Thrust

The thrust is the force produced by a rocket propulsion system acting upon a vehicle. In a simplified way, it is the reaction experienced by its structure due to the ejection of matter at high velocity. It represents the same phenomenon that pushes a garden hose backwards or makes a gun recoil. In the latter case, the forward momentum of the bullet and the powder charge is equal to the recoil or rearward momentum of the gun barrel. Momentum is a vector quantity and is defined as the product of mass times velocity. All ship propellers and oars generate their forward push at the expense of the momentum of the water or air masses, which are accelerated towards the rear. Rocket propulsion differs from these devices primarily in the relative magnitude of the accelerated masses and velocities. In rocket propulsion relatively small masses are involved which are carried within the vehicle and ejected at high velocities.

The thrust, due to a change in momentum, is given below. A derivation can be found in earlier editions of this book. The thrust and the mass flow are constant and the gas exit velocity is uniform and axial.

dm w

dt g0

This force represents the total propulsion force when the nozzle exit pressure equals the ambient pressure.

The pressure of the surrounding fluid (i..e, the local atmosphere) gives rise to the second contribution that influences the thrust. Figure 2-1 shows schematically the external pressure acting uniformly on the outer surface of a rocket chamber and the gas pressures on the inside of a typical thermal rocket engine. The size of the arrows indicates the relative magnitude of the pressure forces. The axial thrust can be determined by integrating all the pressures acting on areas that can be projected on a plane normal to the nozzle axis. The forces acting radially outward are appreciable, but do not contribute to the axial thrust because a rocket is typically an axially symmetric chamber. The conditions prior to entering the nozzle are essentially stagnation conditions.

Because of a fixed nozzle geometry and changes in ambient pressure due to variations in altitude, there can be an imbalance of the external environment or atmospheric pressure p3 and the local pressure p2 of the hot gas jet at the exit plane of the nozzle. Thus, for a steadily operating rocket propulsion system moving through a homogeneous atmosphere, the total thrust is equal to

The first term is the momentum thrust represented by the product of the propellant mass flow rate and its exhaust velocity relative to the vehicle. The second term represents the pressure thrust consisting of the product of the cross-sectional area at the nozzle exit A2 (where the exhaust jet leaves the

Atmosphere (3) Converging nozzle section

Atmosphere (3) Converging nozzle section

FIGURE 2-1. Pressure balance on chamber and nozzle interior walls is not uniform. The internal gas pressure (indicated by length of arrows) is highest in the chamber (p{) and decreases steadily in the nozzle until it reaches the nozzle exit pressure pi- The external or atmospheric pressure p3 is uniform. At the throat the pressure is pt. The four subscripts (shown inside circles) refer to the quantities A, v, T, and p at specific locations.

FIGURE 2-1. Pressure balance on chamber and nozzle interior walls is not uniform. The internal gas pressure (indicated by length of arrows) is highest in the chamber (p{) and decreases steadily in the nozzle until it reaches the nozzle exit pressure pi- The external or atmospheric pressure p3 is uniform. At the throat the pressure is pt. The four subscripts (shown inside circles) refer to the quantities A, v, T, and p at specific locations.

vehicle) and the difference between the exhaust gas pressure at the exit and the ambient fluid pressure. If the exhaust pressure is less than the surrounding fluid pressure, the pressure thrust is negative. Because this condition gives a low thrust and is undesirable, the rocket nozzle is usually so designed that the exhaust pressure is equal or slightly higher than the ambient fluid pressure.

When the ambient atmosphere pressure is equal to the exhaust pressure, the pressure term is zero and the thrust is the same as in Eq. 2-13. In the vacuum of space pi = 0 and the thrust becomes

The pressure condition in which the exhaust pressure is exactly matched to the surrounding fluid pressure (p2 = Pi) is referred to as the rocket nozzle with optimum expansion ratio. This is further elaborated upon in Chapter 3.

Equation 2-14 shows that the thrust of a rocket unit is independent of the flight velocity. Because changes in ambient pressure affect the pressure thrust, there is a variation of the rocket thrust with altitude. Because atmospheric pressure decreases with increasing altitude, the thrust and the specific impulse will increase as the vehicle is propelled to higher altitudes. This change in pressure thrust due to altitude changes can amount to between 10 and 30% of the overall thrust, as is shown for a typical rocket engine in Fig. 2-2. Table 8-1 shows the sea level and high altitude thrust for several rocket engines. Appendix 2 gives the properties of the Standard Atmosphere (ambient pressure).

0 20 40 60 80 100 120 140 160 Altitude, ft x 103

FIGURE 2-2. Altitude performance of RS 27 liquid propellant rocket engine used in early versions of the Delta launch vehicle.

0 20 40 60 80 100 120 140 160 Altitude, ft x 103

FIGURE 2-2. Altitude performance of RS 27 liquid propellant rocket engine used in early versions of the Delta launch vehicle.

Was this article helpful?

0 0
Project Management Made Easy

Project Management Made Easy

What you need to know about… Project Management Made Easy! Project management consists of more than just a large building project and can encompass small projects as well. No matter what the size of your project, you need to have some sort of project management. How you manage your project has everything to do with its outcome.

Get My Free Ebook


Post a comment