9.2.D - Launches


A rocket or rocket vehicle is a missile, spacecraft, aircraft or other vehicle which obtains thrust from a rocket engine. In all rockets, the exhaust is formed entirely from propellants carried within the rocket before use. Rocket engines work by action and reaction. Rocket engines push rockets forwards simply by throwing their exhaust backwards extremely fast.

Rockets for military and recreational uses date back to at least 13th century China. Significant scientific, interplanetary and industrial use did not occur until the 20th century, when rocketry was the enabling technology of the Space Age, including setting foot on the moon.

Rockets are used for fireworks, weaponry, ejection seats, launch vehicles for artificial satellites, human spaceflight and exploration of other planets. While comparatively inefficient for low speed use, they are very lightweight and powerful, capable of generating large accelerations and of attaining extremely high speeds with reasonable efficiency.

In this unit you will learn about:

  • The launch velocity needed to escape the gravitational field of a planet
  • The changing forces and acceleration during a typical rocket launch
  • Ways to increase a rockets velocity using the Earth's rotational and orbital motion
  • Factors that must be considers to ensure the safety of astronauts re-entering the Earth's atmosphere
  • How the motion of planets can be used to enhance the velocity of a deep space probe


Escape Velocity

Newtons Ideas on Escape Velocity

Newton's ideas on escape velocity show
that only object E will have enough kinetic
energy to escape the Earth's gravitational
field completely.

Isaac Newton surmised that if you climb to the top of a mountain and fire a cannon, the cannon ball will travel a certain distance and then hit the ground (A).

If you fired the cannon so that the cannon ball had a larger velocity it would travel even further (B).

If you kept increasing the velocity of the cannon ball and there was no air resistance, a point would come when the cannon ball would be travelling part-way around the world. If the ball could be fired at just the right velocity, it would travel completely around the Earth and hit you in the back of the head (C). In this case it would fall at exactly the same rate as the Earth curves so its also undergoing projectile motion.

If it was fired much faster than that, the canon ball would go into an elliptical orbit (D) or even faster it would travel off into space and never return (E).

The smallest speed at which this can occur (E) is known as the escape velocity.

Escape Velocity

Deriving escape
velocity by equating
the change in GPE
and KE.

Escape velocity is defined as the smallest speed that we need to give an object in order to allow it to completely escape from the gravitational pull of the planet on which it is sitting. To calculate it we need only realise that as an object moves away from the centre of a planet, its kinetic energy gets converted into gravitational potential energy. Thus we need only figure out how much gravitational potential energy an object gains as it moves from the surface of the planet off to infinity and equate this with the kinetic energy lost.

Note that the mass of the object moving into space has cancelled so that the escape velocity of any object is independent of its mass. This means that if you want to throw a grain of rice or an elephant into outer space, you need to give them both the same initial velocity that for the Earth works out to be 11.2 kms-1.

Of course, an elephant has a greater mass so a larger force is needed to accelerate it to the escape velocity.


Equation - Escape Velocity

v

G

m1

r

escape velocity

universal gravitation constant (6.673 x 10-11)

mass of central body (not escaping body)

radius of central body

metres per second (ms-1)

N m2 kg-2

kilograms (kg)

metres (m)

Use this equation when determining the orbital velocity required for a stable orbit at a certain radius.


Some other things to note about escape velocity:

  • After being given the escape velocity initially, an object will come to rest and infinity where GPE is maximum (GPE=0). All of the initial kinetic energy is converted into gravitational potential energy.

  • Escape velocity will always be greater than the orbital velocity as it will take an object out of a stable (closed) orbit to infinity.

 

Forces

Weight and thrust forces add to give a net force that
gives a rocket its acceleration.

During the launch of the space shuttle two solid rocket boosters each provide a whopping 12.5 million newtons of thrust at lift-off. Shown in white in the diagram on the right, these rockets sit either side of the external fuel tank (red) which delivers the liquid oxygen and hydrogen fuel to the engines. The solid rocket boosters provide 83% of the total thrust needed for lif-off, the remaining 17% coming from the three engines mounted on the orbiter itself.

