Capstone Design (Aircraft or CubeSat)
A full design project from requirements to review: pick an electric drone or a 3U CubeSat track, write requirements, select a concept, size it, close power, link, structural and thermal budgets, plan cost, schedule and risk, test, and present at a design review, with six spreadsheet labs. Free, self-paced, and tied to NASA’s CubeSat Launch Initiative, the PREFIRE CubeSats and NASA’s Sustainable Flight National Partnership.
Courses › AERO 490
About this course
This is a free self-study course outline written by Saving Planets. It is not a university course, it carries no academic credit, and no school is involved.
Its scope follows a one-semester senior aerospace capstone. It is modeled on the conceive-design-implement-operate approach of MIT 16.83X Space Systems Engineering (free on MIT OpenCourseWare) and on the NASA Systems Engineering Handbook, which we link where they help. Neither MIT nor NASA endorses this page.
What we add: two parallel tracks (a small electric drone or a 3U CubeSat), every unit tied to real work with a cited public source, every number on the page re-computed by a checking script before it goes live, and every lab in a free spreadsheet.
Work through it in order, alone or with a team. Each unit has goals, key ideas, equations, step-by-step examples, practice with full answers, common mistakes, flashcards and a quiz. Your progress is saved only in this browser.
How this course helps save the planet
Capstone teams build the satellites and aircraft that measure and protect the planet: student CubeSats fly through NASA’s CubeSat Launch Initiative, and small satellites like PREFIRE study how the Arctic sheds heat.
On the aircraft side, NASA’s Sustainable Flight National Partnership aims for 25–30% energy-efficiency gains. Each unit ends with a short, sourced section. Values that are not from a source are labeled as sample or textbook values.
Before you start
Prerequisites
- Avionics & Systems Engineering: requirements, reliability and verification.
- Spacecraft Design: power, thermal and link budgets.
- Aircraft Performance: lift, drag, range and climb.
- Aerospace Structures: stress, safety factors and margins.
How to study
- Keep one design notebook or spreadsheet that every number flows from.
- Trace every design choice to a requirement.
- Close budgets with margin before adding detail.
- Hold short weekly reviews, even when working alone.
- Write as you go: every unit adds a section to your final report.
- Do every practice problem on paper before opening the answer, and retake the quizzes a few days later.
Lab equipment (for the wet labs)
- Spreadsheet software (any free one works), or Python.
- The free NASA Systems Engineering Handbook in a web browser.
- Free slide software for your design reviews.
- A calculator.
Suggested 15-week schedule
About 6 to 9 hours a week: reading, practice problems and, in lab weeks, the lab.
| Week | Unit | Topics | Reading |
|---|---|---|---|
| 1 | Mission, Stakeholders and Requirements | Mission and requirements; Lab A | NASA SE Handbook |
| 2 | Concept Generation and Selection | Concept selection; Lab B | MIT 16.83X |
| 3 | Aircraft Track: Weight Sizing and Range | Aircraft weight sizing | NASA SFNP |
| 4 | Aircraft Track: Weight Sizing and Range | Range and sizing loop; Lab C | MIT 16.83X |
| 5 | Aircraft Track: Wing Loading and Power | Wing loading and power | NASA SFNP |
| 6 | CubeSat Track: Sizing and Orbit | CubeSat sizing and orbit; Lab D | NASA PREFIRE |
| 7 | CubeSat Track: Power and Link Budgets | Power and link budgets; Lab E; midterm practice | NASA SST SOA |
| 8 | Structural and Thermal Checks | Structural and thermal checks | MIT 16.83X |
| 9 | Cost, Schedule and Risk | WBS and schedule | NASA SE Handbook |
| 10 | Cost, Schedule and Risk | Earned value and risk; Lab F | NASA SE Handbook |
| 11 | Prototype, Test and Verification | Prototype planning | MIT 16.83X |
| 12 | Prototype, Test and Verification | Testing | NASA CSLI |
| 13 | Prototype, Test and Verification | Verification closure | NASA SE Handbook |
| 14 | Design Reviews and the Final Report | Critical design review | MIT 16.83X |
| 15 | Design Reviews and the Final Report | Final report; final practice | NASA SE Handbook |
Your progress
Tick units and labs as you finish them, and take the quizzes. Progress and quiz scores are saved only in this browser, never sent to us.
Turn on JavaScript to track progress.
Unit 1 · Week 1
Mission, Stakeholders and Requirements
Choosing a track, defining the mission, identifying stakeholders, writing verifiable requirements and setting allocations with margin.
Learning objectives
By the end of this unit you can:
- Write a one-sentence mission statement.
- List stakeholders and their needs.
- Write verifiable requirements.
- Compute margin against an allocation.
Key concepts
- Pick one track: a small electric drone that carries a sensor, or a 3U CubeSat that observes Earth.
- A mission statement says who needs what and why; requirements make it measurable.
- Stakeholders include users, funders, launch or airspace authorities, and the team itself.
- Each requirement has a number, a unit and a verification method (test, analysis, inspection or demonstration).
- Allocations carry margin early, because estimates grow as designs mature.
Key equations
Worked examples, step by step
Example 1.1 A 3U CubeSat has a 4.0 kg allocation (textbook value) and a 3.4 kg estimate. Margin?
Show the steps
- (4.0 − 3.4)/3.4.
Answer: 17.6%.
Example 1.2 A drone sensor estimate is 0.8 kg. Allocate with 25% margin (sample values).
Show the steps
- 0.8 × 1.25.
Answer: 1.0 kg.
Example 1.3 Write a verifiable requirement for drone endurance.
