Thirteen lessons, three applications. Can you design a rotating detonation engine that runs — and keeps running?
There's no multiple choice here. You get a mission, an envelope and a set of tests, and every coupling in the course pulling against the others.
How an RDE designer thinks
RDE design starts from a single number: the cell width λ of the mixture at the conditions in the chamber. Almost everything else follows from it, in a chain you now know link by link:
- What mixture, at what pressure? Fuel, oxidizer, equivalence ratio and chamber pressure set the CJ state and the cell size (Lessons 3–5). Smaller cells make every other constraint easier.
- Can a wave survive? The fill layer each wave sees must exceed ; the mass flux, the annulus size and the wave speed decide how tall it gets and how many waves the engine runs (Lessons 9 and 11).
- Does the geometry fit the wave? Channel width above about , chamber length above about twice the fill height (Lesson 9).
- Can the injectors keep up? Quick recovery after each wave, no flashback into the plenum, mixing complete in the microseconds before the wave returns — each bought with injector stiffness (Lesson 10).
- Will it start, and will it survive? A spark needs room for DDT, otherwise use a pre-detonator (Lesson 6); the walls need cooling to match the heat flux (Lesson 13).
- Is it worth it? Pressure recovery, thrust or Isp, after every loss is paid (Lesson 12) — and, for a gas turbine, an exhaust the turbine can live with (Lesson 13).
The studio
Choose an application, then shape your engine. The end-on view shows your annulus inside the vehicle's envelope, with the waves your engine would choose to run; the section shows the chamber, its fill layer and the critical height . Each failing test explains why and links to the lesson that holds the fix. Your designs are saved in this browser.
Design reviews
Stuck? These reviews explain one route to a running engine for each mission. Try on your own first: the struggle is where the understanding forms.
Going deeper
Rocket thrust chamber: plenty of margin, if you cool it
With oxygen, cell sizes at tens of atmospheres are a fraction of a millimetre, so the detonation itself is easy. The default design fails elsewhere: its heat-sink walls overheat long before 60 seconds, its plain fuel jets don't mix in the few tens of microseconds between waves, and it doesn't flow enough propellant for 20 kN.
Switch to film or regenerative cooling; use impinging injection so the propellants mix fast; and raise the mass flow to around 6–8 kg/s. Keep the injector stiffness moderate (1.3–1.6): a stiffer injector recovers faster but costs Isp against the conventional chamber. Both hydrogen and methane work, over a range of mixture ratios. Notice how little the detonation does for the Isp: the compactness is the prize.
Going deeper
Gas-turbine combustor: hot enough, but not too hot
Two constraints fight. The turbine accepts at most 1800 K, which with 700 K air means a very lean overall mixture — but lean mixtures have huge cells. The way out is the core fraction: send only part of the air (around half) through the RDE, run that core at a detonable equivalence ratio, and dilute the products with the remaining air afterwards, as conventional combustors do.
Then the cells: with methane–air, even at 15 atm, the critical fill height is tens of centimetres and the envelope can't hold it. Hydrogen makes it work comfortably (ethylene only just fits, in a narrow corner of the design space). A compact annulus with a high mass flux gives two or more waves — which also keeps the turbine-inlet fluctuations within ±8% — and a soft injector (stiffness around 1.3) with impinging injection keeps the studio's pressure recovery above a conventional combustor's. That is exactly the industry's current conclusion: hydrogen-fuelled RDE gas turbines are the near-term prospect.
Treat that last green light as a target, not a promise. The studio's pressure-recovery gauge is its most optimistic: the course's own solver (Lesson 12) loses about half the supply pressure through standard injectors, and only the softest injectors just break even. Real pressure gain is the test no RDE gas turbine has yet passed.
Going deeper
Mach 3 ramjet: little pressure, little room
At 4 atm at most, and less after the injectors, air mixtures have cells of a centimetre or more. With propane or methane, the critical fill height is longer than the chamber allowed and wider than the channel can be. Ethylene only just fits, with the widest channel and nearly the full chamber length. Hydrogen gets there: a moderate plenum pressure (around 3 atm), a soft injector, a wide channel (about 30 mm), a chamber close to the full 40 cm, and enough air flow for 8 kN (around 9 kg/s). One more trap: a minute-long flight outlasts heat-sink walls, so switch to film cooling.
Notice the payoff on the gauges: with almost no compression before the combustor, the detonation's ideal pressure gain is at its largest, so the ramjet is where the RDE's thermodynamic advantage shows most clearly — exactly what Lesson 1's cycle analysis predicted.
The whole picture
Follow one last parcel of fresh mixture through the engine, and notice that you now know why each thing happens.
It waits in a plenum, separated from the chamber by an injector whose stiffness is a pressure tax paid to keep the wave out (Lesson 10). The passing wave blocks the injector, then lets it recover; the parcel enters and must mix in microseconds. It rides up in a fill layer that has to be a dozen cells tall (Lessons 5 and 9), and the number of waves sharing the fuel is the engine's own choice (Lesson 11). Then the wave arrives: a shock (Lesson 2) jumps it to the von Neumann spike, an induction zone holds it for a microsecond (Lesson 4), and it burns, pushing the shock at the Chapman–Jouguet speed (Lesson 3), in a front carved into cells by triple points (Lesson 5). The products are flung along the annulus, pass an oblique shock and a slip line, and expand to the exit (Lesson 9). Whether the engine gained pressure — the reason it exists (Lesson 1) — depends on how much of the fuel burned in the wave, how fast the wave ran and how much the injectors charged for the privilege (Lesson 12).
Every one of these pulls against the others. That isn't a flaw in the technology. It is what engineering at the frontier looks like, and you have just done it yourself.
- A detonation is a shock and a flame locked together. It runs at the CJ speed, set by thermodynamics, and adds heat with less entropy than any steady flame.
- The cell size is the ruler. Fill heights, channel widths, critical diameters and initiation energies all scale with λ — and λ shrinks with pressure.
- The wave is its own valve. Injectors must survive it, recover from it and refill behind it, and the stiffness they need is paid out of the pressure gain.
- The engine chooses its waves. Mass flow, mixing and history decide the mode, not the designer.
- The prize is real but conditional. Pressure gain survives only if the losses are smaller than the detonation's ideal advantage.
If you can now look at a ring of soot-streaked metal and see the waves that ran inside it — and the price each design choice paid somewhere else — the course has done its job.