21--L6A

Rotational analog of Lurch 6 Linear. Procedure for calculating speed of rearward lurch of upper body from bullet, body, conical cloud, and 3-D motion of large fragments, and body. Sets v_frags = v_cloud and solves for m_cloud and v_bodyafter.

Conservation of angular X-momentum

Conservation of total energy

Solutions to simultaneous equations

Distributions of momentum and energy

Angular momentum		Energy, ft-lb
Before	After	Before	After
Ω_bullet = 3.71	Ω_bulletafter = 0.43	KE_bullet = 1164	KE_bulletafter = 14
	Ω_bodyafter = -3.36		KE_bodyafter = 1
	Ω_cloud = 5.94		KE_cloud = 884
	Ω_frag1 = 0.58		KE_frag1 = 47
	Ω_frags23 = 0.10		KE_frags23 = 18
			PE = 200

m_bullet	v_lurch	m_body	v_lurch	PE	v_lurch	v_bullet	v_lurch	v_bulletafter	v_lurch
156	-1.088					1750	-1.024
157	-1.097	65	-1.485	0	-1.592	1760	-1.046	0	-1.022
158	-1.107	70	-1.379	50	-1.477	1770	-1.068	50	-1.056
159	-1.116	75	-1.287	100	-1.363	1780	-1.090	100	-1.086
160	-1.126	80	-1.206	150	-1.249	1790	-1.113	150	-1.113
161	-1.135	85	-1.135	200	-1.135	1800	-1.135	200	-1.135
162	-1.144	90	-1.072	250	-1.021	1810	-1.158	250	-1.153
163	-1.154	95	-1.015	300	-0.907	1820	-1.180	300	-1.167
164	-1.163	100	-0.965	350	-0.793	1830	-1.203	350	-1.177
165	-1.173	105	-0.919	400	-0.679	1840	-1.226	400	-1.183
166	-1.182					1850	-1.250
Sensitivity = [(-1.154 + 1.116)/4]/ [1.135/161] = -1.35		Sensitivity = [(-1.015 + 1.287)/20]/ [1.135/85] = 1.02		Sensitivity = [(-1.021 + 1.363)/100]/ [1.135/200] = 0.60		Sensitivity = [(-1.180 + 1.090)/40]/ [1.135/1800] = -3.57		Sensitivity = [(-1.167 + 1.086)/200]/ [1.135/200] = -0.071
Range = 0.094		Range = 0.57		Range = 0.91		Range = 0.23		Range = 0.161

Q	v_lurch	m_frag1	v_lurch	m_frags23	v_lurch	Q_frag1	v_lurch	Q_frags23	v_lurch

12	-1.106	0.022	-1.118	0.005	-1.139
13	-1.111	0.023	-1.122	0.006	-1.138	20	-1.180	50	-1.164
14	-1.117	0.024	-1.125	0.007	-1.137	25	-1.171	55	-1.157
15	-1.122	0.025	-1.128	0.008	-1.137	30	-1.161	60	-1.150
16	-1.129	0.026	-1.132	0.009	-1.136	35	-1.149	65	-1.143
17	-1.135	0.027	-1.135	0.01	-1.135	40	-1.135	70	-1.135
18	-1.142	0.028	-1.138	0.011	-1.134	45	-1.120	75	-1.127
19	-1.149	0.029	-1.142	0.012	-1.134	50	-1.103	80	-1.119
20	-1.157	0.03	-1.145	0.013	-1.133	55	-1.085	85	-1.111
21	-1.165	0.031	-1.148	0.014	-1.132	60	-1.066	90	-1.102
22	-1.173	0.032	-1.155	0.015	-1.131

Sensitivity = [(-1.149 + 1.122)/4]/ [1.135/17] = -0.101		Sensitivity = [(-1.142 + 1.128)/0.004]/ [1.135/0.027] = -0.083		Sensitivity = [(-1.134 + 1.137)/0.004]/ [1.135/0.010] = 0.0066		Sensitivity = [(-1.103 + 1.161)/20]/ [1.135/40] = 0.102		Sensitivity = [(-1.119 + 1.150)/20]/ [1.135/70] = 0.096
Range = 0.067		Range = 0.037		Range = 0.008		Range = 0.114		Range = 0.062

Q_cl	v_lurch	f_kefrag1	v_lurch	f_kebody	v_lurch	f_I	v_lurch
						1.06	-1.189
25	-2.169					1.07	-1.177
30	-1.856					1.08	-1.167
35	-1.584	1	-1.165	1.0	-1.135	1.09	-1.156
40	-1.346	1.1	-1.153	1.1	-1.135	1.10	-1.145
45	-1.135	1.25	-1.135	1.2	-1.135	1.11	-1.135
50	-0.946	1.4	-1.117	1.3	-1.135	1.12	-1.125
55	-0.776	1.5	-1.105	1.4	-1.135	1.13	-1.115
60	-0.622					1.14	-1.105
65	-0.481					1.15	-1.096
						1.16	-1.086
Sensitivity = [(-0.946 + 1.346)/10]/ [1.135/45] = 1.59		Sensitivity = [(-1.105 + 1.165)/0.5]/ [1.135/1.25] = 0.13		Sensitivity = [(-1.135 + 1.135)/0.4]/ [1.135/1.2] = 0.000		Sensitivity = [(-1.086 + 1.189)/0.1]/ [1.135/1.11] = 1.007
Range = 1.69		Range = 0.060		Range = 0.000		Range = 0.103

m_bullet = 161 gr	v_bullet = 1800 ft s^-1	m_frag1 = 0.027 gr
m_body = 85 lb	v_bulletafter = 200 ft s^-1	m_frags23 = 0.01 gr
v_cloud = 300 ft s^-1	Q_frag1 = 40°	f_kefrag1 = 1.25
Q = 17°	Q_frags23 = 70°	f_kebody = 1.2
PE = 200 ft-lb	Q_cl = 45°	f_I = 1.11