Rocket equation

The so-called rocket equation describes the fundamental equations of rocket propulsion. If we consider the simplest case, in which a monostage rocket accelerates in a gravity-free vacuum, i.e. a slow-down due to gravitation and friction is not taken into consideration. When the rocket has a velocity of zero at the start and ejects the propellant with a constant ejection velocity ue, the velocity u of the rocket after time t corresponds to ... 

In addition to the gravitation of Earth a rocket launched from earth must also overcome the air resistance of the atmosphere, which means that the rocket equation for such cases is only an approximation. Planes, RAM and SCRAM jets which are propelled by jet engines, transport their fuel with them, but they also suck air in and use the oxygen from the air for the combustion of the fuel. They only carry the fuel but not the oxidizer with them. The rocket equation is not valid for such vehicles, which are referred to as air-breathing engines. 

This equation often referred to as the rocket equation or the burnout velocity equation, indicates the limitation on possible speeds of various kinds of rockets. 

Rocket propulsion moves a vehicle by ejecting mass out of the backside of the vehicle. Since there is no atmosphere in space, all of the reaction (i.e. propellant) mass must be carried on board and is usually released as a heated gas (i.e. the exhaust) expanding through a nozzle. All launches from earth into space have used chemical propulsion systems (i.e. reactions between a fuel and an oxidizer). The performance of a rocket vehicle is represented by the so-called first rocket equation ... 

This equation is referred to as the second rocket equation. Actually, from the expression midoldt) = (dmldt)v, it follows that dv = (dmlm)o y By integration, the expression presented above can be derived. 

Because of the use of ammonium perchlorate as a soHd oxidizer for rocket propeUants, the thermal decomposition has been much studied (29—32). Three separate activation energies have been observed for AP decompositions an activation energy of 123.8 kJ/mol (29.6 kcal/mol) is found below 240°C of 79.1 kj/mol (18.9 kcal/mol) above 240°C and finally, of 307.1 kj/mol (73.4 kcal/mol) between 400—440°C (33,34). Below 300°C, the equation... 

The products of equation 11 are separated by controlled crystalLi2ations to produce high purity crystalline anhydrous ammonium perchlorate and sodium chloride. The main use for ammonium perchlorate is as an oxidi2er in the propellant of rockets and missiles (see Explosives and propellants). 

As developed from the equation for conservation of momentum (Ref 27), the thrust, F, on a rocket motor is... 

A rocket fuel would be useless if its oxidation were not spontaneous. Although rockets operate under conditions that are far from standard, an initial estimation of the potential of a rocket fuel might assess whether its oxidation at the high temperatures reached in a rocket is spontaneous. A chemist exploring potential fuels for use in space considered using vaporized aluminum chloride in a reaction for which the skeletal equation is... 

C04-0156. Decaborane, Bio H14, was used as fuel for the Redstone rockets of the 1950s. Decaborane reacts violently with molecular oxygen according to the following equation ... 

The liquid propellant rocket combination nitrogen tetroxide (N204) and IJDMII (unsymmetrical dimethyl hydrazine) has optimum performance at an oxidizer-to-fuel weight ratio of 2 at a chamber pressure of 67 atm. Assume that the products of combustion of this mixture are N2, C02, H20, CO, H2, O, H, OH, and NO. Set down the equations necessary to calculate the adiabatic combustion temperature and the actual product composition under these conditions. These equations should contain all the numerical... 

Example 2.10. Probably the best contemporary example of a variable-mass system would be the equations of motion for a space rocket whose mass decreases as fuel is consumed. However, to stick with chemical engineering systems, let us consider the problem sketched in Fig. 2.8. Petroleum pipelines are sometimes used for transferring several products from one location to another on a batch basis, i.e., one product at a time. To reduce product contamination at the end of a batch transfer, a leather ball or pig that just fits the pipe is inserted in one end of the hne. Inert gas is introduced behind the pig to push it through the hne, thus purging the hne of whatever hquid is in it. 

Finally, the thrust F) of a rocket motor is also known to be related to the rate of burning and is obtained via the mass flow rate using the relationship given in equation (3.8) ... 

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