These massive forces are needed for two things. Firstly, to overcome the force of gravity (weight) of the spacecraft needed to get it into orbit around the Earth and secondly to provide the acceleration needed to get the space shuttle to the speed required for a stable orbit. In the case of deep space probes or spacecraft destined for the moon, the force produced by the engines must provide the acceleration needed to ensure the space probe moves through space at a high speed.

During a launch there are two main forces that act in opposite directions to produce an upwards net force and they are thrust and weight. A net upwards force is produced because the thrust from the engines is larger than the weight and this causes the space shuttle or rocket to accelerate upwards.

Thrust

The thrust arises in the combustion chamber from collisions of gas
molecules with the top of the chamber. Collisions on each side of
the chamber cancel each other out so there is no net force in the
dimension perpendicular to the thrust.

After the engines of the rocket have ignited, fuel mixes with oxygen in the combustion chamber and produces hot gases as products of the reaction. As such, the combustion chamber contains extremely hot gases moving at very high speeds in all directions. When gas molecules strike the walls of the combustion chamber, they strike the wall with a force. The collisions of billions upon billions of gas molecules with the combustion chamber combine to produce the enormous thrust that gets a rocket off the ground.

We can also analyse the thrust using the law of conservation of momentum. During the collision of a gas molecule with the combustion chamber, momentum must be conserved. The momentum lost by a gas molecule is equal to the momentum gained by the rocket. Said another way, the backward momentum of the gases is exactly equal in magnitude to the forward momentum of the rocket. This is what gives the rocket its forward velocity. Imagine yourself on a snow sled with a pile of bricks. You could get yourself (and the sled) to move forward by throwing the bricks off the sled in the opposite direction.

In the equation on the right, the negative sign denotes the direction of velocity of the gases being opposite to that of the rocket. In the above example, forwards would be positive (or upwards if a rocket is launched vertically).

You should note that because at any time instant the mass of the gases is much less than the mass of the rocket, the velocity of the gases will, therefore, be much higher in magnitude than the velocity of the rocket. Although the mass of the gas emitted per second is comparatively small, it has a very large momentum on account of its high velocity. An equal momentum is imparted to the rocket in the opposite direction. This means that the rocket, in spite of its large mass, builds up a high velocity.

Going back to our sled example, throwing one brick is only going to give you a very small velocity due to the large mass of the you and the sled.

Changing Forces and Acceleration

As a rocket rises during lift-off, it lightens because fuel is consumed, and the ratio of thrust to vehicle mass increases. An additional positive effect on the rocket is the decrease in aerodynamic drag with increasing altitude. The combination of these two factors accounts for the increase in acceleration during the launch of the rocket and helps the spacecraft reach the high velocity that is needed for space flight.

To simplify matters we will ignore the drag from air resistance. Considering the net forces acting on a rocket at lift-off, the net force can be determined by adding the thrust and weight, giving us the following expression.

Because the net force and thrust are both in the upwards direction, they have been given a positive sign for direction. Weight has a negative sign because it is acting downwards (in the opposite direction). The second line could easily have been written as:

Fnet = T + (-mg)

As we have discussed above, a rocket's mass will decrease due to loss of fuel. Additionally, the gravitational field reduces slightly with increasing altitude and so will the value for the acceleration due to gravity, g. The result is that a rocket's rate of acceleration will increase as the flight progresses and its velocity will increase at an increasing rate. Consequently, the equation above can only apply at an instant in time provided that the mass and thrust are known at that instant.

Forces on Astronauts and G-Forces

The forces on an astronaut during lift-off. The net force will be the
sum of the reaction force and the weight of the astronaut.

The net force on an astronaut in a rocket can be determined using the same procedure that we did for a rocket. In this case though the force acting in the opposite direction to weight is the reaction force. This is the force of the chair pushing up on the astronaut and also the force that scales use to measure mass.

If you were standing on a set of scales inside an elevator that was at rest, the scales would actually measur the force with which they push up on you. They are calibrated to convert this force to a mass in kilograms by essentially dividing the force by the acceleration due to gravity (F=ma). When the lift is at rest, this force is of the same magnitude (but opposite direction) to your weight force, so the scales can easily measure your weight and calculate your mass.

