Automotive sensors: MAP, MAF, O2, knock, crank position

Why it matters

An engine ECU is only as good as the numbers it receives. To meter fuel within about 1 % of the stoichiometric ratio and time the spark to within a degree, it must know how much air is entering, where the crankshaft is, whether the mixture is rich or lean and whether the engine is knocking. These five sensors — MAP, MAF, oxygen, knock and crank position — are behind most driveability complaints and fault codes.

Key ideas

MAP (manifold absolute pressure) sensor. Measures the absolute pressure in the intake manifold, i.e. pressure referred to a sealed vacuum, not to atmosphere. A thin silicon diaphragm with piezoresistive strain gauges in a bridge gives an output of typically about 0.5–4.5 V. At idle a naturally aspirated petrol engine has a MAP of roughly 30–40 kPa; at wide-open throttle it approaches atmospheric (about 100 kPa at sea level); a turbocharged engine goes above atmospheric. MAP is a direct indicator of engine load. In a speed-density system the ECU calculates air mass from MAP, intake air temperature, engine speed and a stored volumetric-efficiency map.

MAF (mass air flow) sensor. Placed between the air filter and throttle, it measures air mass flow directly. In the common hot-wire or hot-film type, an element is kept at a fixed temperature above intake air temperature; the electrical power needed to do so rises with the mass flow rate (King's law, non-linear). Because it measures mass, it automatically accounts for air density, altitude and changes in volumetric efficiency (wear, valve timing). It must see smooth flow, and contamination or unmetered air leaks after it cause errors.

Oxygen (lambda) sensor. Mounted in the exhaust before (and another after) the catalytic converter.

• Narrow-band zirconia: a ZrO₂ ceramic thimble with platinum electrodes, exhaust on one side and reference air on the other. At operating temperature (above about 300–350 °C, so most are electrically heated), oxygen ions conduct through the ceramic and a Nernst voltage appears: about 0.8–0.9 V when rich (little exhaust oxygen) and about 0.1 V when lean, switching sharply at λ = 1. It tells the ECU only "rich" or "lean", so closed-loop control makes the mixture oscillate about stoichiometric.
• Wide-band (planar, pumping cell): measures the actual λ over a wide range by the current needed to pump oxygen into or out of a measuring chamber; used for lean-burn and diesel engines.
• Titania: a resistive type whose resistance changes with oxygen content (less common).
• The downstream sensor monitors catalyst efficiency for on-board diagnostics.

Knock sensor. Knock is spontaneous auto-ignition of the unburnt end gas after the spark, which sets up pressure oscillations in the chamber (typically about 5–15 kHz depending on bore). A piezoelectric accelerometer bolted to the block picks up this vibration. The ECU filters the signal in a window around TDC, compares it with a threshold, and retards timing on the knocking cylinder, then advances it again step by step. This lets the engine run near the timing for best torque with higher compression ratio. Knock is different from pre-ignition, where the charge is ignited by a hot spot before the spark.

Crankshaft position sensor (CKP). Reads a toothed reluctor wheel, commonly "60-2" (60 equally spaced positions with two teeth missing to mark a reference). Two types:

• Inductive (variable reluctance): a magnet and coil; produces an AC voltage whose amplitude and frequency rise with speed. Needs no supply but gives a weak signal at cranking speed.
• Hall-effect (or magnetoresistive): powered, gives a clean square wave independent of speed, so it works down to zero speed. The ECU gets engine speed from tooth frequency and crank angle from tooth counting after the gap. A camshaft sensor tells which stroke the cylinder is on (needed for sequential injection and coil-on-plug).

Other sensors in the same family: throttle position (potentiometer or Hall), coolant and intake air temperature (NTC thermistors), vehicle speed.

Formulas

λ = AFR_actual / AFR_stoich

• λ: excess-air ratio (dimensionless), AFR: air–fuel ratio by mass; AFR_stoich ≈ 14.7 for petrol. λ < 1 rich, λ > 1 lean.

ρ_im = MAP / (R × T_im)

• ρ_im: intake air density (kg/m³), MAP: absolute manifold pressure (Pa), R = 287 J/(kg·K) for air, T_im: intake temperature (K).