Show the steps
- Number, unit, method.
Answer: “The drone shall fly at least 30 minutes at 15 m/s, verified by flight test.”
Practice problems
Work each on paper first, then check.
Margin if the estimate grows to 3.8 kg?
Show answer
5.26%.
Three textbook 1.33 kg units?
Show answer
3.99 kg, about 4 kg.
Name four stakeholders for a student CubeSat.
Show answer
For example: science users, the university, the launch provider and the radio regulator.
Is “the CubeSat shall be reliable” verifiable?
Show answer
No; add a number and a method.
Common misconceptions
Myth: Requirements describe the design.
Actually: They state needs, not solutions.
Myth: Margin can be added later.
Actually: It is cheapest to hold early.
Myth: One stakeholder is enough.
Actually: Missed stakeholders cause late surprises.
Flashcards
Mission statement
Who needs what and why.
Stakeholder
Anyone with a need or say.
Requirement
Verifiable need.
Allocation
Budgeted share.
Margin
Reserve over estimate.
Track
Drone or CubeSat project path.
Self-check quiz
How this helps save the planet
NASA’s CubeSat Launch Initiative provides opportunities for CubeSats built by U.S. educational institutions and non-profit organizations, including museums and science centers, to fly on upcoming launches; NASA says it has launched over 150 CubeSats.
NASA says its Announcement of Partnership Opportunity is typically released each August with proposals due in November, so a capstone can be shaped like a real proposal.
On Saving Planets: Spacecraft Design · Avionics & Systems Engineering
Sources: NASA: CubeSat Launch Initiative
Free learning resources
- NASA Systems Engineering Handbook: Free NASA handbook.
- NASA: CubeSat Launch Initiative: NASA CSLI.
Unit 2 · Week 2
Concept Generation and Selection
Brainstorming, morphological charts, Pugh matrices, weighted decision matrices and sensitivity to weights.
Learning objectives
By the end of this unit you can:
- Generate several concepts.
- Build a morphological chart.
- Score concepts in a weighted matrix.
- Test sensitivity to weights.
Key concepts
- Generate many concepts before judging any; quantity first, quality later.
- A morphological chart lists options for each function and combines them into concepts.
- A Pugh matrix compares concepts to a datum with +, 0 and −.
- A weighted decision matrix multiplies scores by weights and sums them.
- If small weight changes flip the winner, the decision needs more data.
Key equations
Worked examples, step by step
Example 2.1 Concept A scores 6 (cost), 9 (performance), 5 (risk); B scores 8, 6, 8. Weights 0.3, 0.5, 0.2. Winner?
Show the steps
- A = 1.8 + 4.5 + 1.0 = 7.3.
- B = 2.4 + 3.0 + 1.6 = 7.0.
Answer: A, 7.3 to 7.0.
Example 2.2 Change weights to 0.4, 0.3, 0.3.
Show the steps
- A = 2.4 + 2.7 + 1.5 = 6.6.
- B = 3.2 + 1.8 + 2.4 = 7.4.
Answer: B wins: the choice is sensitive to weights.
Example 2.3 A chart has 3 power options, 2 structures and 4 sensors. Combinations?
Show the steps
- 3 × 2 × 4.
Answer: 24.
Practice problems
Work each on paper first, then check.
Pugh: 4 pluses, 1 minus. Net?
Show answer
+3.
Combinations for 2 × 3 × 3 × 2?
Show answer
36.
Why test weight sensitivity?
Show answer
To see if the winner is robust.
Why brainstorm before scoring?
Show answer
Early judging kills good ideas.
Common misconceptions
Myth: The highest score is always right.
Actually: Check sensitivity and assumptions.
Myth: Weights are objective.
Actually: They encode judgment.
Myth: One concept is enough.
Actually: Compare several.
Flashcards
Morphological chart
Options per function.
Pugh matrix
Compare to a datum.
Datum
Reference concept.
Weighted matrix
Scores times weights.
Sensitivity
How results change with inputs.
Down-select
Choosing a concept.
Self-check quiz
How this helps save the planet
NASA’s Sustainable Flight National Partnership works in three areas: advanced vehicle technologies, efficient airline operations and sustainable aviation fuels.
Weighing options across areas like these is a concept-selection problem: the right weights depend on what the stakeholders value, including emissions.
On Saving Planets: Solutions · Aircraft Performance
Sources: NASA Aeronautics: Sustainable Flight National Partnership
Free learning resources
- MIT OpenCourseWare 16.83X Space Systems Engineering (Spring 2002 – Spring 2003): Free MIT capstone materials.
- NASA Systems Engineering Handbook: Free NASA handbook.
Unit 3 · Weeks 3–4
Aircraft Track: Weight Sizing and Range
Takeoff-weight estimation from weight fractions, the Breguet range equation, and how efficiency gains change range and fuel.
Learning objectives
By the end of this unit you can:
- Estimate takeoff weight from fractions.
- Apply the Breguet range equation.
- Show how L/D changes range.
- Iterate a sizing loop.
Key concepts
- Takeoff weight equals payload divided by one minus the empty and energy fractions.
- If the empty plus energy fractions approach 1, the design does not close.
- For jet aircraft, Breguet range is (V/c)(L/D) ln(W_i/W_f).
- Range is proportional to L/D, so a 30% L/D gain gives 30% more range at the same fuel fraction.
- Sizing is iterative: estimate, compute, update fractions, repeat until the weight converges.
Key equations
Worked examples, step by step
Example 3.1 A drone carries 1 kg payload with empty fraction 0.5 and battery fraction 0.3 (sample values). Takeoff mass?
