Radial Engine Simulator
Aircraft Radial, 5 to 18 Cylinders, in 2D & 3D — Animate • Learn • Practice • Quiz
Display Controls
Drag the slider or press ↑/↓. The throttle sets the manifold pressure between the idle-air pressure (where the engine just carries its idle load) and the preset’s own take-off value, so a supercharged engine keeps its boost. Crank speed follows a stated spool model, I·dω/dt = Tbrake − c·ω² − b·ω, between idle and the take-off rpm; the propeller is the load. The sound is synthesised at the firing frequency, rpm × cylinders / 120.
⚙ Cylinder & rod geometry, breathing & valve timing
The master rod ratio is L/r (rod length over crank radius); the knuckle-pin radius rk is how far the knuckle pins sit from the crank-pin centre. Each link rod is cut to bring its piston to the master’s TDC height. Valve timings move the valves on the drawing; 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 of the followed cylinder
⚙ Rods & cam ring — every cylinder’s stroke, TDC offset and compression ratio
💡 What-if coach — insights from the current operating point
1 Overview
The Radial Engine Simulator runs a four-stroke aircraft radial: 5, 7 or 9 cylinders in one row, or 14 or 18 in two rows, all on one crankshaft. It is drawn seen from the rear, as radial cylinders are numbered, with the front of the crankcase cut away so you can see the master rod, the link rods on their knuckle pins, the crank pin, the counterweight and the cam ring.
Every piston position comes from the real linkage: the master piston is an exact slider-crank, and each articulated piston follows its knuckle pin on the swinging master rod. Every cylinder runs the air-standard Otto cycle, and the simulator reports the followed cylinder’s state, the engine’s performance (IMEP, power, torque, BSFC, efficiencies), the firing order and the crankshaft torque.
2 Configuring the Engine
- Preset — six real engines and one representative one: the Wright R-1820 Cyclone 9 (B-17, DC-3 variants), the Pratt & Whitney R-1340 Wasp and R-985 Wasp Junior, the seven-cylinder Continental W-670 of the Stearman trainer, a representative five-cylinder sport radial, and the twin-row R-1830 Twin Wasp (14 cylinders) and R-2800 Double Wasp (18). Bore, stroke, cylinder count and compression ratio are the published figures; the heat input is set so the model’s brake power lands near the published take-off rating. Changing any value switches the preset to Custom.
- Cylinders (the pills above the canvas) set 5, 7, 9, 14 or 18 cylinders. Follow cylinder picks the cylinder whose state the readouts, the P–V and T–s diagrams and the state table show; you can also click a cylinder on the drawing.
- 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, L ↔ in³, kJ/kg ↔ BTU/lb, g/kWh ↔ lb/hp·h). The choice is remembered across the site.
- Engine speed is the real crankshaft rpm and drives power and fuel flow; Animation speed only changes how fast you watch.
- Compression ratio (of the master cylinder), heat input qin and manifold pressure (throttle or supercharger boost) set the operating point. Every slider has a number box and −/+ steppers; hold a stepper to repeat.
- Cylinder & rod geometry, breathing & valve timing holds the bore, stroke, master rod ratio L/r, knuckle-pin radius, air–fuel ratio, mechanical efficiency, exhaust back-pressure, charge temperature and the four valve timings.
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 the followed cylinder by one stroke (180° of crank), and the arrow keys nudge the crank by 5°. Press inside the crankcase and drag to turn the crankshaft by hand; click a cylinder to follow it.
The gas in each cylinder is coloured by what it is doing: fresh charge blue, compressed charge violet, the flame white-yellow just after both plugs fire, expanding gas orange and exhaust grey. The valves open on the cylinder heads, the exhaust stubs glow while the exhaust valve is open, and the firing order strip at the top lights the cylinder whose power stroke is the latest to start.
The first readout row is the instantaneous state of the followed cylinder and the gas torque on the crankshaft at this instant; the second is the engine’s cycle result at the operating point.
4 The Five Diagrams
- P–V — pressure against volume for the followed cylinder, with the four state points numbered, a large marker for it and small markers for every other cylinder. The inset zooms on the gas-exchange loop.
- T–s — temperature against entropy for the followed cylinder: vertical isentropes and constant-volume curves.
- Firing — the stroke of every cylinder over 720° of crank, listed in firing order, so the staircase of power strokes 720/n degrees apart is plain to see.
- Torque — the gas torque on the crankshaft, T = Σ(p − p0)·dV/dθ, for the followed cylinder alone and for the whole engine, with the mean.
- Pistons — how far each articulated piston sits below the master piston at the same angle past its own top dead centre: the signature of the master-and-link-rod mechanism.
