The purpose of the research outlined in this Master Thesis is to provide a feasibility study and a first approach to the design of a nozzle for a multi-tube Pulse Detonation Engine embedded on a Suborbital Single-Stage spaceplane. A Quasi-One-Dimensional model of an isentropic expansion applied exclusively to the supersonic blowdown phase of the pulse detonation cycle, combined with a 2D method for the geometry design of an Aerospike nozzle was developed in MATLAB. Additional research on shock wave propagation through reactant flow inside bent tubes was made so that the curvature of the tubes due to the throat inclination of an Aerospike didn't affect the combustion process. NASA Chemical Equilibrium with Applications (CEA) code was used to obtain the combustion parameters for Kerosene and Oxygen, and Endo-Fujiwara method was adapted to predict the flow parameters at the inlet of the nozzle at the beginning of the blowdown phase. A mechanism to keep constant reactants pressure before detonation has been found to be imperative for the operation at high altitudes. In such case, Average Thrust and Specific Impulse increases of 16% to 18% for rocket mode, and 19% to 25% for jet mode can be achieved. Despite the performance increase of the nozzle, an estimated Specific Impulse lower than 200 s for rocket mode appears to be too low for Single-Stage-to-Orbit applications.