Show the steps
- 1/(1 − 0.5 − 0.3).
Answer: 5 kg.
Example 3.2 A transport flies at 230 m/s with c = 0.6 per hour, L/D = 17 and W_i/W_f = 1.25 (textbook values). Range?
Show the steps
- c = 1.667 × 10⁻⁴ s⁻¹.
- R = (230/1.667 × 10⁻⁴) × 17 × ln 1.25 = 1.38 × 10⁶ × 17 × 0.2231.
Answer: About 5235 km.
Example 3.3 Raise L/D by 30%.
Show the steps
- Range scales with L/D.
Answer: About 6805 km.
Practice problems
Work each on paper first, then check.
Takeoff mass if the battery fraction rises to 0.35?
Show answer
6.67 kg.
Weight of the 5 kg drone?
Show answer
49.0 N.
Why can’t fractions sum to 1?
Show answer
Nothing would be left for payload.
ln 1.25?
Show answer
0.223.
Common misconceptions
Myth: More battery always means more range.
Actually: It also raises weight; the fraction matters.
Myth: Breguet fits electric aircraft.
Actually: Batteries don’t get lighter; use an energy form.
Myth: One pass is enough.
Actually: Iterate until weight converges.
Flashcards
Empty fraction
Empty over takeoff weight.
Fuel fraction
Fuel over takeoff weight.
Breguet
Range equation.
L/D
Lift-to-drag ratio.
TSFC
Thrust-specific fuel consumption.
Sizing loop
Iterate to convergence.
Self-check quiz
How this helps save the planet
NASA says the Sustainable Flight National Partnership aims to enable 25–30% energy-efficiency improvements in next-generation transports that can use 100% sustainable aviation fuel and fly optimal trajectories.
Its centerpiece is a full-scale X-plane demonstrator testing an ultra-efficient aerodynamic design, with first flight no earlier than late 2026; higher L/D is exactly the lever this unit’s Breguet equation rewards.
On Saving Planets: Aircraft Performance · Solutions
Sources: NASA Aeronautics: Sustainable Flight National Partnership
Free learning resources
- NASA Aeronautics: Sustainable Flight National Partnership: NASA SFNP.
- MIT OpenCourseWare 16.83X Space Systems Engineering (Spring 2002 – Spring 2003): Free MIT capstone materials.
Unit 4 · Week 5
Aircraft Track: Wing Loading and Power
Constraint sizing: wing loading from stall speed, wing area, and climb power for a small electric aircraft.
Learning objectives
By the end of this unit you can:
- Find wing loading from stall speed.
- Size the wing area.
- Compute climb power.
- Draw a simple constraint diagram.
Key concepts
- Stall speed sets the maximum wing loading: W/S = ½ρV_s²C_Lmax.
- Wing area follows from weight divided by wing loading.
- Shaft power for climb covers drag (W V/(L/D)) plus the climb term (W × rate of climb), divided by propulsive efficiency.
- Each requirement draws a line on a W/S versus power-to-weight plot; the design point lies in the region meeting all.
- Small drones fly at low Reynolds numbers, so check airfoil data for small scales.
Key equations
Worked examples, step by step
Example 4.1 Stall at 12 m/s, C_Lmax = 1.2, sea level. Wing loading?
Show the steps
- ½ × 1.225 × 144 × 1.2.
Answer: 105.8 N/m².
Example 4.2 Wing area for the 5 kg drone?
Show the steps
- 49.03/105.84.
Answer: 0.463 m².
Example 4.3 Climb power at 15 m/s, L/D = 10, 2 m/s climb, η = 0.7?
Show the steps
- 49.03 × (1.5 + 2) = 171.6 W.
- 171.6/0.7.
Answer: 245 W.
Practice problems
Work each on paper first, then check.
Wing loading for a 10 m/s stall?
Show answer
73.5 N/m².
Power without the climb term?
Show answer
105.1 W.
Dynamic pressure at 15 m/s?
Show answer
137.8 Pa.
Why does stall set a maximum W/S?
Show answer
Higher W/S needs higher stall speed.
Common misconceptions
Myth: Bigger wings are always better.
Actually: They add weight and drag.
Myth: Climb power is small.
Actually: It can dominate small drones.
Myth: η = 1.
Actually: Propellers and motors lose energy.
Flashcards
Wing loading
Weight per wing area.
C_Lmax
Maximum lift coefficient.
Constraint diagram
Requirements on one plot.
Rate of climb
Vertical speed.
Propulsive efficiency
Useful power fraction.
Stall speed
Minimum steady speed.
Self-check quiz
How this helps save the planet
NASA’s Sustainable Flight National Partnership also targets efficient airline operations and optimal trajectories, where power and climb choices meet fuel use.
Small electric drones sized well in this unit are already used for crop, forest and coastline surveys. Values in this unit are sample values.
On Saving Planets: Aircraft Performance · Aerodynamics I
Sources: NASA Aeronautics: Sustainable Flight National Partnership
Free learning resources
- NASA Aeronautics: Sustainable Flight National Partnership: NASA SFNP.
- MIT OpenCourseWare 16.83X Space Systems Engineering (Spring 2002 – Spring 2003): Free MIT capstone materials.
Unit 5 · Week 6
CubeSat Track: Sizing and Orbit
CubeSat form factors, mass allowance, orbit period, passes per day and eclipse fraction for a low Earth orbit.
Learning objectives
By the end of this unit you can:
- Size a 3U CubeSat mass budget.
- Compute orbit period.
- Compute orbits per day.
