Rotary Engine Simulator
Wankel Engine in 2D & 3D — Animate • Learn • Practice • Quiz
Display Controls
Drag the slider or press ↑/↓. The throttle sets the intake pressure between the idle-air pressure (where the engine just carries its idle load) and the preset’s own value, so a turbo keeps its boost. Shaft speed follows a stated spool model, I·dω/dt = Tbrake − c·ω² − b·ω, between idle and the rev limiter. The sound is synthesised at the firing frequency, rpm × rotors / 60 — one firing per rotor per shaft revolution.
⚙ Engine geometry, breathing & port timing
Port timings are given in degrees of the eccentric shaft. IPO is after TDC (negative = before), IPC after BDC, EPO before BDC and EPC after TDC. Overlap = EPC − IPO. They move the ports on the drawing and the colours of the gas; the P–V cycle is the ideal air-standard cycle, closed at TDC and BDC.
Σ Live equations — values substituted from the current engine
📋 Cycle state points — P, V and T at states 1 to 4
◯ Trochoid geometry — K factor, gears, seals and the rotor recess
💡 What-if coach — insights from the current operating point
1 Overview
The Rotary Engine Simulator runs a Wankel engine: a three-sided rotor turning in an epitrochoid housing on an eccentric shaft. The housing, the rotor flank (the exact inner envelope of the housing), the apex seals, the 3 : 2 phasing gears, the spark plugs and the ports are all drawn from the engine’s own eccentricity e, generating radius R and rotor width b, so a change to any of them changes the picture and the numbers together.
Each of the rotor’s three faces forms a working chamber labelled A, B and C. Every chamber runs the air-standard Otto cycle once per turn of the rotor — three turns of the eccentric shaft — and the simulator reports the chamber state, the cycle performance (IMEP, power, torque, BSFC, efficiencies) and the geometry (displacement, K factor, apex seal lean, gear sizes).
2 Configuring the Engine
- Preset — six real Mazda rotaries: the 13B-REW twin-turbo (RX-7 FD), the Renesis 13B-MSP (RX-8), the 12A (early RX-7), the 20B three-rotor (Eunos Cosmo), the R26B four-rotor that won Le Mans in the 787B, and the 8C single rotor used as a range extender in the MX-30 R-EV. Changing any value switches the preset to Custom.
- Rotors (the pills above the canvas) set the number of rotors on the shaft, 1 to 4. Rotors are phased 360/n degrees apart; the Torque diagram shows the effect on smoothness.
- Units — SI or Imperial converts every readout, every diagram axis and every input box (mm ↔ in, kPa ↔ psi, K ↔ °F, kW ↔ hp, N·m ↔ lb·ft, cm³ ↔ in³, kJ/kg ↔ BTU/lb, g/kWh ↔ lb/hp·h). The choice is remembered across the site.
- Engine speed is the real eccentric-shaft rpm and drives power and fuel flow; Animation speed only changes how fast you watch.
- Compression ratio, heat input qin and intake pressure (throttle or boost) set the operating point. Every slider has a number box and −/+ steppers; hold a stepper to repeat.
- Engine geometry, breathing & port timing holds e, R, b, air–fuel ratio, mechanical efficiency, exhaust back-pressure, intake temperature and the four port timings. The compression ratio is limited by the geometry: with the rotor on the true envelope the chamber can never be smaller than the gap at the waist, so the highest ratio the trochoid allows is shown and the slider stops there. Below it, the rotor recess grows to give the ratio you set.
3 Running the Engine
The engine runs as soon as the page opens (unless your system asks for reduced motion). Play/Pause stops and starts it, Step advances chamber A by one stroke (270° of shaft), and the arrow keys nudge the shaft by 5°. When the engine is paused you can also drag the rotor round with the mouse or a finger.
