PH508: Course reviewDr. Mark Price – Spring 2011

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.

Learning outcomes

Introduction: Space mission architecture

Basic elementsof a space mission

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

Review

Crude overview: [Read: chapter 2, F&S]

1. Ground phase (vehicle construction)

2. Pre-launch phase (payload and rocket integration)

3. Launch phase

4. Space operations phase

5. Other (planetary, asteroid belt, cometary environments, de-orbital/end of life phase)

Spacecraft environment

Can be sub-divided further into:

Manufacture stage Assembly stage Test and checkout stage Handling stage Transportation stage Storage (prior to rocket/payload integration)

Ground phase

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.

Summary of NEO lectures (lectures #1 - #4)

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.

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.

NEO lectures: What you should now know at this point!

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.

Review

The drag force, F, is defined as:

CD is 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.

Space operations phase: drag force

2

21 vACF D

The NEO environment: debris distribution graph

[F&S, Fig. 2.21, Pg. 35 Probably out of date!]

The NEO environment: spacecraft damage from debris

Impact damage on Endeavour (STS-118)and Challenger window (STS-7)

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’.

The space environment: calculation of the solar constant

[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.

The space environment

Derivation of escape velocity: I

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

A: Think about the energies involved!

Initial state:

Kinetic energy = 0 (planet) +

Gravitational potential energy =

Derivation of escape velocity: II

2

21 mv

rGMm

Final state:

Kinetic energy = 0 (planet) + 0 (spacecraft)

Gravitational potential energy =

Initial state energy must equal final state energy

Derivation of escape velocity: III

0

GMm

Therefore:

Derivation of escape velocity: IV00

21 2

rGMmmv

rGMv

rGMv

rGMv

rGMmmv

2

22121

2

2

2

LEARN THIS DERIVATIONAND THE FINAL EQUATION!

Propulsion systems: I

4 major tasks:

1. Launch

2. Station/trajectory acquisition

3. Station/trajectory keeping (staying where it should be, or going in the correct direction).

4. Attitude control (pointing in the correct direction)

Propulsion systems: II

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).

Propulsion systems: III

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.

Propulsion systems: IV

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.

Propulsion systems: VI

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...”

Propulsion systems: VII

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

So, now some maths...

Rocket equation: II

mmVVV

mmVVVmmVVV

mVV

mdmVdV

oeo

oeo

oeo

mme

VV

V

V

m

me

oo

o o

ln

lnln]ln[ln

ln

Tsiolkovsky’s Equation (the rocket equation).

•dm is the mass ejected

•dV is the increase in speed dueto the ejected mass (dm)

•Ve is the exhaust velocity (ie. thevelocity 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.

Recall (in zero g):

Now add gravity: (diagram)

Rocket equation: III (with gravity)

dtdmV

dtdVm e

Bfo

o

s tmm

me

V

e

e

e

gdtdmm

VdV

gdtdmm

VdV

gdtdm

mV

dtdV

mgdtdmV

dtdVm

00

1

1

1

Bfo

oes

Bfooes

Bmm

mes

tmm

me

V

gtmm

mVV

gtmmmVV

gtmVV

gdtdmm

VdV

fo

o

Bfo

o

s

ln

lnln

ln

1

00

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

Define R as:

Rocket equation: V (with gravity)

fo

o

mmmR

e

Bs

es

e

Bses

e

Bsees

Bses

VtgRR

RVV

VtgRVV

VtgVRVV

tgRVV

exp

ln

expln

ln

ln

R’ is the “effective mass ratio” (with gravity)

•Vs =spacecraft velocity•Ve= exhaust velocity•gs = accl. of gravity acting on spacecraft•tB = rocket burn time•mf= mass of fuel

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:

Multi-stage rockets

RSSRP

mm

mmm

S

mmP

mmm

mmmR

s

f

s

sf

p

o

fo

o

sp

o

1

1

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 mEquatorial velocity = 4.007 x 107 / 86400 =

463.83 ms-1

Geographical velocity boost: I

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.

Geographical velocity boost: II

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.

Propulsion systems: overview

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:

Multi-stage rockets

RSSRP

mm

mmm

S

mmP

mmm

mmmR

s

f

s

sf

p

o

fo

o

sp

o

1

1

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:

Multi-stage rockets

1

oi

oii m

mP

(ie. The payload ratio of stage 1 = mass of stage 1/ mass of stage 2)

Thus the total payload ratio, P is:

The structural payload, S is:

And the mass ratio, R is:

Multi-stage rockets

np

o PPPPmmP 321

1

si

sifii m

mmS

fioi

oii mm

mR

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…)

Multi-stage rockets ieis RVVV lnmax

n

e

ne

ie

RRRRRRVV

RRRVV

RVV

321

max

21max

max

lnlnlnln

ln

Function: the Spacecraft’s ‘skeleton’.

Principal design driver: minimise mass without compromising reliability.

Design aspects: ◦ Materials selection◦ Configuration design◦ Analysis◦ Verification testing (iterative process).