- Compute the worst-case eclipse.
Key concepts
- CubeSats come in 10 cm units (U); a 3U is about 10 × 10 × 34 cm (textbook value).
- Mass allowance is roughly 1.33 kg per U (textbook value); confirm with the launch provider.
- Orbit period depends only on the semi-major axis: T = 2π√(a³/μ).
- In the worst case (Sun in the orbit plane), eclipse fraction is asin(R_E/a)/π.
- Low orbits decay faster from drag; most student CubeSats re-enter within years.
Key equations
Worked examples, step by step
Example 5.1 Period at 500 km altitude?
Show the steps
- a = 6878.1 km.
- T = 2π√(6878.1³/398,600.4).
Answer: 94.6 min.
Example 5.2 Orbits per day?
Show the steps
- 1440/94.6.
Answer: 15.2.
Example 5.3 Worst-case eclipse?
Show the steps
- asin(6378.1/6878.1)/π = 0.378.
- 0.378 × 94.6.
Answer: 35.8 min.
Practice problems
Work each on paper first, then check.
3U mass allowance at 1.33 kg/U?
Show answer
3.99 kg.
Sunlit time per orbit?
Show answer
58.9 min.
Does period depend on CubeSat mass?
Show answer
No.
Why do low orbits decay?
Show answer
Atmospheric drag.
Common misconceptions
Myth: Heavier satellites orbit slower.
Actually: Period depends only on a.
Myth: Eclipse is always 50%.
Actually: It depends on altitude and Sun angle.
Myth: Use altitude in Kepler’s law.
Actually: Use a = R_E + h.
Flashcards
CubeSat
Standard small satellite in 10 cm units.
3U
Three-unit CubeSat.
Period
Time per orbit.
Eclipse fraction
Share of orbit in shadow.
Semi-major axis
R_E + h for circular orbits.
Decay
Orbit loss from drag.
Self-check quiz
How this helps save the planet
NASA says PREFIRE uses a pair of tiny satellites, CubeSats launched in May 2024, to measure a little-studied part of the radiant energy Earth emits, for clues about sea ice loss, ice-sheet melting and a warming Arctic.
NASA calls the Arctic the region that behaves like our planet’s thermostat, venting excess energy received in the tropics, which is why a pair of small satellites there matters.
On Saving Planets: Earth Observation · Orbital Mechanics
Sources: NASA Science: PREFIRE (Polar Radiant Energy in the Far-InfraRed Experiment)
Free learning resources
- NASA Science: PREFIRE (Polar Radiant Energy in the Far-InfraRed Experiment): NASA PREFIRE.
- NASA Small Spacecraft Technology State of the Art: Free NASA report.
Unit 6 · Week 7
CubeSat Track: Power and Link Budgets
Solar-array output, orbit-average power, battery sizing for eclipse, UHF link path loss and daily data volume.
Learning objectives
By the end of this unit you can:
- Compute array output in sunlight.
- Compute orbit-average power.
- Size a battery for eclipse.
- Estimate path loss and data per day.
Key concepts
- Array power is solar flux × cell efficiency × area × cos(angle).
- Orbit-average generation is reduced by the eclipse fraction (and by pointing in practice).
- The battery covers the eclipse load; limiting depth of discharge extends cycle life.
- Free-space path loss grows as 20 log₁₀(4πd/λ); UHF amateur bands are common for student CubeSats.
- Data volume per day is bit rate × pass time × passes.
Key equations
Worked examples, step by step
Example 6.1 Panels of 0.06 m² with 28% cells face the Sun (sample values). Output?
Show the steps
- 1361 × 0.28 × 0.06.
Answer: 22.9 W.
Example 6.2 Orbit average with Unit 5’s eclipse fraction of 0.378?
Show the steps
- 22.86 × 0.622.
Answer: 14.2 W.
Example 6.3 Battery for 8 W through a 35.8 min eclipse at 30% depth of discharge?
Show the steps
- 8 × 35.75/60 = 4.77 Wh.
- 4.77/0.3.
Answer: 15.9 Wh.
Practice problems
Work each on paper first, then check.
Path loss at 437 MHz over 1000 km?
Show answer
λ = 0.686 m; L = 145.3 dB.
Data per day at 9600 bit/s, four 10-minute passes?
Show answer
23.04 Mbit = 2.88 MB.
Output at a 60° Sun angle?
Show answer
11.4 W.
Why limit depth of discharge?
Show answer
More cycles before the battery wears out.
Common misconceptions
Myth: Sun power is constant around the orbit.
Actually: Eclipse and pointing cut it.
Myth: Battery = eclipse energy.
Actually: Divide by DoD.
Myth: More bits per second is free.
Actually: It needs more link margin.
Flashcards
Orbit-average power
Generation over a full orbit.
DoD
Depth of discharge.
Path loss
Spreading loss.
UHF
Ultra-high-frequency band.
Pass
Time a ground station sees the satellite.
Data volume
Bits downlinked per day.
Self-check quiz
How this helps save the planet
NASA’s small spacecraft report says that when its first edition was published in 2013, 247 CubeSats and 105 other small spacecraft under 50 kg had been launched worldwide, less than 2% of the mass launched to orbit.
NASA says small spacecraft have since become the primary means for commercial, government, private and academic institutions to access space, so careful power and link budgets now support a large share of Earth observation.
On Saving Planets: Spacecraft Design · Earth Observation
Free learning resources
- NASA Small Spacecraft Technology State of the Art: Free NASA report.
- MIT OpenCourseWare 16.83X Space Systems Engineering (Spring 2002 – Spring 2003): Free MIT capstone materials.
