Case Study: Choosing and Sizing the Propellant for a Mars Ascent Vehicle

"The cheapest kilogram of propellant is the one you never had to launch from Earth."

Executive Summary

In the first case study we took three finished engines apart. Here we do the harder thing: we make a propellant decision under real constraints, and then size the vehicle it implies. The mission is a Mars Ascent Vehicle (MAV) — the small rocket that lifts a sample (or, one day, a crew) from the Martian surface back to Mars orbit. It is the single most unforgiving element of any Mars return: it must sit on another planet for months or years and then, with no possibility of repair, ignite and fly on the first attempt. The classic answer is storable hypergolics, chosen for exactly that reliability. The disruptive answer is methane and oxygen manufactured on Mars from the local atmosphere. We will weigh the two with this chapter's chemistry, size each with the rocket equation, and discover that the winning argument is not specific impulse at all — it is the rocket equation applied to the whole journey.

Skills applied

• Turning propellant properties (storability, restart, $I_{sp}$, manufacturability) into a mission decision (§18.3–18.6).
• Reconstructing $I_{sp}$ from chamber conditions with the exhaust-velocity formula (§18.2).
• Inverting the rocket equation to size a stage (§18.5 method from Chapter 3).
• Tracing an in-situ-resource-utilization advantage through the rocket equation of the outbound legs.

Background

The requirement

• Payload: $m_L = 500\ \text{kg}$ (a sample-return capsule and its orbit-insertion kit) to low Mars orbit.
• Delta-v: Mars surface to low Mars orbit costs about $\Delta v = 4.0\ \text{km/s}$ including gravity and drag losses (Mars's thin atmosphere and low gravity make this far cheaper than Earth's $9.4\ \text{km/s}$; Tier 2).
• The hard constraint: the vehicle must survive an unattended surface stay and ignite reliably, once, with no repair. Theme 2 in its starkest form.

The two candidate propellants

The hypergolic looks like the safe pick: no cryogenics to keep, no igniter to fail, decades of flight heritage. Methalox looks harder: two cryogens to keep cold on Mars for a year, and an ignition system. But methalox has a card that changes the entire calculation — you can make it there.

Phase 1: Reconstruct the two specific impulses

We verify the table's $I_{sp}$ values with the chapter's formula rather than trusting them. For the methalox engine ($\gamma = 1.20$, $T_c \approx 3{,}500\ \text{K}$, $\mathcal{M} \approx 0.020\ \text{kg/mol}$, expanding from $p_c = 60\ \text{bar}$ to $p_e = 0.05\ \text{bar}$):

$$ v_e = \sqrt{\frac{2(1.2)}{0.2}\cdot\frac{8.314 \times 3500}{0.020}\left[1 - \left(\tfrac{0.05}{60}\right)^{0.1667}\right]} = \sqrt{1.746\times10^{7} \times 0.693} \approx 3{,}479\ \text{m/s}, $$

so $I_{sp} = 3479 / 9.81 \approx 355\ \text{s}$. The same method applied to the hypergolic (cooler, heavier exhaust, and a lower pressure-fed chamber) gives about $320\ \text{s}$. Methane's lighter exhaust buys roughly $35$ seconds — worth having, but as we will see, not the decisive factor.

Phase 2: Size each vehicle with the rocket equation

Using the stage-sizing formula from Chapter 3, $m_{\text{stage}} = m_{\text{above}}\,(R-1)/(1 - R\varepsilon)$, with a structural coefficient $\varepsilon = 0.10$ and $m_{\text{above}} = m_L = 500\ \text{kg}$. First the mass ratios, $R = e^{\Delta v/v_e}$:

$$ R_{\text{hyp}} = e^{4000/3139} = e^{1.274} = 3.58, \qquad R_{\text{methalox}} = e^{4000/3482} = e^{1.149} = 3.16. $$

Then the stage masses:

$$ m_{\text{stage,hyp}} = 500 \cdot \frac{3.58 - 1}{1 - 3.58(0.10)} = 500 \cdot \frac{2.58}{0.642} = 2{,}010\ \text{kg}, $$ $$ m_{\text{stage,methalox}} = 500 \cdot \frac{3.16 - 1}{1 - 3.16(0.10)} = 500 \cdot \frac{2.16}{0.684} = 1{,}575\ \text{kg}. $$

The methalox vehicle is lighter at liftoff (higher $I_{sp}$, so a smaller mass ratio). But look at the last column, which is the one that matters: because the methalox propellant is manufactured on Mars, only the empty vehicle and its payload — about $660\ \text{kg}$ — must be delivered from Earth. The hypergolic vehicle must arrive fully fueled, so all $2{,}510\ \text{kg}$ crosses interplanetary space and lands on Mars.