When the lift begins to accelerate upwards, the reading on the scales increases and your weight also seems to increase. The same thing happens to an astronaut accelerating upwards in a rocket. The thrust from the rocket's engines increases the reaction force and this makes the astronaut feel much heavier than he actually is. This apparently heavier feeling of weight is known as apparent weight and it always increases during lift-off.

Adding the forces acting on an astronaut during lift-off gives an expression for net force and apparent weight. During lift-off the astronaut will feel the chair pushing up on him with increasing force as the rocket accelerates upwards. Humans can only withstand an upper limit for the reaction force and remain conscious and this is why the concept of g-forces is used when discussing the the forces on astronauts.

G-force can be determined by
dividing the apparent weight by the
actual weight.

The term g-force simply refers to the multiple of an astronaut's actual weight they are feeling due to the upward reaction force against their bodies. Their weight appears to increase during lift-off and the number of times by which it increases is the number we asign as the g-force in operation. As discussed in the section above, because of the loss of mass and the reduction in acceleration due to gravity as altitude increases, the acceleration of a rocket will increase. This means that astronauts will experience g forces many times higher than 1g (their actual weight). In fact, the g forces will increase up to about a 3g maximum.

The problem with high acceleration launches is that astronauts and payload suffer from the high g-forces produced. If an astronaut was sitting upright to the direction of motion, mental confusion and unconsciousness can follow g-forces. Internal organs are pulled down into the body cavity and blood pressure falls because blood gravitates to the feet.

Astronauts usually lie facing upwards on a specially designed, cushioned couch. This makes the g-forces more tolerable, although breathing can become a problem and an astronaut may need extra oxygen to make up for the decline in blood oxygen at these concentrations. Specially designed pressurised g-suits also act to circulate blood in the extremities and ensure the health and safety of the astronauts is maintained during lift-off.

 

Velocity Boost

A spacecraft can be given a
velocity boost from the Earth's
rotation if it launches towards
the east.

The Earth rotates on its own axis in an easterly direction. At the latitude of NASA’s Cape Canaveral launch site, the speed of rotation is about 400 ms-1. It makes good sense to launch a rocket in the easterly direction as it will already have a speed of 400 ms-1 in the direction it needs to go. The closer to the equator, the faster the velocity due to the increasing radius of the Earth. You will recall that one way to work out orbital velocity is to use v = 2πr/T. Since the radius increase as you move towards the equator, so will the orbital velocity. This is why launch sites are always located as close to the equator as possible.

To penetrate the dense lower portion of the atmosphere by the shortest possible route, rockets are initially launched vertically from the launch pad. As the rocket climbs, its trajectory is tilted in the easterly direction by the guidance system to take advantage of the Earth’s rotational motion. Eventually, the rocket is travelling parallel to the Earth’s surface immediately below and can then be maneuvered into Earth orbit.

A velocity boost from the Earth's orbit around the
Sun can only be taken advantage of at certain
times of the year known as launch windows.

For a spacecraft to go on a mission to another planet or into deep space, it is first necessary for the spacecraft to achieve escape velocity and to go into its own elliptical orbit around the Sun. The Earth orbits the Sun at about 30 kms-1. Again it makes good sense to use this speed to help a spacecraft achieve escape velocity for trips to other planets. So, if the spacecraft is to go on a mission to planets beyond the Earth’s orbit, it is launched in the direction of Earth’s orbital motion and achieves a velocity around the Sun greater than the Earth’s 30 kms-1. Thus, the spacecraft’s orbit is larger than that of the Earth and is arranged to intersect with the orbit of the planet to which it is heading at a time when the planet will be at that point. Given that the Earth's orbital velocity vector changes constantly, there are only certain places in its orbit (and times of year) that make a launch suitable. The velocity vector must be pointing in the intended direction of motion.

 

Safe Re-Entry

The safe return of a spacecraft into the Earth's atmosphere and subsequent descent to Earth requires consideration of two main issues:

  • How to handle the intense heat generated as the spacecraft enters the Earth's atmosphere, and

  • How to keep the g-forces of deceleration within safe limits for the astronauts.

