Why Cooling Tower Capacity Cannot Exceed Entering Wet-Bulb Temperature
A cooling tower's leaving water temperature is bounded below by entering wet-bulb temperature. This is a thermodynamic limit, not a design tolerance. Per ASHRAE Fundamentals 2021 Chapter 1 Section 1.7 (Adiabatic Saturation), wet-bulb temperature represents the equilibrium state where sensible heat transfer from water to air equals latent heat transfer through evaporation. Once water temperature reaches T_wb, evaporation stops regardless of tower fill depth, air velocity, or tower height. No mechanical workaround exists.
Engineers who use dry-bulb temperature for cooling tower selection in humid climates (ASHRAE Climate Zones 1A, 2A, 3A summer conditions) systematically oversize towers by 30–50% per Brentwood Industries cooling tower performance documentation, because dry-bulb fails to capture the moisture content that limits evaporation. The opposite error applies in dry climates (Zones 2B, 3B): dry-bulb-based selection in Phoenix or Las Vegas underestimates the achievable approach, producing undersized towers and chiller performance shortfalls. Per Cooling Technology Institute Standard STD-201RS, tower acceptance criteria are evaluated exclusively against entering wet-bulb. CTI ATC-105-2019 Section 5 specifies wet-bulb measurement protocol for commissioning; ASHRAE Standard 90.1-2022 Section 6.4.3.10 ties minimum cooling tower efficiency requirements to wet-bulb conditions. This calculator derives wet-bulb from one of three input combinations using iterative Newton-Raphson solution on the Sprung psychrometric equation per ASHRAE Fundamentals 2021 Chapter 1 Equations 33–34, with Magnus saturation pressure per Alduchov & Eskridge (1996) providing ±0.4% accuracy over −40°C to +50°C.
Sprung Equation, Iterative Newton-Raphson Solution, and Three Input Combinations
Saturation vapor pressure uses the Magnus approximation:
Metric: P_sat(T) = 0.61078 × exp(17.625 × T / (243.04 + T)) [kPa]
Imperial: P_sat(T) = 0.08855 × exp(17.625 × Tc / (243.04 + Tc)) [psi], where Tc = (T_°F − 32) / 1.8
The constant 0.08855 = 0.61078 × 0.1450377, the kPa-to-psi conversion factor. Magnus accuracy is ±0.4% from −40°C to +50°C per Alduchov & Eskridge (1996); ASHRAE Fundamentals 2021 Chapter 1 Equations 5–6 (Hyland-Wexler) provide ±0.05% for temperatures outside this range.
The Sprung psychrometric equation in forward direction (given T_db and T_wb):
Metric: W_sat_wb = 621.945 × P_sat(T_wb) / (P_atm − P_sat(T_wb)) [g/kg]
W = W_sat_wb − A × (T_db − T_wb) × (1000 + W_sat_wb)
Imperial: W_sat_wb = 4350 × P_sat(T_wb) / (P_atm − P_sat(T_wb)) [gr/lb]
W = W_sat_wb − A × (T_db − T_wb) × 7000
Sprung psychrometric constant A: 0.000799 °C⁻¹ (metric), 0.000437 °F⁻¹ (imperial). These values apply to mechanically aspirated wet-bulb sensors with air velocity ≥ 3 m/s (600 fpm) per ASHRAE Standard 41.6-2014 (RA2021). Section 4 covers naturally ventilated sensors, which require a different constant.
The calculator's typical use case is the reverse problem: given dry-bulb and one moisture parameter, find T_wb. The Sprung equation is implicit in T_wb with no closed-form solution. Newton-Raphson iteration solves:
f(T_wb) = W_sat(T_wb) − A × (T_db − T_wb) × K − W_actual = 0
where K = (1000 + W_sat(T_wb)) metric or 7000 imperial. Convergence criterion: |ΔT_wb| < 0.001°C (0.002°F) per ASHRAE Fundamentals 2021 Chapter 1 commentary on iterative psychrometric solutions.
Three input combinations are supported:
Combination A (T_db + RH): standard BMS or weather station input. Step 1: P_sat from Magnus at T_db. Step 2: P_v = (RH/100) × P_sat. Step 3: W = 621.945 × P_v / (P_atm − P_v) metric or 4350 × P_v / (P_atm − P_v) imperial. Step 4: T_wb via iterative Sprung solver.