2D and 3D, at the left of the strip above the canvas, switch views. The page opens in 3D on a computer or tablet and in 2D on a phone; your last choice is remembered for that kind of device, and a link ending ?view=2d or ?view=3d opens that view. The 3D engine is the same linkage: every piston, link rod, knuckle pin and the cam ring is placed by the engine model each frame. Drag to turn it, Ctrl + scroll or pinch to zoom, right-drag or Shift-drag to pan, double-click to reset the camera, and click a part to read what it does (clicking a cylinder part also follows that cylinder). Cutaway cuts the crankcase, crankshaft and cylinders open on the plane of the row (on a twin-row engine, the rear row), so seen from the Rear camera the 3D engine is the 2D drawing; Propeller shows or hides the hub, which is drawn direct drive; Labels names the main parts. The diagrams live in 2D.
🎓 Explain walks through the engine in seven steps (it switches to 2D), turning the crank to each position and naming what is happening. Rev it adds a throttle, a spool model and a synthesised engine sound. Right-click (long-press on touch) the canvas for a menu: copy the cylinder state, copy a performance summary, export CSV or PNG, or reset.
5 Calculations, Learning Panels and Export
The calculator icon opens a step-by-step derivation for the operating point on screen: displacement, firing interval and order, the followed cylinder’s volumes from the linkage, trapped charge, compression and combustion, net work, power, torque, IMEP and BSFC. The learning panels show the live equations, the followed cylinder’s four state points, a table of every cylinder’s stroke, TDC offset, link-rod length and compression ratio with the cam ring, and a what-if coach.
Export CSV writes the setup, the performance, the per-cylinder table and a 2°-resolution sweep of the followed cylinder’s volume, pressure and temperature with the crankshaft torque. Export PNG saves the canvas.
6 Explore, Practice and Quiz
Explore has sixteen cards in four groups — Fundamentals, Rods & cam ring, Thermodynamics and Design — several with a small drawing made from the same engine model. Practice draws from twelve problem types (displacement, firing interval, firing order, cam ring speed, firing frequency, mean piston speed, Otto efficiency, clearance volume, power from IMEP, torque, link-rod count, specific output); type an answer, press Check, or Show Solution for the working. Problems are worked in SI. Quiz asks six questions drawn from a pool of twenty, with the options shuffled each time.
7 What the Model Assumes
Each cylinder runs the ideal air-standard Otto cycle (γ = 1.4) with heat added at constant volume at firing TDC and rejected at BDC; real combustion takes time, and heat loss, friction, leakage and the rich take-off mixture are lumped into the mechanical efficiency and the heat input. The valve timings only move the valves on the drawing. The linkage is exact: link rods are cut so every piston reaches the master piston’s TDC height, and the remaining spread in stroke and compression ratio is what the geometry gives. Inertia forces of the reciprocating parts, the propeller reduction gear and the supercharger’s own thermodynamics are not modelled.
How a Radial Engine Works — Interactive Radial Engine Simulator
A radial engine arranges its cylinders in a ring round a single crankshaft, like the spokes of a wheel. It is an ordinary four-stroke piston engine — intake, compression, power, exhaust — but every piston of a row drives the same crank pin. A nine-cylinder radial such as the Wright R-1820 Cyclone has a crankshaft with one throw, and from the 1920s to the 1950s engines like it powered the DC-3, the B-17, the P-47 Thunderbolt and the Stearman trainer.
Radial Engine Parts
- Crankcase — a round, usually forged aluminium case that carries the crankshaft bearings and has a pad for every cylinder.
- Cylinders — steel barrels with deep cooling fins and aluminium heads, each with two valves and two spark plugs. Every cylinder stands in the airstream, so radials are air-cooled.
- Master rod — the one connecting rod in each row that runs on the crank pin. Its big end is a flange carrying a knuckle pin for every other cylinder.
- Link (articulated) rods — the other connecting rods, each pinned to the master rod by a knuckle pin. A row of nine cylinders has one master rod and eight link rods.
- Cam ring — a ring of cam lobes round the crankshaft, geared down, that opens every valve through tappets, push rods and rockers.
- Supercharger — on most large radials, a gear-driven centrifugal compressor at the rear that feeds every cylinder through equal-length intake pipes.
Radial Engine Firing Order — Why the Cylinders Are Odd
Each cylinder reaches top dead centre once per turn of the crank, but a four-stroke cylinder fires only every other turn. A single row therefore fires every other cylinder: on a nine-cylinder engine 1, 3, 5, 7 and 9 on the first turn and 2, 4, 6 and 8 on the second, giving the firing order 1-3-5-7-9-2-4-6-8 with a power stroke every 80° (720/9). This only spaces the firings evenly when the row has an odd number of cylinders, which is why single-row radials have 5, 7 or 9. A seven-cylinder engine fires 1-3-5-7-2-4-6 every 102.9°; a five-cylinder engine fires 1-3-5-2-4 every 144°.