The gas in each chamber is coloured by what it is doing: fresh charge blue, compressed charge violet, the flame orange-yellow just after the plugs fire, expanding gas amber and exhaust grey. The ports glow while they are open. A dotted circle shows the path of the rotor centre — the eccentric — and the shaft mark turns three times for each turn of the rotor.
The first readout row is the instantaneous state of chamber A and the gas torque on the shaft at this instant; the second is the cycle result at the operating point.
4 The Four Diagrams
- P–V — pressure against chamber volume, with the four state points numbered and a marker for each of the three chambers. The area of the loop is the net work of one chamber per cycle.
- T–s — temperature against entropy: vertical isentropes and constant-volume curves.
- Phasing — the volume of chambers A, B and C over 1080° of shaft (one full cycle), with the intake and exhaust port-open periods drawn under each. It shows that each stroke lasts 270° and that the three chambers are 360° apart.
- Torque — the gas torque on the eccentric shaft over one revolution, T = Σ(p − p0)·dV/dφ, for one rotor and for the whole engine, with the mean drawn as a line. Its mean times 2π equals the net work per revolution.
🎓 Explain walks through one turn of the rotor in eight steps, turning the engine to each position and naming what is happening. Rev it adds a throttle and engine sound synthesised at the firing frequency.
2D section and 3D, in the View strip above the canvas, switch views. The page always opens on the 2D section, on a phone and on a computer; press 3D (or open a ?view=3d link) for the 3D engine. In 3D you can turn the engine (drag), zoom (pinch or Ctrl + scroll), cut it open, lift the front housing off, and click any part for a card that says what it does. Every part moves by the same rotor kinematics as the 2D drawing.
Right-click (long-press on touch) the 2D canvas for a menu: copy the chamber state, copy a performance summary, export CSV or PNG, or reset the view.
5 Calculations, Learning Panels and Export
The calculator icon opens a step-by-step derivation for the operating point on screen: displacement, minimum volume and rotor recess, trapped charge, the four state points, net work, IMEP, power, torque and fuel figures, in classical notation. The learning panels under the readouts give the live equations, a state-point table, the trochoid geometry and a what-if coach.
Export CSV writes the setup, the performance, the state points and a 3°-resolution sweep of chamber volume, pressure, temperature and shaft torque. Export PNG saves the canvas (the 3D view when 3D is showing).
6 Explore, Practice and Quiz
Explore has sixteen cards in four groups — Fundamentals, Geometry, Thermodynamics, and Design & seals — several with a small drawing made from the same geometry. Practice generates twelve kinds of problem (displacement, equivalent displacement, apex seal lean, rotor speed, power strokes, firing frequency, Otto efficiency, minimum volume, indicated power, torque, gear size, stroke time); they are worked in SI and graded to the precision the answer is printed to. Quiz draws six questions from a pool of twenty, shuffling the questions and the order of the options.
7 What the Model Assumes
The housing is the true epitrochoid with no parallel offset and the rotor flank is its exact envelope; real engines offset the housing by the apex seal tip radius and cut the rotor slightly inside it. Each chamber runs the cold air-standard Otto cycle (γ = 1.4, heat added instantly at TDC, no wall heat transfer, no seal leakage). Intake is at the set pressure and temperature; the exhaust and intake strokes enclose the pumping loop. Real rotaries burn slower and lose more heat than this, so their efficiency is lower; the coach says so.
How a Rotary Engine Works — Interactive Wankel Engine Simulator
A rotary engine, or Wankel engine, makes power without pistons, connecting rods or valves. A rounded triangular rotor orbits inside a housing shaped like a fat figure eight — an epitrochoid — riding on an offset lobe of the output shaft, the eccentric shaft. The gaps between the rotor’s three faces and the housing are three working chambers. As the rotor turns, each chamber grows and shrinks twice, and in doing so it draws in a charge, compresses it, burns it and pushes the exhaust out: the four strokes of an ordinary petrol engine, done in different places round the housing rather than one after another in a cylinder. This rotary engine simulator draws that mechanism from its real geometry, in a 2D section and as a 3D model you can turn and cut open, and runs the thermodynamic cycle in every chamber at once.