Combination B (T_db + T_dp): when a chilled-mirror hygrometer provides direct dew point. Step 1: P_v = P_sat(T_dp) from Magnus at T_dp. Step 2: W from vapor pressure. Step 3: T_wb via iterative solver.
Combination C (T_db + W): when humidity ratio is already specified in design documents per ASHRAE Fundamentals 2021 Chapter 14 outdoor design data or AHRI Standard 540-2020. Step 1: P_v = P_atm × W / (621.945 + W) metric or P_atm × W / (4350 + W) imperial. Step 2: T_wb via iterative solver.
Variable definitions and typical ranges: T_db dry-bulb −10 to +50°C HVAC range; T_wb ≤ T_db by definition, survivability limit 35°C (95°F); T_dp ≤ T_wb ≤ T_db always; RH 0–100%; W 0–30 g/kg HVAC, to 100+ g/kg industrial drying; P_atm 101.325 kPa standard, altitude correction per ASHRAE Fundamentals 2021 Chapter 1 Equation 3. Verification: at RH = 100%, T_wb = T_db = T_dp and wet-bulb depression ΔT = 0; ΔT increases monotonically as RH decreases.
Aspiration Velocity, Sensor Type, and Why Constant 0.000437 Doesn't Apply to All Wet-Bulb Measurements
The Sprung constant A is sensor-type specific. ASHRAE Fundamentals 2021 Chapter 1 commentary defines three cases:
Aspirated sensor (≥ 3 m/s air velocity): A = 0.000437 °F⁻¹ (0.000799 °C⁻¹) — calculator default.
Naturally ventilated sensor: A ≈ 0.000750 °F⁻¹ (0.0013 °C⁻¹) — approximately 1.7× larger.
Screen-shielded ambient sensor: A varies with screen geometry, typically 0.0005–0.0007 °F⁻¹.
Field implications per HVAC-Talk forum thread 305312 (Psychrometer Questions): a sling psychrometer aspirated above 1000 fpm uses A = 0.000437 correctly; below 500 fpm aspiration, the sensor reads systematically high humidity because computed W is lower than actual, introducing 1–3°F wet-bulb error. A stationary wet-bulb thermometer without forced air never reaches thermodynamic wet-bulb.
Aspirated psychrometers (Assmann-type with motorized fan) provide consistent ≥ 3 m/s and are preferred for cooling tower commissioning per CTI ATC-105-2019 Section 5.3. Cost range: $400–1,500. For in-duct measurements, a Shortridge wet-sock probe installed through a drilled 1/4-inch hole captures actual coil-entering wet-bulb after duct heat infiltration. Per HVAC-Talk thread 1764071, return ducts in unconditioned attic spaces gain 1–3°F wet-bulb from infiltration, a heat gain that ASHRAE Standard 90.1-2022 Section 6.4.4.1 limits by requiring R-6 minimum return duct insulation.
Chilled-mirror hygrometers (RH Systems 933, Vaisala DM70) measure dew point directly at ±0.1–0.2°C per ASTM E337-15, eliminating the Sprung constant question entirely when using Combination B. Cost: $3,000–15,000, appropriate for commissioning-grade reference measurements. Capacitive RH sensors (Vaisala HUMICAP HMP110, Honeywell HIH-4030) provide Combination A input at ±2–3% RH per manufacturer specifications, with calibration drift ±1–2%/year requiring annual recalibration per ASHRAE Standard 111-2008; the resulting wet-bulb uncertainty is ±0.5–1.0°C.
Sensor selection summary: cooling tower commissioning per CTI ATC-105-2019 requires aspirated psychrometer; HVAC equipment commissioning uses in-duct wet-sock probe; BMS design specification uses capacitive RH sensor through Combination A; reference calibration uses chilled-mirror hygrometer through Combination B; ASHRAE Climatic Design Conditions tabulate wet-bulb directly for design applications per ASHRAE Fundamentals 2021 Chapter 14.
Cooling Tower Selection in Indianapolis: Approach Sizing at 78°F Design Wet-Bulb
Project: 200-ton cooling tower for a commercial HVAC chiller plant in Indianapolis, Indiana. ASHRAE Fundamentals 2021 Chapter 14 design data for Indianapolis International Airport (Site 724380): 0.4% summer design wet-bulb 78°F (25.6°C); 1% summer design wet-bulb 76°F (24.4°C); coincident dry-bulb at 0.4% wet-bulb 86°F (30°C). The tower cannot cool water below 78°F regardless of size; approach (leaving water temperature minus entering wet-bulb) is the design variable trading capital cost against operating efficiency.
