The variations of parameters method was used to determine the optimum nose shape for a reentry vehicle having a transpiration-cooled nosetip (TCNT). Three families of nose shapes were considered - The oblate ellipsoid, the flat face - round shoulder, and the spherical arc - round shoulder. These families are bounded by the flat face - sharp corner at one extreme and the hemisphere at the other extreme. The amount of coolant required by each nose shape during reentry was determined by using a high speed computer to couple the aerodynamic equations with the trajectory equations. The optimum shape is the shape which requires the least amount of coolant for reentry. The flat face - sharp corner shape was found to require the least amount of coolant, about 60 percent less water than the hemisphere. Although the time to impact is longer for the flat face, the smaller surface area and lower heating intensity more than offsets the increased reentry time. The possibility of an optimum flat face height was also investigated; no face height was found that minimized the total heating to the vehicle during reentry. (Author).