PH508: Course review

1. PH508: Course review Dr. Mark Price – Spring 2011

2. Learning outcomes • An understanding of the way in which space missions are configured both from the point-of-view of the constituent subsystems, mission profile (i.e., the project aims) including the influence of the space environment. • Appreciate the constraints and trade-offs which led to one mission configuration over another. • Appreciate space activities from a commercial viewpoint and be familiar with basic management tools for planning work (e.g., Gant charts, Pert charts etc.) • Make (valid) approximations and solve problems using a mathematical approach.

3. Introduction: Space mission architecture Basic elements of a space mission

4. Review • Definition of different phases of a mission • Concept • Design • Integration • Testing • Launch • Operations • End-of-life • The different space environments • NEO • Deep space • Other bodies • The differing conditions (gravity, radiation, micrometeoroid, debris etc.) within each space environment • How all this influences a spacecraft’s design

5. Spacecraft environment Crude overview: [Read: chapter 2, F&S] • Ground phase (vehicle construction) • Pre-launch phase (payload and rocket integration) • Launch phase • Space operations phase • Other (planetary, asteroid belt, cometary environments, de-orbital/end of life phase)

6. Ground phase Can be sub-divided further into: • Manufacture stage • Assembly stage • Test and checkout stage • Handling stage • Transportation stage • Storage (prior to rocket/payload integration)

7. Summary of NEO lectures (lectures #1 - #4) • Summary – you should now have an understanding of the various environments that a spacecraft could encounter: • Gravity • Vacuum • Thermal • Radiation • Debris • Also an understanding of how these environments affect the Spacecraft and its subsystems • General case of deep space • Specific case of NEO and the differences between the two. • Other areas around Solar System bodies.

8. NEO lectures: What you should now know at this point! Conceptually • The various phases of a space mission from ‘concept’ through to ‘end-of-life’ phase. • An appreciation of some of the details of each of these phases and how financial, engineering and science constraints etc. affect mission design. • How a spacecraft’s environment changes from ground level, near earth orbit and deep space. • How these environments (radiation, thermal, dust etc.) feedback into the final mission design.

9. NEO lectures: What you should now know at this point! Mathematically • Understand how to use the drag equation to work out the force on a body as it travels through the atmosphere • Calculate the solar constant for Earth and (other bodies) making justifiable assumptions. • Derive the escape velocity of a body.

10. Review • Things to ‘take home’ • The design and implementation of a space mission is a complicated and expensive task. • Each separate phase has to implement the highest possible level of quality control. It has to work, and it has to work first time! • Many different things to consider when designing a mission: power requirements, weight, thermal control, mechanical robustness, system redundancy, etc.

11. Space operations phase: drag force • The drag force, F, is defined as: • CDis the drag coefficient - a function of atmospheric density, ρ. Typical values are between 0.5 – 2. A function of altitude • A is the cross-sectional area of the spacecraft in line of flight • v is the velocity.

12. The NEO environment: debris distribution graph [F&S, Fig. 2.21, Pg. 35 Probably out of date!]

13. The NEO environment: spacecraft damage from debris Impact damage on Endeavour (STS-118) and Challenger window (STS-7)

14. The space environment: calculation of the solar constant • The Sun’s radiation density at the Earth. • Assume Earth – Sun distance = 149.6 million km = 1.49 x 1011 metres. • Surface area of sphere at that distance (4πr2) = 2.81 x 1023 m2. • Solar output = 3.85 x 1026 Watts • Radiation density at earth’s surface = 3.85 x 1026/ 2.81 x 1023 = 1369 Watts m-2 (ignoring attenuation from atmosphere etc.) – generally referred to as the ‘solar constant’.

15. The space environment [Will crop up again in PH608, and probably PH711] • Can be broadly categorised into: • Near Earth Environment • Deep Space • Other ‘local’ environment (planetary orbits, asteroid belt, cometary etc.). • As ‘Near Earth’ is local space we’ll start with the general case: deep space.

16. Derivation of escape velocity: I Q; What velocity, v, do I need to just escape the gravitational pull of the planet? (the escape velocity).