Phase 3: The rocket-equation cascade

Now the insight that makes ISRU revolutionary. Every kilogram landed on Mars is the survivor of a brutal chain of rocket equations: launch from Earth, trans-Mars injection, and a powered/aero descent to the surface. As a rough figure (Tier 3, illustrative), delivering one kilogram to the Martian surface costs on the order of $5$–$10\ \text{kg}$ in Earth-launch mass. Take the middle, $\sim 7$:

$$ \Delta(\text{Earth-launch mass}) \approx 7 \times \left(2{,}510 - 660\right)\ \text{kg} = 7 \times 1{,}850 \approx 13{,}000\ \text{kg}. $$

Not having to ship the ascent propellant from Earth saves on the order of thirteen tonnes of mass off the Earth-launch requirement — vastly more than the $35$ seconds of $I_{sp}$ ever could. The methane advantage that decides the mission is not the number in the $I_{sp}$ column; it is that the propellant column can be filled on arrival, cutting the outbound rocket-equation chain off near its root.

💡 Intuition: The rocket equation punishes propellant you carry before you need it exponentially harder than propellant you make where you need it. Hypergolics ask you to haul the ascent fuel across the entire solar system and soft-land it; ISRU lets you arrive nearly empty and fill up from the air. This is the same logic as staging — stop carrying mass you do not yet need — pushed to its planetary limit.

Phase 4: The chemistry of making propellant on Mars

The methalox case rests on a chemical claim, so we should be able to write it down. Mars's atmosphere is ~95% carbon dioxide, and water ice is accessible in the subsurface. Split the water for hydrogen (and oxygen) by electrolysis, then combine hydrogen with carbon dioxide in the Sabatier reaction:

$$ \text{CO}_2 + 4\,\text{H}_2 \;\rightarrow\; \text{CH}_4 + 2\,\text{H}_2\text{O}, $$

which yields methane and water; the water is recycled back through electrolysis, and additional electrolysis of water supplies the liquid oxygen. The net inputs are Martian CO$_2$, Martian water, and electrical power; the outputs are exactly the LOX and LCH$_4$ the ascent engine needs. This is why methane, almost alone among high-performance fuels, closes the Mars-return problem — its feedstocks are lying on the ground and floating in the air.

🔧 Engineering Reality: what the clean formula hides. ISRU is not free. The Sabatier plant, its electrolyzers, and above all its power source (a fission reactor or acres of arrays) are mass and complexity that must be landed, deployed, and run unattended for a year before the crew or the return depends on it — and it must keep two cryogens cold on a planet with dust storms. That is a monstrous reliability demand (Theme 2). The propellant is cheaper; the machine that makes it is not. A real trade study weighs the ~13 tonnes of Earth-launch mass saved against the mass, power, and risk of the plant — which is precisely the kind of analysis your Mission Design Review teaches you to run.

Discussion Questions

1. Methalox has only ~35 s more $I_{sp}$ than the hypergolic, yet it wins the mission decisively. In one sentence, where does the real advantage come from?
2. Why does the "mass that must arrive from Earth" column matter more than the "liftoff mass" column for a Mars mission?
3. The hypergolic needs no cryogenic keep-alive and no igniter. Under what mission assumptions would those reliability advantages outweigh the ISRU mass saving?
4. The Sabatier reaction consumes hydrogen. If that hydrogen must be shipped from Earth (rather than made from Martian water), how does the ISRU advantage change?

Your Turn: Extensions

• Option A (design). Redo Phase 2 for a crewed MAV with $m_L = 4{,}000\ \text{kg}$. Does the Earth-delivered mass saving scale linearly with payload? Which propellant's advantage grows faster?
• Option B (computation). Write mav_sizing(mL, dv, isp, eps) returning propellant, structure, and liftoff mass, and a wrapper that reports the Earth-delivered mass for the ISRU and non-ISRU cases. Reproduce the table. Do not run it — hand-trace with # Expected output:.
• Option C (your mission). If your mission (Track B/C) involves a landing and return, add an ISRU-versus- storable propellant trade to your MDR: state the delta-v, size both options, and record the Earth-delivered mass for each.

Key Takeaways

1. A propellant decision is a whole-mission decision. Sizing only the ascent stage favors the higher-$I_{sp}$ methalox modestly; sizing the journey favors it overwhelmingly, because its propellant need not be launched from Earth.
2. ISRU attacks the rocket equation at its root. Not carrying ~1,850 kg of ascent propellant from Earth saves on the order of ten times that in Earth-launch mass — the exponential chain working in your favor.
3. Methane is the fuel that closes Mars return, because its feedstocks (CO$_2$, water) are available on Mars via the Sabatier reaction — a chemical fact, not a preference.
4. The cheaper propellant demands a harder machine. ISRU trades propellant mass for plant mass, power, and a severe unattended-reliability requirement — exactly the trade a Mission Design Review exists to make.