Valve timing, port timing and volumetric efficiency

Why valves and ports open and close away from the dead centres, valve overlap and VVT, symmetric two-stroke port timing, and how to define and calculate volumetric efficiency.

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Why it matters

An engine's torque is roughly proportional to the mass of air it can trap per cycle, so how well the cylinder breathes sets the power ceiling. Valve timing (four-stroke) and port timing (two-stroke) decide when gas can flow in and out, and volumetric efficiency is the number that tells you how well that breathing works across the speed range.

Key ideas

Why valves do not open and close at TDC and BDC. Gas has inertia and valves need time to lift. If the inlet valve opened exactly at TDC and closed at BDC, the cylinder would be far from full at speed. Practical timings therefore lead and lag the dead centres:

  • Inlet valve opens (IVO) about 10–25° before TDC, so it is well open when the piston starts down.
  • Inlet valve closes (IVC) about 30–60° after BDC. The moving charge keeps flowing in (ram effect) even as the piston starts rising. Late IVC is the single most important timing for volumetric efficiency at high speed.
  • Exhaust valve opens (EVO) about 35–55° before BDC, so most of the gas blows down under its own pressure and the piston pushes less on the exhaust stroke.
  • Exhaust valve closes (EVC) about 5–20° after TDC, using the momentum of the outgoing gas to scavenge the clearance volume.
  • Valve overlap is the period near TDC when both valves are open (IVO-before-TDC plus EVC-after-TDC). It helps scavenging at high speed but lets exhaust flow back into the inlet at low speed and idle, raising residual gas and HC. CI engines can use more overlap than SI engines because only air is being scavenged. The figures are typical; the exact values come from the manufacturer's valve timing diagram.

Variable valve timing (VVT). No fixed timing suits all speeds: late IVC helps at high speed but pushes charge back out at low speed. Cam phasers and variable-lift systems shift IVC and overlap with speed and load, improving low-speed torque, high-speed power, and part-load efficiency (less throttling and internal EGR for lower NOx).

Port timing (two-stroke). In a piston-ported two-stroke engine the piston uncovers and covers the exhaust port and the transfer (scavenge) port. Because the piston controls both, the timing is symmetric about BDC: a port opening θ° before BDC closes θ° after BDC. The exhaust port is placed higher, so it opens first (exhaust lead, for blowdown) and closes last, which lets some fresh charge escape (short-circuiting), a main source of HC and fuel loss in carburetted two-strokes. Typical figures: exhaust port open about 60–75° each side of BDC, transfer port about 50–60° each side. Reed valves, rotary valves or tuned expansion chambers are used to break the symmetry.

Volumetric efficiency (ηv). The mass of fresh air actually inducted per cycle divided by the mass that would fill the swept volume at a reference density, usually ambient (or, for supercharged engines, intake-manifold) conditions. It is a mass ratio, not a volume ratio at whatever conditions happen to apply. Typical full-throttle values: 75–90 % for naturally aspirated SI engines, 85–95 % for CI engines; tuned intakes can exceed 100 % over a narrow speed band.

Factors that lower ηv: throttling (part load SI), friction losses in air filter, manifold, valve and port; heating of the charge by hot walls; residual exhaust gas; fuel vapour displacing air (port-injected or carburetted petrol, and especially gaseous fuels such as CNG); backflow at low speed with late IVC; choking of the inlet valve at high speed (the inlet Mach index, a valve-flow parameter, should stay below about 0.5); high altitude (lower ambient density, though ηv referred to local ambient changes little). ηv versus speed is a hump: limited by backflow at low speed and by flow friction and choking at high speed.

Formulas

ηv = m_a / (ρ_a · V_s) (per cylinder per cycle) m_a fresh air mass inducted per cycle (kg); ρ_a reference air density (kg/m³); V_s swept volume (m³).

ηv = ṁ_a / (ρ_a · V_s,total · N/n_R) ṁ_a measured air flow (kg/s); V_s,total total swept volume (m³); N speed (rev/s); n_R = 2 for four-stroke, 1 for two-stroke.

ρ_a = p_a / (R·T_a) p_a in Pa, T_a in K, R = 287 J/kg·K for air.

θ_open = (lead before dead centre) + 180° + (lag after dead centre) Valve open period in crank degrees, e.g. inlet = IVO-before-TDC + 180 + IVC-after-BDC.

t = θ / (6·N_rpm) Time in s for θ crank degrees at N_rpm rev/min (1 rev/min = 6 °/s).

x = r·(1 − cos θ) + l − √(l² − r²·sin²θ) Piston displacement from TDC (m) at crank angle θ from TDC; r crank radius = stroke/2 (m); l connecting-rod length (m). Used to find port opening angles. Ignoring the rod (l → ∞) gives x = r(1 − cos θ), which is only approximate.

