Chapter 08 of 11 · ETO

Instrumentation & Calibration

Every reading on a panel has already passed through a sensor, a transmitter and a run of cable, and each of those can go wrong in its own particular way. This chapter works through the whole chain, so a disputed number can be traced to its real cause rather than blamed on the instrument by default.

Worked examples3, fully stepped
Read time≈ 14 min
PrerequisiteNone

1. The measurement chain, and why it matters

Every reading a bridge or engine control room displays has travelled through a chain: a sensing element responds to a physical change, a transmitter converts that response into a standard signal, wiring carries the signal to a marshalling cabinet, and a display or logic system turns it back into a number or an action. A fault, a drift, or a disputed value can sit at any link in that chain, and the instrument itself is only one of them.

When a reading looks wrong — a temperature that will not settle, a level that jumps, a pressure that disagrees with a local gauge — the first useful question is not "is the sensor broken?" but "where in the chain would this symptom appear?" A sensor fault, a wiring fault, an installation fault and a genuine process change can all produce a similar-looking trace on a screen, and a competent engineer works back through the chain rather than reaching straight for a replacement part.

The key idea

Diagnose the chain, not the display. The instrument is usually innocent; the installation, the wiring or the process is usually guilty.

2. Pressure, level and flow: establishing the reference

Pressure only means something once its reference is stated. Gauge pressure is measured relative to local atmosphere and is what most engine-room gauges show; absolute pressure is measured relative to a perfect vacuum and is what a condenser or a refrigerant chart needs; differential pressure (DP) is the difference between two points and is what a level transmitter or an orifice-plate flow meter actually measures. Confusing gauge and absolute is a common source of "impossible" readings, particularly around vacuum systems.

Gauge = Absolute − Atmospheric state the reference before comparing two pressures

Level is very often not measured directly at all — it is inferred from the hydrostatic pressure a liquid column exerts at the bottom of a tank, using a DP cell referenced to atmosphere (or to the vapour space, for a closed tank).

h = ΔP / (ρg) a level reading is only as good as the density used to calculate it

Because the formula divides by density, any error in ρ — the wrong liquid, a temperature-dependent density change, or a calibration table built for fresh water applied to a denser cargo or ballast — becomes a level error, even though the transmitter itself is functioning exactly as designed and calibrated. Flow measurement follows related logic: DP flow meters (orifice plates, venturis) infer flow from the pressure drop across a restriction, so the same reference and density sensitivities apply, while other technologies (turbine, electromagnetic, ultrasonic) sense flow more directly but bring their own installation requirements — usually a minimum straight run of pipe upstream and downstream to let the flow profile settle before it reaches the sensor.

3. Thermocouples and RTDs: two different mechanisms

Two temperature-sensing technologies dominate marine instrumentation, and they work on genuinely different physics. A thermocouple is two dissimilar metal wires joined at a measuring junction; the junction generates a small voltage — microvolts per degree — and that voltage is a function of the temperature difference between the measuring junction and the reference ("cold") junction, not of the measuring junction's absolute temperature alone. That is why a thermocouple circuit needs cold junction compensation: the instrument measures or assumes the temperature at its own terminals and adds the correction electronically, so the displayed value represents the true temperature at the measuring end. Without it, the reading silently carries the error of whatever temperature the terminal box happens to be at.

A resistance temperature detector (RTD), typically a Pt100 element, works differently: it exploits the fact that a pure metal's electrical resistance rises predictably with temperature. A Pt100 is defined as 100 Ω at 0 °C, rising by roughly 0.385 Ω per °C near that point, and because resistance — not a microvolt signal — is being measured, lead wire resistance sits directly in series with the element and adds straight onto the reading unless it is removed. A three-wire connection uses a bridge arrangement to cancel the lead resistance in the two current-carrying legs; a four-wire connection removes it completely by separating the current-carrying and voltage-sensing leads. A simple two-wire hookup is only acceptable for a short run where the lead resistance is negligible next to the element's own resistance change.

