An approximate method of calculating the minimum total weight of the two-insulation--two-coolant thermal protection system is developed. The equations derived in the development of the approximate method enable insight into the parameters that control the system weight. Two cases are considered: the case where the outer coolant location is unrestricted within the insulating wall and the case where the outer coolant location is restricted within the insulating wall. The effects on system weight of material properties and the outer coolant location within the insulating wall are discussed. A comparison of weights predicted by the approximate method and numerical solutions is shown. / Master of Science