Step 1: Tower nominal duty per CTI STD-201RS-2017 nominal rating conditions. Entering hot water 95°F (35°C); leaving cold water 85°F (29.4°C); entering wet-bulb 78°F (25.6°C); range = 95 − 85 = 10°F (5.6°C); approach = 85 − 78 = 7°F (3.9°C). One cooling tower ton = 15,000 BTU/hr per CTI definition (versus refrigeration ton = 12,000 BTU/hr).
Step 2: Required water flow rate. Heat load Q = 200 × 15,000 = 3,000,000 BTU/hr. Water flow = 3,000,000 / (500 × 10) = 600 GPM.
Step 3: Wet-bulb verification using Combination A. Indianapolis 0.4% summer outdoor: T_db = 86°F, coincident wet-bulb = 78°F per ASHRAE Fundamentals 2021 Chapter 14. Cross-check calculation:
Tc = (86 − 32) / 1.8 = 30°C; P_sat(86°F) = 0.08855 × exp(17.625 × 30 / 273.04) = 0.6143 psi.
For T_wb = 78°F: Tc_wb = 25.56°C; P_sat(25.56°C) = 0.08855 × exp(17.625 × 25.56 / 268.6) = 0.4721 psi.
W_sat_wb = 4350 × 0.4721 / (14.696 − 0.4721) = 144.3 gr/lb.
W = 144.3 − 0.000437 × (86 − 78) × 7000 = 144.3 − 24.5 = 119.8 gr/lb.
P_v = 14.696 × 119.8 / (4350 + 119.8) = 0.394 psi.
RH = (0.394 / 0.6143) × 100 = 64%.
ASHRAE-tabulated coincident RH at 78°F WB / 86°F DB for Indianapolis is approximately 65% — within 2% of the calculated value. Calculation confirmed.
Step 4: Approach decision matrix per Brentwood Industries documentation and CTI thermal performance correlations:
| Approach | Tower size | Capital cost | Notes |
|---|---|---|---|
| 5°F (2.8°C) | Largest | +30–40% | LEED or high-runtime industrial |
| 7°F (3.9°C) | Standard (CTI nominal) | Baseline | Typical commercial chiller plant |
| 10°F (5.6°C) | Smaller | −25–30% | Seasonal or space-constrained |
| 15°F (8.3°C) | Very small | −40–50% | Highest operating cost |
Per CED Engineering Module M08-020: the practical range is 5–7°F (2.8–3.9°C) approach. Below 5°F (2.8°C), tower size grows exponentially per CTI thermal performance curves.
Step 5: Engineering decision. Option A at 5°F (2.8°C) approach delivers leaving water at 83°F (28.3°C); larger tower required, capital +30–40%, but chiller IPLV improves 8–12% per AHRI Standard 550/590-2023 at the lower condenser temperature. Option B at 7°F (3.9°C) approach (CTI nominal) delivers leaving water at 85°F (29.4°C) with standard tower size and standard cost: appropriate for typical commercial chiller plant. Option C at 10°F (5.6°C) approach delivers leaving water at 88°F (31.1°C) with a smaller tower saving 25–30% capital, but chiller IPLV degrades 10–15% per AHRI 550/590-2023. Selected design: Option B for a standard commercial plant. Specification: 200 nominal tons, 600 GPM, 95°F (35°C) EWT, 85°F (29.4°C) LWT, 78°F (25.6°C) design wet-bulb, verify against CTI STD-201RS thermal performance curves.
Evaporative Cooler Effectiveness: When Wet-Bulb Depression Exceeds 20°F vs. When It's Below 5°F
Direct evaporative cooler supply temperature approaches T_wb through evaporation along the constant-T_wb line per ASHRAE Fundamentals 2021 Chapter 1 Section 1.9. Saturation efficiency expresses this relationship:
η_sat = (T_db_in − T_db_out) / (T_db_in − T_wb_in) × 100%
High-quality direct evaporative coolers with 10–12 inch rigid media (CELdek or GlasDek) achieve 85–93% saturation efficiency per Building America Solution Center documentation. Legacy 2-inch excelsior media achieves 50–80%.
