Appendix E - Finite Difference Method

Appendix E - Finite Difference Method - Appendix E : Finite...

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Unformatted text preview: Appendix E : Finite Difference Method The finite difference method is a useful tool in order to evaluate the first- and second-order kinematic coefficients. For the first-order kinematic coefficients, the finite difference method can be written as (44) The second-order kinematic coefficients are evaluated using the following equation (45) The values obtained for the first-and second-order kinematic coefficients using the method described in the analysis section are compared to the method of finite differences. It is clear that there is little error when using the two methods. It is important to note that the error in using the finite difference method is decreased in case 2 & case 3 due to the smaller increment in the input. Table : First-Order Kinematic Coefficients for Case 1 Comparison for Finite Difference Method [Degrees] [in. / in.]- Finite Difference [in. / in.] [in. / in.]- Finite Difference [in. / in.] [in. / in.]- Finite Difference [in. / in.]-0.5--0.5876--0.6267- 10-0.5-0.5-0.6698-0.6632-0.5613-0.5546 20-0.5-0.5-0.7127-0.7065-0.4561-0.4518 30-0.5-0.5-0.7186-0.7140-0.3252-0.3239 40-0.5-0.5-0.6971-0.6944-0.1862-0.1874 50-0.5-0.5-0.6594-0.6582-0.0539-0.0566 60-0.5-0.5-0.6141-0.6136 0.0625 0.0592 70-0.5-0.5-0.5658-0.5657 0.1588 0.1552 80-0.5-0.5-0.5159-0.5159 0.2333 0.2298 90-0.5-0.5-0.4632-0.4635 0.2853 0.2822 100-0.5-0.5-0.4039-0.4049 0.3129 0.3108 110-0.5-0.5-0.3328-0.3347 0.3128 0.3124 120-0.5-0.5-0.2435-0.2457 0.2806 0.2825 130-0.5-0.5-0.1318-0.1327 0.2138 0.2175 140-0.5-0.5 0.0002 0.0023 0.1173 0.1214 150-0.5-0.5 0.1409 0.1455 0.0062 0.0093 160-0.5-0.5 0.2717 0.2763-0.0989-0.0971 170-0.5-0.5 0.3770 0.3795-0.1831-0.1819 180-0.5-0.5 0.4516 0.4516-0.2427-0.2414 190-0.5-0.5 0.4989 0.4975-0.2817-0.2805 200-0.5-0.5 0.5256 0.5237-0.3068-0.3058 210-0.5-0.5 0.5369 0.5351-0.3235-0.3229 220-0.5-0.5 0.5361 0.5343-0.3360-0.3359 230-0.5-0.5 0.5243 0.5224-0.3473-0.3475 240-0.5-0.5 0.5011 0.4990-0.3600-0.3607 250-0.5-0.5 0.4649 0.4621-0.3769-0.3782 260-0.5-0.5 0.4120 0.4083-0.4018-0.4040 270-0.5-0.5 0.3367 0.3314-0.4402-0.4438 280-0.5-0.5 0.2294 0.2216-0.5003-0.5058-0.5-0.5876 0.0000-0.6267 0.0000 10-0.5-0.5-0.6698-0.6632-0.5613-0.5546 20-0.5-0.5-0.7127-0.7065-0.4561-0.4518 30-0.5-0.5-0.7186-0.7140-0.3252-0.3239 40-0.5-0.5-0.6971-0.6944-0.1862-0.1874 50-0.5-0.5-0.6594-0.6582-0.0539-0.0566 60-0.5-0.5-0.6141-0.6136 0.0625 0.0592 70-0.5-0.5-0.5658-0.5657 0.1588 0.1552 80-0.5-0.5-0.5159-0.5159 0.2333 0.2298 90-0.5-0.5-0.4632-0.4635 0.2853 0.2822 100-0.5-0.5-0.4039-0.4049 0.3129 0.3108 [Degrees] [in. / in.]- Finite Difference [in. / in.] [in. / in.]- Finite Difference [in. / in.] [in. / in.]- Finite Difference [in. / in.] 110-0.5-0.5-0.3328-0.3347 0.3128 0.3124 120-0.5-0.5-0.2435-0.2457 0.2806 0.2825 130-0.5-0.5-0.1318-0.1327 0.2138 0.2175 140-0.5-0.5 0.0002 0.0023 0.1173 0.1214 150-0.5-0.5 0.1409 0.1455 0.0062 0.0093 160-0.5-0.5 0.2717 0.2763-0.0989-0.0971 170-0.5-0.5 0.3770 0.3795-0.1831-0.1819 180-0.5-0.5 0.4516 0.4516-0.2427-0.2414 190-0.5-0.5 0.49890....
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Appendix E - Finite Difference Method - Appendix E : Finite...

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