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142 Homogeneous Linear Gradient Strut Loading Criterion Strut Loading Criterion 2.5 2.5 0 0 37.5 30 37.5 30 Strength Depth Strength Depth 100 18 100 18 Figure 12-9. Strut loading trends for 29.0-in. tire with homogeneous (left) and linear (right) depth gradient. over-penetration and the resulting overload behavior. This arrestor bed models. These profiles were compared with one trend was not true for the homogeneous material shown on another and with the currently used homogeneous material the left. This contrast implies a superior geometric coupling approach. of the depth-varying material with the tire size and load. An initial down-selection eliminated the exponential pro- The strut loading plot on the right side of Figure 12-9 file from consideration; subsequent analysis eliminated the shows a long, dual-tire optimal region where the boundary quadratic profile. The final analysis compared the linear pro- curves overlap one another at between 24 and 30 in. of bed file material with the homogeneous approach. depth. In that region, both aircraft struts are ideally loaded at A dual-tire optimum design can be obtained with either a factor of 0.8. homogeneous or linear depth-varying arrestor beds. However, This long overlap is superior to the crisscross intersection the optimum designs for each differ in several substantial ways: of the homogeneous material plot on the left. It implies that additional tires, either larger or smaller than the two subject The homogeneous material strut-loading metamodels for tires, could also find optimal responses with such a design. the two tires had different shapes and magnitudes; the depth- After all, a larger tire would generally require a deeper bed; varying material did much to bridge the response chasm, such a bed would not disturb the response of either existing resulting in similar surfaces for the two tires. tire, since neither feels the effects of the additional depth. The The optimal design for the homogeneous material exhibited tires would tend to settle to their own equilibrium levels. This high sensitivity to changes in the arrestor material strength behavior contrasts with the homogeneous material, where for the smaller tire; the depth-varying system reduced the the only dual-tire optimum point was a chance intersection sensitivity difference between the tires by 50%. of the two tire curves. The likelihood of a third tire happen- The homogeneous material did not lend itself to multiple ing to intersect those two curves at the same junction point is simultaneous aircraft optimizations; the depth-varying sys- minimal. tem offered a dual-tire optimized region rather than a single Therefore, three behaviors emerge in the optimal design intersection point, and likely could support multiple simul- region of the linear depth gradient material: taneous aircraft optimizations. With the depth-varying material, each tire ignored unneeded 1. Each tire ignores unneeded depth, and "sees" the bed as bed depth, settling to its own natural equilibrium depth. tailor-fit to its dimensions; 2. The strength sensitivity of the smaller tire is reduced, mov- ing closer to that of the larger tire; and 12.5. Transition to Fielded System 3. The behavior suggests the feasibility of multi-tire simulta- 12.5.1. Comparison with Other neous optimization due to the depth insensitivity. Candidate Evaluations The depth-varying foam material was assessed as part of a 12.4.6. Summary of Metamodel Analysis parallel study to the overall research effort. The focal point of The metamodel analysis explored linear, quadratic, and the investigation differed from that of the other candidate exponential depth-varying material profiles using stratified arrestor concepts, and the final evaluation is less mature.