The purpose of this paper is to derive and solve equations for the fuel required by internal combustion engine airplanes on trajectories with a constant rate of climb or descent. Three modes of flight are considered: constant angle of attack, constant speed, and constant Mach number.
Newton's second law of motion is used to derive the equations. These are Riccati equations or reduced to such equations after neglecting a small term. A change of variable transforms them into second order linear differential equations that are solved exactly.
Formulas are found for the weight of fuel, speed, altitude, horizontal distance, time to climb, and power required.
The formulas obtained have direct applications for the analysis of aircraft performances and mission planning.
The formulas obtained are new and fundamental for the analysis of aircraft dynamics.
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