29b--Constraints for 70 deg

As before, the results are presented sequentially for weights of 5, 6, 7, and 8 lb, with a summary at the end. All the allowable answers except one case give negative lurches, and all the ranges center on the observed -0.8 ft s^-1. The lurches for the 8-lb head are again less negative than for the other weights.
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	1075	1071	1067
*100*	1090	1074	1059	1043	1028	1012	996	981	965	949
*150*	1070	1035	1000	965	930	895	859	824	788	752
*200*	1043	981	918	856	793	730	667	603	540	476
*250*	1008	911	813	715	616	518	491	320	221	121
*300*	965	825	684	542	401	259	116	-27	-170	-313
*350*	914	723	531	339	146	-48	-242	-436	-632	-827
*400*	856	606	355	103	-149	-402	-655	-909	-1164	-1420
*450*	789	473	155	-163	-483	-803	-1124	-1446	-1768	-2092
*500*	715	324	-68	-461	-856	-1251	-1647	-2045	-2443	-2843
*550*	633	160	-315	-791	-1268	-1746	-2226	-2070	-3190	-3673
*600*	543	-20	-585	-1152	-1720	-2289	-2860	-3433	-4007	-4583

The allowed values for v_lurch are -0.2 to -3.8 ft s^-1. They are less negative than found for Θ_cl = 30°, and center on the observed value of -0.8 ft s^-1. This makes 5 lb and 30° an acceptable combination for m_head and Θ_cl.

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	0.86	0.77	0.67	0.58	0.48	0.39	0.30	0.20	0.11	0.01
*100*	0.76	0.58	0.39	0.20	0.01	-0.18	-0.37	-0.56	-0.75	-0.94
*150*	0.67	0.39	0.11	-0.18	-0.46	-0.75	-1.03	-1.32	-1.60	-1.89
*200*	0.58	0.20	-0.18	-0.56	-0.94	-1.32	-1.70	-2.08	-2.46	-2.84
*250*	0.48	0.01	-0.46	-0.93	-1.41	-1.88	-2.36	-2.84	-3.32	-3.80
*300*	0.39	-0.18	-0.74	-1.31	-1.88	-2.45	-3.02	-3.60	-4.17	-4.75
*350*	0.29	-0.37	-1.03	-1.69	-2.36	-3.02	-3.69	-4.36	-5.03	-5.70
*400*	0.20	-0.55	-1.31	-2.07	-2.83	-3.59	-4.35	-5.12	-5.88	-6.65
*450*	0.11	-0.74	-1.59	-2.45	-3.30	-4.16	-5.02	-5.88	-6.74	-7.61
*500*	0.01	-0.93	-1.88	-2.82	-3.77	-4.73	-5.68	-6.64	-7.60	-8.56
*550*	-0.08	-1.12	-2.16	-3.20	-4.25	-5.30	-6.34	-7.40	-8.45	-9.51
*600*	-0.18	-1.31	-2.44	-3.58	-4.72	-5.86	-7.01	-8.16	-9.31	-10.46

For m_head = 6 lb
The same inverse property of m_cloud and v_cloud is seen here. PE ranges between 120 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	1064	1060	1056	1052	1048	1044	1040	1036
*100*	1060	1044	1029	1013	997	982	966	950	935	919
*150*	1040	1005	970	935	900	864	829	793	758	722
*200*	1013	951	888	825	762	699	636	573	509	446
*250*	978	880	782	684	586	487	389	289	190	90
*300*	935	794	653	512	370	228	86	-57	-207	-344
*350*	884	693	501	308	115	-78	-273	-467	-662	-858
*400*	826	575	324	73	-179	-432	-686	-940	-1195	-1451
*450*	759	442	125	-194	-513	-833	-1154	-1476	-1799	-2123
*500*	685	294	-99	-492	-886	-1282	-1678	-2076	-2474	-2874
*550*	603	129	-345	-821	-1299	-1777	-2257	-2738	-3221	-3704
*600*	513	-51	-616	-1182	-1750	-2320	-2891	-3464	-4038	-4614

The allowed values for v_lurch are -0.2 to -3.4 ft s^-1, very similar to the 5-lb results. They center on 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	0.90
50	0.80	0.71	0.62	0.52	0.43	0.33	0.24	0.14	0.05	-0.05
*100*	0.71	0.52	0.33	0.14	-0.04	-0.24	-0.42	-0.62	-0.81	-1.00
*150*	0.61	0.33	0.05	-0.24	-0.52	-0.80	-1.09	-1.38	-1.66	-1.95
*200*	0.52	0.14	-0.23	-0.61	-0.99	-1.37	-1.75	-2.14	-2.52	-2.90
*250*	0.43	-0.04	-0.52	-0.99	-1.46	-1.94	-2.42	-2.90	-3.37	-3.85
*300*	0.33	-0.23	-0.80	-1.37	-1.94	-2.51	-3.08	-3.66	-4.23	-4.81
*350*	0.24	-0.42	-1.08	-1.75	-2.41	-3.08	-3.75	-4.42	-5.09	-5.76
*400*	0.14	-0.61	-1.37	-2.12	-2.88	-3.65	-4.41	-5.18	-5.94	-6.71
*450*	0.05	-0.80	-1.65	-2.50	-3.36	-4.22	-5.07	-5.94	-6.80	-7.66
*500*	-0.04	-0.99	-1.93	-2.88	-3.83	-4.78	-5.74	-6.70	-7.65	-8.62
*550*	-0.14	-1.18	-2.22	-3.26	-4.30	-5.35	-6.40	-7.46	-8.51	-9.57
*600*	-0.23	-1.37	-2.50	-3.64	-4.78	-5.92	-7.07	-8.22	-9.37	-10.52

