Thrust and Specific Impulse

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)  

In this equation F(th) is the theoretical thrust, R is the average rate of burning, /gp is a performance parameter related to the propellant called the specific impulse, D is the propellant density and Ap is the average area of the burning surface. 

The performance of rocket propellants is commonly studied by means of the specific impulse which can be expressed as the thrust delivered per unit weight of propellant consumed as shown by equation (3.9). 

In the above equation W is the weight of propellant and h and t2 are the times between which the thrust is measured. 

The specific impulse, under fixed pressure conditions, is invariant for any propellant system and is the basic chemical comparison parameter used in evaluation. 

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A thermal rocket of recent development which produces low thrust and specific impulse for satellite control purposes is the subliming propellant rocket. In this rocket the propellant is ordinarily a high vapor pressure solid. Propellant flow rate is controlled by the addition of heat to the subliming propellant. Desirable properties of propellants for such rockets is stability in the solid phase, high vapor pressure, and, as for all thermal rocket propellants, low molecular weight of the vapor produced. 

The jet power of the propellant, Pj, leaving the engine is deterntined by thrust and specific impulse ... 

The above discussion is considerably oversimplified, in that it applies only for constant-thrust trajectories. Interplanetary missions may, in actuality, require considerable variation in thrust and specific impulse [2,3], Nevertheless, the simplified approach provides preliminary information concerning the ranges of propulsion parameters of interest for space missions. 

Liquid rocket propellants are subdivided into monopropellants and bipropellants. Monopropellants are liquids which burn in the absence of external oxygen. They have comparatively low energy and specific impulse and are used in small missiles which require low thrust. Hydrazine is currently the most widely used monopropellant however, hydrogen peroxide, ethylene oxide, isopropyl nitrate and nitromethane have all been considered or used as monopropellants. Information on the performance of some monopropellants is presented in Table 8.3. 

The mass of heat sink material required to satisfactorily condense the rocket gas flow for a specified run time is a function of several rocket parameters and heat sink material properties. To a suitable approximation, the specific impulse of the rocket fuel determines the amount of energy per unit fuel mass that must be removed by the heat sink, and the fuel mass flow is determined by the ratio of rocket thrust to specific impulse. The heat capacity of the heat sink material along with the allowable material temperature rise during the rocket firing imply the required heat sink mass ... 

In addition to the research effort at the Lewis Research Center, NASA has recently awarded a research and development contract for an ion thrust generator capable of producing 0.01 lbs thrust at specific impulses in the 4000-sec range. A similar contract was earlier awarded by the Air Force. These thrust units may eventually be suitable for clustering to produce jet power of the order of 30 kw for eventual use with the SNAP-8 power supply. 

The specific impulse is the thrust per unit weight rate of flow and so,... 

The specific hiats of NPN product gases (primarily carbon monoxide and carbon dioxide) arising from combustion are Cp 0.346cal/g/° and Cv 0.252cal/g/° at 300°K. The specific impulse of these gases (calc at 400psi) is 155 lbs/thrust/lb/sec... 

The ratio of rocket thrust to propellant mass flow, commonly called the specific impulse (/9p) of the propellant, represents a measure of the force developed per unit mass flow of propellant. From Eq. (2), it is apparent that high propellant-flame temperatures and low molecular-weight combustion products are required to produce high 7sp. 

Figure 30.5 Comparison of specific impulse and flight Mach number for hydrogen (1) and hydrocarbons (2). PDE performance estimated using ASI Performance deck turbojet, ramjet, and scramjet performance levels reflect well-designed systems for man-rated thrust classes. TJ — turbojets RJ — ramjets SJ — scramjets PDE — pulse detonation engines PIL — preignition hmit [12]...

In addition, the specific impulse is given by the thrust coefficient and the characteristic velocity according to... 

The specific impulse of a rocket motor, I, as defined in Eq. (1.75), is dependent on both propellant combushon efficiency and nozzle performance. Since is also defined by Eq. (1.79), rocket motor performance can also be evaluated in terms of the characterishc velocity, c, defined in Eq. (1.74) and the thrust coefficient, Cp, defined in Eq. (1.70). Since c is dependent on the physicochemical parameters in the combustion chamber, the combushon performance can be evaluated in terms of c. On the other hand, Cp is dependent mainly on the nozzle expansion process, and so the nozzle performance can be evaluated in terms of Cp. Experimental values of and Cpgxp are obtained from measurements of chamber pressure, p, and thrust, F ... 

Nozzleless rockets are very simplified and low-cost rockets because no nozzles are used. Their specific impulse is lower than that of conventional rockets even when the same mass of propellant is used. Normally, a convergent-divergent nozzle is used to expand the chamber pressure to the atmospheric pressure through an isentropic change, which is the most effective process for converting pressure into propulsive thrust The flow process without a nozzle increases entropy and there is stagnahon pressure loss. 

The combustion temperature in a gas generator is maximized at the stoichiometric mixture of 8 = 5. The specific impulse increases with increasing e (fuel-lean mixture). However, the thrust decreases as e is increased. The maximum thrust is obtained at the stoichiometric mixture ratio. It is evident that L increases with increasing b- The I p of a pyrolant containing 1b(0-2) is 1100 s and its T)-is about 1600 K at e = 20. 

F = thrust in pounds and W = wt flow rate of proplnt in ib/ sec Specific impulse must vary with changes in alti-... 

Specific impulse, Isp, probably the most accepted measure of LP performance, was defined in Sect 1 and tabulated in Tables 1 2. The thrust, F, of a rocket is given by... 

In organizing the symposium, we made the usual division into solid and liquid rocket propellants. Most readers no doubt already know the relative merits of solid vs. liquid systems—viz., the instant readiness of solids (compared with cryogenic liquids), their higher density (important in volume-limited systems), and the relative simplicity of rocket construction liquids offer easy variation in thrust level and the attainment of higher specific impulses, the latter because physical separation permits the use of fuels and oxidizers that would be incompatible if premixed. 

The specific impulse Is is used to compare the performances of rocket propellants and is dependent on the thrust and flow rate of the gases through the nozzle as shown in Equation 8.4. 

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