Case Study: Choosing the Propulsion for a Cargo Lunar Lander

"Every engine on a spacecraft is an answer to a question about the mission. Ask the wrong question and the best engine in the world is the wrong one."

Executive Summary

In the first case study we audited a finished engine. Here we do the harder thing: we choose and size a propulsion system from a blank page, given only a mission. Our mission is Track B — deliver cargo to the lunar surface — and the decision is not "which engine has the best specific impulse" but "which propellant class and cycle actually fit the job, and how much propellant will they demand." We will use the four selection questions from the chapter's Mission Design Checkpoint to pick a propellant and a cycle, size the propellant load with the rocket equation of Chapter 3, check that the engine can actually land the vehicle using the thrust-to-weight idea of Chapter 16, and then iterate to see what a higher-$I_{sp}$ propellant would change. This is exactly the reasoning that opens a real lander program — and the reasoning you will run on your own mission in the MDR.

Skills applied

  • Turning mission needs into propellant/cycle requirements (§17.1, §17.3, §17.4).
  • Selecting a propellant class against thrust, restart, throttle, and storability (§17.1, Checkpoint).
  • Sizing propellant mass by inverting the rocket equation (§17.1 use; Ch. 3).
  • Checking landing feasibility with thrust-to-weight in lunar gravity (Ch. 16).

Background

The mission and the leg

Our lander must carry cargo from a low lunar orbit (LLO) down to a soft landing on the surface. The descent is the propulsion-defining leg. From the delta-v map you built in Chapter 3, a soft landing from low lunar orbit costs roughly $1.7\ \text{km/s}$; add margin for hover, redesignation of the landing site, and gravity losses during the descent, and we will design to $$\Delta v = 2.0\ \text{km/s}.$$

The vehicle masses (our design inputs)

  • Dry lander (structure, avionics, legs, tanks, engine): $m_{\text{dry}} = 1{,}500\ \text{kg}$.
  • Cargo delivered to the surface: $m_{\text{cargo}} = 1{,}000\ \text{kg}$.
  • So the mass at engine cutoff (touchdown) is $m_f = m_{\text{dry}} + m_{\text{cargo}} = 2{,}500\ \text{kg}$.

The four questions

The Mission Design Checkpoint gave us the interrogation every propulsion choice must survive. For a lunar descent:

  1. How much thrust, and where? In-space and near-surface — modest thrust, but it must be finely controllable.
  2. Must it restart or throttle? Emphatically yes: the engine must throttle deeply to arrest the descent and hover, and ideally restart for a go-around.
  3. How long must the propellant wait? Days of transit from Earth, then a coast in lunar orbit — long enough that cryogenic boiloff is a real concern.
  4. How much $I_{sp}$ can we trade for reliability? For a one-shot landing with cargo aboard, a fair amount — reliability and control outrank a few seconds of $I_{sp}$.

Phase 1: Choose the propellant class

Question 2 immediately eliminates a solid motor: you cannot throttle or restart one (§17.4), and you certainly cannot hover on one. A lander must use a liquid (or, in principle, a hybrid). That leaves the liquid propellants of §17.1, and questions 3 and 4 decide among them.

Question 3 — the long wait with boiloff — argues against cryogenics. Hydrolox and methalox both boil away over days unless actively cooled (a mass and power cost we would rather avoid on a cargo lander). The hypergolic propellants (N₂O₄ with a hydrazine-family fuel) are storable as liquids at room temperature for months, ignite on contact with no ignition system to fail, and restart reliably — which is why the Apollo Lunar Module descent engine was hypergolic, and why so many deep-space craft are. We choose hypergolic bipropellant, accepting its modest $I_{sp} \approx 311\ \text{s}$ and its toxicity (a ground-handling problem, not a flight problem) in exchange for storability, restart, and heritage.