Twin-row radials add a second odd row behind the first, staggered so its cylinders sit in the gaps, on a crankshaft with two throws 180° apart. The rows fire alternately. The 14-cylinder Pratt & Whitney R-1830 Twin Wasp fires 1-10-5-14-9-4-13-8-3-12-7-2-11-6 and the 18-cylinder R-2800 Double Wasp fires 1-12-5-16-9-2-13-6-17-10-3-14-7-18-11-4-15-8. The simulator does not store these orders: it derives them from the cylinder angles and crank throws, and they come out exactly as published.
Master Rod and Articulated Rods
Because the knuckle pins ride on the swinging master rod and not on the crank pin, an articulated piston does not move like the master piston. Its stroke is a little longer and its top dead centre arrives a few degrees early or late. In the simulator’s R-1820 the master piston sweeps exactly 174.6 mm while the longest articulated stroke is about 1.5 mm more, and the TDC of the cylinders furthest round the row is up to about 5° off its nominal angle. Engine designers place the knuckle pins and size the link rods so that every piston reaches the same height at TDC; the simulator cuts each link rod to do exactly that, so every cylinder’s compression ratio sits between 6.45 and 6.50 : 1 instead of dropping by several tenths. The Pistons diagram plots the difference for every cylinder.
The Cam Ring
A radial has no camshaft per bank. A single cam ring round the crankshaft carries the lobes for every cylinder of the row. With (n − 1)/2 lobes it turns against the crank at 1/(n − 1) of crank speed; with (n + 1)/2 lobes it turns with the crank at 1/(n + 1). A nine-cylinder engine typically uses a four-lobe ring at one eighth of crank speed. Each lobe is shared by two cylinders, and the arithmetic only works because the firing order skips every other cylinder.
Worked Example — Displacement, Firing Frequency and Efficiency of the R-1820
The Wright R-1820 has 9 cylinders of 155.6 mm (6.125 in) bore and 174.6 mm (6.875 in) stroke. Its displacement is 9 × (π/4) × 155.6² × 174.6 mm³ = 29.9 L (1823 in³). At its 2500 rpm take-off speed it fires 2500 × 9 / 120 = 187.5 times a second, which is the fundamental of its exhaust note. At a compression ratio of 6.45 : 1 the air-standard Otto efficiency is 1 − 6.45−0.4 = 52.6 %; with the take-off manifold pressure of about 152 kPa (45 inHg) the model gives about 895 kW (1200 hp) of brake power and a brake thermal efficiency near 23 %, because take-off mixtures run rich to keep the cylinders cool.
Why Radial Engines Run Smoothly
The gas torque on the crankshaft from one cylinder is its gauge pressure times the rate at which its volume changes with crank angle, T = (p − p0) dV/dθ. With a power stroke starting every 720/n degrees, the pulses overlap and the total torque never strays far from its mean. Open the Torque diagram and switch between 5, 9 and 18 cylinders: the peak-to-mean ratio falls steadily. Averaged over two turns, the drawn torque equals the engine’s total cycle work divided by 4π — the simulator’s gate checks that to five digits.
Who Uses This Simulator?
Aviation maintenance (A&P and EASA Part-66) students learning powerplant theory, mechanical engineering students studying IC engines and mechanisms, instructors who want to show the master-and-link-rod mechanism and the firing order without a cutaway engine, and enthusiasts who want to know why a radial sounds the way it does.
Frequently Asked Questions
How does a radial engine work?
A radial engine arranges its cylinders in a ring round one crankshaft. Every piston of a row drives the same crank pin: one piston through the master rod, which runs on the crank pin, and the others through link rods pinned to the master rod's big end. Each cylinder runs the ordinary four-stroke cycle, and the cylinders fire in turn so that a power stroke starts every 720/n degrees of crank rotation.
Why do radial engines have an odd number of cylinders?
A four-stroke radial row fires every other cylinder as the crank goes round: 1-3-5-7-9 on the first turn and 2-4-6-8 on the second. That gives evenly spaced power strokes only when the number of cylinders in the row is odd. Twin-row engines such as the 14-cylinder R-1830 and 18-cylinder R-2800 are two odd rows on a two-throw crankshaft.
What is the firing order of a 9 cylinder radial engine?
1-3-5-7-9-2-4-6-8. The cylinders are numbered round the engine, cylinder 1 at the top, and a power stroke starts every 80 degrees of crank rotation (720/9).
What is a master rod in a radial engine?
The master rod is the one connecting rod in each row that runs directly on the crank pin. Its big end is a flange carrying knuckle pins, and every other piston of the row drives a link (articulated) rod pinned to one of those knuckle pins. The articulated pistons move slightly differently from the master piston, with a slightly longer stroke and a top dead centre a few degrees early or late.
Explore Related Simulators
- Four Stroke Engine Simulator — the same Otto cycle in a single cylinder, with valve timing and multi-cylinder inline and V engines.
- Rotary Engine Simulator — the Wankel, which has no pistons at all.
- Two Stroke Engine Simulator — ports instead of valves, a power stroke every turn.
- Slider-Crank Mechanism — the linkage the master piston follows.
- Gas Turbine Simulator — the engine that replaced the radial in aircraft.
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