Unit 7 · Week 8
Structural and Thermal Checks
Load factors, margins of safety, launch and flight loads, and a first thermal equilibrium estimate for both tracks.
Learning objectives
By the end of this unit you can:
- Compute a design load from a load factor.
- Compute a margin of safety.
- Estimate equilibrium temperature.
- Decide what needs detailed analysis.
Key concepts
- Design loads are weight times a load factor (launch or maneuver), times a factor of safety.
- Margin of safety MS = allowable/(FS × applied) − 1 must be positive.
- Aluminum 6061-T6 yields near 276 MPa (textbook value), a common choice for both drones and CubeSat frames.
- A first thermal estimate balances absorbed sunlight with emitted infrared; for α = ε a sunlit body near Earth sits near 278 K on average.
- Hand checks find the critical cases; finite-element and thermal models then refine them.
Key equations
Worked examples, step by step
Example 7.1 A 4 kg CubeSat sees 10 g (sample load factor). Load?
Show the steps
- 10 × 4 × 9.80665.
Answer: 392 N.
Example 7.2 A rail sees 80 MPa; yield is 276 MPa; FS = 1.25. MS?
Show the steps
- 276/(1.25 × 80) − 1.
Answer: 1.76, positive.
Example 7.3 Average equilibrium temperature with α = ε?
Show the steps
- (1361/(4 × 5.670374419 × 10⁻⁸))^¼.
Answer: 278 K.
Practice problems
Work each on paper first, then check.
MS if stress rises to 200 MPa?
Show answer
0.10.
Load at 6 g on 5 kg?
Show answer
294 N.
In °C, 278.3 K is?
Show answer
5.2 °C.
Why a factor of safety?
Show answer
Uncertain loads, materials and analysis.
Common misconceptions
Myth: MS = 0 is fine.
Actually: Keep it positive.
Myth: Space is cold, so no thermal problem.
Actually: Sunlit parts can overheat.
Myth: Hand checks replace analysis.
Actually: They guide it.
Flashcards
Load factor
Multiple of weight.
Factor of safety
Multiplier on loads.
Margin of safety
Allowable over required minus one.
Yield strength
Stress for permanent set.
Equilibrium temperature
Absorbed = emitted.
FEA
Finite element analysis.
Self-check quiz
How this helps save the planet
NASA says PREFIRE’s twin CubeSats measure far-infrared emission from Earth, the same radiation this unit balances in its thermal estimate.
NASA reports the PREFIRE mission was extended so the twin satellites operate through at least September 2026, expanding focus from the poles to the whole planet, a payoff of a design that survived launch and orbit.
On Saving Planets: Aerospace Structures · Heat Transfer
Sources: NASA Science: PREFIRE (Polar Radiant Energy in the Far-InfraRed Experiment)
Free learning resources
- MIT OpenCourseWare 16.83X Space Systems Engineering (Spring 2002 – Spring 2003): Free MIT capstone materials.
- NASA Systems Engineering Handbook: Free NASA handbook.
Unit 8 · Weeks 9–10
Cost, Schedule and Risk
Work breakdown structures, critical-path schedules, earned value, risk matrices and mitigation plans.
Learning objectives
By the end of this unit you can:
- Build a work breakdown structure.
- Find the critical path.
- Compute CPI, SPI and estimate at completion.
- Score and mitigate risks.
Key concepts
- A work breakdown structure splits the project into deliverable pieces that can be estimated and assigned.
- The critical path is the longest chain of dependent tasks; any delay on it delays the project.
- Earned value compares planned value, earned value and actual cost.
- CPI = EV/AC and SPI = EV/PV; values under 1 mean over budget or behind schedule.
- Risks are scored likelihood × consequence and tracked with owners and mitigations.
Key equations
Worked examples, step by step
Example 8.1 PV = $50k, EV = $45k, AC = $48k (sample values). CPI and SPI?
Show the steps
- CPI = 45/48.
- SPI = 45/50.
Answer: CPI = 0.9375, SPI = 0.90.
Example 8.2 Budget at completion is $100k. EAC?
Show the steps
- 100/0.9375.
Answer: $106.7k.
Example 8.3 Tasks in sequence take 3, 4, 5 and 2 weeks in a 15-week term. Slack?
Show the steps
- Path = 14 weeks.
- 15 − 14.
Answer: 1 week.
Practice problems
Work each on paper first, then check.
Risk score for likelihood 4, consequence 5?
Show answer
20 of 25.
CPI = 1.1 means?
Show answer
Under budget.
Variance at completion for EAC $106.7k?
Show answer
−$6.7k.
What is a WBS?
Show answer
Work breakdown structure.
Common misconceptions
Myth: Spending on plan means on schedule.
Actually: Compare earned value, not spend.
Myth: Every task is critical.
Actually: Only the longest path is.
Myth: Risks disappear when listed.
Actually: They need owners and actions.
Flashcards
WBS
Work breakdown structure.
Critical path
Longest dependent chain.
Earned value
Value of work done.
CPI
EV/AC.
SPI
EV/PV.
Risk matrix
Likelihood × consequence.
Self-check quiz
How this helps save the planet
NASA’s Systems Engineering Handbook includes a full section on crosscutting technical management, alongside system design and product realization.
Projects that stay on budget and schedule launch sooner, and Earth-observing data starts flowing sooner. Cost values in this unit are sample values.
On Saving Planets: Solutions · Avionics & Systems Engineering
Sources: NASA Systems Engineering Handbook
Free learning resources
- NASA Systems Engineering Handbook: Free NASA handbook, Section 6.