🔧 Engineering Reality: This is a genuinely contested call, not a slam-dunk. Methalox ($I_{sp} \approx 350\ \text{s}$) would cut the propellant load, and a Mars-bound architecture might prefer it for commonality and ISRU (§17.6). We will quantify exactly what hypergolic costs us in Phase 5. The point of §17.1 is that there is no universally "best" propellant — only the best fit for a stated mission, and storable and restartable is what a wait-then-land cargo mission values most.

Phase 2: Choose the cycle

How should we feed the chamber? A lander needs only modest chamber pressure — it is not fighting for the last second of $I_{sp}$ like a launch first stage — but it needs supreme reliability and deep, smooth throttling. That is the textbook case for a pressure-fed engine (§17.3): no turbopump, no preburner, no spinning machinery to fail, just helium pressure pushing propellant into the chamber. The Apollo LM descent engine was pressure-fed and throttleable over roughly a 10 : 1 range, and it landed six crews. We adopt the same architecture: pressure-fed hypergolic, one deeply throttleable main descent engine plus small reaction-control thrusters for attitude.

The cost of pressure-feeding — a low chamber pressure and therefore a slightly lower $I_{sp}$ and a heavier pressurized tank — is exactly the kind of penalty a lander can afford, because its total $\Delta v$ is small and its premium is on not-failing over on-orbit refinement. Simplicity is the feature.

Phase 3: Size the propellant

Now the rocket equation earns its keep. With $I_{sp} = 311\ \text{s}$, the effective exhaust velocity is $$c = I_{sp}\,g_0 = 311 \times 9.81 = 3{,}051\ \text{m/s}.$$ The required mass ratio for $\Delta v = 2{,}000\ \text{m/s}$ is $$\frac{m_0}{m_f} = e^{\Delta v/c} = e^{2000/3051} = e^{0.656} = 1.926.$$ So the fully fueled lander at the start of descent masses $$m_0 = 1.926 \times 2{,}500\ \text{kg} = 4{,}815\ \text{kg},$$ and the propellant it must carry is $$m_p = m_0 - m_f = 4{,}815 - 2{,}500 = 2{,}315\ \text{kg}.$$

Sanity check. Propellant is $2{,}315/4{,}815 \approx 48\%$ of the loaded lander — a believable propellant fraction for a modest-$\Delta v$ lander (far below the ~90% an orbital launch demands, exactly as Chapter 3 would predict for a leg of only 2 km/s). The cargo we actually deliver is $1{,}000/4{,}815 \approx 21\%$ of the descent mass — respectable for a lander.

Phase 4: Can the engine actually land it?

Propellant mass is only half the design; the engine must also produce the right thrust. Landing is a thrust-to-weight problem, and the weight is set by lunar gravity, $g_{\text{moon}} = 1.62\ \text{m/s}^2$ (about one-sixth of Earth's).

At the start of descent the lander is heaviest, $m_0 = 4{,}815\ \text{kg}$, so its lunar weight is $$W_0 = m_0\,g_{\text{moon}} = 4{,}815 \times 1.62 = 7{,}800\ \text{N} \approx 7.8\ \text{kN}.$$ To decelerate from orbital descent we want a thrust comfortably above this. Choose a main engine with a maximum thrust of $F_{\max} = 10\ \text{kN}$. Then the starting thrust-to-weight (in lunar gravity) is $$\frac{F_{\max}}{W_0} = \frac{10{,}000}{7{,}800} \approx 1.28,$$ enough to brake and control the descent.

Now the crucial check at the other end. At touchdown the lander is lightest ($m_f = 2{,}500\ \text{kg}$), so to hover it needs only $$F_{\text{hover}} = m_f\,g_{\text{moon}} = 2{,}500 \times 1.62 = 4{,}050\ \text{N} \approx 4.05\ \text{kN}.$$ That is just $4{,}050/10{,}000 = 40\%$ of the engine's maximum thrust. The engine must throttle down to about 40% to hover at touchdown — and lower still to settle gently. This is precisely why a lander cannot use a solid motor (no throttle) and why deep-throttle capability, not peak thrust or $I_{sp}$, is the driving engine requirement. A pressure-fed hypergolic engine like the LM descent engine, throttleable to ~10% of maximum, clears this requirement with room to spare.

