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+---
+schema: cxf-library/fault-card/v1
+id: AHU-FC-005
+name: SAT too low vs MAT in heating
+equipment: ahu
+status: verified
+phase: 1
+method: rule
+severity: 3
+category: EXCESS_CONSUMPTION
+confidence: MEDIUM
+estimation_method: PROXY_ESTIMATION
+source:
+  - "HVAC FDD Reference v1.0 §5.8.1 (index; card abbreviated)"
+  - "G36 §5.16.14 FC#5 (text per Addendum u public review)"
+  - "NISTIR 7365 (defaults provenance)"
+g36: "§5.16.14 FC#5"
+clusters: [CLU-01]
+suppresses: []
+suppressed_by: [AHU-FC-062]
+related: [AHU-FC-050, AHU-FC-007, AHU-FC-062]
+playbooks: [simultaneous-hc]
+operating_states: "OS#1 (heating) — host-gated"
+preconditions: "The unit must have a MAT sensor; G36 omits FC#5 where there is none. Evaluate only in OS#1, whose actuator signature per G36 Table 5.16.14.2 is heating coil > 0, cooling coil = 0, OA damper at minimum position — outside it a SAT below MAT is the intended result of cooling, not a fault. Supply fan running, since neither MAT nor SAT means anything in still air. Suspend evaluation for ModeDelay (30 min) after any operating-state change, while the coils and damper are still stroking and the sensors still report the previous state's mixture. Silence this rule while AHU-FC-062 is active: MAT is an input here and FC-062 is its integrity gate. When any gate is unmet the verdict is NO_EVAL, not healthy."
+points:
+  - mat
+  - sat
+outputs:
+  - name: yFault
+    description: True while SAT has stayed more than mat_sat_gap_threshold below MAT for at least alarm_delay
+params:
+  mat_sat_gap_threshold:
+    default: 3.0
+    unit: "°C"
+    description: "Shortfall of SAT below MAT that counts as heat being removed rather than sensor and fan-rise uncertainty. Composed from the G36 §5.16.14 internal variables as eSAT + eMAT − dTSF = 1 + 3 − 1; a site that retunes any of the three recomputes the sum (a larger measured fan rise lowers the threshold, a looser sensor band raises it)"
+    cxf: gapBig.t
+  alarm_delay:
+    default: 1800.0
+    unit: s
+    description: Continuous fault persistence required before the alarm asserts (G36 AlarmDelay, 30 min)
+    cxf: persist.delayTime
+energy_impact:
+  affected_subsystem: AHU heating (and the cooling source cancelling it)
+  savings_range: "1-4% of site energy (HVAC FDD Reference §5.8.1 index row, mapped there to PNNL-25985 EEM-05)"
+  climate_sensitivity: heating-dominant
+  runtime_estimation: "waste_kw >= supply_airflow_m3s × 1.2 kg/m³ × 1.005 kJ/kg·K × ((mat + dTSF) − sat) — the thermal power being removed from air the heating coil just paid to warm. A floor, not an equality: it credits the coil with no rise at all, and design airflow stands in for a measured one"
+emissions:
+  scope: "1+2"
+  method: PROXY_EMISSIONS
+verified:
+  engine_rev: e2ff2f8
+  content_id: "cxf:fnv1a128:23c2dc854e3fd583e7f98f40f298a24a"
+  date: 2026-08-17
+---
+
+## Description
+
+In heating, air leaves the unit warmer than it arrived. It crosses the supply
+fan, which adds about a degree of shaft work, and then a heating coil the
+sequence has called for. SAT sitting several degrees *below* MAT under those
+conditions is not a control error — it means something in the unit is taking
+heat back out. A cooling coil valve leaking or stuck open, a DX circuit stuck
+on, or a sensor pair that disagrees by more than either instrument is rated for.
+
+This is G36 §5.16.14 FC#5, applicable in OS#1 (heating) only. Elsewhere a SAT
+below MAT is exactly what the sequence asked for. The leaking-cooling-coil
+diagnosis is simultaneous heating and cooling seen from the air side, which is
+why the fault sits in cluster CLU-01 behind AHU-FC-050: FC-050 catches the two
+valve commands overlapping, this rule catches the case where only one command is
+raised and the other device is passing water or refrigerant anyway.
+
+## Detection Logic
+
+```
+gap    = mat − sat
+yFault = gap > mat_sat_gap_threshold,
+         sustained continuously for alarm_delay
+```
+
+Block graph (`rule.cxf.jsonld`):
+
+![AHU-FC-005 block graph](diagram.svg)
+
+`gap` subtracts SAT from MAT and `gapBig` compares that shortfall against
+`mat_sat_gap_threshold`, which is G36's `SAT_AVG + eSAT <= MAT_AVG − eMAT +
+dTSF` rearranged so one positive number carries the whole allowance (see
+Deviations). The threshold is not a sensor tolerance: it is the two sensor
+bands *minus* the fan rise the air is known to get for free, so it fires on
+heat removal that neither instrument error nor the fan can explain. The
+comparison is strict, so a gap sitting exactly on 3.0 °C reads healthy.