- MIT OpenCourseWare 16.83X Space Systems Engineering (Spring 2002 – Spring 2003): Free MIT capstone materials.
Unit 9 · Weeks 11–13
Prototype, Test and Verification
Verification matrices, test planning, measurement statistics, comparing results with predictions, and closing requirements.
Learning objectives
By the end of this unit you can:
- Build a verification matrix.
- Compute mean and standard deviation.
- Compare a measurement with an allocation.
- Close or waive a requirement.
Key concepts
- A verification matrix lists each requirement, its method, the test or analysis, and the result.
- Repeat measurements to estimate the mean and spread; report both.
- Compare results with predictions; large differences reveal model errors early.
- Test as you fly: use flight-like configurations and procedures.
- MIT’s 16.83X follows conceive, design, implement and operate phases, ending with testing in the intended environment.
Key equations
Worked examples, step by step
Example 9.1 Five mass measurements: 3.38, 3.42, 3.40, 3.45, 3.35 kg. Mean?
Show the steps
- Sum 17.00/5.
Answer: 3.40 kg.
Example 9.2 Sample standard deviation?
Show the steps
- Deviations −0.02, 0.02, 0, 0.05, −0.05.
- √(0.0058/4).
Answer: 0.038 kg.
Example 9.3 Margin against the 4.0 kg allocation?
Show the steps
- (4.0 − 3.40)/3.40.
Answer: 17.6%: the requirement closes.
Practice problems
Work each on paper first, then check.
Predicted 3.30 kg, measured 3.40 kg. Error?
Show answer
+3.03%.
Why repeat measurements?
Show answer
To estimate spread and catch mistakes.
What does “test as you fly” mean?
Show answer
Use flight-like hardware and procedures.
Who approves a waiver?
Show answer
The project’s review board or customer.
Common misconceptions
Myth: One measurement is enough.
Actually: Report mean and spread.
Myth: Tests prove a design perfect.
Actually: They show it meets requirements under test conditions.
Myth: Disagreeing data is bad.
Actually: It teaches you about the model.
Flashcards
Verification matrix
Requirement-to-evidence table.
Mean
Average.
Standard deviation
Spread.
Test as you fly
Flight-like testing.
Waiver
Approved exception.
CDIO
Conceive, design, implement, operate.
Self-check quiz
How this helps save the planet
MIT OpenCourseWare describes 16.83X as following a conceive-design-implement-operate model, with a final phase in which the system is tested and readied for its intended environment.
NASA’s CubeSat Launch Initiative flies student satellites that pass this kind of testing, turning capstones into working instruments in orbit.
On Saving Planets: Avionics & Systems Engineering · Probability & Statistics
Sources: MIT OpenCourseWare 16.83X Space Systems Engineering (Spring 2002 – Spring 2003) · NASA: CubeSat Launch Initiative
Free learning resources
- MIT OpenCourseWare 16.83X Space Systems Engineering (Spring 2002 – Spring 2003): Free MIT capstone materials.
- NASA Systems Engineering Handbook: Free NASA handbook, Section 5.
Unit 10 · Weeks 14–15
Design Reviews and the Final Report
Preliminary and critical design reviews, presenting trades and budgets, answering questions, and writing the final report.
Learning objectives
By the end of this unit you can:
- Plan a design review.
- Present budgets with margins.
- Track review action items.
- Write a clear final report.
Key concepts
- A preliminary design review shows the concept meets requirements with margin; a critical design review shows the detailed design is ready to build.
- Lead with requirements, then the design, then budgets, risks, test plans and open issues.
- Every review produces action items with owners and due dates.
- The final report tells the story from need to verified design, with numbers that trace to the spreadsheet.
- Honest discussion of what didn’t work is part of good engineering.
Key equations
Worked examples, step by step
Example 10.1 A 20-minute review at 1.5 minutes per slide. Slides?
Show the steps
- 20/1.5.
Answer: About 13.
Example 10.2 A review leaves 12 action items; 9 are closed. Closure?
Show the steps
- 9/12.
Answer: 75%.
Example 10.3 30 of 32 requirements are verified. Coverage?
Show the steps
- 30/32.
Answer: 93.75%.
Practice problems
Work each on paper first, then check.
Slides for a 30-minute review at 2 min each?
Show answer
15.
What follows PDR?
Show answer
CDR.
Closure with 11 of 12 closed?
Show answer
91.7%.
Why show open issues?
Show answer
Reviewers can help, and it builds trust.
Common misconceptions
Myth: Reviews are exams.
Actually: They help the project.
Myth: More slides is better.
Actually: Clarity beats volume.
Myth: Hide problems.
Actually: Show them with plans.
Flashcards
PDR
Preliminary design review.
CDR
Critical design review.
Action item
Task from a review.
Final report
Need-to-verification story.
Coverage
Share of verified requirements.
Lessons learned
What to do differently.
Self-check quiz
How this helps save the planet
NASA says its Sustainable Flight National Partnership supports the aviation community’s goal of net-zero carbon emissions by 2050.
NASA says PREFIRE’s extended mission now looks at the whole planet; strong reviews and reports are how student and professional designs reach that kind of impact.
On Saving Planets: Solutions · Earth Observation
Sources: NASA Aeronautics: Sustainable Flight National Partnership · NASA Science: PREFIRE (Polar Radiant Energy in the Far-InfraRed Experiment)
Free learning resources
- NASA Systems Engineering Handbook: Free NASA handbook.
- MIT OpenCourseWare 16.83X Space Systems Engineering (Spring 2002 – Spring 2003): Free MIT capstone materials.