ṁ_air = η_v × ρ_im × V_d × n / 120 (four-stroke, speed-density)

• ṁ_air: air mass flow (kg/s), η_v: volumetric efficiency (dimensionless, from the ECU map), V_d: total swept volume (m³), n: engine speed (rpm).

ṁ_fuel = ṁ_air / AFR

f_tooth = N_t × n / 60

• f_tooth: tooth-position frequency (Hz), N_t: tooth positions per revolution (including the missing ones for a 60-2 wheel), n: crank speed (rpm).

f_knock ≈ 1.841 × c / (π × B), c = √(γ × R × T)

• f_knock: first circumferential acoustic mode of the chamber (Hz, Draper's relation), B: bore (m), c: speed of sound in the burnt gas (m/s), γ: ratio of specific heats, T: gas temperature (K). An estimate; use the engine maker's value for real calibration.

Worked examples

Example 1 (standard). A 1.6 L four-cylinder four-stroke petrol engine runs at 3000 rpm with MAP = 60 kPa, intake air at 37 °C, volumetric efficiency 0.85 and λ = 1 (AFR 14.7). Find the air mass flow, fuel flow and fuel mass per injection (one injection per cylinder per cycle).

1. ρ_im = 60,000 / (287 × 310.15) = 0.674 kg/m³.
2. ṁ_air = 0.85 × 0.674 × 0.0016 × 3000 / 120 = 0.0229 kg/s.
3. ṁ_fuel = 0.0229 / 14.7 = 1.56 × 10⁻³ kg/s = 1.56 g/s.
4. Injections per second = (3000 / 120) × 4 = 100; fuel per injection = 1.56 g/s / 100 = 15.6 mg.

Answer: 0.0229 kg/s air, 1.56 g/s fuel, about 15.6 mg per injection.

Example 2 (GATE level). (a) A 60-2 crank wheel turns at 2400 rpm. Find the tooth-position frequency, the time per 6° tooth pitch and the number of real teeth passing per second. (b) A wide-band sensor reports AFR = 16.2 on a petrol engine. Find λ and state what a narrow-band sensor would read. (c) Estimate the knock frequency for a bore of 86 mm with burnt gas at 2500 K, γ = 1.3.

1. f_tooth = 60 × 2400 / 60 = 2400 Hz; time per pitch = 1 / 2400 = 0.417 ms; real teeth per second = 58 × (2400 / 60) = 2320.
2. λ = 16.2 / 14.7 = 1.10 → lean; a narrow-band zirconia sensor would read about 0.1 V.
3. c = √(1.3 × 287 × 2500) = 966 m/s; f_knock = 1.841 × 966 / (π × 0.086) = 6.58 × 10³ Hz.

Answer: 2400 Hz, 0.417 ms, 2320 teeth/s; λ = 1.10 (lean, about 0.1 V); about 6.6 kHz.

Common mistakes

• Treating MAP as "vacuum" (atmospheric minus manifold pressure). MAP is absolute; at idle MAP is low and vacuum is high.
• Reading a narrow-band O₂ voltage as a measure of how rich or lean the mixture is — it is essentially a switch at λ = 1.
• Confusing knock (end-gas auto-ignition after the spark) with pre-ignition (ignition before the spark).
• Expecting an inductive crank sensor to give a usable signal at very low speed, or forgetting that its amplitude changes with speed.
• Forgetting the factor 120 (not 60) for air flow in a four-stroke engine.
• Using °C instead of K in the ideal-gas density.

For GATE ME

These sensors tie into IC-engine numericals: air mass flow from volumetric efficiency and manifold conditions, fuel flow from air–fuel ratio, λ, ideal-gas density, and conversion between engine speed, signal frequency and crank angle. Conceptual questions test which sensor measures what and the difference between knock and pre-ignition.

Quick check

1. Does MAP rise or fall when the throttle is opened suddenly?
2. Why does a MAF sensor not need altitude correction?
3. What voltage does a narrow-band zirconia sensor give when the mixture is rich?
4. A 36-1 wheel at 1500 rpm: what is the tooth-position frequency?
5. What does the ECU do when the knock sensor reports knock?

Answers: 1. It rises towards atmospheric pressure. 2. It measures air mass directly, so density changes are already included. 3. About 0.8–0.9 V. 4. 36 × 1500 / 60 = 900 Hz. 5. Retards ignition timing on the knocking cylinder, then advances it again gradually.