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	983	979	975	971	967	963	959
*100*	982	967	951	936	920	904	889	873	857	841
*150*	963	928	893	858	822	787	751	716	680	644
*200*	936	873	811	748	684	622	559	495	432	368
*250*	901	803	705	607	509	410	311	212	112	12
*300*	856	717	576	435	293	151	8	-135	-278	-422
*350*	807	615	423	231	38	-156	-350	-545	-740	-936
*400*	748	498	247	-5	-257	-510	-764	-1018	-1273	-1529
*450*	682	365	47	-271	-591	-911	-1232	-1554	-1877	-2201
*500*	608	216	-176	-569	-964	-1359	-1756	-2154	-2552	-2952
*550*	526	52	-423	-899	-1376	-1855	-2335	-2816	-3299	-3783
*600*	436	-128	-693	-1260	-1828	-2398	-2969	-3542	-4117	-4692

The lurch with the 7-lb head is virtually identical to that with the 6-lb head, -0.2 to -3.5 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	0.70	0.60	0.51	0.42	0.32	0.23	0.13	0.04	-0.06	-0.15
*100*	0.60	0.42	0.23	0.04	-0.15	-0.34	-0.53	-0.72	-0.91	-1.10
*150*	0.51	0.23	-0.06	-0.34	-0.62	-0.91	-1.20	-1.48	-1.77	-2.06
*200*	0.42	0.04	-0.34	-0.72	-1.10	-1.48	-1.86	-2.24	-2.62	-3.01
*250*	0.32	-0.15	-0.62	-1.10	-1.57	-2.05	-2.52	-3.00	-3.48	-3.96
*300*	0.23	-0.34	-0.91	-1.48	-2.04	-2.62	-3.19	-3.76	-4.34	-4.91
*350*	0.13	-0.53	-1.19	-1.85	-2.52	-3.18	-3.85	-4.52	-5.19	-5.86
*400*	0.04	-0.72	-1.47	-2.23	-2.99	-3.75	-4.52	-5.28	-6.05	-6.82
*450*	-0.06	-0.90	-1.76	-2.61	-3.46	-4.32	-5.18	-6.04	-6.90	-7.77
*500*	-0.15	-1.09	-2.04	-2.99	-3.94	-4.89	-5.84	-6.80	-7.76	-8.72
*550*	-0.25	-1.28	-2.32	-3.36	-4.41	-5.46	-6.51	-7.56	-8.62	-9.67
*600*	-0.34	-1.47	-2.61	-3.74	-4.88	-6.03	-7.17	-8.32	-9.47	-10.63

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	593	578	562	546	530
*150*	652	617	582	547	511	476	440	404	369	333
*200*	625	562	500	437	374	311	247	184	120	56
*250*	589	492	394	296	197	98	-1	-100	-200	-300
*300*	547	406	265	123	-19	-161	-304	-447	-591	-735
*350*	496	304	112	-81	-274	-468	-662	-857	-1053	-1249
*400*	437	187	-64	-316	-569	-822	-1076	-1331	-1586	-1842
*450*	371	54	-264	-583	-903	-1223	-1545	-1867	-2190	-2514
*500*	297	-95	-488	-881	-1276	-1672	-2069	-2467	-2866	-3266
*550*	215	-259	-735	-1211	-1689	-2168	-2648	-3130	-3613	-4097
*600*	125	-439	-1005	-1572	-2141	-2711	-3282	-3856	-4430	-5007

As before, v_lurch retains its basic range, but it shifts toward weaker lurches (+0.1 to -2.9 ft s^-1. Only a single value is greater than zero.

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	0.44	0.34	0.25	0.15	0.06	-0.04	-0.13	-0.23	-0.32	-0.42
*100*	0.34	0.15	-0.04	-0.22	-0.42	-0.60	-0.80	-0.99	-1.18	-1.37
*150*	0.25	-0.04	-0.32	-0.60	-0.89	-1.17	-1.46	-1.75	-2.03	-2.32
*200*	0.15	-0.22	-0.60	-0.98	-1.36	-1.74	-2.12	-2.51	-2.89	-3.27
*250*	0.06	-0.41	-0.89	-1.36	-1.84	-2.31	-2.79	-3.27	-3.75	-4.23
*300*	-0.04	-0.60	-1.17	-1.74	-2.31	-2.88	-3.45	-4.03	-4.60	-5.18
*350*	-0.13	-0.79	-1.45	-2.12	-2.78	-3.45	-4.12	-4.79	-5.46	-6.13
*400*	-0.22	-0.98	-1.74	-2.49	-3.26	-4.02	-4.78	-5.55	-6.31	-7.08
*450*	-0.32	-1.17	-2.02	-2.87	-3.73	-4.58	-5.44	-6.31	-7.17	-8.04
*500*	-0.41	-1.36	-2.30	-3.25	-4.20	-5.15	-6.11	-7.07	-8.02	-8.99
*550*	-0.51	-1.54	-2.59	-3.63	-4.67	-5.72	-6.77	-7.83	-8.88	-9.94
*600*	-0.60	-1.73	-2.87	-4.01	-5.15	-6.29	-7.44	-8.58	-9.74	-10.89

Summary of constraints
This summary table is very similar to the one for Θ_cl = 30°. Its main results are again that m_cloud has no real constraints, that v_cloud may usually not drop below 200 ft s^-1, and that v_lurch is (nearly always) always negative, includes the observed value but is centered above it, and has a range that is nearly independent of m_head.

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	-0.2 to -3.8	110–540
6	0.1 to 1.0	200–600	-0.2 to -3.4	110–590
7	0.1 to 1.0	200–600	-0.2 to -3.5	110–580
8	0.1 to 1.0	100–600	+0.1 to -2.9	110–590
9	—	—	—	—
10	—	—	—	—