17. Derivation of escape velocity: II A: Think about the energies involved! Initial state: Kinetic energy = 0 (planet) + Gravitational potential energy =

18. Derivation of escape velocity: III Final state: Kinetic energy = 0 (planet) + 0 (spacecraft) Gravitational potential energy = Initial state energy must equal final state energy

19. Derivation of escape velocity: IV • Therefore: LEARN THIS DERIVATION AND THE FINAL EQUATION!

20. Propulsion systems: I

21. Propulsion systems: II • 4 major tasks: • Launch • Station/trajectory acquisition • Station/trajectory keeping (staying where it should be, or going in the correct direction). • Attitude control (pointing in the correct direction)

22. Propulsion systems: III Launch • Need lift-off acceleration, a, to be greater than gravitational acceleration, g. (“a>g”) for an extended period. • This implies a very high thrust for a long duration. E.g., the shuttle main engine: 2 x 106 N for 8 minutes. • Typical Δv ≥ 9.5 km s-1 (including drag and gravity losses).

23. Propulsion systems: IV Launch phase (continued) • Still difficult to achieve with current technology • Only achievable with chemical rockets • Massive launch vehicles required for relatively small payloads • Major constraint for spacecraft and mission design is the mass cost: £1000s - £10,000s per kilogram.

24. Propulsion systems: VI Earth Escape • Δv ~ 7.6 km s-1 (Mars flyby) • Δv ~ 16 km s-1 (Solar system escape velocity) • Without using gravity assist manoeuvres. Station/trajectory keeping • Low thrust levels required (mN – 10s N) pulsed for short durations. • Δv ~ 10s – 100s m s-1 over duration of mission.

25. Propulsion systems: VII Attitude control (‘pointing’) • Very low thrust levels for short duration • Small chemical rockets • Reaction wheels (diagram). Principle of operation of all propulsion systems is Newton’s third law “...for every action, there is an equal and opposite reaction...”

26. Rocket equation: I Derivation: Need to balance exhaust (subscript ‘e’) momentum with rocket momentum. ∑momenta = 0 (Conservation of linear momentum) (Recall: momentum = mass x velocity) ∴ m dV = -dm Ve dV = -Ve dm/m

27. Rocket equation: II So, now some maths... • dm is the mass ejected • dV is the increase in speed due • to the ejected mass (dm) • Ve is the exhaust velocity (ie. the • velocity of the ejected mass • relative to the rocket) • m is the rocket mass (subscript • ‘o’ denotes initial values) • In practice, drag reduces Vmax by • ~0.3 – 0.5 km s-1. Tsiolkovsky’s Equation (the rocket equation).

28. Rocket equation: III (with gravity) • Recall (in zero g): • Now add gravity: (diagram)

29. Rocket equation: IV (with gravity) Integrating previous equation:

30. Rocket equation: V (with gravity) • Define R as: • Vs =spacecraft velocity • Ve= exhaust velocity • gs = accl. of gravity acting • on spacecraft • tB = rocket burn time • mf= mass of fuel R’ is the “effective mass ratio” (with gravity)

31. Multi-stage rockets Assume a simple rocket where: • mf = mass of propellant • ms = mass of structure • mp = mass of payload • mo = mf + ms + mp • Define mass ratio, R: • Payload ratio, P: • Structure ratio, S:

32. Geographical velocity boost: I Because the Earth revolves on its axis from West to East once every 24 hours (86400 secs) a point on the Earth’s equator has a velocity of 463.83 ms-1. Reason: radius of the Earth, RE = 6.3782 x 106 metres. Earth’s circumference = 2πRE = 4.007 x 107 m Equatorial velocity = 4.007 x 107 / 86400 = 463.83 ms-1

33. Geographical velocity boost: II • Therefore, a spacecraft launched eastwards from the Earth’s equator would gain a free increment of velocity of 463.83 ms-1. • Away from the equator the Earth has a smaller circumference which is determined by multiplying the equatorial circumference by the cosine of the latitude in degrees. • For example, the Russian Baikonur Cosmodrome is at 45° 55’ north. The Earth’s rotational velocity at that point is: 322.69 m s-1.

34. Propulsion systems: overview • System classification: • Various possible schemes (see F&S, Fig. 6.1) • Other ‘exotic’ systems possible (“Project Orion”) • Function: • “Primary propulsion” – launch • “Secondary propulsion” • Station/trajectory acquisition and keeping • Attitude control • Recall: vastly different requirements for different purposes: • ΔV of m s-1 – km s-1 • Thrust of mN – MN • Accelerations of μg - >10g • Different technologies applicable to different functions/regimes.

