Rotating Detonation Engine: A Shock Wave Chasing Its Own Tail Thousands of Times a Second

What It Is: A Detonation Trapped in a Ring

Rocket and jet engines in service burn propellant in a deflagration: a subsonic flame across which pressure dips slightly, so pumps, compressors or pressurized tanks must supply all of the pressure in advance. A detonation is a different kind of combustion. It is a shock wave moving at roughly Mach 5–7 relative to the fresh gas, with combustion locked right behind it. The shock heats the mixture so hard that it ignites almost instantly, and the energy released keeps pushing the shock forward.

A rotating detonation engine (RDE, or RDRE when built as a rocket) traps that wave in a loop. The combustor is two coaxial cylinders, an outer wall and a solid centerbody, separated by a narrow annular gap that is closed at the injector end and open at the exhaust end. NASA's 2022 RDRE used an annular gap 8.4 mm (0.33 in) around a 142 mm (5.59 in) centerbody. Propellant sprays in through small injector orifices in the closed end; exhaust leaves the open end, through a converging throat or over a centerbody extended into a short aerospike-like plug. The word rotating describes only the wave. No hardware spins, and the combustor has no valves, pistons or turbines.

How It Works, Step by Step

• 1. Fill. Fuel and oxidizer spray axially through small injector orifices into the annulus and mix.
• 2. Ignite. An igniter, often a small predetonator tube that fires a detonation into the channel, starts a front running circumferentially around the ring. The wave then sustains itself while propellant flows.
• 3. Consume. Ahead of the front lies a triangular layer of fresh mixture that has refilled since the wave last passed. It is tallest just ahead of the front, where it has had almost the whole interval since the previous front passed to refill, and tapers to nothing just behind it. The leading shock compresses this layer. In an ideal fuel–air detonation the pressure at the end of the reaction zone (the Chapman-Jouguet, or CJ, state) is ~15–20× the starting pressure, and the spike just behind the shock briefly reaches roughly twice that. The heat released keeps the shock driving.
• 4. Stall and expand. For an instant the gas behind the front is at higher pressure than the propellant manifolds, so the injectors stall and may briefly backflow. The burned gas expands axially toward the open end. A weaker oblique shock trails from the top of the front into exhaust left over from the previous lap, and a slip line separates the new products from the old.
• 5. Recover and repeat. As pressure behind the front decays, the injectors recover and the fresh layer rebuilds before the wave comes around again. Averaged over any useful interval, the kilohertz pulses give nearly steady thrust.

The number of fronts organizes itself, generally rising with mass flow. NASA's 2022 engine often ran with 2–5 co-rotating fronts, and their direction of travel sometimes flipped.

The Governing Numbers, Worked Through

Lap rate. A front travelling at speed U around a channel of mean diameter D completes f = U/(πD) laps per second. NASA measured wave speeds of ~1.2–1.8 km/s (4,000–6,000 ft/s) in its 2022 RDRE. The mid-gap diameter is about 0.150 m (the 142 mm centerbody plus one 8.4 mm gap), so the circumference is π × 0.150 ≈ 0.47 m. A wave at 1.5 km/s therefore laps 1,500 ÷ 0.47 ≈ 3,200 times a second, one at 1.8 km/s about 3,830 times, and one at 1.2 km/s about 2,550 times. NASA's quoted per-wave frequencies of ~2,800–3,850 laps per second, from waves running ~1.3–1.8 km/s, match that span, with one lap taking about 0.3 ms. A fixed sensor sees n times that rate: four fronts at 3,200 laps per second pass it ~12,800 times a second.

Wave speed and pressure. The ideal CJ detonation speed is set by the mixture's energy content: ≈ 1,970 m/s for stoichiometric hydrogen–air and ~2.4 km/s for methane–oxygen. Momentum conservation across a strong detonation gives the CJ pressure approximately as p_CJ ≈ ρ₀U²/(γ + 1). For hydrogen–air at 1 atm and 25 °C, the density is ρ₀ ≈ 0.86 kg/m³, and the hot products have γ ≈ 1.16–1.2. That gives p_CJ ≈ 0.86 × 1,970² ÷ 2.2 ≈ 1.5 MPa, about 15 times the 0.101 MPa starting pressure and the low end of the ~15–20× range. Real RDE waves run slower: NASA's 1.2–1.8 km/s, measured burning methane with oxygen (ideal CJ ~2.4 km/s), is only about half to three-quarters of that ideal and below even the hydrogen–air value, largely because fill layers are imperfectly mixed, some mixture burns before the front arrives, and the front leaks strength sideways into the product gas above the layer.

