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Torque, power & mean effective pressure

“How much power?” is really three questions multiplied together: how big is each bang, how big is the engine, and how often does it fire. Engineers separate them with one wonderfully honest number — mean effective pressure — and once you have it, torque and power curves stop being marketing and start being arithmetic.

Mean effective pressure

Take the PV-loop work from the second article and ask: what constant pressure, pushing the piston down one single stroke, would do the same work? That fictitious pressure is the MEP:

MEP=WcycleVd⟺Wcycle=MEP⋅Vd\text{MEP} = \frac{W_{\text{cycle}}}{V_d} \qquad\Longleftrightarrow\qquad W_{\text{cycle}} = \text{MEP}\cdot V_d(1)
VdV_d
displacement (swept volume) of the cylinder or whole engine [m³]
IMEP\text{IMEP}
from the indicated (PV-loop) work [Pa]
BMEP\text{BMEP}
from brake work at the crankshaft — IMEP minus friction [Pa]

MEP is the great equaliser: it strips out engine size. A 1960s road engine, a modern hatchback and a Formula 1 V6 might all have similar peak pressures, but their BMEPs — 8, 13 and 30+ bar — tell you instantly how hard each one works every litre of its displacement. Naturally-aspirated petrol tops out near 13–14 bar (limited by how much air fits in a cylinder at atmospheric pressure); everything above that is boost.

Torque is BMEP with units on

A four-stroke completes one cycle per two revolutions, i.e. per 4π4\pi radians. Work per cycle over angle per cycle is, by definition, average torque:

T=Wcycle4π=BMEP⋅Vd4π(four-stroke)T = \frac{W_{\text{cycle}}}{4\pi} = \frac{\text{BMEP}\cdot V_d}{4\pi}\qquad\text{(four-stroke)}(2)

(A two-stroke divides by 2π2\pi — one cycle per revolution — which is its power-density advantage stated as an equation.) Note what is absent from (2): rpm. Torque measures the size of each push, not how often you push. That is why a torque curve is really a “breathing curve” — it is flat wherever the engine fills its cylinders equally well, and it droops at high rpm exactly as filling (volumetric efficiency) droops.

Power multiplies the push by the push-rate:

P=T ω=T⋅2πN60P = T\,\omega = T \cdot \frac{2\pi N}{60}(3)
200040006000torque T ∝ BMEPpower P = Tωengine speed [rpm]
Fig. 1. Schematic full-throttle curves for a naturally-aspirated petrol engine. Torque (orange) mirrors the engine's breathing; power (green) is that same curve multiplied by speed, so it keeps climbing past the torque peak until breathing collapses faster than revs rise.

Assemble a whole engine from its three factors below:

T=BMEP⋅Vd4πT = \frac{\text{BMEP}\cdot V_d}{4\pi}T=191 N⋅m,P=90 kWT = 191\ \text{N·m},\quad P = 90\ \text{kW}

A healthy naturally-aspirated engine at full throttle (~10–14 bar). Power is just torque × speed: P=T ωP = T\,\omega.

The real ceiling: mean piston speed

If power is torque × speed, why not just rev to 20 000? Because the piston’s average speed — two strokes per revolution —

Vˉp=2 S N\bar V_p = 2\,S\,N(4)

turns out to be capped near 20–25 m/s for almost every reciprocating engine ever built, from ship diesels to F1. Inertia loads grow with ω2\omega^2 (last two articles), ring lubrication fails, valve springs float. So stroke and rpm trade off directly: that’s why an F1 engine (S ≈ 53 mm) could spin 15 000 rpm while a marine diesel (S ≈ 2.5 m) idles at 100 — both run the same piston speed.

Vˉp=2SN=2×0.086×650060\bar V_p = 2 S N = 2 \times 0.086 \times \tfrac{6500}{60}Vˉp=18.6 m/s\bar V_p = 18.6\ \text{m/s}

sports/motorbike engines — forged internals required. Note the trade: a long stroke must rev lower for the same piston speed — exactly why undersquare engines make torque and oversquare engines make rpm.