Chapter 29 — Key Takeaways (Mission Design)

A one-page reference. Reread this before an exam, before a design review, or before you size any mission.

The mission-design funnel (and it spirals)

Step Question it answers Home
Objective what do we want? (from outside engineering)
Requirements what must be true? §29.2
Orbit where does it fly? Ch. 9
Trajectory / delta-v budget how does it get and stay there? Ch. 3, 10, §29.3
Spacecraft what hardware provides it? Part IV
Launch vehicle what lifts it? Ch. 30
Operations how is it flown / disposed? Ch. 31, 35
Cost does it fly at all? (the closing number)

The funnel is a spiral, not a waterfall: each trip down teaches you something that sends you back up. A design closes when every budget balances at once, with margin.

The core equations

Relationship Meaning
$v_e = I_{sp}\,g_0$ exhaust velocity from specific impulse ($g_0=9.81$ m/s²)
$m_0/m_f = e^{\Delta v/v_e}$ mass ratio (the amplifier) from the delta-v budget
$m_0 = (m_0/m_f)\,m_f$ wet mass from dry mass
$\Delta m_0 = (m_0/m_f)\,\Delta m_f$ every kg of dry mass drags $m_0/m_f$ kg of wet mass

First-defined terms

Term One-line definition
Mission design Converting an objective into a self-consistent architecture that closes.
Requirement A single, testable, verifiable "shall" statement; flows down mission → system → subsystem.
Trade study A documented comparison of architectures against weighted criteria.
Delta-v budget The margined sum of every velocity change; the master constraint (sizes the vehicle).
Margin Deliberate reserve against uncertainty/growth; bought down as the design matures.
Systems engineering Designing the whole — interfaces and shared budgets — not the parts.
Driving requirement The requirement the coupled design is most sensitive to.
Design review A gated, independent evaluation of design maturity (MDR/PDR/CDR).

The delta-v budget as master constraint

  • A mission is a route across the delta-v map; its budget is the sum of the legs (Ch. 3 / Appendix G).
  • Split legs by who pays: launch vehicle (surface → drop-off orbit) vs. spacecraft's own propulsion.
  • Roll up with per-leg margins, then invert the rocket equation to size the vehicle.
  • Worked (Track A comsat): GTO→GEO 1,800 (5%) + SK 750 (10%) + disposal 11 → ideal 2,561, margined 2,726 m/s. At $I_{sp}=320$ s, dry 1,500 kg → mass ratio 2.38, propellant ~2,076 kg, wet ~3,576 kg.

Margins — how much, and when

Phase / gate Typical mass margin Principle
Concept / MDR 25–30% almost everything is estimated
PDR 15–20% components chosen, many on paper
CDR 5–10% most hardware defined
Weighed, pre-launch 0–3% you now know the mass

Buy down margin by buying knowledge — never by hoping. Margin protects against the unknown; contingency covers identified risks. Spacecraft dry mass grows ~20–30% over development — budget for it.

Systems engineering — the mass–power–cost coupling

payload↑ → power↑ → array mass↑ → dry mass↑ → propellant↑ (×mass ratio) → wet mass↑ → launch↑ → cost↑
  • The dry-mass → propellant arrow is the amplifier (runs through the rocket equation). Comsat ~2.38; lunar lander ~6.72. Higher delta-v → longer lever → mass growth hurts more.
  • The systems engineer tracks the shared budgets (delta-v, mass, power, link, pointing) and the interfaces. Missions are lost at unmanaged interfaces (Mars Climate Orbiter: a units mismatch).
  • Find the driving requirement first — it is where margin and effort pay off most.

The review lifecycle

Gate Confirms In one line
MDR requirements/orbit/budget/architecture consistent does the mission close?
PDR preliminary subsystem designs meet requirements w/ margin will the design work?
CDR detailed build-to design complete and verified is it ready to build?

The review timeline is the margin-buy-down schedule. The cost of fixing a flaw rises ~10× per gate.

Common pitfalls

Pitfall Reality
"Design flows straight down the funnel." It spirals; the arrows go back up.
"Cut margin to the computed budget." The estimate is uncertain and grows; you'll fall short.
"Electric is just better." Best for a weighting; the trade study and driving requirement decide.
"Optimize each subsystem independently." Coupling means local wins can lose for the system.
"The mission's delta-v is launch + spacecraft summed." Different staged vehicles — never merge their budgets.

Numbers worth remembering

  • Track-A comsat spacecraft-own budget ≈ 2.6 km/s ideal (~2.7 margined); wet ~3.6 t (chemical), ~1.75 t (electric).
  • Lunar cargo lander (LEO→surface, one way) ≈ 5.5 km/s ideal; mass ratio ~6.7 at $I_{sp}=320$ s.
  • Amplifier = mass ratio: every dry kg drags $m_0/m_f$ wet kg.

Mission / astrotools additions this chapter

  • MDR: the synthesis checkpoint — assemble requirements + orbit + delta-v budget + mass/power into one coherent architecture; name the driving requirement.
  • mission.py: roll_up_dv(budget) (ideal + margined totals) and size_vehicle(dv, isp, payload) (propellant + wet mass). These carry into the Chapter 40 capstone.