R(T) ≈ R₀(1 + αT), R₀ = 100 Ω, α ≈ 0.385 Ω/°C a linear approximation good enough for shipboard estimates

4. The 4–20 mA loop and the live zero

Almost every transmitter on board, whatever it senses, ends up speaking the same language: a 4–20 mA current loop. The choice of 4 mA as the zero point rather than 0 mA is deliberate. Current, unlike voltage, does not fall off along a long run of cable — the same current flows at every point in a series loop regardless of cable resistance, so the signal is immune to the volt drop that would otherwise distort a voltage-based reading over a long run between the engine room and a remote sensor.

The "live zero" is the other half of the design. Because the bottom of the range is 4 mA and not 0 mA, a genuine zero reading (empty tank, atmospheric pressure, zero flow) still produces a small, positive, alive current. A current of exactly 0 mA can only mean the loop itself has failed — a broken wire, a disconnected transmitter, a blown fuse — and the control system can distinguish that instantly from a real zero process value and raise a fault rather than quietly displaying a false "empty" or "zero" reading.

Output (mA) = 4 + 16 × (reading − LRV) / (URV − LRV) straight-line scaling across the calibrated range

LRV and URV are the lower and upper range values the transmitter was configured for — not necessarily the physical limits of the sensor, but the span chosen for this particular installation.

5. Zero, span and the calibration procedure

Calibrating a transmitter means adjusting two separate parameters, and treating them as one is the single most common calibration mistake. Zero sets where the output sits at the bottom of the range — it shifts the whole output line up or down without changing its slope. Span sets how much the output changes for a given change in the input — it rotates the line about the zero point, changing the slope, or gain, of the relationship between the process value and the signal.

Zero shifts the line; span rotates it the two adjustments are independent and must be set in order

Because span is defined relative to zero, the correct order is always zero first, then span, then re-check zero — adjusting the span control on a transmitter that is not first sitting at the correct zero moves the zero point too, and a technician can chase their tail between the two adjustments if they lose track of which was set last. A proper calibration check does not stop at one point either: the instrument is checked at several points across its range — commonly 0 %, 50 % and 100 %, or five points for a more rigorous check — because a transmitter can be correct at zero and wrong at span, correct in the middle and wrong at the ends, or drifting non-linearly in a way a single-point check would never reveal.

Every calibration check is recorded twice: the as-found value, read before any adjustment is made, and the as-left value, read after adjustment. The as-found value is the evidence — it shows how far the instrument had actually drifted since the last check, which feeds decisions about calibration intervals and instrument reliability, and it is what a surveyor or auditor will ask to see. Recording only the as-left value throws that evidence away.

6. Installation errors and calibration records

A transmitter can be perfectly calibrated on the bench and still give a wrong reading once it is installed, because installation introduces error sources that have nothing to do with the instrument's own accuracy. Impulse lines — the small-bore tubing connecting a process tap to a DP transmitter — can trap air in a liquid-filled line or trap condensate in a gas-filled line, and either changes the effective pressure the transmitter actually sees at its diaphragm. A thermowell that has worked loose, or was never fully seated in good thermal contact with the process, insulates the sensor from the temperature it is supposed to be measuring and produces a slow, sluggish, understated reading. A level transmitter referenced to the wrong liquid density will calculate a level that is systematically wrong by a fixed ratio across the whole range, even though every milliamp it produces is exactly what its own internal calibration says it should be.

The practical consequence is procedural: before condemning a transmitter that is "reading wrong", check the installation — vent the impulse lines, verify the thermowell is seated and the sensor is fully inserted, confirm the density or reference used in the level calculation matches the actual product — because replacing a transmitter that was never at fault fixes nothing and leaves the real cause live.

