52	-0.88	-1.23	-1.59	-1.95	-2.31	-2.67
*450*	0.50	0.10	-0.30	-0.70	-1.10	-1.50	-1.90	-2.31	-2.71	-3.12
*500*	0.45	0.01	-0.43	-0.88	-1.32	-1.77	-2.22	-2.66	-3.11	-3.56
*550*	0.41	-0.08	-0.56	-1.05	-1.54	-2.04	-2.53	-3.02	-3.52	-4.01
*600*	0.37	-0.16	-0.70	-1.23	-1.77	-2.30	-2.84	-3.38	-3.92	-4.46

For m_head = 7 lb
Again the inverse pattern between m_cloud and v_cloud.

v_cloud, ft s^-1 ↓ m_cloud, lb →	*0.1*	*0.2*	*0.3*	*0.4*	*0.5*	*0.6*	*0.7*	*0.8*	*0.9*	*1.0*
0	998	998	998	998	998	998	998	998	998	998
50	994	990	986	982	979	975	971	967	963	959
*100*	982	966	951	936	920	904	889	873	858	842
*150*	963	928	893	858	822	787	752	717	682	647
*200*	956	873	811	748	686	623	561	498	435	373
*250*	900	803	705	608	510	412	314	216	119	21
*300*	857	717	576	436	295	154	13	-128	-269	-410
*350*	807	615	424	233	41	-151	-343	-535	-727	-919
*400*	748	498	248	-2	-252	-503	-753	-1004	-1255	-1506
*450*	682	365	49	-268	-585	-902	-1219	-1536	-1854	-2172
*500*	608	217	-174	-565	-956	-1348	-1739	-2131	-2523	-2916
*550*	526	53	-420	-893	-1367	-1840	-2314	-2789	-3263	-3738
*600*	436	-127	-690	-1253	-1816	-2380	-2944	-3509	-4074	-4639

The lurch with the 7-lb head is very similar to that with the 6-lb head, +0.3 to -1.2 ft s^-1. This brackets the observed value.

v_cloud, ft s^-1 ↓ m_cloud, lb →	*0.1*	*0.2*	*0.3*	*0.4*	*0.5*	*0.6*	*0.7*	*0.8*	*0.9*	*1.0*
0	0.79	0.79	0.79	0.79	0.80	0.80	0.80	0.80	0.80	0.80
50	0.75	0.70	0.66	0.62	0.57	0.53	0.48	0.44	0.40	0.35
*100*	0.70	0.62	0.53	0.44	0.35	0.26	0.17	0.08	-0.00	-0.09
*150*	0.66	0.53	0.39	0.26	0.13	-0.00	-0.14	-0.27	-0.41	-0.54
*200*	0.62	0.44	0.26	0.08	-0.09	-0.27	-0.45	-0.63	-0.81	-0.99
*250*	0.57	0.35	0.13	-0.09	-0.32	-0.54	-0.76	-0.99	-1.21	-1.44
*300*	0.53	0.26	-0.00	-0.27	-0.54	-0.81	-1.07	-1.34	-1.61	-1.88
*350*	0.48	0.17	-0.14	-0.45	-0.76	-1.07	-1.39	-1.70	-2.02	-2.33
*400*	0.44	0.08	-0.27	-0.63	-0.98	-1.34	-1.70	-2.06	-2.42	-2.78
*450*	0.39	-0.00	-0.40	-0.80	-1.20	-1.61	-2.01	-2.41	-2.82	-3.22
*500*	0.35	-0.09	-0.54	-0.98	-1.43	-1.87	-2.32	-2.77	-3.22	-3.67
*550*	0.30	-0.18	-0.67	-1.16	-1.65	-2.14	-2.63	-3.13	-3.62	-4.12
*600*	0.26	-0.27	-0.80	-1.34	-1.87	-2.41	-2.94	-3.48	-4.02	-4.57

For m_head = 8 lb
As previously, the pattern of allowed values for PE is broader vertically and horizontally than with the lighter heads, particularly for small m_cloud and v_cloud. The "smearing" is especially evident for m_cloud = 0.1 lb. The lowest values of v_cloud now reach down to 100 ft s^-1.