Climate suitability per Building America Solution Center criteria: design wet-bulb below 70°F (21°C) indicates excellent suitability for direct evaporative cooling as a primary system; 70–74°F (21–23°C) is marginal and indirect-direct two-stage systems are preferred; above 74°F (23°C) direct evaporative is inadequate and mechanical refrigeration is required.
Wet-bulb depression defines performance potential across four ranges:
Depression above 20°F (11°C) — dry climates, ASHRAE Climate Zones 2B and 3B. Phoenix summer T_db = 110°F, T_wb = 70°F, depression = 40°F. A direct evaporative cooler at 90% efficiency delivers supply air at 110 − 0.90 × 40 = 74°F. Adequate space cooling without mechanical refrigeration.
Depression 10–20°F (5.6–11°C) — moderate climates, Zone 3C coastal. San Francisco summer T_db = 75°F, T_wb = 60°F, depression = 15°F. Supply air at 75 − 0.85 × 15 = 62°F; marginal for residential, inadequate for commercial loads.
Depression 5–10°F (3–5.6°C) — humid climates, Zones 2A and 3A. Sarasota, Florida: T_db = 92°F, T_wb = 79°F, depression = 13°F per Building America documentation. Supply air at 92 − 0.85 × 13 = 81°F — inadequate cooling. Indirect-direct two-stage evaporative cooling can in theory deliver supply approaching T_dp per Eng-Tips forum thread 423615 (cooling below wet-bulb), but only with a first-stage indirect heat exchanger that reduces both T_db and T_wb of the primary stream.
Depression below 5°F (3°C) — very humid climates, Zone 1A. Miami peak hours: T_db = 90°F, T_wb = 80°F. Mechanical refrigeration required per ASHRAE Standard 90.1-2022 Section 6.4. Direct evaporative cooling raises indoor humidity above the 60% RH ceiling per ASHRAE Standard 55-2023 Section 5.2.4.
For ASHRAE Climate Zones 2B–3B with design wet-bulb below 70°F, evaporative cooling primary systems deliver 60–80% energy savings versus vapor compression per ANSI/ASHRAE Standard 133-2008 (Method of Testing Direct Evaporative Air Coolers) testing methodology. ANSI/ASHRAE Standard 143-2015 covers indirect unit performance rating.
WBGT Heat Stress and the 35°C Wet-Bulb Survivability Threshold
Wet-bulb temperature is the dominant term in the Wet Bulb Globe Temperature heat stress index per ACGIH 2024 TLV for Heat Stress and Strain (American Conference of Governmental Industrial Hygienists). OSHA Technical Manual Section III Chapter 4 (Heat Stress) cites WBGT as the primary occupational heat stress indicator.
WBGT formulation: outdoors with solar load: WBGT = 0.7 × T_nwb + 0.2 × T_g + 0.1 × T_db. Indoors or outdoors without solar load: WBGT = 0.7 × T_nwb + 0.3 × T_g. Variables: T_nwb = natural wet-bulb (no forced aspiration); T_g = globe thermometer reading; T_db = dry-bulb. Per ASHRAE Fundamentals 2021 Chapter 1 commentary, natural wet-bulb T_nwb typically reads 1–3°F (0.5–1.7°C) higher than the thermodynamic wet-bulb computed by this calculator. The 0.7 weighting makes T_nwb the dominant WBGT component.
ACGIH 2024 TLV thresholds for continuous work (unacclimatized): light work ≤ 30°C (86°F) WBGT; moderate work ≤ 26.7°C (80°F); heavy work ≤ 25°C (77°F); very heavy work ≤ 25°C only with full acclimatization. Beyond these thresholds, the work-rest cycle shifts to 75/25, then 50/50, then 25/75, then work cessation.
