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Parametric DesignPrinciples of Space Systems Design

Parametric Design

• The Design Process• Example: Project Diana

Akin’s Laws of Spacecraft Design - #3

Design is an iterative process. Thenecessary number of iterations is onemore than the number you havecurrently done. This is true at anypoint in time.

Overview of the Design Process

System-level Design(based on discipline-

oriented analysis)

Vehicle-level Estimation(based on a few

parameters from prior art)

System-level Estimation(system parameters based

on prior experience)

Program Objectives ✑System Requirements

Increasing complexity

Increasing accuracy

Decreasing abilityto comprehend the “bigpicture”

Basic Axiom:

Relative rankings betweencompeting systems willremain consistent fromlevel to level

Regression Analysis of Existing Vehicles

Veh/Stage prop mass gross mass Type Propel lants Isp vac isp sl sigma eps delta( l b s ) ( l b s ) ( s e c ) ( s e c )

Delta 6925 Stage 2 13 ,367 15 ,394 Storab N2O4-A50 319.4 0.152 0.132 0.070Delta 7925 Stage 2 13 ,367 15 ,394 Storab N2O4-A50 319.4 0.152 0.132 0.065Titan II Stage 2 59 ,000 65 ,000 Storab N2O4-A50 316.0 0.102 0.092 0.087Titan III Stage 2 77 ,200 83 ,600 Storab N2O4-A50 316.0 0.083 0.077 0.055Titan IV Stage 2 77 ,200 87 ,000 Storab N2O4-A50 316.0 0.127 0.113 0.078Proton Stage 3 110 ,000 123 ,000 Storab N2O4-A50 315.0 0.118 0.106 0.078Titan II Stage 1 260 ,000 269 ,000 Storab N2O4-A50 296.0 0.035 0.033 0.027Titan III Stage 1 294 ,000 310 ,000 Storab N2O4-A50 302.0 0.054 0.052 0.038Titan IV Stage 1 340 ,000 359 ,000 Storab N2O4-A50 302.0 0.056 0.053 0.039Proton Stage 2 330 ,000 365 ,000 Storab N2O4-A50 316.0 0.106 0.096 0.066Proton Stage 1 904 ,000 1 ,004 ,000 Storab N2O4-A50 316.0 285.0 0.111 0.100 0.065

average 3 1 2 . 2 2 8 5 . 0 0 . 1 0 0 0 . 0 8 9 0 . 0 6 1standard deviation 8 . 1 0 . 0 3 9 0 . 0 3 3 0 . 0 1 9

Regression Analysis

• Given a set of N data points (xi,yi)• Linear curve fit: y=Ax+B

– find A and B to minimize sum squared error

– Analytical solutions exist, or use Solver in Excel

• Power law fit: y=AxB

• Polynomial, exponential, many other fits possible

error Ax B yi ii

N= + −( )∑

error A x B yi ii

N= + −[ ]∑

=log( ) log( )

Regression Analysis of Inert Mass Fraction

Hypergolic stages

1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07

Hypergolic stages

Stage Gross Mass (lbs)

Inert MassFraction

Regression Values for Design Parameters

Isp (vac) delta Max DV( s e c ) ( m / s e c

LOX/LH2 4 3 3 0.078 1 0 8 2 5L O X / R P - 1 3 2 0 0.063 8 6 7 0Storables 3 1 2 0.061 8 5 5 2Solids 2 8 3 0.087 6 7 7 2

Project Diana - Mission Statement

Design a system to return humans tothe moon within the shortest feasibletime span for the minimum achievablecost.

Project Diana - Requirements Document

• System must be based on the use ofAmerican launch vehicles in operationalstatus as of 2005

• System shall be at least as capable forlunar exploration as the J-mission Apollosystem– Two landed crew– 72 hour stay time, 3 x 6 hour EVAs– 300 kg of science payload (each way)

American Heavy-Lift Vehicles (2005)

• Space Shuttle -27K kg to LEO

• Delta IV Heavy -23K kg to LEO

∆∆∆∆V Requirements for Lunar MissionsTo:

Low EarthOrbit

LunarTransferOrbit

Low LunarOrbit

LunarDescentOrbit

LunarLanding

Low EarthOrbit

3.107km/sec

LunarTransferOrbit

3.107km/sec

0.837km/sec

3.140km/sec

Low LunarOrbit

0.837km/sec

0.022km/sec

LunarDescentOrbit

0.022km/sec

2.684km/sec

LunarLanding

2.890km/sec

2.312km/sec

Mission Scenario 1

• What can be accomplished with a single shuttlepayload (27K kg)?

• Assume δ=0.1, Isp=320 sec• Direct landing

– LEO-lunar transfer orbit ∆V=3.107 km/sec– Lunar transfer orbit-lunar landing ∆V=3.140 km/sec– Lunar surface-earth return orbit ∆V=2.890 km/sec– Direct atmospheric entry to landing

Scenario 1 Analysis• Trans-lunar injection

• Lunar landing– r=0.3674– mLS=1958 kg

• Earth return– r=0.3978– mER=583 kg

r eTLI

sp= =−

0 3713.

m m r kgTLI o TLI= −( ) =δ 7325

This scenario would work for amoderate robotic sample returnmission, but is inadequate for ahuman program.