The lab (Design studio)
The design studio is the hands-on part of the course. Here it is free and for practice only, with no credit.
Every lab is a spreadsheet design tool, so there are no hazards. Do not build or fly a real drone, charge lithium batteries or handle launch hardware for this course without qualified supervision and local rules. Take screen breaks, sit with good posture, and keep cables out of walkways.
Safety reference: OSHA: Walking-working surfaces (slip, trip and fall hazards)
Lab A: Requirements and margin tracker
Week 1
Goal: Build the requirements spreadsheet your whole project will use, with live margins.
Procedure
- List 10–20 requirements with number, unit and verification method.
- Enter a 4.0 kg mass allocation (textbook 3U value) or a 5 kg drone allocation.
- Enter estimates of 3.4, 3.6 and 3.8 kg and compute margin.
- Color margins under 10% red.
Data table
| Estimate (kg) | Margin |
|---|---|
| 3.4 | 17.6% |
| 3.6 | 11.1% |
| 3.8 | 5.26% |
Computed sample values.
Sample calculation
- (4.0 − 3.6)/3.6 = 11.1%.
- (4.0 − 3.8)/3.8 = 5.26%.
Safety
- Computer only.
Home or virtual alternative
- Any spreadsheet works.
NASA Systems Engineering Handbook
Planet link: NASA’s CubeSat Launch Initiative has launched over 150 CubeSats. NASA: CubeSat Launch Initiative
Lab B: Concept-selection matrix with sensitivity
Week 2
Goal: Score two concepts and test how weights change the winner.
Procedure
- Enter Unit 2’s scores: A (6, 9, 5), B (8, 6, 8).
- Score with three weight sets.
- Plot the winner against the performance weight.
- Write one paragraph defending your choice.
Data table
| Weights (cost, perf., risk) | A | B |
|---|---|---|
| 0.3, 0.5, 0.2 | 7.3 | 7.0 |
| 0.4, 0.3, 0.3 | 6.6 | 7.4 |
| 0.2, 0.6, 0.2 | 7.6 | 6.8 |
Computed sample values.
Sample calculation
- A = 0.2 × 6 + 0.6 × 9 + 0.2 × 5 = 7.6.
- B = 0.2 × 8 + 0.6 × 6 + 0.2 × 8 = 6.8.
Safety
- Computer only.
Home or virtual alternative
- Any spreadsheet works.
MIT OpenCourseWare 16.83X Space Systems Engineering (Spring 2002 – Spring 2003)
Planet link: NASA’s SFNP works across vehicles, operations and sustainable fuels. NASA Aeronautics: Sustainable Flight National Partnership
Lab C: Drone sizing loop
Week 4
Goal: Size the drone track’s takeoff mass for several battery fractions.
Procedure
- Enter 1 kg payload and empty fraction 0.5.
- Compute takeoff mass for battery fractions 0.25, 0.30 and 0.35.
- Add wing area from W/S = 105.84 N/m².
- Pick a design point and justify it.
Data table
| Battery fraction | Takeoff mass (kg) |
|---|---|
| 0.25 | 4.0 |
| 0.30 | 5.0 |
| 0.35 | 6.67 |
Computed sample values.
Sample calculation
- 1/(1 − 0.5 − 0.25) = 4.0 kg.
- 1/(1 − 0.5 − 0.35) = 6.67 kg.
Safety
- Computer only.
Home or virtual alternative
- Any spreadsheet works.
MIT OpenCourseWare 16.83X Space Systems Engineering (Spring 2002 – Spring 2003)
Planet link: NASA’s SFNP targets 25–30% energy-efficiency gains. NASA Aeronautics: Sustainable Flight National Partnership
Lab D: CubeSat orbit and eclipse
Week 6
Goal: Compute period and worst-case eclipse for candidate altitudes.
Procedure
- Enter altitudes 400, 500 and 600 km.
- Compute T and orbits per day.
- Compute worst-case eclipse minutes.
- Choose an altitude and note the drag-lifetime trade.
Data table
| Altitude (km) | T (min) | Eclipse (min) |
|---|---|---|
| 400 | 92.6 | 36.1 |
| 500 | 94.6 | 35.8 |
| 600 | 96.7 | 35.5 |
Computed sample values.
Sample calculation
- T(600) = 2π√(6978.1³/398,600.4) = 96.7 min.
- Eclipse(400) = 0.390 × 92.6 = 36.1 min.
Safety
- Computer only.
Home or virtual alternative
- Any spreadsheet works.
NASA Small Spacecraft Technology State of the Art
Planet link: NASA: PREFIRE’s CubeSats launched in May 2024. NASA Science: PREFIRE (Polar Radiant Energy in the Far-InfraRed Experiment)
Lab E: Power and data budget
Week 7
Goal: Close the CubeSat power and data budgets with margin.
Procedure
- Enter array output 22.9 W and orbit average 14.2 W.
- List loads and compare with the orbit average.
- Compute data per day at 9600 bit/s for 2, 4 and 6 ten-minute passes.
- Compare with your payload’s daily data.
Data table
| Passes per day | Data (Mbit) |
|---|---|
| 2 | 11.52 |
| 4 | 23.04 |
| 6 | 34.56 |
Computed sample values.
Sample calculation
- 9600 × 600 × 2 = 11.52 Mbit.
- 9600 × 600 × 6 = 34.56 Mbit.
Safety
- Computer only.
Home or virtual alternative
- Any spreadsheet works.
