Iii

0 2000 4000 6000 8000 m/sec

Average effective exhaust velocity

20,000

10,000

"0 20 40 60 80 100120140160180 Mass ratio m,Jmf- 1/A/R

FIGURE 4-2. Maximum vehicle velocity in a gravitationless, drag-free space for different mass ratios and specific impulses (plot of Eq. 4-6). Single-state vehicles can have values of 1/IVR up to about 20 and multistage vehicles can exceed 200.

20,000

10,000

"0 20 40 60 80 100120140160180 Mass ratio m,Jmf- 1/A/R

FIGURE 4-2. Maximum vehicle velocity in a gravitationless, drag-free space for different mass ratios and specific impulses (plot of Eq. 4-6). Single-state vehicles can have values of 1/IVR up to about 20 and multistage vehicles can exceed 200.

not only is true of interplanetary spaceships in a vacuum but applies to almost all types of rocket-powered vehicles. For this reason, importance is placed on saving inert mass on every vehicle component, including the propulsion system.

Equation 4-6 can be modified and solved for the effective propellant mass mp required to achieve a desired velocity increment for a given initial takeoff mass or a final burnout mass of the vehicle. The final mass consists of the payload, the structural mass of the vehicle, the empty propulsion system mass (which includes residual propellant), plus a small additional mass for guidance, communications, and control devices. Here mp = w0 — rrif.

The flight velocity increment up is proportional to the effective exhaust velocity c and, therefore, to the specific impulse. Thus any improvement in Is (such as better propellants, more favorable nozzle area ratio, or higher chamber pressure) reflects itself in improved vehicle performance, provided that such an improvement does not also cause an excessive increase in rocket propulsion system inert mass, which causes a decrease in the effective propellant fraction.

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