💡 Intuition: A lander's engine spends its life fighting not to accelerate. Because the vehicle gets lighter as it burns propellant, the thrust needed to hover falls throughout the descent — so the engine must be able to throttle down, and keep throttling down, all the way to touchdown. An engine that could only run at full thrust would slam the lander into the surface; the whole art is in the throttle.

Phase 5: Iterate — what would methalox change?

Design is iteration, so let us test our contested Phase-1 call. Suppose we accept cryogenic boiloff management and switch to methalox, $I_{sp} = 350\ \text{s}$, so $c = 350 \times 9.81 = 3{,}434\ \text{m/s}$. The mass ratio drops: $$\frac{m_0}{m_f} = e^{2000/3434} = e^{0.582} = 1.790,$$ giving $m_0 = 1.790 \times 2{,}500 = 4{,}476\ \text{kg}$ and propellant $m_p = 4{,}476 - 2{,}500 = 1{,}976\ \text{kg}$.

Methalox saves $2{,}315 - 1{,}976 = 339\ \text{kg}$ of propellant — about a $15\%$ reduction in propellant mass — for the same delivered cargo. That is a real prize. But it comes with cryogenic tanks, insulation, and boiloff losses over the transit and lunar-orbit coast, plus the complexity of colder propellant handling. For a single cargo lander that must sit and wait, the hypergolic system's storability and dead-simple restart may well be worth the extra 339 kg. For a reusable or refuelable lander, or one in a methalox-based architecture like Starship's (§17.6), the calculus flips and methalox wins. There is no context-free answer — only the trade, laid out honestly. That is the whole discipline of propulsion selection.

Discussion Questions

  1. We eliminated solid motors in one sentence. Restate the physical reason, and explain why it applies to every landing mission, not just this one.
  2. The engine must throttle to ~40% to hover at touchdown. Trace why the hover thrust falls during descent, and what would go wrong with an engine that could not throttle.
  3. Methalox saves ~15% of propellant mass but adds cryogenic complexity. For which of the four mission tracks (A comsat, B lander, C Mars orbiter, D asteroid) would you most and least favor cryogenics, and why?
  4. We chose a pressure-fed cycle over a pumped one. What did that cost us in performance, and why is that cost acceptable here but not on a launch first stage?

Your Turn: Extensions

  • Option A (design). Redo Phases 3–4 for a heavier lander: $m_{\text{dry}} = 2{,}000\ \text{kg}$, $m_{\text{cargo}} = 2{,}000\ \text{kg}$. Does the propellant fraction stay the same? Does the required hover throttle setting change? Explain both results physically.
  • Option B (computation). Write size_lander(m_dry, m_cargo, dv, isp) that returns the propellant mass and loaded mass, and hover_throttle(m_final, m_start, f_max, g_body) that returns the touchdown throttle fraction. Reproduce this study's 2,315 kg and 40%. (Do not run it — hand-trace and add # Expected output:.)
  • Option C (your mission). Apply the four selection questions to your mission's main propulsive stage, pick a propellant and cycle, and size the propellant with the rocket equation. Record the choice and the number in your MDR.

Key Takeaways

  1. Selection precedes sizing. The mission's need for throttle, restart, and storability chose a pressure-fed hypergolic system before any number was computed — and ruled out solids outright.
  2. The rocket equation sizes the propellant. A 2 km/s descent at $I_{sp} = 311\ \text{s}$ needs a mass ratio of 1.93, i.e. ~2,315 kg of propellant for a 2,500 kg landed mass (~48% propellant).
  3. Landing is a throttle problem, not a thrust problem. Because the lander lightens as it burns, the engine must throttle to ~40% (and below) to hover — the requirement that makes deep throttling, not peak $I_{sp}$, the design driver.
  4. The best propellant is mission-dependent. Methalox would save ~15% propellant but adds cryogenic risk; the honest output of §17.1 is a trade, not a winner.