Calibration itself needs to be traceable: the standard used to check a transmitter (a deadweight tester, a precision loop calibrator, a certified thermometer) must itself carry a current calibration certificate that, ultimately, traces back to a national or international standard. A calibration record without a traceable standard behind it is just a number — it cannot demonstrate that the checking instrument was itself trustworthy on the day the check was made.

7. Worked examples

Three worked checks: catching a zero error and separating it from a span error, correcting a Pt100 reading for lead resistance on a long two-wire run, and tracing a DP level display back to the true liquid height when the product density does not match the calibration.

Worked example 1

Diagnosing a zero shift on a tank-level DP transmitter loop

A ballast tank DP level transmitter is ranged 0–8 m (LRV 0 m, URV 8 m), output 4–20 mA. During a routine bench check the empty condition (true level 0 m) reads 4.6 mA as-found, and the full condition (true level 8 m) reads 20.6 mA as-found. Is this a zero error or a span error, what correction is needed, and what would the loop show at a true level of 6 m before that correction is made?

Given

Range: 0–8 m (LRV 0 m, URV 8 m), output 4–20 mA As-found reading at true 0 m = 4.6 mA As-found reading at true 8 m = 20.6 mA Third check point: true level = 6 m

  1. First find what the loop should read at each end of the range if it were perfectly calibrated, using the standard straight-line scaling.

    Output=4 + 16 × (level − LRV)/(URV − LRV) At 0 m: 4 + 16 × 0/8=4.0 mA (ideal) At 8 m: 4 + 16 × 8/8=4 + 16 = 20.0 mA (ideal)
  2. Compare the as-found readings against these ideal values at both ends.

    Error at 0 m=4.6 − 4.0 = +0.6 mA Error at 8 m=20.6 − 20.0 = +0.6 mA Equal at both ends → zero error only; span (gain) is correct

    A span (gain) error would grow across the range; a zero error stays the same size everywhere because it is a constant offset.

  3. Express the 0.6 mA offset in engineering units.

    ΔLevel=(ΔmA / 16) × span =(0.6 / 16) × 8 =0.3 m (transmitter reads 0.3 m high, uniformly)

    Since the technician will most usefully log and discuss it as a level error.

  4. Finally, state what the loop is showing right now at the true 6 m check point, before the zero adjustment is made, so the as-found value for that point can be logged too.

    Ideal (as-left target) output at 6 m=4 + 16 × 6/8 =4 + 12 =16.0 mA As-found output at 6 m=16.0 + 0.6 = 16.6 mA

AnswerZero error of +0.6 mA (+0.3 m) across the whole range; span is correct as supplied. Adjust the zero screw by −0.6 mA, re-check span is unchanged, then log as-found 4.6 / 16.6 / 20.6 mA against as-left 4.0 / 16.0 / 20.0 mA.

The trap: touching the span adjustment because the full-scale reading is wrong — when the error is a constant offset at every point, adjusting span only drags the error to a different part of the range instead of removing it; zero is corrected first, and only then is span re-checked.

Worked example 2

Pt100 lead resistance on a long two-wire run

A Pt100 sensor (R₀ = 100 Ω at 0 °C, α ≈ 0.385 Ω/°C) is wired two-wire over a long cable run to a fuel settling tank. The total lead resistance of the two conductors, measured before commissioning, is 0.77 Ω. At the marshalling cabinet the resistance measured across the two terminals is 123.87 Ω. Find the true tank temperature, and the error a technician would see if they read the terminal resistance directly without allowing for the leads.

Given

Pt100: R₀ = 100 Ω at 0 °C, α ≈ 0.385 Ω/°C (linear approximation) Total lead resistance (two-wire run) = 0.77 Ω Resistance measured at the marshalling cabinet terminals = 123.87 Ω

Required

Find the true tank temperature, and the error a technician would see if they read the terminal resistance directly without allowing for the leads

  1. In a two-wire hookup both lead resistances sit in series with the element.

    R(element, true)=R(measured) − R(leads) =123.87 − 0.77 =123.10 Ω

    Inside the same measurement, so the true element resistance is found by subtracting the known lead resistance first.