Spacecraft structures: I

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!

Spacecraft structures: II

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!

Spacecraft structures: III

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!

Spacecraft structures: IV

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).

Spacecraft structures: V

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.

Spacecraft structures: VI

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).

Spacecraft structures: VII

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.

Spacecraft thermal balance and control: I

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).

Spacecraft thermal balance and control: II

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

Spacecraft thermal balance and control: III

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.).

Spacecraft thermal balance and control:VI

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

Spacecraft thermal balance and control:VII

Balance equation for Spacecraft equilibrium temperature is thus constructed:

Heat radiated from space = Direct solar input + reflected solar input +Heat radiated from Earth (or nearby body)

+Internal heat generation

We will start to quantify these in a minute...

Spacecraft thermal balance and control:X

Spacecraft thermal balance and control:XI

Heat radiated into space, J, from our Spacecraft. Assume:◦ Spacecraft is at a temperature, T, and radiates like a

blackbody (σT4 W m-2 , σ = Stefan’s constant = 5.670 x 10-8 J s-1 m-2 K-4)

◦ It radiates from it’s entire surface area, ASC – we will ignore the small effect of reabsorption of radiation as our Spacecraft is probably not a regular solid.

◦ Has an emissivity of ε.

Therefore:J = ASCεσ T4

Spacecraft thermal balance and control:XII

Now we start to quantify the other components.

Direct solar input, need:◦ JS, the solar radiation intensity (ie., the solar constant

at 1 AU for our Earth orbiting spacecraft).◦ A’S the cross-section area of our spacecraft as seen

from the Sun (A’S ≠ ASC!)◦ The absorbtivity, α, of our spacecraft for solar radiation

(how efficient our spacecraft is at absorbing this energy)

◦ Direct solar input = A’S α JS

Spacecraft thermal balance and control:XIII

Reflected solar input. Need:◦ JS – the solar constant at our nearby body.◦ A’P the cross-sectional area of the spacecraft seen

from the planet◦ Absorbtivity, α, for spacecraft of solar radiation◦ The albedo of the planet, and what fraction, a, of

that albedo is being seen by the spacecraft (function of altitude, orbital position etc.)

◦ Define: Ja = albedo of planet x JS x a◦ Reflected solar input = A’p α Ja

Spacecraft thermal balance and control:XIV

Heat radiated from Earth (nearby body) onto spacecraft. Need:◦ Jp = planet’s own radiation intensity◦ F12, a viewing factor between the two bodies. Planet is not a point

source at this distance.◦ A’P cross-sectional area of spacecraft seen from the planet.◦ Emissivity, ε, of spacecraft

◦ Heat radiated from Earth onto spacecraft= A’P ε F12 JP

◦ Q: Why ε and not α? α is wavelength (i.e., temperature) dependent. Planet is cooler than Sun and at low temperature α = ε)

Spacecraft internally generated heat = Q

Spacecraft thermal balance and control:XV

So, putting it all together...

Divide by ASCε (and tidy) to get:

Therefore α/ε term is clearly important.

Spacecraft thermal balance and control:XVI

QJFAJAJATA PpapSSSC 124

SCP

SC

Pa

SC

PS

SC

S

AQJF

AAJ

AAJ

AAT

12

4

Of the other terms, JS, Ja, JP and Q are critical in determining spacecraft temperature.

Q: How can we control T? (for a given spacecraft).◦ In a fixed orbit JS, Ja, JP are all fixed.◦ Could control Q◦ Could control α/ε (simply paint it!)

So select α/ε when making spacecraft. Table on next slide gives some values of α/ε.

Spacecraft thermal balance and control:XVII

Spacecraft thermal balance and control:XVIII

Spacecraft thermal balance and control:XX

These use solar radiant energy and convert it directly into electricity, via the photovoltaic effect.

An array is made up of thousands of individual cells (2 cm x 4 cm typically), connected in series to provide DC power (28 V typical, 120 V can be found today).

Power levels can be in range of a few Watts to 100’s of kW.

An individual cell is just a semiconductor p-n junction.

Solar cells

Solar Cells

Silicon was typical, today (Gallium Arsenide) GaAs has been used but is not universal.

 Silicon is doped with boron to produce p-type (electron deficient) material and phosphorous for n-type (electron excess) material.

In dark conditions an equilibrium is reached where no significant current flows. If illuminated, by photons of sufficient energy, electron-hole pairs are created, these flow creating a potential difference across the device.

Solar cells

Solar cells

To cause the hole-electron production the photon energy has to exceed the band-gap energy. If photons have excess energy this can be deposited as heat.

We can define hf Eg where h is Planck’s constant, f is the frequency of the radiation and Eg is the band gap in Joules.

You can characterise a solar cell by its I-V curve. The best operating point is the maximum power point, given by Vmp and Imp

Solar cells

You can also define:◦ Open circuit voltage (i.e. no current drawn) Voc

◦ Short circuit current Isc◦ A fill factor (FF) which says how “square” the I-V

curve is. The “squarer” the better. FF is defined as:

FF = (Vmp Imp)/(Voc Isc)

The closer to 1 this is the “squarer” it is.