Worked examples

Example 1 (standard): volumetric efficiency and valve open time. A four-cylinder, four-stroke petrol engine of 1.6 L total swept volume runs at 4000 rpm and inducts 0.050 kg/s of air. Ambient conditions are 100 kPa and 27 °C. The inlet valve opens 15° BTDC and closes 45° ABDC. Find ηv, the inlet valve open period and the time it is open.

  1. ρ_a = p_a/(R·T_a) = 100 000/(287 × 300) = 1.1614 kg/m³.
  2. Power strokes per second per cylinder: N/2 = (4000/60)/2 = 33.33 s⁻¹.
  3. Ideal air flow = ρ_a · V_s,total · N/2 = 1.1614 × 1.6 × 10⁻³ × 33.33 = 0.06194 kg/s.
  4. ηv = ṁ_a / ideal = 0.050/0.06194 = 0.807 (80.7 %).
  5. θ_open = 15 + 180 + 45 = 240° of crank rotation.
  6. t = θ/(6·N_rpm) = 240/(6 × 4000) = 0.010 s = 10 ms.

Example 2 (GATE level): port timing with connecting-rod obliquity. A piston-ported two-stroke engine has a stroke of 100 mm and a connecting rod of 200 mm. The top edge of the exhaust port is 25 mm above the piston crown position at BDC; the top edge of the transfer port is 15 mm above it. Find the crank angles at which the ports open and their open durations.

  1. r = 50 mm, l = 200 mm. Distance from TDC to BDC = 100 mm, so the exhaust port opens when x = 100 − 25 = 75 mm; the transfer port opens when x = 100 − 15 = 85 mm.
  2. Use x = r(1 − cos θ) + l − √(l² − r² sin²θ) and solve by trial. For θ = 113.1°: cos θ = −0.3928, r(1 − cos θ) = 69.64 mm; r sin θ = 45.98 mm; √(200² − 45.98²) = 194.64 mm; x = 69.64 + 200 − 194.64 = 75.0 mm. So exhaust opens at 113.1° after TDC (66.9° before BDC).
  3. For θ = 128.5°: r(1 − cos θ) = 81.14 mm; r sin θ = 39.12 mm; √(200² − 39.12²) = 196.14 mm; x = 81.14 + 200 − 196.14 = 85.0 mm. So transfer opens at 128.5° after TDC (51.5° before BDC).
  4. The piston controls both edges, so timing is symmetric about BDC: exhaust open period = 2 × 66.9 = 133.7°; transfer open period = 2 × 51.5 = 103.0°. Exhaust lead = 128.5 − 113.1 = 15.4°.
  5. Check without obliquity: r(1 − cos θ) = 75 mm gives cos θ = −0.5, θ = 120°, an error of about 7°. With a finite rod the piston is lower than the simple formula predicts at angles past 90°, so the port opens earlier.

Common mistakes

  • Computing the inlet valve period as 180° plus only one of the lead or lag; add both.
  • Defining ηv as a ratio of volumes measured at different conditions. Use mass of air, referred to ambient density.
  • Forgetting n_R = 2 for four-stroke engines, which doubles the ideal air flow and halves ηv.
  • Using °C in ρ = p/(RT).
  • Ignoring the connecting rod when the question gives its length; at angles past 90° the error is several degrees.
  • Assuming two-stroke port timing can be made asymmetric with the piston alone; it cannot.
  • Thinking more overlap is always better. It helps at high speed and hurts idle and low-speed running.

For GATE ME

Expect numericals on volumetric efficiency from measured air flow (often with an orifice or air-box reading), on valve open periods and overlap from a timing diagram, and occasionally on port opening angles using the slider-crank relation. Conceptual questions test why IVC is after BDC, why EVO is before BDC, the effect of speed on ηv, and why two-stroke port timing is symmetric. Practise drawing the four-stroke valve timing diagram and the two-stroke port timing diagram from given angles.

Quick check

  1. Inlet valve opens 12° BTDC and closes 48° ABDC. What is the inlet valve open period?
  2. Exhaust valve closes 10° ATDC and inlet opens 12° BTDC. What is the valve overlap?
  3. Why does a CNG-fuelled SI engine have lower volumetric efficiency than the same engine on petrol?
  4. Why is two-stroke piston-port timing symmetric about BDC?
  5. A 2 L four-stroke engine at 3000 rpm takes in 0.045 kg/s of air; ambient density is 1.18 kg/m³. What is ηv?

Answers: 1. 240°. 2. 22°. 3. The gaseous fuel occupies about 10 % of the intake volume and displaces air. 4. The same piston edge uncovers and covers the port. 5. 0.045/(1.18 × 0.002 × 25) = 0.763, i.e. about 76 %.

Interview questions

All Automotive Engines, Emissions and Alternate Fuels interview questions

Try answering each one aloud before you open it.