+`persist` requires 30 minutes of continuous violation, which rides out the
+minutes after a mode change, a hot-water loop coming up to temperature, and a
+valve stroking through its span.
+
+Nothing about the size of the heating call reaches this rule. A unit whose
+heating coil does nothing at all still shows SAT about a fan rise above MAT, so
+the gap runs slightly negative and this rule reads healthy; that failure belongs
+to the inactive-coil rules. What this rule tests is the sign and size of the
+temperature change across the unit, which is the one thing two temperature
+sensors can settle between them.
+
+## Possible Diagnoses
+
+G36 §5.16.14 FC#5, transcribed:
+
+1. SAT sensor error
+2. MAT sensor error
+3. Cooling coil valve leaking or stuck open
+4. Heating coil valve stuck closed or actuator failure
+5. Fouled or undersized heating coil
+6. HW temperature too low or HW unavailable
+7. Gas or electric heat unavailable
+8. DX cooling stuck on
+
+Diagnoses 4 through 7 — a dead heating coil, whatever killed it — explain a
+missing temperature rise on their own, but not a rise of the wrong sign. They
+reach this rule only in company: nothing is being added while something else is
+taking heat out. So read the list as two groups. Either the sensors are lying
+(1, 2), or a heat sink is running against the heating call (3, 8), and a dead
+coil behind it (4–7) makes the gap wide enough to clear the threshold sooner.
+
+## Energy Impact
+
+EXCESS_CONSUMPTION, MEDIUM confidence, PROXY_ESTIMATION, all three taken from
+the reference's §5.8.1 index row. The waste is a cancellation: the heating
+source pays to warm air and a leaking cooling coil or a stuck DX circuit
+immediately unpays it, so both sides of the exchange bill. The runtime proxy
+sizes the removal rather than the addition, because the removal is what the two
+temperatures observe:
+
+```
+waste_kw >= supply_airflow_m3s × 1.2 × 1.005 × ((mat + dTSF) − sat)
+```
+
+That is a floor rather than an equality, because it credits the heating coil
+with no rise at all; whatever the coil did add is being removed on top of it.
+Design airflow stands in for a measured one, and the split between "heat never
+added" and "heat added then removed" is not observable from two temperatures —
+between them, that is what keeps this an estimate. The same
+formula shape carries AHU-FC-050's simultaneous heating and cooling waste term.
+The index puts the recoverable range at 1–4% of site energy and maps the fault
+to PNNL-25985 EEM-05 (supply air temperature reset), the nearest measure in
+PNNL's catalog rather than a measure-specific study of this failure — the repair
+this fault actually dispatches is a valve, coil, or sensor, so treat the range
+as an order-of-magnitude bound. Heating-dominant by climate: the fault can only
+be evaluated in OS#1, so its hours are heating hours.
+
+## Emissions Impact
+
+PROXY_EMISSIONS, MEDIUM confidence. Scope is recorded as `1+2` because the two
+halves of the exchange run at once and land in different inventories: hot water from a gas boiler or a gas furnace section is Scope 1,
+electric resistance or a heat pump is Scope 2, and the cooling side that eats
+the heat is Scope 2 in nearly every building. A site with gas heat and electric
+cooling is genuinely paying into both at once, which is the CLU-01 signature
+the reference's §5A.8 table describes. Avoided-emissions basis: marginal
+operating emissions rate (MOER) for the electric half, static combustion factor
+for the fuel half.
+
+## Deviations
+
+- **The reference card for this fault is abbreviated; G36 is the normative
+  source.** HVAC FDD Reference v1.0 carries AHU-FC-005 as a §5.8.1 index row —
+  name, impact category, confidence, estimation method, EEM link, savings range
+  — with no chapter 9 card behind it, so it publishes no equation, no tunable
+  defaults, no diagnoses, no operating-state applicability, no severity, and no
+  test vectors. Everything in Detection Logic and Possible Diagnoses is
+  transcribed from ASHRAE Guideline 36 §5.16.14 FC#5 as it appears in Addendum u
+  to Guideline 36-2018 (first public review, 2021), with the internal-variable
+  defaults of Table 5.16.14.5 (NISTIR 7365 provenance, which the addendum notes
+  are biased toward minimizing false alarms).
+- **Severity 3 is the library's.** No reference card exists to state one and the
+  §5.8.1 index carries no severity column. The value matches the scaffold row in
+  this chapter's README and the treatment of every other G36 comparison rule
+  here: a fault worth a work order inside a week, not a same-day dispatch.