Mission Scenario 2

• Assume a single shuttle payload is used to sizethe lunar descent and ascent elements

• Assume δ=0.1, Isp=320 sec• Direct landing

– LEO-lunar transfer orbit ∆V=3.107 km/sec– Lunar transfer orbit-lunar landing ∆V=3.140 km/sec– Lunar surface-earth return orbit ∆V=2.890 km/sec– Direct atmospheric entry to landing

Scenario 2 Analysis• Lunar landing

– r=0.3674– mLS=7219 kg

• Earth return– r=0.3978– mER=2150 kg

• Trans-lunar injection– r=0.3713

Payload mass still too low forhuman spacecraft. TLI stagemass of 72,520 kg is too largefor any existing launch vehicle.(Ideal situation is to ensure 100%load factors on all launches.)

rkgLEO

=−( )

99 520,

Mission Scenario 3

• Assume three Delta-IV Heavy missions carryidentical boost stages which perform TLI andpart of descent burn

• Space shuttle payload completes descent andperforms ascent and earth return

• All other factors as in previous scenarios

Scenario 3 Standard Boost Stage

• mo=23,000 kg• mi =2300 kg• mp =20,700 kg• LEO departure configuration is three boost

stages with 27,000 kg descent/ascentstage as payload

• mLEO =96,000 kg

Scenario 3 TLI Performance• Boost stage 1

– VTLI remaining=2345 m/sec• Boost stage 2

– r=0.7; ∆V2=1046 m/sec– VTLI remaining=1300 m/sec

• Boost stage 3– r=0.55; ∆V3=1300 m/sec– Residual ∆V after TLI=376 m/sec

∆V gIm m

spLEO prop

LEO1 762= −

=ln sec

Alternate Staging Possibilities

• Three identical stages• Serial staging (previous chart) ∆V=3483 m/sec• Parallel staging (all three) ∆V=3264 m/sec• Parallel/serial staging (2/1) ∆V=3446 m/sec• Pure serial staging is preferred

Scenario 3 Ascent/Descent Performance

• 376 m/sec of lunar descent maneuver performedby boost stage 3

• Remaining descent requires 2764 m/sec– r=0.4143– mi=2700 kg– mLS=8485 kg

• Earth return– r=0.3978– mi=849 kg– mER=2528 kg

Return vehicle mass is stillsignificantly below that of theGemini spacecraft - need toexamine other numbers of boostvehicles

Effect of Number of Boost Stages

Number of Boost Modules

Payload 583 1068 1809 2528 32290 1 2 3 4

Baseline System Schematic - Project Diana

Boost Stage 123,000 kg

Descent/Landing Stage

16,160 kg

Ascent Stage7611 kg

Crew Cabin3299 kg

Alternate Lunar Transport Architectures

• Transportation node at intermediate point (low lunarorbit, Earth-Moon L1)

• Leave systems at node if not needed on the lunarsurface, e.g.:– TransEarth injection stage– Orbital life support module– Entry, descent, and landing systems

• Will increase payload capacities at the expense ofadditional operational complexity, potential for safetycritical failures

Mass Breakdown of Payload Systems• 27,000 kg assembly delivered to LEO by space shuttle• mi,orbit = orbital maneuvering module inert mass• mp,node = propellants for arrival at transport node• mp,TEI = trans Earth injection propellants• mi,asc = inert mass of lunar ascent vehicle• mp,asc = propellant mass of lunar ascent vehicle• mi,des = inert mass of lunar descent vehicle• mp,des = propellant mass of lunar descent vehicle• mL,node = payload transported to node and back• mL,LS = payload transported to/from lunar surface only• mL,thru = payload transported to/from lunar surface and

returned to Earth (assumed to be ≥500 kg)

Variation 1: Lunar Orbit Staging• Assume same process as baseline, but use lunar

parking orbit before/after landing• Additional DV’s required for LLO stops

– Lunar landing additional ∆V=+31 m/sec– Lunar take-off additional ∆V=+53 m/sec

• Low lunar orbit waypoint changes baseline payloadto 3118 kg (-3.5%)

• Not useful without taking advantage of node tolimit lunar landing mass

Variation 2: Lunar Orbit Rendezvous• Use specialized vehicle for descent/ascent• Use four boost stages as per baseline• Boost stage 4 residual propellants

– 10,680 kg following trans lunar insertion– 1315 kg following lunar orbit insertion– Use remaining stage 4 capacity to aid descent stage

• Leave TEI stage in lunar orbit during ascent/descent– Descent ∆V=2334 m/sec– Ascent ∆V=2084 m/sec– TEI ∆V=837 m/sec

Baseline System Schematic - Project Diana

16,160 kg

Ascent Stage7611 kg

Crew Cabin3299 kg

LOR System Schematic - Project Diana

15,010 kg

TEI Stage

Ascent Stage5811 kg

Crew Cabin4114 kg

2066 kg

The Next Steps From Here

• Perform parametric sensitivity analyses– Inert mass fractions– Specific impulse– Size of entry package left in orbit

• Investigate reduction from 4 to 3 boost stagesfor minimal system

• Examine growth options allowed by system– One-way cargo variants– Larger module with more boost modules

Recovered File 1 -...

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