  1. 1.What is valve timing in an internal combustion engine?Concept

    Valve timing is the crank angle at which each inlet and exhaust valve opens and closes, shown on a valve timing diagram. Valves deliberately lead and lag the dead centres: typically the inlet opens 10–25° before TDC and closes 30–60° after BDC to use the inertia (ram effect) of the incoming charge, and the exhaust opens 35–55° before BDC for blowdown and closes 5–20° after TDC to scavenge the clearance volume. These leads and lags raise volumetric efficiency and reduce pumping work compared with opening and closing exactly at TDC and BDC.

  2. 2.Explain port timing in a two-stroke engine.Concept

    In a piston-ported two-stroke engine the piston itself uncovers and covers the exhaust and transfer ports in the cylinder wall, so there are no valves. The exhaust port is higher, so it opens first, letting the gas blow down before the transfer port opens and admits fresh charge from the crankcase. Because the same piston edge opens and closes each port, the timing is symmetric about BDC: a port that opens θ before BDC closes θ after BDC, and the exhaust port closes after the transfer port.

  3. 3.What is volumetric efficiency in the context of automotive engines?Concept

    Volumetric efficiency is the mass of fresh air actually inducted per cycle divided by the mass of air that would fill the swept volume at a reference density, normally ambient (or intake-manifold for supercharged engines). It is a mass ratio: ηv = ṁ_a/(ρ_a·V_s·N/2) for a four-stroke engine. Naturally aspirated SI engines reach about 75–90 % at full throttle and CI engines about 85–95 %. Because torque is roughly proportional to the air trapped, ηv sets the shape of the full-load torque curve.

  4. 4.Why is variable valve timing used in modern engines?Application

    A fixed cam is a compromise: a late inlet closing and large overlap fill the cylinder well at high speed but push charge back into the manifold and raise residual gas at low speed. Variable valve timing shifts the cam phase (and sometimes lift) with speed and load, giving better low-speed torque and high-speed power from the same engine. At part load it can reduce throttling losses through early or late inlet closing and provide internal EGR via overlap, lowering fuel consumption and NOx.

  5. 5.What happens if the valve timing is incorrect in an engine?Application

    If the cam timing is retarded or advanced, for example after a timing belt jumps a tooth, the cylinder fills poorly, so torque and power fall, the engine idles roughly and may be hard to start, and fuel consumption and emissions rise. Effective compression changes because the inlet closes at the wrong point. In an interference engine a badly wrong timing or a broken belt lets the valves hit the piston, bending valves and damaging the piston.

  6. 6.How does port timing affect the performance of a two-stroke engine?Application

    Larger port open angles allow more time for flow at high speed, giving more peak power, but they shorten the effective expansion stroke and waste fuel at low speed. The exhaust lead (the gap between exhaust and transfer opening) must be enough for blowdown, otherwise exhaust flows back into the crankcase. Because the exhaust closes after the transfer port, some fresh charge short-circuits into the exhaust, raising HC and fuel consumption; tuned expansion chambers, reed or rotary valves and direct injection are used to reduce this.

  7. 7.Calculate the volumetric efficiency of an engine with a swept volume of 2 litres that inducts 1.8 litres of air per cycle, both measured at ambient conditions.Numerical

    Volumetric efficiency is the inducted air mass divided by the mass that would fill the swept volume at ambient density. With both volumes at the same (ambient) density, the densities cancel: ηv = 1.8/2.0 = 0.90, i.e. 90 %. If the inducted air were measured at another temperature or pressure, it would first have to be converted to ambient density.

  8. 8.What is the impact of high volumetric efficiency on engine performance?Application

    Brake torque is roughly proportional to volumetric efficiency, because the fuel that can be burnt is limited by the air trapped; so a higher ηv gives more torque and power from the same displacement, raising specific output. It also allows a smaller engine for a given power (downsizing). It does not by itself improve thermal efficiency; a high ηv achieved by large overlap may even raise idle HC emissions.

  9. 9.Explain how valve overlap can affect engine emissions.Application

    During overlap both valves are open near TDC. At high speed the outgoing exhaust helps draw in fresh charge and scavenge the clearance volume. At low speed and idle, especially with a low manifold pressure, exhaust flows back into the inlet, increasing residual gas; this dilution lowers peak temperature and NOx (internal EGR) but can cause unstable combustion and higher HC. In port-injected or carburetted engines, some fresh mixture can also flow straight through to the exhaust, raising HC.

  10. 10.A four-stroke engine has its inlet valve opening at 10° BTDC and closing at 40° ABDC. Calculate the inlet valve open period in crank degrees.Numerical

    The inlet valve is open from 10° before TDC, through the 180° of the suction stroke, to 40° after BDC. Open period = 10 + 180 + 40 = 230° of crank rotation. At 3000 rpm this corresponds to 230/(6 × 3000) = 0.0128 s, which is why the lead and lag are needed.

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