Solar cells

For a silicon cell Voc is typically 0.5 to 0.6 V, Isc depends on the illumination level, and FF can be 0.7 to 0.85.

To find the peak power, you draw output power vs. output voltage. A clear peak can be found, which defines Vmp and hence Imp can be determined.

If you heat a solar cell you will find its performance changes. Its efficiency falls as its temperature increases.

Solar cells

There is a packing factor for a solar panel, which describes how much of its surface area is really solar cells, 0.9 is good. The rest is structure, edges, gaps etc. So the effective area is less than the actual surface area of a solar panel.

Solar panels need to be face on to the Sun for maximum efficiency. If they are tilted then a geometric correction has to be applied to give the cross-section projected orthogonal to the solar direction. If the angle between the normal to the surface of the panel and the solar direction is θ, then there is a factor cos θ that has to be applied when finding the effective surface area illuminated and hence the power output.

Solar cells

Solar cells in orbit do suffer degradation with time. Due to:◦Accumulation of micrometeorite impact damage,◦Attack by atomic oxygen on the wiring◦Radiation damage to the semi-conductor.

There is thus a factor for loss of efficiency with time – power output falls slowly with time.

Estimating this loss rate, and over-sizing the solar array at the Beginning of Life (BOL) so it over-produces power but produces the correct power at the End of Life (EOL).

Solar panels at the BOL in Earth orbit can produce 30 – 50 Watts per kg of mass.

Current state-of-the-art Multi-Junction (MJ) solar cells have efficiencies approaching 50%.

Solar cells

RTGs: II

A practical device is shown in F&S page 340

Isotope Fuel form Decay product Power density (W/g)

τ½ (years)

Polonium 210 Gd Po α 82 0.38

Plutonium 238 Pu O2 α 0.41 86.4

Curium 242 Cm2 O3 α 98 0.4

Strontium 90 SrO β 0.24 28.0

RTGs: III

Various radioactive materials for possible use in a RTG.

RTGsPellet of glowing 238PuO2 – generating 62 watts of heat

RTGs: IV

Cassini RTG – source, NASA

When considering a design, care has to be made to ensure that in the event of an accident during launch, the radioactive material does not escape into the environment. Clean-up costs would be expensive in terms of money, and public support!

The power generated by a RTG is not constant with time, the material decays so there is less as time goes on and hence less power can be generated.

RTGs: V

RTGsMuch better…..New Horizons’ RTG (mission to Pluto)[Cassini flight spare, using 11 kg of Plutonium pellets]

When considering a design, care has to be made to ensure that in the event of an accident during launch, the radioactive material does not escape into the environment. Clean-up costs would be expensive in terms of money, and public support!

The power generated by a RTG is not constant with time, the material decays so there is less as time goes on and hence less power can be generated.

RTGs: V

You need: 

Where Pt is power at time t, and P0 is the initial power at t = 0.

τ½ (years) is given in the table above.

RTGs: VI

tPP ot

2/1

693.0exp

You need: 

Where Pt is power at time t, and P0 is the initial power at t = 0.

τ½ (years) is given in the table above.

RTGs: VI

tPP ot

2/1

693.0exp

So you have to calculate what power you need for the mission and start the mission (Beginning Of Life - BOL) with too much power. Then as the source decays, the RTG’s output falls and you plan it so you have just the right amount of power at the end of the mission lifetime (End Of Life – EOL)

RTGs: VII

So you have to calculate what power you need for the mission and start the mission (Beginning Of Life - BOL) with too much power. Then as the source decays, the RTG’s output falls and you plan it so you have just the right amount of power at the end of the mission lifetime (End Of Life – EOL)

RTGs: VII

Derivation of the rocket equation WITH and WITHOUT gravity.

How to break the equation up into P, S and R and apply that to multi-staging.

Understand and use the drag force equation Calculate the solar constant and understand

that the radiation intensity falls off as 1/r2. Be able to describe in broad terms the

different phases of a mission, from concept phase through to end-of-life phase.

PH508: Core material you should know

Why thermal control is vital to spacecraft operations

How to calculate the equilibrium temperature of spacecraft given it’s emittance, absorptance, distance from the Sun and it’s orbital parameters.

Using energy balance arguments derive a mathematical expression for the temperature of a spacecraft.

PH508: Core material you should know

What the main drivers and constraints are in designing and implementing a space mission.

Be able to describe the three main power sources used by spacecraft and how each works.

What the approximate power output is (as a function of weight) for each of the power sources

The advantages and disadvantages of each power source.

PH508: Core material you should know

How a Spacecraft’s eventual operational environments (NEO, deep space etc.) determines the materials from which it is constructed.

What materials are generally used in spacecraft construction

Know the meaning of:◦ Apogee◦ Perigee◦ Albedo◦ Absorptance◦ Emittance

PH508: Core material you should know