  2. Convert the true element resistance to temperature with the linear Pt100 approximation.

    T(true)=(R(element) − R₀) / α =(123.10 − 100) / 0.385 =23.10 / 0.385 =60.0 °C
  3. Now find what a technician unaware of the lead resistance would read off.

    T(indicated, uncorrected)=(R(measured) − R₀) / α =(123.87 − 100) / 0.385 =23.87 / 0.385 =62.0 °C Error=62.0 − 60.0 = +2.0 °C (reads high)

    Applying the same formula to the raw terminal resistance without subtracting the leads — this is the installation error, not an instrument fault.

AnswerTrue tank temperature is 60.0 °C. An uncorrected two-wire reading shows 62.0 °C, 2.0 °C high, purely from lead resistance — the element itself is not faulty.

The trap: assuming a Pt100's resistance can be read straight off the terminals — on any run long enough for the lead resistance to matter, a two-wire hookup adds that resistance directly onto the reading; a three- or four-wire connection is what cancels it.

Worked example 3

A DP level display that ignores the actual product density

A DP level transmitter on a cargo tank is spanned 0–20 kPa = 0–2.00 m (LRV 0, URV 2.00 m), with the display scaled assuming fresh water, SG 1.00. The tank actually holds a caustic soda solution, SG 1.25, and the loop is currently at 20 mA (100 % of span). The transfer pump's minimum safe suction level is a true physical height of 1.00 m. Find the true liquid height right now, and the display reading (in mA) that will actually be showing when the pump's minimum safe level is reached.

Given

Span: 0–20 kPa = 0–2.00 m, calibrated for SG 1.00 (fresh water) Actual product: caustic soda solution, SG 1.25 Current loop output = 20 mA (100 % of span) Minimum safe true suction height = 1.00 m

Required

Find the true liquid height right now, and the display reading (in mA) that will actually be showing when the pump's minimum safe level is reached

  1. Level by DP works from h = ΔP/(ρg).

    For a fixed ΔP, height is inversely proportional to density, so a denser liquid than the one the display was scaled for needs a shorter column to produce the same pressure — the true height is less than the displayed one.

  2. At 20 mA the loop is at 100 % of span.

    Displayed height (as configured)=2.00 m h(true)=h(displayed) × (SG(cal) / SG(actual)) =2.00 × (1.00 / 1.25) =1.60 m

    So the display (scaled for SG 1.00) is showing its full-scale value. Convert that displayed height to the true height using the ratio of densities.

  3. Now work the same ratio in reverse to find what the display will read.

    h(displayed-equivalent)=h(true) × (SG(actual) / SG(cal)) =1.00 × (1.25 / 1.00) =1.25 m mA=4 + 16 × (1.25 / 2.00) =4 + 16 × 0.625 =4 + 10 = 14.0 mA

    In metres and in mA, at the moment the true liquid surface reaches the pump's minimum safe height of 1.00 m.

AnswerTrue liquid height right now is 1.60 m, not the 2.00 m the display shows. The pump's minimum safe suction level (true 1.00 m) will be reached while the display still reads 1.25 m / 14.0 mA — well above the bottom of the range, not near it.

The trap: reading a DP level display as if it were a direct height measurement — it is a pressure measurement converted to height using an assumed density, and if the actual product is denser than the one used at calibration the true level is always lower than the number shown, right up to the point a low-level trip is needed.

Reference sheet
60-second recall
  1. Current, not voltage, ignores cable resistance — that is why loops are 4–20 mA.
  2. A thermocouple measures a junction difference; an RTD measures its own resistance.
  3. Span rotates the line, zero shifts it — order matters, and zero is checked again after span.
  4. A DP level reading is only correct for the density it was calibrated against.
  5. Check the impulse line or the thermowell before condemning the transmitter.