Instantaneous velocity measurement method of projectile with double ballistic zone-block apparatus

解算测速点变化量	第二幕面距离变化量
解算测速点变化量	1	2	3	4	5	6	7	8
1	0.02×10⁻⁵	0.01	0.02	0.03	0.04	0.05	0.06	0.07
2	0.01	0.07×10⁻⁵	0.01	0.02	0.03	0.04	0.05	0.06
3	0.02	0.01	0.01×10⁻⁴	0.01	0.02	0.03	0.04	0.05
4	0.03	0.02	0.01	0.03×10⁻⁴	0.01	0.02	0.03	0.04
5	0.04	0.03	0.02	0.01	0.04×10⁻⁴	0.01	0.02	0.03
6	0.05	0.04	0.03	0.02	0.01	0.06×10⁻⁴	0.01	0.02
7	0.06	0.05	0.04	0.03	0.02	0.01	0.08×10⁻⁴	0.01
8	0.07	0.06	0.05	0.04	0.03	0.02	0.01	0.01×10⁻³

Table 2. Test data of slingshot shooting 6 mm steel ball

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Table 2. Test data of slingshot shooting 6 mm steel ball

序号	v_1-2/m·s⁻¹	v_1-3/m·s⁻¹	b_12-13	v_t/m·s⁻¹	v_2-3/m·s⁻¹	误差/m·s⁻¹	相对误差/%
1	39.966	39.826	0.009 362	39.686	39.687	0.000	−1.23×10⁻⁵
2	46.978	46.812	0.009 421	46.647	46.648	−0.001	−1.25×10⁻⁵
3	39.052	38.923	0.008 872	38.793	38.794	0.000	−1.11×10⁻⁵
4	41.572	41.431	0.009 075	41.290	41.290	0.000	−1.15×10⁻⁵
5	44.371	44.240	0.007 877	44.109	44.110	0.000	−8.68×10⁻⁶
6	41.247	41.111	0.008 858	40.974	40.975	0.000	−1.1×10⁻⁵
7	42.132	41.986	0.009 272	41.841	41.841	−0.001	−1.2×10⁻⁵
8	42.522	42.380	0.008 905	42.239	42.239	0.000	−1.12×10⁻⁵

Table 3. Test data of slingshot shooting 10 mm mud pellet

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Table 3. Test data of slingshot shooting 10 mm mud pellet

序号	v_1-2/m·s⁻¹	v_1-3/m·s⁻¹	b_12-13	v_t/m·s⁻¹	v_2-3/m·s⁻¹	误差/m·s⁻¹	相对误差/10⁻⁵ %
1	42.450	42.213	0.014 901	41.978	41.979	−0.001	−3.09
2	27.511	27.394	0.011 371	27.277	27.278	0.000	−1.82
3	41.393	41.051	0.022 131	40.712	40.714	−0.003	−6.83
4	44.392	44.129	0.015 816	43.868	43.870	−0.002	−3.49
5	54.301	53.982	0.015 689	53.665	53.667	−0.002	−3.43
6	57.467	57.073	0.018 326	56.682	56.685	−0.003	−4.69
7	58.009	57.648	0.016 655	57.289	57.291	−0.002	−3.87
8	54.921	54.571	0.017 032	54.224	54.226	−0.002	−4.05

Table 4. Test data of air gun shooting 6 mm steel ball

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Table 4. Test data of air gun shooting 6 mm steel ball

序号	v_1-2/m·s⁻¹	v_1-3/m·s⁻¹	b_12-13	v_t/m·s⁻¹	v_2-3/m·s⁻¹	误差/m·s⁻¹	相对误差/10⁻⁵ %
1	189.251	188.584	0.009 404	187.921	187.923	−0.002	−1.24
2	154.607	154.004	0.010 424	153.403	153.406	−0.002	−1.52
3	146.456	145.758	0.012 728	145.064	145.068	−0.003	−2.27
4	150.784	150.150	0.011 235	149.519	149.522	−0.003	−1.77
5	148.839	148.207	0.011 354	147.577	147.580	−0.003	−1.8
6	143.349	142.884	0.008 651	142.422	142.423	−0.001	−1.05
7	136.190	135.685	0.009 908	135.182	135.184	−0.002	−1.38
8	126.753	126.220	0.011 243	125.689	125.691	−0.002	−1.77

Table 5. Test data of rifle

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Table 5. Test data of rifle

序号	v_1-2/m·s⁻¹	v_1-4/m·s⁻¹	b_12-14	v_t/m·s⁻¹	v_2-4/m·s⁻¹	误差/m·s⁻¹	相对误差/%
1	824.402	822.740	0.000 734	822.438	822.438	0.000	−4.86×10⁻⁷
2	853.971	851.304	0.001 138	850.819	850.820	−0.001	−1.06×10⁻⁶
3	855.432	854.213	0.000 519	853.992	853.992	0.000	−2.34×10⁻⁷
4	839.631	837.155	0.001 074	836.706	836.707	−0.001	−8.37×10⁻⁷
5	838.926	836.940	0.000 862	836.579	836.579	0.000	−5.98×10⁻⁷
6	839.631	838.127	0.000 652	837.854	837.854	0.000	−3.58×10⁻⁷
7	829.187	826.402	0.001 224	825.897	825.898	−0.001	−1.33×10⁻⁶
8	838.223	835.756	0.001 072	835.308	835.308	−0.001	−9.58×10⁻⁷

Table 6. Test statistics

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Table 6. Test statistics

测试模式	B均值	B标准差σ	速度相对误差均值/%	速度相对误差标准差σ/%
弹弓发射钢珠	0.008 955	0.000 490	−1.13×10⁻⁵	1.2×10⁻⁶
弹弓发射泥丸	0.016 490	0.003 055	−3.91×10⁻⁵	1.44×10⁻⁵
气枪发射钢珠	0.010 618	0.001 290	−1.6×10⁻⁵	3.85×10⁻⁶
步枪发射7.62 mm	0.000 909	0.000 255	−7.33×10⁻⁷	3.77×10⁻⁷

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Hai LI, Chenhao ZHENG, Pingwei ZHAO, Jinping NI, Zhichao WU. Instantaneous velocity measurement method of projectile with double ballistic zone-block apparatus[J]. Journal of Applied Optics, 2023, 44(3): 571

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