v_cloud, ft s^-1 ↓ m_cloud, lb →	*0.1*	*0.2*	*0.3*	*0.4*	*0.5*	*0.6*	*0.7*	*0.8*	*0.9*	*1.0*
0	687	687	687	687	687	687	687	687	687	687
50	683	679	676	672	668	664	660	656	652	648
*100*	672	656	640	625	609	594	578	562	547	531
*150*	652	617	582	547	512	476	441	406	371	335
*200*	625	562	500	437	375	312	250	187	124	61
*250*	590	492	394	297	199	101	3	-95	-193	-291
*300*	547	406	265	125	-16	-157	-298	-439	-580	-722
*350*	496	305	113	-79	-270	-462	-654	-846	-1038	-1231
*400*	437	187	-63	-313	-564	-814	-1065	-1316	-1567	-1818
*450*	371	54	-262	-579	-896	-1213	-1531	-1848	-2166	-2484
*500*	297	-94	-485	-876	-1267	-1659	-2051	-2443	-2835	-3228
*550*	215	-258	-731	-1204	-1678	-2152	-2626	-3101	-3575	-4050
*600*	125	-438	-1001	-1564	-2128	-2692	-3256	-3821	-4386	-4951

As before, v_lurch retains its basic range, but it shifts toward weaker lurches (+0.3 to -1.1 ft s^-1). Most of the values are still below aero, however, and the range still includes the observed lurch.

v_cloud, ft s^-1 ↓ m_cloud, lb →	*0.1*	*0.2*	*0.3*	*0.4*	*0.5*	*0.6*	*0.7*	*0.8*	*0.9*	*1.0*
0	0.53	0.53	0.53	0.53	0.53	0.53	0.53	0.53	0.53	0.54
50	0.48	0.44	0.40	0.35	0.31	0.26	0.22	0.18	0.13	0.09
*100*	0.44	0.35	0.26	0.18	0.09	-0.00	-0.09	-0.18	-0.27	-0.36
*150*	0.40	0.26	0.13	-0.00	-0.14	-0.27	-0.40	-0.54	-0.67	-0.81
*200*	0.35	0.18	-0.00	-0.18	-0.36	-0.54	-0.72	-0.89	-1.07	-1.25
*250*	0.30	0.09	-0.14	-0.36	-0.58	-0.80	-1.03	-1.25	-1.48	-1.70
*300*	0.26	-0.00	-0.27	-0.54	-0.80	-1.07	-1.34	-1.61	-1.88	-2.15
*350*	0.22	-0.09	-0.40	-0.71	-1.02	-1.34	-1.65	-1.96	-2.28	-2.60
*400*	0.18	-0.18	-0.53	-0.89	-1.25	-1.60	-1.96	-2.32	-2.68	-3.04
*450*	0.13	-0.27	-0.67	-1.07	-1.47	-1.87	-2.27	-2.68	-3.08	-3.49
*500*	0.09	-0.36	-0.80	-1.24	-1.69	-2.14	-2.59	-3.04	-3.48	-3.94
*550*	0.04	-0.44	-0.93	-1.42	-1.91	-2.40	-2.90	-3.39	-3.89	-4.38
*600*	-0.00	-0.53	-1.07	-1.60	-2.14	-2.67	-3.21	-3.75	-4.29	-4.83

Summary of constraints
This summary table is very similar to the one for Θ_cl = 70°. Its main difference is that v_lurch is shifted toward more-positive values. For example, all of the lurch's upper limits are now 0.3 or 0.4 ft s^-1, whereas previously only one was positive. Nevertheless, all the ranges for the lurch still include the observed -0.8 ft s^-1.

M_head, lb	m_cloud, lb	v_cloud, ft s^-1	v_lurch, ft s^-1	PE, ft-lb
5	0.1 to 1.0	200–600	+0.4 to -1.3	110–540
6	0.1 to 1.0	200–600	+0.4 to -1.1	130–590
7	0.1 to 1.0	200–600	+0.3 to -1.2	120–580
8	0.1 to 1.0	100–600	+0.3 to -1.1	100–590
9	—	—	—	—
10	—	—	—	—