+- **The energy profile is the index row's; the emissions split is the
+  library's.** `category`, `confidence`, `estimation_method`, and
+  `savings_range` are copied from §5.8.1 (EXCESS_CONSUMP / MED / PROXY / 1–4%
+  site), as every 001-range card verified before this one did. The index carries
+  no emissions column, so `scope` and `method` are assigned here: `1+2` follows
+  AHU-FC-050's convention for simultaneous heating-and-cooling waste — both
+  inventories fill at once, and only the heating half's fuel varies by plant
+  (matching mirror card AHU-FC-012). The runtime formula is the library's too, mirrored from AHU-FC-050's
+  simultaneous-heating-and-cooling waste term.
+- **Combined-epsilon threshold.** G36 states the test as `SAT_AVG + eSAT <=
+  MAT_AVG − eMAT + dTSF` across three separate internal variables. Rearranged,
+  that is `MAT − SAT >= eSAT + eMAT − dTSF`, so one positive threshold binds one
+  CXF path: 1 + 3 − 1 = 3.0 °C at the Table 5.16.14.5 defaults. A site that
+  retunes any input recomputes the sum rather than the parameter — measure the
+  fan rise at 2 K on a high-static unit and the threshold drops to 2.0 °C
+  (sharper, because more free heat is expected); loosen eMAT to 4 K for a
+  poorly mixed plenum and it rises to 4.0 °C. Same rearrangement as AHU-FC-062
+  and AHU-FC-001, and it can disagree with the four-term form by one ulp on a
+  value straddling the threshold, which no temperature sensor resolves.
+- **G36's `<=` becomes a strict `>`.** CDL `Reals` offers no greater-or-equal
+  comparison, so a gap of exactly 3.0 °C reads healthy where G36 would call it a
+  fault. The disagreement has measure zero on a real temperature pair and errs
+  toward silence. The vectors pin both sides (3.0 clear, 3.1 faulted).
+- **Instantaneous samples instead of averaged signals.** G36 computes every
+  signal as a five-minute rolling average of one-minute samples (`SAT_AVG`,
+  `MAT_AVG`). This rule compares raw samples and leans on the 30-minute
+  `persist` delay to reject noise. The two are not equivalent: averaging
+  tolerates a signal that keeps crossing back while its mean stays outside the
+  band, and persistence does not — an oscillating gap resets the timer on every
+  compliant tick and can hide indefinitely. The `oscillating_gap_never_persists`
+  vector is that case, recorded rather than hidden. A steady offset, which is
+  what a leaking valve or a drifted sensor produces, reads the same way under
+  either treatment. Same note as AHU-FC-002.
+- **Operating-state applicability and ModeDelay are frontmatter, not graph.**
+  G36 scopes FC#5 to OS#1 and suspends every fault condition for 30 minutes
+  after a mode change. Both are host concerns under this library's stance
+  (precedent AHU-FC-063): the graph computes the fault given valid data, and a
+  verdict outside OS#1 or inside the transition window is NO_EVAL, never
+  healthy. The OS#1 signature the host gates on is G36 Table 5.16.14.2's:
+  heating coil > 0, cooling coil = 0, OA damper at minimum position.
+- **Suppression is declared, not encoded.** MAT is an input, so AHU-FC-062 — the
+  mixing-box integrity gate that tests MAT against the OAT/RAT envelope —
+  silences this rule while it is active. The engine is status-blind and cannot
+  express that; it lives in `suppressed_by` and the host enforces it.
+- **No published test vectors.** The reference publishes vectors only for faults
+  with full chapter cards. Every scenario in `vectors.json` is authored from the
+  G36 equation: both sides of the threshold edge, a transient shorter than
+  `alarm_delay`, a recovery that clears, and the oscillation case above.
+- `persist.delayOnInit = true` (Modelica/CDL default is `false`), the library's
+  standing choice: a gap already present at load waits out the full 30 minutes
+  rather than alarming on the first tick after a controller restart.
+
+## Notes
+
+This rule and AHU-FC-007 are the two G36 heating-side SAT tests, and they fail
+differently on purpose. FC-007 compares SAT against its setpoint with the valve
+saturated and answers "the unit cannot make the air it was asked for". This one
+compares SAT against MAT and answers "the unit is making the air colder than it
+found it". A fouled coil or a dead boiler trips FC-007 and leaves this rule
+quiet, because nothing is removing heat. A leaking cooling valve trips both:
+the unit is short of setpoint *and* running a heat sink. Both firing on the same
+unit points at diagnosis 3 or 8 before anything else on the list.
+
+Order of work: confirm MAT before believing the gap. AHU-FC-062 exists for
+exactly this and runs a shorter delay, so if the mixing box or the MAT sensor is
+the problem the operator sees that alarm first and this one is suppressed. If
+MAT checks out, the [simultaneous-hc](../../../playbooks/simultaneous-hc.md)
+playbook covers the leaking-valve half of the diagnosis list — the same
+isolation-valve and actuator checks apply whether the overlap shows up as two
+open valve commands (AHU-FC-050) or as air that mysteriously loses heat crossing
+a unit in heating.