Dependence of the Modified Lockheed Calibration Coefficient on Analysis Conditions for Cryogenic Transfer-Line Multilayer Insulation

The solid/contact conduction coefficient in the Modified Lockheed correlation for cryogenic transfer-line multilayer insulation (MLI) may depend on calibration conditions. Using 11 consistent cases from a published dataset, we examined heat-transfer area, emissivity and layer-density definitions. A common temperature potential gives a closed-form total heat leak for a cylindrical layerwise model, while internal temperatures are obtained by numerical inversion. Nested leave-one-out cross-validation with internal order selection separated in-sample fit from held-out prediction. The equally weighted quadratic fit yielded a 2.56% mean absolute percentage error (MAPE) and 5.10% maximum error in layerwise evaluation; nested cross-validation gave 11.22% MAPE. Recalibration at emissivities of 0.02-0.06 gave 2.51-3.31% MAPE despite an approximately threefold variation in the mean coefficient. Applying outer-area-calibrated coefficients to layerwise evaluation gave 17.09% MAPE, including an area-definition mismatch. Across 14 cases, three with inconsistent layer information, reported and thickness-based layer densities yielded 4.28% and 17.20% MAPE, respectively. The fitted coefficient is therefore a residual-based calibration coefficient conditional on the analysis conditions and underlying heat-transfer submodels.