## Action and Reaction

Why does exhausting a hot gas through a nozzle produce a force that propels the rocket vehicle to high speeds? Once again, Isaac Newton comes to the rescue in answering this question.

There are two main thrust effects occurring to allow the rocket vehicle to accelerate in the atmosphere, and in the vacuum of space where there is nothing to push against! They are referred to as pressure thrust and impulse thrust, the latter being by far the dominant source of thrust force in a rocket system.

The way that pressure thrust works is easily understood by thinking about a bottle of carbonated soda (Fig. 5.4). When the bottle is sealed, the pressure forces inside are equal on all sides of the container, and there is no resultant force. However, if we remove the cap, an imbalance occurs producing a net force (which is small in this case). The bottle with the cap removed is analogous to the rocket engine combustion chamber with the open exit nozzle; there is some propulsive force produced by the pressure imbalance.

Figure 5.4: A pressure imbalance produces pressure thrust.

To understand the dominant propulsive effect, the impulse thrust, we need to recall Newton's laws of motion discussed in Chapter 1, and in particular his third law: to every action there is an equal and opposite reaction. Put simply, the action of a rocket engine is to throw lots of mass at high speed out the back of a launch vehicle, and the reaction is to cause the vehicle as a whole to accelerate in the opposite direction. To see this more clearly, we can propose an experiment to demonstrate the principle, but, again, do not try this at home! All you need for this is a high-velocity rifle, a skateboard, and a good sense of balance to stop you falling off the skate board when you fire the gun! A fired rifle produces a "kick": when the trigger is pulled, the bullet flies out of the barrel at high speed in one direction, and the gun reacts alarmingly by kicking back on the shooter's shoulder. It is this kick that can be harnessed as a propulsive force if we fire the gun while standing on the skateboard (Fig. 5.5). Let's suppose that the combined mass of the shooter, the rifle, and the skateboard is 75 kg. Let's suppose that the bullet has a mass of 50 g and leaves the barrel of the gun at 1500 m/sec (4920 feet/sec). We can

Figure 5.5: A "thought experiment" involving a high-velocity rifle and a skateboard!

Figure 5.5: A "thought experiment" involving a high-velocity rifle and a skateboard!

do some simple calculations to show that if the shooter gets on the skateboard and fires the gun, the kick will give them a speed of 1 m/sec (3 feet/sec) in the other direction. That's just over 2 mph, which is less than a good walking pace, so our improvised rocket system is not that good at producing propulsive force. But it does illustrate the effect of impulsive thrust. In a real rocket system, the designers strive to eject lots of "bullets"— in this case the exhaust gases from the engine nozzle—at high speed to maximize the reaction to accelerate the vehicle in the opposite direction.

Note that the two sources of rocket thrust are closely related. Clearly, the hole in the combustion chamber where the nozzle exit is located causes a pressure imbalance, giving a measure of pressure thrust. Also, equally clearly, if you have a hole with high pressure gas inside and low pressure gas outside, then you are definitely going to get mass coming out, providing impulse thrust. Although the two effects are distinguishable in the mathematics of rockets systems, physically they are closely linked.