This paragraph contains guidance and recommendations for the output, filtering, and the general methods of reporting numerical data. The purpose is to achieve uniformity in the practice of reporting numerical results. The use of the following recommendations will provide a basis for a meaningful comparison to test results from different sources.
12.7.1 Energy Balance.
If the numerical analysis uses an explicit finite element formulation, the applicant should evaluate the presence of hourglass modes, also known as zero energy modes, to determine if they are located at critical structural components. If this evaluation determines that these modes are present, the applicant should assess the hourglass modes to quantify their influence on the accuracy of the analysis. The applicant should correct the model if it does not attain the appropriate energy balance. The VAR should contain a summary of the ratio of initial energy to final energy and provide a comparison of hourglass energy to total energy.
12.7.2 Data Output.
12.7.2.1 The transient analysis should generate data at a minimum frequency of 10,000 Hz for electronic data and 1,000 Hz for trajectories. This will maintain an equivalent practice with the instrumentation and data requirements specified in SAE J211, and it will allow for a meaningful comparison between numerical data and test data.
12.7.2.2 If the output of the data channels is dependent on the integration time step of the analysis, and its sample rate is higher than the rate of the test data, the reported simulation data should be subsampled for comparison. If any post-analysis filtering is to be applied, the generated data may need to be reported at a higher frequency than 10,000 Hz (or 1,000 Hz) to remain consistent with the requirements outlined in SAE J211. The VAR should document any deviations to this practice.
12.7.3 Data Filtering.
The filtering practices of SAE J211 apply for all applications.
12.8 Ultimate Margin of Safety.
12.8.1 The ultimate margin of safety represents the ultimate strength of the structure in relation to the strength required to carry the ultimate load. In this AC, it is presented as a decimal value defined as:
MS ultimate = ([Ultimate Strength / Ultimate Load] - 1)
12.8.2 For the structural substantiation of the seat/restraint system and attachment structure, the ultimate margin of safety must show a positive value. The VAR should document the ultimate margins of safety for those structural elements the applicant or the FAA identifies as critical.
Appendix A Appendix A. Occupant Trajectory and Head Injury Criteria (HIC) A.1 OVERVIEW.
This appendix serves as an example of items to consider and document when validating occupant trajectory and HIC. Refer to paragraphs 8.3.1 and 8.3.5 of this AC for validation criteria regarding occupant trajectory and HIC. This is not meant to be a universal example. Other situations may require more or less stringent validation efforts.
A.2 TEST SETUP.
A.2.1 The scenario is a front-row seat with a foam-covered bulkhead 25 inches forward of the occupant. Refer to Figure A-1 below. The launch seat has been represented by a rigid fixture for simplicity. The seat cushion is one-half inch thick stiff foam covered in fabric. The occupant is represented by a 50th Percentile Male (Hybrid II) ATD and is restrained by a standard nylon lap belt. The impact condition is from § 25.562(b)(2), with no yaw or floor misalignment. The anthropomorphic test device (ATD) has been instrumented with three linear accelerometers in the head (Endevco model 7264B).
Based on the specific geometry of this aircraft configuration, it was determined that femur compression was not an issue. Therefore, no femur load cell was installed (refer to paragraph 8.3.6 of this AC). Webbing transducers were attached to both ends of the lap belt to record belt loads (Denton model 3255).
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Appendix A Figure A-1. Test Setup (xz-plane) A.2.2 Pre-test measurements included the head center of gravity (CG), hip-point (H-point), knee, and ankle of the ATD, along with the SRP, belt anchor location, multiple points on the lap belt, points on the floor, foot stop, bulkhead (including the foam), and targets required for photometric scaling and validation.
A.2.3 The model was generated using MADYMO 6.1. The seat is represented by rigid planes and the seat cushion was excluded from the model. Refer to figure A-2 below. The friction coefficient between the ATD and seat was defined to represent the effect of the fabric-covered foam. The occupant model is the MADYMO Hybrid II 50th Percentile Male (p572 version 3.3). The lap belt is represented by simple springs with material properties derived from high rate tests of the webbing. The foam on the bulkhead is modeled by finite elements, and the material properties were determined by load frame tests. The sled pulse from the physical test was applied to the ATD in the x-direction and gravity was applied in the z-direction. No penetration contacts were defined between the ATD and all rigid surfaces, bulkhead, seat, floor, and foot stop, as well as between the individual parts of the ATD. A kinematic contact was defined between the ATD and the foam on the bulkhead.