Fill height. Fronts arrive every πD/(nU) seconds, and during that time the fresh layer grows at the axial fill velocity u, so h ≈ u·πD/(nU). With four fronts at 1.5 km/s on the 0.47 m circumference, a front arrives every ~78 µs. At an illustrative fill velocity of 100 m/s, the layer is therefore ~8 mm tall. Bykovskii's empirical rule says a stable front needs a layer about h* ≈ (12 ± 5) detonation cell widths tall. Cell width λ, the diamond pattern that the wave's triple-shock points etch on a sooted foil, shrinks roughly in inverse proportion to pressure. Stoichiometric hydrogen–air at 1 atm has λ ≈ 1 cm and so needs a layer of roughly 7–17 cm. Oxygen-based propellants at several MPa have cells far smaller than a millimetre, which is how a rocket RDE fits several fronts into a short, narrow channel.

Pressure-Gain Combustion: The Prize and the Fine Print

A conventional combustor loses a little stagnation pressure as it burns. Adding heat to a moving gas at nearly constant pressure (the Brayton idealization) always costs some total pressure, and liquid-rocket injectors add a deliberate pressure drop, often around 15–20% of chamber pressure, to keep combustion stable. A detonation instead approximates constant-volume heat addition, idealized as the Humphrey or Fickett–Jacobs cycle. The burned gas can therefore leave at a higher mean stagnation pressure than the mixture had when it entered the combustor. Less entropy is generated for the same heat release, which means higher thermal efficiency and, for a rocket, potentially higher specific impulse (Isp).

Cycle analyses show the largest gains where incoming pressure is low, as in gas turbines and ramjets; rocket chambers already run at several MPa, which shrinks the ideal advantage. Astrobotic claims specific-impulse gains of up to 15%. Hardware is more sobering: JAXA's 2021 flight measured an Isp close to the constant-pressure ideal rather than clearly above it. To compare engines fairly, researchers use equivalent available pressure (EAP). EAP is the steady total pressure that, with the same mass flow and total temperature, would produce the measured thrust when ideally expanded. Net pressure gain means EAP above the supply-plenum pressure, a bar that injector losses, slow waves and unsteady exhaust have made hard to clear.

Real Hardware and How It Is Tested

NASA's Marshall Space Flight Center worked with IN Space LLC and Purdue University on its RDRE. It was printed by laser powder bed fusion from GRCop-42 and GRCop-84, NASA-developed copper–chromium–niobium alloys that keep their strength when hot while carrying heat away from walls scoured by kilohertz shock loading. In summer 2022 it produced 4,171 lbf (~18.6 kN) at 622 psia (~4.3 MPa) chamber pressure. In fall 2023 the program logged a 251 s burn above 5,800 lbf (~25.8 kN).

Because the flow repeats every fraction of a millisecond, testing leans on fast diagnostics:

• High-speed pressure transducers are mounted at the outer wall or in the propellant manifolds, usually recessed to survive the heat, and sampled at 100 kHz or faster. A Fourier transform gives the dominant frequency. Dividing by the wave count gives the lap rate, and multiplying by the circumference gives the wave speed.
• High-speed video looking up the annulus from the exhaust end, at tens of thousands of frames per second, counts fronts and their direction. Unwrapping the ring's brightness into a time–angle map shows each wave as a diagonal streak whose slope is its speed.
• Capillary-tube attenuated pressure (CTAP) ports damp out the kilohertz swings to read a time-averaged chamber pressure.
• Thrust-stand load cells, combined with metered propellant flow, give thrust, Isp and EAP.
• Detonation-tube experiments, including soot-foil records, supply the cell width λ and CJ behavior used to size channels with Bykovskii's rule.

