Sky-high science: building rockets at school

Space science is a fascinating field of study, whether at school or, in our case, at the one-week European Space Camp in Norway (see box). One hands-on aspect that can be easily introduced in the classroom is rocketry.

Paper rockets are small and relatively simple to construct, and can achieve flight distances of 50 metres or more, enabling students to compete in terms of either height or distance, depending on the space available. Students can also be creative, designing visually appealing rockets or using different types of material. Making a paper rocket is the perfect way to have fun and learn plenty of physics at the same time. Here, we describe a simple rocket that we built and launched during the 2011 European Space Camp.

Building paper rockets enables students to tie together many different concepts in physics – in particular, the equations of motion linking velocity, acceleration, distance and time, as well as the principles of aerodynamics. It also provides an exciting introduction to what it is like to be a scientist: designing a rocket from theoretical principles, carrying out an experiment by launching rockets, and finally analysing the results, drawing conclusions and identifying points for improvement for the future.

Building your rocket

Materials

• Two pieces of A4 paper
• Scissors
• Sticky tape
• Putty or Plasticine^®

Procedure

The aim when building the rocket is to minimise drag (air resistance). Drag is mostly dependent on the velocity, but also on the frontal surface area of the rocket and its overall shape – important considerations when designing a rocket.

Rocket body:

1. Roll one piece of paper into a cylinder to form the body of the rocket.
2. Seal one of the open ends of the cylinder with tape, making the front of the rocket. Check that the seal is airtight by blowing into it.

Nosecone:

1. From the other piece of paper, cut out a circle (diameter 7.5 cm), then cut a sector of approximately 90 degrees from the circle.
2. Twist the remaining piece into a cone and place a small ball of putty inside the tip of the cone before fastening the cone to the sealed end of the rocket body with tape.

Fins:

1. Cut four paper triangles of exactly the same size and fold one of the sides of each triangle to form a flap, which will be attached to the rocket.
   Students should think about the optimal shape of the fin – some fin profiles will cause the rocket to spin more, others less. Is spin desirable in a rocket?

Stability

The stability of a rocket depends on where the centre of gravity and the centre of pressure are in relation to each other. For a stable rocket, the centre of gravity should be in front of the centre of pressure at all times. Simply put, the centre of pressure is where the sum of all drag forces acts.

If the centre of pressure is in front of the centre of gravity, a turning moment will occur, causing the rocket to flip over in mid-flight. This is why ballast is usually applied to the nosecone.

If the relative distance between the centre of gravity and centre of pressure is too large, either because too much mass has been applied to the front of the rocket or because the fins are oversized, the rocket will be more sensitive to wind.

Launching the rocket

To launch the rocket, you will need a launcher, which for safety reasons should be built by the teacher. There are many types of launcher, but all are essentially a stable tube with the same three constituents.

1. A compression chamber in which the air is pressurised, using either a compressor or a bicycle pump with a built-in pressure gauge (Figure 1, A+B).
2. A launch tube on which the rocket is placed (Figure 1, D). An adjustable launch tube allows the angle of elevation of the rocket at take-off to be determined.
3. A mechanism (e.g. a lever or a battery-powered valve) to release the pressure from the compression chamber into the launch tube (Figure 1, C). The sudden release of pressurised air launches the rocket.

We would recommend building a robust launcher out of metal piping, with an adjustable launch tube. This allows reproducible launches, with different angles of elevation. At the European Space Camp, we used a launching system in which air was pumped into a copper pipe system using a low-cost air compressor, a robust and stable system that can be used over and over again. For downloadable instructions, see below^w1. A robust launcher can also be built out of PVC, using materials readily available from hardware shops, as described on the NASA website^w2.

When launching your rocket, note that higher air pressure does not necessary lead to better flight performances. This is because aerodynamic drag on the rocket increases with velocity: the rocket’s fins may be distorted, increasing drag and reducing performance.

Before deciding on the angle at which to launch their rocket, the students should think about how the angle of elevation affects the total distance travelled and the rocket’s apogee (its highest point above the ground).

Follow-up

After the launch, the students can analyse the rocket’s trajectory to calculate the maximum height (apogee) attained by the rocket and also its initial velocity. To perform the trajectory analysis, some measurements need to be taken before the launch (see Figure 2):

• Length of the rocket body (h, in m)
• Inner diameter of the launch tube (D_i , in m)
• Pressure within the launcher (P, in Pascal) before launch while the valve is closed; this can be read off the foot pump or the compressor, and converted from psi or bar into Pascal. (The pressure is assumed to be constant across the length of the tube.)
• Mass of the rocket (m_r , in kg)
• Angle of elevation (θ, in degrees; Figure 3).
   

1. The first step is to calculate the initial velocity (n₀) of the rocket. This is equal to the acceleration (a) of the rocket multiplied by the time (t₀) for which the force was acting on it:

2. The force acting on the rocket can be calculated using two equations. A_i is the cross-sectional area of the rocket body.

3. The acceleration of the rocket can be expressed by combining these two equations:

4. By time t₀ , the rocket has travelled a distance equal to the length of the rocket body (h), and this length can be expressed by:

5. To find an expression for t₀ , Equation 5 can be rearranged:

The rocket’s initial velocity (ν₀) can now be expressed in terms of known variables, by inserting the expressions for the time t₀ (Equation 6) and the acceleration a (Equation 4) into the equation for the initial velocity (Equation 1):

We assume that the rocket has a parabolic flight path, and this allows us to calculate the equation for the trajectory of the rocket.

1. By decomposing the initial velocity vector n₀ into the x and y directions, the distance travelled by the rocket in these directions will then be:

where g is the gravitational constant.

2. From the equation for the distance travelled in the x direction (Equation 8), an expression of the time t can be inserted into the equation for the distance travelled in the y direction (Equation 9), and this gives us the equation for the trajectory of the rocket:

3. The apogee of the rocket (H) can then be calculated by:

Each rocket will probably be able to be launched only once, as the nosecones are usually damaged on landing. However, if the rockets are still intact, the students can carry out repeat experiments and perhaps vary the launch angle.

On the basis of their results, the students could discuss the following questions:

1. How does the weight of the rocket affect the height and distance it travels?

2. Why does wind affect the performance of the paper rocket?
3. What would happen if you placed the fins near the nosecone?
4. Where should the launcher be pointed in relation to the wind direction?