Appendix A Figure A-4. Comparison of Head Resultant Acceleration A.2.9 The simulation produced a HIC value within the required 100 HIC units, test HIC of 700, simulation HIC of 650. The initial and final integration times selected by the HIC calculator was similar: t1 for the test is 144 ms; t1 for the simulation is 139 ms; and t2 for both test and simulation is 164 ms. The HIC duration differs by 5 ms, which meets the 5 ms limit listed in paragraph 8.3.5.5 of this AC. The average acceleration value during the HIC window is 65.3 g for the test and 57.2 g for the simulation.
A.2.10 The proposed simulation achieved the required error metrics, all below 10 percent. The simulation was not a conservative one, so any future use will require that it is limited to simulations where the expected HIC will be below 840 HIC units. Other limitations include that this model is pursuant to § 25.562 Test 2 (16 G) pulse with a 50th Percentile Male (Hybrid II) ATD for determining head accelerations and belt loads for this particular seat geometry near a padded bulkhead.
A-6
Appendix B Appendix B. Test-Simulation Comparison Methodology B.1 OVERVIEW.
This appendix describes one method to calculate the error between the results of a numerical simulation and the results of a physical test. Unless otherwise specified, for each required channel, two features should be evaluated: magnitude error and curve shape error. Time histories should be evaluated beginning with the onset of the test pulse and through significant system response, often the motion of the anthropomorphic test device(s), as seen in the physical test. Channel inputs should have consistent units, appropriate sampling rates, minimum 10,000 Hz for electronic instrumentation data and 1000 Hz for photometric data, and equal time lengths. Test and simulation position data need to have the same global origin, typically the SRP. If necessary, units, data set length, and origin offsets can be corrected during post processing.
B.2 TEST CALCULATIONS AND SIMULATIONS.
B.2.1 The magnitude error for load, moment, acceleration, or velocity can be calculated using a relative error on the peak in equation 1. In figure B-1 below, the simulation peak is 1,360 lbs and the test peak is 1,315 lbs. The magnitude error, using equation 1, is
3.4 percent.
Peak − Peak test simError = ∗100% Peaktest [1] B-1
Appendix B Figure B-1. Test and Simulated Results from Dynamic Tests: Example 1 B.2.2 The curve shape error is calculated using the Sprague and Geers Comprehensive Error, equations 2-7. For Figure B-1 above, the Sprague and Geers Comprehensive Error is 7.2 percent. (Refer to Sprague, M.A. and Geers, T.L. A Spectral-Element Method for Modeling Cavitation in Transient Fluid-Structure Interaction, International Journal for Numerical Methods in Engineering, Volume 60, Issue 15, pages 2467-2499, dated August 21, 2004).
t2 I = (t − t )−1 ∫ m2 (t)dtmm 2 1 t1 [2] t −1 2Icc = (t2 − t1) c (t)dt∫ 2 t1 [3] t2 Imc = (t2 − t1)−1 ∫ m(t) ⋅ c(t)dt 1t [4] B-2
Appendix B The magnitude error, biased towards the test, is then defined as— M = I / I −1SG cc mm [5] The phase error is defined as— 1 −1P = cos (I / I I )SG π mc mm cc [6] The comprehensive error is defined as— 2 2C = M + PSG SG SG [7] B .2.3 Based on the quantitative results above, the simulation meets the requirements set forth in paragraph 8.3 of this AC. The simulation curve shows that the magnitude guidelines are met, that is, peak load within 10 percent. A good correlation of the time-history plot is also established, with the curve shape error within 10 percent. In addition, note that the analysis tends to be conservative (simulation load is greater than the test load).
B.2.4 As a stark contrast to Figure B-1 of this AC, figure B-2 shows relying on peak value is not always sufficient to determine correlation. Although the relative error on the peak is
0.3 percent, from a qualitative view, the analysis is clearly not simulating the same physical phenomenon as the test. Calculation of the Sprague and Geers Comprehensive Error yields a 60.4 percent curve shape error providing a quantitative confirmation of the poor correlation.
B-3
Appendix B Figure B-2. Test and Simulated Results from Dynamic Tests: Example 2 B.2.5 Photometric/motion data should be handled differently than force, acceleration, velocity, or moment data. Position data for the test and simulation should be offset by the test data initial position (IP) as seen in figure B-3 below. This approach preserves any initial differences between the test and simulation results. To accomplish this, subtract the test data IP from the entire time history of both the test data and simulation data. Once the data has been offset, Y’ axis, the magnitude error, whether positive or negative, can be determined by a simple difference, equation 8 of the peak. The curve shape error should be determined using the Sprague and Geers comprehensive error on the offset data. The basis for any differences in the IP should be discussed in the VAR.
B-4
Appendix B Figure B-3. Motion Data Offset Example Error = PeakTest − P eak Sim [8] B-5
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