The 35°C (95°F) wet-bulb survivability threshold per Sherwood and Huber (2010, Proceedings of the National Academy of Sciences) represents the theoretical limit above which the human body cannot dissipate metabolic heat through perspiration regardless of shade, hydration, or air velocity. Skin must maintain temperature above 35°C for metabolic function; when T_wb reaches 35°C, evaporative skin cooling reverses direction and skin gains heat from the air. Hyperthermia results within approximately 6 hours regardless of fitness level or acclimatization. Raymond et al. (2020, Science Advances) documented brief wet-bulb spikes to 35°C in the Persian Gulf, South Asia, and Mexico's Gulf Coast; climate models project T_wb ≥ 35°C events increasing 10–100× from 2000 baseline by 2050. ASHRAE Standard 55-2023 Section 5.2.4 humidity comfort criteria assume T_wb below 26°C (79°F); occupant survival design margins disappear at 30°C wet-bulb.
For occupational heat stress calculations, this calculator provides psychrometric (aspirated) wet-bulb. WBGT calculations require natural wet-bulb measurement or a conversion factor; consult OSHA Technical Manual Section III Chapter 4 for conversion methodology.
Where the Magnus Approximation Fails Above 65°C and Below −40°C
Magnus accuracy bands per Alduchov & Eskridge (1996) and ASHRAE Fundamentals 2021 Chapter 1: ±0.4% from −40°C to +50°C (full HVAC operating range); ±2–3% from −50°C to −40°C or from +50°C to +65°C; above 5% error from +65°C to +100°C; above 10% error below −50°C or above +100°C.
Sprung constant validity: A = 0.000437 °F⁻¹ applies to aspirated sensors at ≥ 3 m/s per ASHRAE Standard 41.6-2014 (RA2021). Naturally ventilated sensors produce A values 1.3–1.7× larger; the resulting humidity ratio error is 5–15%. Solar radiation effects on unshielded dry-bulb sensors can elevate T_db readings by 2–5°F without a radiation shield per ANSI/ASHRAE Standard 41.1-2020 Section 5.4.
Application-specific validity: HVAC design over −10°C to +45°C and RH 20–95% — Magnus plus Sprung within ±1% of true psychrometric values; cooling tower commissioning per CTI ATC-105-2019 — within tolerance provided aspiration velocity ≥ 3 m/s is confirmed; industrial drying at T_db 60–150°C — Magnus inadequate, use Hyland-Wexler formulation per ASHRAE Fundamentals 2021 Chapter 1 Equations 5–6; cryogenic applications below −50°C — Magnus inadequate, use IAPWS-IF97 industrial steam tables; high-altitude installations above 1000 ft — standard atmospheric pressure assumption introduces error, apply altitude correction per ASHRAE Fundamentals 2021 Chapter 1 Equation 3.
Alternative libraries for extended-range applications: ASHRAE LibHuAirProp (C/Python wrapper, full Hyland-Wexler); CoolProp open-source library; NIST REFPROP; IAPWS-IF97 industrial steam tables (−50°C to +800°C, ±0.05% accuracy); Engineering Equation Solver with psychrometric library.
Per Eng-Tips forum thread 210192 (Defining Design Wet Bulb Temperature): for design wet-bulb determination, use ASHRAE-tabulated 0.4% or 1% annual exceedance values from ASHRAE Fundamentals 2021 Chapter 14 Climatic Design Conditions database, not values calculated from peak DB and separate peak RH. ASHRAE tabulation accounts for temperature-moisture co-occurrence statistics over 30-year hourly observation data; calculating peak WBT from peak DB and peak RH separately overestimates design WBT by 2–4°F per forum consensus.
Wet Bulb Temperature Calculator
Wet-bulb temperature calculation with iterative Newton-Raphson solver on the Sprung psychrometric equation, support for three input combinations (T_db + RH, T_db + T_dp, T_db + W), and derived properties including depression, RH, W, dew point, vapor pressure, and enthalpy are available in the Wet Bulb Temperature Calculator.
FAQ
How do I determine design wet-bulb temperature for a cooling tower? Is it the peak summer WBT or something else?
Use ASHRAE Climatic Design Conditions tabulated 0.4% or 1% annual exceedance wet-bulb per ASHRAE Fundamentals 2021 Chapter 14. The 0.4% value means wet-bulb is exceeded for no more than 35 hours per year (0.4% × 8,760 hours); 1% corresponds to 88 hours. Calculating WBT from peak summer DB and peak RH separately overestimates design WBT by 2–4°F per Eng-Tips forum thread 210192 consensus, because peak DB and peak RH rarely coincide. ASHRAE tabulation accounts for temperature-moisture co-occurrence statistics from 30-year hourly observation data.