History: From a Spinning Wave to Spaceflight

• 1926: Campbell and Woodhead discover spinning detonation, a reaction front that spirals down a tube near a mixture's detonation limit.
• 1959–60: Bogdan Voitsekhovskii in Novosibirsk records a detonation circling continuously in a ring-shaped channel fed with acetylene–oxygen, the first rotating detonation.
• 1960s onward: J. A. Nicholls and colleagues at the University of Michigan test the idea as a rocket motor but cannot sustain the wave for long. Over the following decades, Fedor Bykovskii's group in Novosibirsk maps continuous spin detonation across many fuels and distills the (12 ± 5) cell-width rule.
• 2000s–2010s: Better diagnostics, simulation and additive manufacturing drive a worldwide revival.
• 27 July 2021: JAXA's S-520-31 sounding rocket fires a methane–oxygen RDE, developed with Nagoya and Keio universities, in space: 518 N for 6 s, the first RDE operated in space.
• 2022–2023: NASA Marshall's printed RDRE makes 4,171 lbf in summer 2022, then a 251 s burn above 5,800 lbf in fall 2023.
• 14 May 2025: Houston-based Venus Aerospace flight-tests its RDRE on a small vehicle.
• April 2026: Astrobotic's Chakram engine completes a 300 s burn.

Failure Modes, Misconceptions and Look-Alikes

• Dropping to deflagration. If the fill layer is too short, poorly mixed or off-mixture, the shock decouples from the reaction and the chamber falls back to ordinary burning with no pressure gain.
• Counter-rotating and clapping modes. Fronts travelling in opposite directions collide and pass through each other, which weakens the waves and swings loads harder. Wave count or direction can switch mid-run.
• Parasitic combustion and contact burning. Fresh mixture burns early as a slow flame, either ahead of the front (parasitic) or where it touches hot products from the previous lap (contact burning). That lowers wave speed below CJ and wastes the gain.
• Injector backflow and flashback. Pressure behind each front can briefly exceed manifold pressure and push hot gas into the injectors. Stiffer injectors with a larger pressure drop resist this but spend the very pressure gain being sought.
• Heat flux and fatigue. Fronts scrub the walls thousands of times a second, concentrating heat flux near the injector face, while kilohertz pressure cycling drives high-cycle fatigue in walls, centerbody and injectors.

Misconceptions. Nothing spins: the name refers to the wave, not a rotor. Nor is it a chain of separate explosions: the wave is continuous, and while local peaks are high, the time-averaged chamber pressure is moderate. Pressure gain is not free energy. It is a lower-entropy way of releasing the same chemical energy, and losses can easily erase it.

Look-alikes. A pulse detonation engine (PDE) fills a tube, detonates it, blows it down and refills at ~20–100 Hz per tube. It needs valves or timed injection and must start a new detonation every cycle, while an RDE ignites once and runs continuously at thousands of hertz. A tangential combustion instability in a conventional rocket, the kind the F-1 program fought in the 1960s, is also a pressure wave spinning around the chamber. But it is an unwanted acoustic mode that can wreck injectors, not a deliberate detonation. Engine knock is uncontrolled end-gas autoignition, only occasionally a true detonation, that damages piston engines.

Rotating detonation vs pulse detonation vs conventional rocket combustion (representative values)

Attribute	Rotating detonation engine	Pulse detonation engine	Conventional rocket combustor
Combustion mode	Continuous detonation circling an annulus	Intermittent detonation filling a tube	Steady deflagration (subsonic flame)
Cycle rate	~2,800–3,850 laps per second per wave (NASA 2022 RDRE)	~20–100 Hz per tube	No cycle; continuous burning
Valves and ignition	No valves; ignited once, then self-sustaining	Valves or timed injection; detonation re-initiated every cycle	No valves; ignited once
Pressure across combustion	Jumps ~15–20× at the front (ideal, fuel–air); net pressure gain is the goal	Jumps ~15–20× (ideal, fuel–air) in each pulse	Dips slightly
Wave or flame speed	~1.2–1.8 km/s measured (NASA 2022); ideal CJ ≈ 1,970 m/s for hydrogen–air	Close to CJ, ~2 km/s class for fuel–air	Subsonic flame, far below the local sound speed
Flight status	First in space: JAXA S-520-31, 27 July 2021 (518 N for 6 s)	Crewed demo: modified Long-EZ Borealis, 2008	Mature; the basis of every operational rocket engine