20--L5A

Rotational analog of Lurch 5 Linear. Procedure for calculating speed of rearward lurch of upper body from bullet, body, cloud, large fragments, conical motion of cloud, and 3-D motion of large fragments and body.

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 = -3.77		KE_bodyafter = 1.0
	Ω_cloud = 6.37		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	m_cloud	v_lurch	PE	v_lurch	v_bullet	v_lurch
156	-1.274							1750	-1.239
157	-1.276	65	-1.680			0	-1.516	1760	-1.248
158	-1.278	70	-1.559			50	-1.460	1770	-1.257
159	-1.280	75	-1.455	0.1	-0.366	100	-1.403	1780	-1.266
160	-1.282	80	-1.364	0.2	-0.885	150	-1.344	1790	-1.275
161	-1.283	85	-1.283	0.3	-1.283	200	-1.283	1800	-1.283
162	-1.285	90	-1.212	0.4	-1.620	250	-1.221	1810	-1.292
163	-1.287	95	-1.148	0.5	-1.917	300	-1.157	1820	-1.301
164	-1.289	100	-1.090	0.6	-2.187	350	-1.091	1830	-1.310
165	-1.290	105	-1.038	0.7	-2.435	400	-1.023	1840	-1.319
166	-1.292			0.8	-2.666			1850	-1.327
Sensitivity = [(-1.287 + 1.280)/4]/ [1.283/161] = -0.22		Sensitivity = [(-1.212 + 1.364)/10]/ [1.283/85] = 1.01		Sensitivity = [(-1.620 + 0.885)/0.2]/ [1.283/0.3] = -0.86		Sensitivity = [(-1.221 + 1.344)/100]/ [1.283/200] = 0.19		Sensitivity = [(-1.292 + 1.275)/20]/ [1.283/1800] = -1.19
Range = 0.018		Range = 0.64		Range = 2.30		Range = 0.49		Range = 0.088

v_bulletafter	v_lurch	Q	v_lurch	m_frag1	v_lurch	m_frags23	v_lurch	v_frag1	v_lurch
		12	-1.255	0.022	-1.257	0.005	-1.278
0	-1.154	13	-1.260	0.023	-1.263	0.006	-1.279	100	-1.203
50	-1.190	14	-1.265	0.024	-1.268	0.007	-1.280	150	-1.228
100	-1.223	15	-1.271	0.025	-1.273	0.008	-1.281	200	-1.250
150	-1.254	16	-1.277	0.026	-1.278	0.009	-1.282	250	-1.268
200	-1.283	17	-1.283	0.027	-1.283	0.01	-1.283	300	-1.283
250	-1.310	18	-1.290	0.028	-1.289	0.011	-1.285	350	-1.295
300	-1.335	19	-1.298	0.029	-1.294	0.012	-1.286	400	-1.304
350	-1.357	20	-1.305	0.03	-1.299	0.013	-1.287	450	-1.308
400	-1.377	21	-1.313	0.031	-1.304	0.014	-1.288	500	-1.309
		22	-1.322	0.032	-1.309	0.015	-1.289
Sensitivity = [(-1.310 + 1.254)/100]/ [1.283/200] = -0.087		Sensitivity = [(-1.298 + 1.271)/4]/ [1.283/17] = -0.089		Sensitivity = [(-1.294 + 1.273)/0.004]/ [1.283/0.027] = -0.11		Sensitivity = [(-1.286 + 1.281)/0.004]/ [1.283/0.010] = -0.0097		Sensitivity = [(-1.295 + 1.268)/100]/ [1.283/300] = -0.063
Range = 0.22		Range = 0.067		Range = 0.052		Range = 0.011		Range = 0.106

v_frags23	v_lurch	Q_frag1	v_lurch	Q_frags23	v_lurch	Q_cl	v_lurch
100	-1.281	20	-1.328	50	-1.312	25	-1.984
150	-1.283	25	-1.320	55	-1.306	30	-1.794
200	-1.284	30	-1.309	60	-1.299	35	-1.615
250	-1.285	35	-1.297	65	-1.291	40	-1.446
300	-1.283	40	-1.283	70	-1.283	45	-1.283
350	-1.281	45	-1.268	75	-1.275	50	-1.128
400	-1.278	50	-1.252	80	-1.267	55	-0.979
450	-1.273	55	-1.234	85	-1.259	60	-0.835
500	-1.267	60	-1.215	90	-1.251	65	-0.697
Sensitivity = [(-1.281 + 1.285)/100]/ [1.283/300] = 0.0094		Sensitivity = [(-1.268 + 1.297)/10]/ [1.283/40] = 0.090		Sensitivity = [(-1.275 + 1.291)/10]/ [1.283/70] = 0.087		Sensitivity = [(-1.128 + 1.446)/10]/ [1.283/45] = 1.12
Range = 0.014		Range = 0.113		Range = 0.061		Range = 1.29

f_kefrag1	v_lurch	f_kefrags23	v_lurch	f_kebody	v_lurch	f_I	v_lurch
						1.06	-1.344
						1.07	-1.331
						1.08	-1.319
1.0	-1.295	1.0	-1.288	1.0	-1.284	1.09	-1.307
1.1	-1.290	1.1	-1.286	1.1	-1.284	1.10	-1.295
1.25	-1.283	1.25	-1.283	1.2	-1.283	1.11	-1.283
1.4	-1.276	1.4	-1.281	1.3	-1.283	1.12	-1.272
1.5	-1.272	1.5	-1.279	1.4	-1.283	1.13	-1.261
						1.14	-1.250
						1.15	-1.239
						1.16	-1.228
Sensitivity = [(-1.272 + 1.295)/0.5]/ [1.283/1.25] = 0.045		Sensitivity = [(-1.279 + 1.288)/0.5]/ [1.283/1.25] = 0.0175		Sensitivity = [(-1.283 + 1.284)/0.4]/ [1.283/1.2] = 0.0023		Sensitivity = [(-1.228 + 1.344)/0.1]/ [1.283/1.11] = 1.004
Range = 0.023		Range = 0.009		Range = 0.001		Range = 0.116

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
m_cloud = 0.3 lb	Q_frag1 = 40°	v_frag1 = 300 ft s^-1
Q = 17°	Q_frags23 = 70°	v_frags23 = 300 ft s^-1
PE = 200 ft-lb	Q_cl = 45°	f_kefrag1 = 1.25
f_I = 1.11	f_kebody = 1.2	f_kefrags23 = 1.25