Rotary Engine Parts
- Rotor housing — the epitrochoid bore, x = e cos 3α + R cos α, y = e sin 3α + R sin α, with a hard chrome or ceramic running surface and water passages round it. Its narrow waist (the minor axis) is where each chamber is smallest: top dead centre.
- Rotor — three curved flanks meeting at three apexes. Each flank carries a recess that sets the compression ratio. Inside, an internal gear and the rotor bearing.
- Eccentric shaft — the output shaft. Its lobe, offset by the eccentricity e, carries the rotor, so the rotor centre travels round a circle of radius e.
- Phasing gears — the rotor’s internal gear rolling on a fixed gear on the side housing, in the ratio 3 : 2 (51 and 34 teeth on a 13B). They hold the rotor’s orientation so its apexes stay on the housing, and make it turn at one third of shaft speed.
- Apex, side and corner seals — spring-loaded strips at the tips and along the sides of the rotor that keep the chambers apart.
- Side housings and ports — the flat end plates, which on most Mazda engines carry the intake ports (side ports), while the exhaust leaves through a port in the trochoid surface (a peripheral port).
- Spark plugs — usually two per rotor, leading and trailing, beside the waist on the side opposite the ports.
The Four Strokes in a Wankel Engine — 270° Each
Follow one rotor face round the housing. The rotor turns once for every three turns of the eccentric shaft, so one full cycle of a chamber takes 1080° of shaft rotation and each stroke takes 270°, one and a half times as long as in a piston engine. The three faces are 360° of shaft apart, so while one chamber takes in a charge, another is being compressed and the third is on its power stroke.
| Stroke | Shaft angle (chamber phase) | Chamber volume | Where it happens |
|---|---|---|---|
| 1. Intake | 0° → 270° | Vmin → Vmax | The face passes the intake port after the waist on the port side; the chamber grows and draws in charge |
| 2. Compression | 270° → 540° | Vmax → Vmin | Both ports covered; the charge is carried round and squeezed towards the plug-side waist |
| 3. Power | 540° → 810° | Vmin → Vmax | The plugs fire at the waist; burning gas pushes on the flank and turns the eccentric shaft |
| 4. Exhaust | 810° → 1080° | Vmax → Vmin | The leading apex uncovers the exhaust port; the shrinking chamber pushes the gas out |
Because each of the three faces fires once per rotor turn and the rotor turns once per three shaft turns, every rotor fires once per revolution of the shaft. That is the key difference from a four-stroke piston engine, whose cylinders fire once every two revolutions.
Rotary Engine Displacement — the 3√3·e·R·b Formula
With the rotor riding on the true trochoid, each chamber’s volume varies exactly sinusoidally with shaft angle, V(ψ) = Vmin + (Vs/2)(1 − cos(2ψ/3)), and the swept volume of one chamber is
Vs = 3√3 · e · R · b
The simulator checks this formula against the area it measures directly between its drawn housing and its drawn rotor, and they agree to 0.004 %. Applied to Mazda’s engines:
| Engine | e × R × b (mm) | Per chamber | Rotors | Rated displacement | K = R/e | Apex seal lean |
|---|---|---|---|---|---|---|
| 12A | 15 × 105 × 70 | 573 cm³ | 2 | 1146 cm³ | 7.00 | 25.4° |
| 13B (REW, Renesis) | 15 × 105 × 80 | 654.7 cm³ | 2 | 1309 cm³ | 7.00 | 25.4° |
| 20B-REW | 15 × 105 × 80 | 654.7 cm³ | 3 | 1964 cm³ | 7.00 | 25.4° |
| R26B (787B) | 15 × 105 × 80 | 654.7 cm³ | 4 | 2619 cm³ | 7.00 | 25.4° |
| 8C (MX-30 R-EV) | 17.5 × 120 × 76 | 829.3 cm³ | 1 | 829 cm³ | 6.86 | 25.9° |
The “rated” figure is the one Mazda quotes, one chamber per rotor. Since a rotor fires every revolution, a 1.3 L two-rotor makes as many power strokes per minute as a 2.6 L four-stroke — the readout shows this as the four-stroke equivalent — and motorsport rules have used factors of 1.5 to 2. Counting all three faces gives the total swept volume, 3 × 654.7 = 1964 cm³ per 13B rotor, but those three chambers fire over three revolutions.
