Science, Maths & Technology

# Rocket science

Updated Tuesday 26th September 2006

Battle of the the Geeks' Ian Johnston takes us through the science which lifts rockets from launchpad to the skies. We start, though, by asking why buildings don't fall down

Action, Reaction and Propulsion
How does a building stay up? There is a huge downwards force on it, due to gravity, and this is exactly balanced by the upwards force supplied by the ground.

Action (the weight) and reaction (the upthrust) are equal and opposite. This principle is Newton's Third Law and it is extremely useful in analysing static objects, since it tells us that the sum of all the forces acting on a stationary object must be zero.

The forces in a bridge, a human leg or a tent must all be in static equilibrium.

The situation becomes a bit more complicated when we involve moving objects or materials, and to work out what's going on we need a new idea: momentum.

When a force acts on an object which is free to move, the object will accelerate (either by starting to move, or by changing its speed, or by changing its direction of motion).

After a while, a given force can produce a large velocity in a small object, a small velocity in a large object or any combination in between. We can summarize this with the idea of momentum, which is defined as:

the mass of an object multiplied by its velocity,

so the effect of a force acting over a time is a change in momentum, or, to put it another way:

force equals rate of change of momentum.

Small things can move faster than large things.

When a plane flies through the air the shape of the wings gives rise to a flow pattern which drops the pressure above the top surface and increases it below the bottom surface.

The overall result is an upwards force on the wing - called lift - and a downwards force on the surrounding air, which responds by acquiring some momentum downwards.

This is how a propeller or jet engine works, too. Air leaves the back of the device moving a lot faster than it approached the front, and the increase in rearwards momentum is balanced by a forwards force – thrust – on the plane.

All this depends on changing the momentum of the surrounding fluid, and for dolphins, gliders and airliners it works very well. However, it has limitations.

Thrust depends on momentum change which depends on mass flow rate (how much material is affected) and velocity change (how much it is affected), and there are restrictions to both of these.

The amount of material available for a wing, propeller or jet engine to move depends on the surrounding pressure, because that's what fills the gap when some fluid has been accelerated out of the way.

It also depends on the density, because the denser a fluid is the more momentum, and therefore the more force, is involved in moving it. With a fall in pressure, density, or both, it becomes harder to achieve the momentum change required.

That's why we can tread water but not fly, and why every plane has a ceiling above which it can't fly. The extreme case of this is in space, where there is no fluid to move and where wings of any sort are useless.

The answer is to take a store of fluid with us as we travel, and give that a change of momentum instead of the fluid (if any) surrounding. However, that means moving more material, and that's expensive.

So, remembering that momentum is mass times velocity, the solution is to take a small mass, but to move it as quickly as possible when the time comes.

However, that brings its own difficulties. When fluid velocities approach the speed of sound, flow patterns change radically. There is no longer time for fluid to get smoothly out of the way of an oncoming object, and instead shock waves form – regions with very rapid changes in velocity.

Shock waves involve a loss of mechanical energy (as the fluid heats up) and as a result are very inefficient. Mechanical pumping systems (like propellers) are therefore also very inefficient when high velocities are involved.

So we need a way of accelerating a small amount of fluid to high speeds without using any form of pump. The easiest way to do this is to use heating effects.

When gases are heated at a constant pressure they expand, so if we allow gas to flow through a chamber and heat it on its way through it will flow out faster than it flows in. The mass flow rate is the same, but since it is less dense the volume flow rate increases.

Transferring heat into fluids is not easy, and it's even worse for gases: think how big a central heating radiator needs to be for quite a small heat output. It is therefore much more efficient to create the heat within the gas itself, by burning.

And so the logical conclusion of all this is ... a rocket!

Burning material in a small chamber so that it can be ejected at high velocity (and therefore high momentum) to create forward thrust.

Then the engineering fun really begins, as we have to decide how to produce and control a high power burning process in a confined space.

This is perilously close to the definition of a bomb, so when rocket design goes wrong the results can be spectacular – and dangerous.

The Space Shuttle's main engines burn liquid hydrogen and liquid oxygen: they are stored separately in the external tank and then pumped into a combustion chamber where they mix and burn. This give a huge amount of controllable thrust (over 180 tonnes per engine) but at enormous expense.

Not only are the engines fantastically complicated – they cost \$50 million each – the support systems needed to produce, store and deliver large quantities of liquid oxygen and hydrogen are also complicated, expensive and dangerous.

The most familiar rocket motors are probably those in fireworks. They use a black powder (gunpowder) propellant, which is a mixture of fuel (carbon and sulphur) and oxidiser (potassium nitrate).

The Space Shuttle's solid rocket boosters (the two rockets on each side of the main tank) use aluminium powder as the fuel and ammonium perchlorate as the oxidiser bound together with plastic.

These systems have some great advantages (they're simple and robust) but a fundamental disadvantage (lack of control). Once a solid rocket has been started then in general it can't be stopped until the fuel has run out.

This is fine for simple launching applications, but has some unfortunate implications for transport and safety. Airline, shipping companies and customs officials are not keen on materials which burn vigorously and uncontrollably if lit!

For small scale rocketry, as used on Battle of the Geeks, hybrid motors give an elegant solution.

The motors available to the teams used liquid nitrous oxide (laughing gas) as the oxidiser and a plastic fuel, which is also the combustion chamber.

The ignition process is more complicated, because the combustion chamber walls have to be heated up to boiling point before the reaction will start, but without this complicated sequence the entire system - liquid, solid and structure - is completely inert and harmless.

Rockets are spectacular and awe-inspiring to watch. Launching systems like the Space Shuttle or Ariane are extremely complicated and expensive. However, the basic principles on which they work are exactly the same as those for a Bonfire Night rocket – or two engineers with carbon dioxide fire extinguishers, folding chairs and a short length of track!