My cooling tower vendor sized for 78°F design WBT but the local NOAA station shows peak WBT of 81°F on some summer days. Should I oversize to 81°F?
No. Size to the ASHRAE 0.4% or 1% exceedance value, not the absolute peak. For Indianapolis, ASHRAE Fundamentals 2021 Chapter 14 lists 78°F as the 0.4% summer wet-bulb, covering 99.6% of annual hours. Brief excursions to 81°F cause temporary approach excursion of 3°F warmer leaving water; chiller condenser temperature rises proportionally; efficiency degrades 6–9% during those hours per AHRI Standard 550/590-2023 partial-load curves. This is acceptable per ASHRAE Standard 90.1-2022 design philosophy. Sizing to peak 81°F WBT requires a 30–50% larger tower providing marginal benefit for 35–88 hours per year per Eng-Tips forum thread 121173 vendor selection consensus.
I saw a manufacturer claim their evaporative cooler delivers air below wet-bulb temperature. Is this physically possible or marketing?
Physically possible with two-stage indirect-direct evaporative architecture per Eng-Tips forum thread 423615. A single-stage direct evaporative cooler cannot drop supply T_db below entering T_wb. A two-stage system first cools primary air through a heat exchanger without adding moisture, reducing both T_db and T_wb of the primary stream; the second direct stage then evaporates along the new, lower constant-T_wb line. Final supply T_db can theoretically approach entering T_dp in the ideal limit. Real-world products such as Climate Wizard achieve this. The bound for a two-stage system is dew point, not wet-bulb; the bound for a single-stage direct evaporative remains T_wb.
How do I calculate evaporative cooler effectiveness when I know only inlet and outlet dry-bulb temperatures?
Use saturation efficiency per Eng-Tips forum thread 173795: η_sat = (T_db_in − T_db_out) / (T_db_in − T_wb_in) × 100%. You need inlet dry-bulb, inlet wet-bulb (compute with this calculator using Combination A or B), and outlet dry-bulb. Example: T_db_in = 90°F, T_wb_in = 70°F, T_db_out = 75°F. η_sat = (90 − 75) / (90 − 70) × 100% = 75%. Modern 10–12 inch rigid media achieves 85–93% per Building America Solution Center; legacy 2-inch excelsior media achieves 50–80%.
Sling psychrometer reads 75°F WB but a Fluke 971 computes 72°F WB from the same DB and RH. Which is correct for cooling tower commissioning?
A properly aspirated sling psychrometer with whip rate sustaining ≥ 1,000 fpm (3 m/s) air velocity, distilled water, and a clean cotton wick (replaced quarterly per ASHRAE Standard 41.6-2014) provides direct measurement of thermodynamic wet-bulb. The Fluke 971 capacitive sensor inherits ±2–3% RH sensor uncertainty, translating to ±0.5–1.0°F computed wet-bulb. For commissioning per CTI ATC-105-2019 Section 5.3, direct wet-bulb measurement is preferred over computed value. If the sling reads systematically high, verify aspiration velocity, wick condition, and water source (distilled only). A chilled-mirror hygrometer (RH Systems 933) with ±0.2°C dew point accuracy per ASTM E337-15 resolves any sling-versus-computed dispute as a reference instrument per HVAC-Talk thread 305312.
Related Calculations
Cooling tower approach analysis for tower selection and performance evaluation uses the Cooling Tower Calculator, applying entering wet-bulb to approach (T_leaving − T_wb_entering) per CTI STD-201RS-2017 thermal performance methodology. The same tool applies wet-bulb input together with range and approach to compute thermal efficiency per CTI ATC-105-2019.
Complete moist-air state including humidity ratio, enthalpy, and specific volume from dry-bulb and RH is available in the Psychrometric Calculator. Absolute moisture content for latent load calculations is derived in the Humidity Ratio Calculator. Cooling coil total capacity from entering and leaving enthalpy states is calculated in the Enthalpy Calculator per ASHRAE Handbook HVAC Systems 2024 Chapter 23 Section 23.4.
Condensation risk on chilled water piping or supply diffusers requires dew point comparison to surface temperature in the Dew Point Temperature Calculator per ASHRAE Standard 160-2021 Section 5. Cooling coil sensible heat ratio for coil row depth selection is covered by the Sensible Heat Ratio Calculator.