35. Multi-stage rockets Assume a simple rocket where: • mf = mass of propellant • ms = mass of structure • mp = mass of payload • mo = mf + ms + mp • Define mass ratio, R: • Payload ratio, P: • Structure ratio, S:

36. Multi-stage rockets In general: • Vmax = ∑Vs Maximum rocket velocity is the total of the stage velocities. Using conventional definitions (i.e. 1st stage is the first to burn etc.), the payload ratio of the ith stage is, Pi: (ie. The payload ratio of stage 1 = mass of stage 1/ mass of stage 2)

37. Multi-stage rockets Thus the total payload ratio, P is: The structural payload, S is: And the mass ratio, R is:

38. Multi-stage rockets • Therefore, • And if all stages have the same Ve • (Generally, however, this is not the case as Ve isn’t necessarily the same for each stage – Saturn V homework example…)

39. Spacecraft structures: I • Function: the Spacecraft’s ‘skeleton’. • Principal design driver: minimise mass without compromising reliability. • Design aspects: • Materials selection • Configuration design • Analysis • Verification testing (iterative process).

40. Spacecraft structures: II Generalised requirements • Must accommodate payload and spacecraft systems • Mounting requirements etc. • Strength • Must support itself and its payload through all phases of the mission. • Stiffness (related to strength) • Oscillation/resonance frequency of structures (e.g. booms, robotic arms, solar panels). • Often more important than strength!

41. Spacecraft structures: III • Environmental protection • Radiation shielding (e.g., electromagnetic, particle) for both electronics and humans. • Incidental or dedicated • Spacecraft alignment • Pointing accuracy • Rigidity and temperature stability • Critical for missions like Kepler!

42. Spacecraft structures: IV • Thermal and electrical paths • Material conductivity (thermal and electrical) • Regulate heat retention/loss along conduction pathways (must not get too hot/cold). • Spacecraft charging and its grounding philosophy • Accessibility • Maintain freedom of access (docking etc.) For OPTIMUM design require careful materials selection!

43. Spacecraft structures: V Materials selection • Specific strength is defined as the yield strength divided by density. • Relates the strength of a material to its mass (lead has a very low specific strength, titanium a high specific strength). • Stiffness (deformation vs. load) • Stress corrosion resistance • Stress corrosion cracking (SCC).

44. Spacecraft structures: VI • Fracture and fatigue resistance • Materials contain microcracks (unavoidable) • Crack propagation can lead to total failure of a structure. • Extensive examination and non-destructive testing to determine that no cracks exists above a specified (and thus safe) length. • Use alternative load paths so that no one structure is a single point failure and load is spread across the structure.

45. Spacecraft structures: VII • Thermal parameters • Thermal and electrical conductivity • Thermal expansion/contraction (materials may experience extremes of temperature). • Sublimation, outgassing and erosion of materials (see previous lecture notes). • Ease of manufacture and modification • Material homogeneity (particularly composites - are their properties uniform throughout?). • Machineability (brittleness - ceramics difficult to work with) • Toxicity (beryllium metal).

46. Spacecraft thermal balance and control: I Introduction [See F&S, Chapter 11] • We will look at how a spacecraft gets heated • How it might dissipate/generate heat • The reasons why you want a temperature stable environment within the spacecraft. • Understanding the thermal balance is CRITICAL to stable operation of a spacecraft.

47. Spacecraft thermal balance and control: II Object in space (planets/satellites) have a temperature. Q: Why? • Sources of heat: • Sun • Nearby objects – both radiate and reflect heat onto our object of interest. • Internal heating – planetary core, radioactive decay, batteries, etc. • Heat loss via radiation only (heat can be conducted within the object, but can only escape via radiation).

48. Spacecraft thermal balance and control: III To calculate the heat input/output into our object (lets call it a Spacecraft) need to construct a ‘balance equilbrium equation’. First: what are the main sources of heat? For the inner solar system this will be the Sun, but the heat energy received by our Spacecraft depends on: • Distance from Sun • The cross-sectional area of the Spacecraft perpendicular to the Sun’s direction

49. Spacecraft thermal balance and control:VI • Heat output • Solar energy reflected from body • Other incident energy from other sources is reflected • Heat due to its own temperature is radiated (any body above 0K radiates) • Internal sources • Any internal power generation (power in electronics, heaters, motors etc.).

50. Spacecraft thermal balance and control:VII • Key ideas • Albedo – fraction of incident energy that is reflected • Absorptance– fraction of energy absorbed divided by incident energy • Emissivity (emittance) – a blackbody at temperature T radiates a predictable amount of heat. A real body emits less (no such thing as a perfect blackbody). Emissivity, ε, = real emission/blackbody emission