NASA Small Spacecraft Technology State of the Art
Planet link: NASA: small spacecraft are now the primary means for many groups to access space. NASA Small Spacecraft Technology State of the Art
Lab F: Earned-value tracker
Week 10
Goal: Track cost and schedule performance across three status dates.
Procedure
- Enter PV, EV and AC for three dates.
- Compute CPI and SPI.
- Compute EAC with BAC = $100k.
- Write a one-line status for each date.
Data table
| PV, EV, AC ($k) | CPI | SPI |
|---|---|---|
| 20, 20, 22 | 0.909 | 1.00 |
| 50, 45, 48 | 0.9375 | 0.90 |
| 80, 76, 80 | 0.95 | 0.95 |
Computed sample values.
Sample calculation
- 20/22 = 0.909.
- 76/80 = 0.95.
Safety
- Computer only.
Home or virtual alternative
- Any spreadsheet works.
NASA Systems Engineering Handbook
Planet link: NASA’s handbook covers crosscutting technical management. NASA Systems Engineering Handbook
Exam prep practice sets
Time yourself: about 10 minutes per problem. Then compare with the full solutions.
Midterm practice set (Units 1–5)
Margin of a 4.0 kg allocation over a 3.6 kg estimate?
Show full solution
- 0.4/3.6.
Answer: 11.1%.
Takeoff mass for 2 kg payload, empty 0.45, battery 0.3?
Show full solution
- 2/0.25.
Answer: 8 kg.
Wing loading for a 14 m/s stall, C_Lmax 1.3?
Show full solution
- ½ × 1.225 × 196 × 1.3.
Answer: 156.1 N/m².
Period at 400 km?
Show full solution
- a = 6778.1 km.
Answer: 92.6 min.
Breguet range with L/D = 20 instead of 17 (Unit 3 values)?
Show full solution
- 5235 × 20/17.
Answer: 6159 km.
Final practice set (Units 1–10)
Array of 0.09 m² at 30% efficiency?
Show full solution
- 1361 × 0.3 × 0.09.
Answer: 36.7 W.
Battery for 10 W over 36 min at 25% DoD?
Show full solution
- 10 × 0.6/0.25.
Answer: 24 Wh.
MS for 100 MPa, yield 276 MPa, FS 1.4?
Show full solution
- 276/140 − 1.
Answer: 0.971.
EAC with BAC $200k, EV 60, AC 64?
Show full solution
- CPI = 0.9375.
- 200/0.9375.
Answer: $213.3k.
Mean and sample std dev of 2, 4, 6?
Show full solution
- Mean 4.
- √(8/2).
Answer: 4 and 2.
Verification coverage, 45 of 50?
Show full solution
- 45/50.
Answer: 90%.
Formula sheet
Constants
| Constant | Value |
|---|---|
| Earth’s gravitational parameter (textbook value) | μ = 398,600.4418 km³/s² |
| Earth’s equatorial radius (textbook value) | 6378.137 km |
| Standard gravity | g = 9.80665 m/s² |
| Solar constant (textbook value) | 1361 W/m² |
| Sea-level air density (textbook value) | 1.225 kg/m³ |
| Speed of light | c = 299,792,458 m/s (exact) |
Free texts and resources
Use these free handbooks, lectures and mission pages alongside the course.
- NASA Systems Engineering Handbook: Free NASA handbook.
- MIT OpenCourseWare 16.83X Space Systems Engineering (Spring 2002 – Spring 2003): Free MIT capstone materials.
- NASA Small Spacecraft Technology State of the Art: Free NASA small-spacecraft report.
- NASA: CubeSat Launch Initiative: NASA launch opportunities.
- NASA Science: PREFIRE (Polar Radiant Energy in the Far-InfraRed Experiment): NASA CubeSat mission.
- NASA Aeronautics: Sustainable Flight National Partnership: NASA sustainable aviation.
Glossary
- Action item
- Task assigned at a review.
- Allocation
- Budgeted share of a resource.
- Breguet equation
- Aircraft range equation.
- CDR
- Critical design review.
- CPI
- Cost performance index.
- Constraint diagram
- Requirements plotted against wing loading.
- Critical path
- Longest chain of dependent tasks.
- CubeSat
- Small satellite built in 10 cm units.
- Depth of discharge
- Share of battery capacity used.
- Earned value
- Budgeted value of work done.
- Eclipse fraction
- Share of an orbit in shadow.
- Margin of safety
- Allowable over required minus one.
- Morphological chart
- Options for each function.
- PDR
- Preliminary design review.
- Pugh matrix
- Comparison against a datum concept.
- Requirement
- Verifiable statement of need.
- SPI
- Schedule performance index.
- Verification matrix
- Requirement-to-evidence table.
- Wing loading
- Weight per wing area.
- Work breakdown structure
- Project split into deliverables.
Self-assessment rubric
No grade or credit is given. Use this to judge honestly where you are in each unit.
| Level | What it looks like |
|---|---|
| 4 · Mastery | Delivers a design that traces every number to a requirement, closes all budgets with margin, verifies requirements with evidence, and presents trades, risks and lessons clearly. |
| 3 · Proficient | Closes most budgets with margin and presents a clear design with minor gaps. |
| 2 · Developing | Has a concept and some budgets but weak requirement tracing or missing margins. |
| 1 · Beginning | Presents a design without requirements, budgets or verification; needs to revisit the units. |
Suggested weighting if you want a score
| Part | Weight |
|---|---|
| Practice problems | 20% |
| Labs | 25% |
| Midterm practice set | 25% |
| Final practice set | 30% |
Aim for level 3 or better in every unit before moving to the next course.