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Appendix A Figure A-2. Numerical Model Setup (xz-plane) A.2.4 MADYMO 6.1 is a commercially available rigid body dynamics and finite element simulation code. As part of the development process and distribution to its customers, the developer provides a theory and reference manual to assist the user in applying the code and material models appropriately. No formal statement of code conformity or code verification was available from the developer (as discussed in paragraph 7.1 of this AC); however, the user attests that the code is acceptable for its intended use.
A.2.5 The bulkhead foam was modeled using eight-node solid elements that carry tensile, compressive, and shear loads. This type of element provides good accuracy for simple, rectangular shapes. The load frame test used to generate material properties was simulated to show that the mathematical implementation of this foam block is correct.
The time step was controlled by the software, updating as necessary to maintain compliance with the Courant criteria (as discussed in paragraph 7.3.1.1 of this AC). No mass scaling was used in this model. The mesh resolution was evaluated as described in paragraph 7.2.2 of this AC.
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Appendix A A.2.6 The v-ATD selected is the MADYMO Hybrid II 50th Percentile Male (p572 version 3.3). This v-ATD predates the publication of SAE ARP 5765, Revision A, Analytical Methods for Aircraft Seat Design and Evaluation, and, therefore, has not been evaluated by the developer to show compliance with the dynamic calibration paragraph of the ARP (as discussed in paragraph 8.1.3 of this AC). The developer has shown compliance with the head drop test. During end-user evaluation of the head path from the SAE ARP dataset, this v-ATD had acceptable agreement up to 30 inches of head x-direction travel. For this current simulation, this v-ATD can be considered to be conditionally compliant with the limitations that the v-ATD be used for a § 25.562 Test 2 pulse with limited head excursion.
A.2.7 For this test setup, there are two primary occupant trajectory items to consider: head path and pelvic motion. For brevity, only xz-plane head motion is examined here. If there is significant lateral trajectory, the applicant will likely be required to validate the y-axis motion. Y-axis motion is not considered in this example. Figure A-3 of this AC shows the xz-plane motion of the head CG for the test and simulation. The figure also shows the location of the wall and front edge of the foam. The origin of the figure is the SRP. Qualitatively, the impact location was similar, with the measured height and estimated lateral location of initial head contact occurring at roughly the same location between test and simulation. Because the impact surface is completely homogenous, this estimation is sufficient to meet the impact location requirement in paragraph 8.3.5.6 of this AC. Differences exist between the initial position of the head and the depth the head travels into the foam. In general, it is appropriate for the FAA to ask the applicant to explain discrepancies and to present data to defend these explanations. This is not the same as allowing the applicant to rationalize the differences. An explanation can be supported with data. A rationalization cannot usually standup to this type of scrutiny.
Calculation of the curve shape error requires that the x-position versus time and zposition versus time be evaluated separately; curve shape error on the x-position is 5.1 percent and 8.5 percent on the z-position. The magnitude error is 0.3 in on the peak xposition with the simulation under-predicting the motion. For this impact scenario, the maximum position in the z-axis does not have significance. As referenced in paragraph
8.3.3 of this AC, lap belt loads should be evaluated separately from occupant trajectory, omitted for brevity.
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Appendix A Figure A-3. Comparison of Head Path (xz-plane) A.2.8 Before evaluating HIC, aspects of the head CG resultant acceleration should be considered, as illustrated in figure A-4. The test peak is 82.3 g, and the simulation peak is 83.8 g. The difference is 2 percent, well below the 10 percent limit, and the simulation result is conservative. The curve shape error is 9.8 percent. Depending on the impact scenario, the FAA may also ask the applicant to evaluate the components of the resultant acceleration separately. The head resultant velocity at impact was 38.5 feet per second (fps) in the test and 37.7 fps in the simulation (magnitude error of 2.0 percent).
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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.
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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.
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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.
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Appendix B Figure B-3. Motion Data Offset Example Error = PeakTest − P eak Sim [8] B-5