1. Introduction

The space shuttle system pictured right, consists of three main components:

1. One External Tank, loaded with liquid hydrogen (H₂) and liquid oxygen (O₂). This weighs 760 ton and lasts for the first 8.5 minutes of flight.
2. Two Solid Rocket Boosters (SRBs), filled with aluminium (Al) and ammonium perchlorate (NH₄ClO₄) VII each weighing 590 ton. Each SRB ejects 400 tons of exhaust gases, leaving the rocket at about 3600 metres per second, in 2 minutes.
3. One reusable winged orbiter (has three main engines which use fuel and oxygen from External tank) weighs 110 ton. The orbiter main engines (together) eject 720 tons of exhaust gases, leaving at about 3600 metres per second, in 8.5 minutes.

With this explosive mix of chemicals, it's not surprising that space travel is so dangerous.

2. Problems

Given the above, provide solutions to the following.

1. Why does the ejection of gas from the engines produce a forward force on the system? (“System” = orbiter + 2 SRBs + external tank)
2. Calculate the total momentum of the exhaust gases ejected in the first one second of firing, in kg m/s.
3. Calculate the mass of the complete loaded system.
4. Calculate the weight of the complete loaded system.
5. Given that force X time = change of momentum, and therefore force = change of momentum / time, calculate the force on the system produced by all the engines together.
6. What is the unbalanced force on the system, when the force due to the engines is directed upwards? (Note: force is a vector, so the direction must be specified).
7. Calculate the acceleration of the system at lift-off (Note: Acceleration is also a vector)
8. Calculate the acceleration of the system if the engines were fired with the system pointing horizontally.
9. To get into orbit, a horizontal speed of some 8000 m/s is required, so why is the system launched vertically?
10. At 120 seconds after lift-off, when the SRBs are exhausted, the shuttle is 44 km above sea-level. What figure does this give for the average vertical acceleration during the first 120 seconds?
11. Why is the average acceleration greater than the initial acceleration calculated in question 7?
12. Make an estimate of the vertical speed of the system after 120s, using the approximation that acceleration has been steady.
13. The exhausted SRBs, when released, are said to continue upwards for another 23km of height gain! What vertical speed does this indicate at the point of release?
14. How well does your answer to question 13 agree with that to question 12?
15. Justify an approximation you made (unconciously?) in question 13.
16. By a calculation, show whether or not the Shuttle could get off the ground without the assistance of SRBs.
17. 1450m³ of the liquid hydrogen fuel is pumped from the external tank to the oribiters main engines in 8.5 minutes, through a pipe 43cm in diameter. At what speed does the liquid hydrogen travel along this pipe?
18. How high could this pump squirt a liquid hydrogen fountain?
19. How many external-tank-loads of liquid hydrogen could be stored in a large room, e.g. room 44 (suitably modified) measures 3 X 7 X 13.5 metres?
20. What conditions would you suggest for the storage of liquid hydrogen?
21. The density of hydrogen gas under “normal” conditions is about 80 g / m³. The airship Hindenberg, which burned in 1936, was a lot bigger than the Shuttle System - the same height (50m) and 250m long. Its volume was 200,000m³. Which held more hydrogen, the Hindenberg, or the Shuttle External Tank?

3. Solutions

• Sample solutions are available by emailing anthonybrianhull at yahoo dot co dot uk.

4. Further work

DO try this at home!

• A cheaper, quicker and easier way to be a rocket scientist is to build your own water rocket. An empty lemonade bottle will do for your rocket. You can propel your spacecraft using a much less flammable and more abundant liquid called water and a mixture of gases called air, pressurised using a bicycle pump. It won't get your rocket into orbit, but its great fun. See The Leeds Water Rocket Page for further details.

5. References, acknowledgements and copyright

• Supplementary data provided by Space Shuttle System and Mission Profile, from the US National Aeronautics and Space Administration (NASA)
• This work is not copyrighted but please credit the original author if you are going to copy, modify or re-distribute it.
• Thanks to Simon Cornforth for providing the intital data