On re-entry, friction between the spacecraft and the Earth's atmosphere generates a great deal of heat. Early spacecraft such as NASA's Mercury, Gemini & Apollo capsules, used heat shields made from what was called an ablative material that would burn up on re-entry and protect the crew from the high temperatures. The space shuttle uses an assortment of materials to protect its crew from the intense heat. Reinforced carbon-carbon composite, low and high temperature ceramic tiles and flexible surface insulation material all play important protective roles in appropriate positions on the shuttle.

The re-entry angle of the space shuttle must be tightly controlled to ensure
the safety of the astronauts.

It would be easier if a spacecraft could re-enter the atmosphere vertically. Unfortunately, the thick, bottom section of our atmosphere that is used to effectively slow the spacecraft to safe landing speed is not sufficiently thick (about 100 km) to allow for vertical re-entry. So, the spacecraft is forced to re-enter at an angle to the horizontal of between 5.2° and 7.2°. This small angular corridor is called the re-entry window. If the astronauts re-enter at too shallow an angle, the spacecraft will bounce off the atmosphere back into space. If the astronauts re-enter at too steep an angle, both the g-forces and the heat generated will be too great for the crew to survive.

What Can Go Wrong?

The following points represent the main reasons why a safe re-entry must be so carefully controlled.

  • If the angle of re-entry is too shallow, the spacecraft may skip off the atmosphere. The commonly cited analogy is a rock skipping across a pond. If the angle of entry is too steep, the spacecraft will burn up due to the heat of re-entry.

  • Because of collisions with air particles and the huge deceleration, a huge amount of heat is produced from friction. The space shuttle must be able to withstand these temperatures. It uses a covering of insulating tiles which are made of glass fibres but are about 90% air. This gives them excellent thermal insulating properties and also conserves mass. The tile construction is denser near the surface to make the tiles more resistant to impact damage, but the surface is also porous. Damage to the space shuttle Columbia's heat shield is thought to have caused its disintegration and the loss of seven astronauts on 1st February 2003. Investigators believe that the scorching air of re-entry penetrated a cracked panel on the left wing and melted the metal support structures inside.

  • Large g forces are experienced by astronauts as the space shuttle decelerates and re-enters the Earth's atmosphere. Astronauts are positioned in a transverse position with their backs towards the Earth's surface as g forces are easier for humans to tolerate in these positions. Supporting the body in as many places as possible also helps to increase tolerance.

  • There is an ionisation blackout for the space shuttle of about 16 minutes where no communication is possible. This is because as heat builds up, air becomes ionised forming a layer around the spacecraft. Radio signals cannot penetrate this layer of ionised particles.

 

Gravitational Slingshot Effect

In orbital mechanics and aerospace engineering, a gravitational slingshot or 'gravity assist' is the use of the gravity of a planet to alter the path and speed of an interplanetary spacecraft. The slingshot effect is used to accelerate a spacecraft in a planetary flyby. NASA calls this a gravity assist, and exploits it to save fuel in missions to outer planets such as Jupiter and Saturn. The planets continue in their orbits unaffected, so at first sight this seems like something for nothing, a cosmic perpetual-motion trick. But the physics is straightforward, resting only on conservation of momentum and of energy and the huge mass ratio between planet and spacecraft.

The spacecraft's velocity relative to the Sun
is increased by a gravity assist manouvere.

A gravity assist or slingshot manoeuvre around a planet changes a spacecraft's velocity relative to the Sun, even though it preserves the spacecraft's speed relative to the planet - as it must according to the law of conservation of energy. From a large distance, the spacecraft appears to have bounced off the planet. AS an analogy, conisder moving a fast moving magnet past a stationary iron ball without touching it. The ball will accelerate due to the interaction with the moving magnetic field of the magnet.

The slingshot effect can be explained using the law of conservation of momentum and the law of conservation of energy. When a spacecraft approaches the planet, it gains some momentum from the interaction with the planet's gravitational field. The momentum gained by the spacecraft causes a change in its velocity (usually an increase). The planet loses the same amount of momentum but since it mass is so large and p = mv, the change in velocity will be insignificant. The space probe on the other hand has increased its velocity significantly because its mass is only small. The same reasoning can be applied to conservation of energy. The gain in kinetic energy of the spacecraft (KE=1/2mv2) is the same as the loss by the planet with the same mass comparisons.