M rm n n

FIGURE 3-12. Simplified diagrams of several different nozzle configurations and their flow effects.

FIGURE 3-13. Length comparison of several types of nozzles. (Taken in part from G. V. R. Rao, "Recent Developments in Rocket Nozzle Configurations," American Rocket Society Journal, Vol. 31, No. 11, November 1961.)

(shorter nozzles can reduce vehicle length, vehicle structure, and vehicle inert mass).

Cone- and Bell-Shaped Nozzles

The conical nozzle is the oldest and perhaps the simplest configuration. It is relatively easy to fabricate and is still used today in many small nozzles. A theoretical correction factor X can be applied to the nozzle exit momentum of an ideal rocket with a conical nozzle exhaust. This factor is the ratio between the momentum of the gases in a nozzle with a finite nozzle angle 2a and the momentum of an ideal nozzle with all gases flowing in an axial direction:

The variation of X with different values of a is shown in Table 3-3 for any nozzle that has uniform mass flow per unit exit area. For ideal rockets X = 1.0. For a rocket nozzle with a divergence cone angle of 30° (half angle a = 15°), the exit momentum and therefore the exhaust velocity will be 98.3% of the velocity calculated by Eq. 3-15b. Note that the correction factor X only applies

TABLE 3-3. Nozzle Angle Correction Factor for Conical Nozzles

Nozzle Cone Divergence Half Angle, a (deg)

Correction Factor, A

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