allows for the incorporation of high-energy fuel additives such as aluminium, lithium, or metal hydrides. Combustion The governing equation for hybrid rocket combustion shows that the regression rate is dependent on the oxidizer mass flux rate, which means the rate that the fuel will burn is proportional to the amount of oxidizer flowing through the port. This differs from a solid rocket motor, in which the regression rate is proportional to the chamber pressure of the motor. where is the regression rate, is the regression rate coefficient (incorporating the grain length), is the oxidizer mass flux rate, and is the regression rate exponent. As the motor burns, the increase in diameter of the fuel port results in an increased fuel mass flow rate. This phenomenon makes the oxidizer to fuel ratio (O/F) shift during the burn. The increased fuel mass flow rate can be compensated for by also increasing the oxidizer mass flow rate. In addition to the O/F varying as a function of time, it also varies based on the position down the fuel grain. The closer the position is to the top of the fuel grain, the higher the O/F ratio. Since the O/F varies down the port, a point called the stoichiometric point may exist at some point down the grain. Properties Hybrid rocket motors exhibit some obvious as well as some subtle advantages over liquid-fuel rockets and solid-fuel rockets. A brief summary of some of these is given below: Advantages compared with liquid rockets Mechanically simpler – requires only a single liquid propellant resulting in less plumbing, fewer valves, and simpler operations. Denser fuel – fuels in the solid phase generally have higher density than those in the liquid phase, reducing overall system volume. Metal additives – reactive metals such as aluminium, magnesium, lithium or beryllium can be easily included in the fuel grain increasing specific impulse (), density, or both. Combustion instabilities – Hybrid rockets do not typically exhibit high frequency combustion instabilities that plague liquid rockets due to the solid fuel grain breaking up acoustic waves that would otherwise reflect in an open liquid engine combustion chamber. Propellant pressurization – One of the most difficult to design portions of a liquid rocket system are the turbopumps. Turbopump design is complex as it has to precisely and efficiently pump and keep separated two fluids of different properties in precise ratios at very high volumetric flow