The K Factor and the Apex Seals
The shape of a Wankel is fixed by one number, the trochoid constant K = R/e. A small K gives a deep waist and room for a high compression ratio, but the apex seals must lean further from the housing normal as they sweep round — up to asin(3/K), 25.4° at K = 7. A large K gives gentle seal angles but a bulky engine for its displacement. K must exceed 3, or the curve loops. With the rotor on the exact envelope, the waist leaves a minimum gap that limits the compression ratio to about 18 : 1 at K = 7; production rotors run 9 to 10 : 1 and get there with the recess in each face.
Worked Example — Renesis 13B-MSP at 8500 rpm
The Renesis preset: e = 15 mm, R = 105 mm, b = 80 mm, two rotors, compression ratio 10 : 1, intake at 100 kPa and 310 K, exhaust at 105 kPa, qin = 1350 kJ/kg, mechanical efficiency 0.80, air–fuel ratio 13.
| Quantity | Working | Result |
|---|---|---|
| Swept volume per chamber | 3√3 × 15 × 105 × 80 mm³ | 654.7 cm³ |
| Minimum volume | Vs/(r − 1) = 654.7/9 | 72.7 cm³ |
| Trapped charge | p1Vmax/RT1 = 100 kPa × 727.5 cm³ / (287 × 310) | 0.818 g |
| End of compression | T2 = 310 × 100.4; p2 = 100 × 101.4 | 779 K, 2512 kPa |
| Peak of combustion | T3 = 779 + 1350/0.7175 | 2660 K, 8581 kPa |
| Net work per chamber cycle | m cv[(T3 − T2) − (T4 − T1)] − (pexh − pman)Vs | 661.1 J |
| IMEP | 661.1 J / 654.7 cm³ | 1010 kPa |
| Indicated power | Wnet × nr × N/60 = 661.1 × 2 × 8500/60 | 187.3 kW |
| Brake power and torque | 0.80 × 187.3; T = 60P/2πN | 149.9 kW, 168 N·m |
| Air-standard efficiency | 1 − 10−0.4 | 60.2 % |
The divisor is 60, not 120: each rotor fires once per revolution. Mazda quoted about 170 kW for the Renesis at 8200 rpm, so the air-standard model, with its 0.80 mechanical efficiency, lands in the right place.
Torque on the Eccentric Shaft
Gas pressure pushes on each flank, and the eccentric shaft turns that push into torque. By virtual work the torque from one chamber is its gauge pressure times the rate at which its volume changes with shaft angle, T = (p − p0) dV/dφ, with dV/dφ = (Vs/3) sin(2ψ/3). The three chamber volumes always add up to the same total, so the atmosphere puts no net torque on the rotor. Averaged over one revolution, the torque times 2π equals the net work of one chamber cycle for each rotor: a single rotor gives one strong pulse per revolution, two rotors 180° apart give two, and the four-rotor R26B is smoother still. Switch the diagram to Torque and change the rotor count to see it.
Rotary Engine vs Piston Engine
| Wankel rotary engine | Four-stroke piston engine | |
|---|---|---|
| Moving parts in the core | Rotor(s) and eccentric shaft | Pistons, rods, crankshaft, valves, camshafts, timing drive |
| Power strokes per output revolution | 1 per rotor | 1/2 per cylinder |
| Degrees per stroke | 270° of shaft | 180° of crank |
| Gas exchange | Ports uncovered by the rotor | Poppet valves driven by cams |
| Reciprocating mass | None — smooth and free-revving | Pistons and rods; balance shafts on some layouts |
| Combustion chamber | Long, thin and moving: slow burn, high heat loss | Compact: fast burn, lower heat loss |
| Typical compression ratio | 9–10 : 1 | 10–13 : 1 (petrol) |
| Fuel consumption and emissions | Higher (hydrocarbons, oil burned for seal lubrication) | Lower |
| Power-to-weight | Very high | Moderate |
Why Mazda’s Rotary Engines Sound the Way They Do
The firing frequency of a rotary is f = N × nrotors / 60. A two-rotor 13B at 3000 rpm fires at 100 Hz — the same as a four-cylinder four-stroke at 3000 rpm — but its exhaust port opens abruptly as an apex sweeps past it, with no valve to throttle the pulse, giving the sharp, buzzing note. Engines with peripheral intake ports and large overlap idle unevenly, the famous “brap brap”. Press Rev it to hear a synthesised version and to watch the shaft speed follow the throttle.
Who Uses This Simulator?
Students of mechanical and automotive engineering meeting the Wankel in an IC engines or thermodynamics course; instructors who want to show the epitrochoid, the rotor envelope and the 3 : 2 phasing gears move together; car enthusiasts who want to see what is inside an RX-7 or RX-8; and anyone curious how a rotary engine works. Every number comes from the drawn geometry and the cycle, and the step-by-step calculations show the working.
Frequently Asked Questions
How does a rotary engine work?
A Wankel rotary engine has a three-sided rotor that orbits inside an epitrochoid housing on an eccentric shaft. Each rotor face forms a chamber with the housing whose volume grows and shrinks as the rotor turns, so every chamber goes through intake, compression, power and exhaust once per rotor turn. Ports in the housing replace valves, and the rotor turns at one third of the output shaft speed.
How do you calculate the displacement of a rotary engine?
The swept volume of one chamber is Vs = 3 x square root of 3 x e x R x b, where e is the eccentricity, R the generating radius (rotor centre to apex) and b the rotor width. For the Mazda 13B, e = 15 mm, R = 105 mm and b = 80 mm, so Vs = 654 cm3 per rotor and 1.3 L for two rotors.
How many power strokes does a rotary engine make per revolution?
One per rotor per revolution of the eccentric shaft. The rotor turns once for every three shaft turns and fires on each of its three faces, so a two-rotor engine fires twice per shaft revolution, as often as a four-cylinder four-stroke. Each stroke lasts 270 degrees of shaft rotation instead of 180.
What are apex seals and why do they wear?
Apex seals are spring-loaded strips at the three tips of the rotor that seal each chamber from the next. They slide across the housing at around 30 to 40 m/s while leaning up to asin(3e/R), about 25 degrees on a 13B, under combustion pressure and with little oil, so they wear and can chatter the housing surface.
What are the advantages and disadvantages of a Wankel engine?
A Wankel is compact, light and smooth, with few moving parts, no valves and no reciprocating masses, so it makes high power for its size and revs freely. Its long, thin moving combustion chamber loses heat and burns incompletely, and the apex seals leak and wear, so fuel consumption, oil use and emissions are higher than a piston engine's.
Explore Related Simulators
- Four Stroke Engine Simulator: the piston engine running the same Otto cycle, with valves, a crankshaft and a 3D cutaway.
- Two-Stroke Engine Simulator: the other ported engine — a power stroke every revolution, like a rotor.
- Planetary Gear Simulator: internal and external gears in mesh, like the rotor’s 3 : 2 phasing gears.
- Thermodynamics Simulator: Otto, Diesel and Brayton cycles side by side.
- Gas Turbine Simulator: the other continuous-rotation engine, on the Brayton cycle.
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