1. The Thermal Model

Newton's Law of Cooling

An engine sitting outside behaves like any warm object in a cold environment: it loses heat to the air at a rate proportional to how much warmer it is than that air. This is Newton's Law of Cooling. Left long enough, the engine will reach the same temperature as the ambient air — it converges.

The continuous form of the equation is:

Because the weather data arrives in hourly steps, the model is discretized — one step per hour. At each hour boundary, the engine temperature advances by:

What tau means physically

Tau is the time it takes the engine to close roughly 63% of the gap between its current temperature and the ambient temperature. After 3×tau the engine is 95% of the way there; after 5×tau it has converged to within 1%.

For a freshly shut-down engine on a cold night, that gap starts large — maybe 300°F or more. The engine is well within 5°F of ambient after roughly five time constants, which is 9–15 hours depending on the engine.

Initial conditions

The model starts from the oldest weather data point in the fetch window (48 hours of history by default) and initializes engine temperature equal to the ambient temperature at that moment. The assumption is that any flight activity or pre-existing heat has long since dissipated. If you just landed, you can override this with the Engine Temp advanced setting to set a realistic starting point.

2. Engine Data and Thermal Capacity

Where the engine specs come from

Each engine entry in the database was compiled from published manufacturer specifications and type certificate data. The data recorded for each engine:

• Dry weight (lbs) — the engine mass without oil or fuel
• Cylinder count — used in surface area scaling
• Displacement (cubic inches) — used in surface area scaling
• Oil capacity (quarts) — oil contributes meaningfully to thermal mass
• Aluminum fraction / Steel fraction — estimated material breakdown by weight

Lycoming four-cylinder engines (O-235, O-320, O-360, IO-360) use 68% aluminum / 32% steel. Six-cylinder engines from both Lycoming and Continental use 65% aluminum / 35% steel — slightly more steel due to larger crankcases and heavier crankshafts. Continental's O-200 runs 70% aluminum / 30% steel, reflecting its lighter all-aluminum construction.

Computing thermal capacity

The thermal capacity C (in BTU/°F) tells us how much energy is required to change the engine's temperature by one degree. It is computed from the material breakdown and the specific heat of each material:

Example worked out for the Lycoming O-320:

Surface area factor

How fast an engine sheds heat depends not just on how much thermal mass it has, but on how much surface area it exposes to the air. More cylinders and larger displacement both increase surface area. The model approximates the exposed surface area using:

The exponent 2/3 comes from the geometric relationship between volume and surface area for similar shapes — if you scale a cylinder up by a volume factor k, its surface area scales by k^2/3. Each cylinder of larger displacement has more surface area, and more cylinders multiply that further.

Computing tau for any engine

The O-320 is the reference engine, with a calibrated tau of 3.0 hours. This value was chosen to match observed real-world cold soak behavior — an O-320 on a still winter night is well within 5°F of ambient after about 15 hours. Every other engine's tau is scaled from this reference by the ratio of thermal capacities and the inverse ratio of surface area factors:

A bigger engine with more thermal mass (higher C) takes longer to cool — tau goes up. A bigger engine also has more surface area (higher SA), which speeds cooling — tau goes down. These two effects partially cancel. In practice, displacement matters more than cylinder count alone, and larger engines tend to have slightly shorter tau than you might expect because their surface area scales faster than their mass.

3. Cowl Plugs

Cowl plugs block the openings in the engine cowling through which most convective cooling occurs. With plugs installed, the air movement across cylinder fins is sharply reduced, and the engine loses heat primarily through conduction to the cowling structure rather than by forced or natural convection across exposed metal.

The model accounts for this with a simple multiplier on tau:

A 40% increase in the time constant means the engine retains heat noticeably longer. For an O-320 at tau = 3.0h, plugs extend that to 4.2h. The 63% convergence milestone — the point where the engine has closed most of the gap to ambient — shifts from 3.0h to 4.2h: 72 minutes later.

The 1.4 factor is a calibrated estimate. Real-world cowl plug performance varies by installation, ambient wind, and how well the plugs seal. If your engine consistently reads warmer than the model predicts with plugs installed, you can fine-tune using the tau override in Advanced settings.

4. Solar Heating Model

Why solar matters

On a clear winter morning, direct sunlight on a dark cowling can add 5–15°F to an engine's temperature compared to a shaded or overcast situation. This isn't cosmetic — it can push an engine from RED into YELLOW, or YELLOW into GREEN. Ignoring solar on a clear day produces a meaninglessly pessimistic result.

Cowl color absorptivity

Different surface colors absorb different fractions of incident solar radiation. The model uses standard solar absorptivity values for common aircraft finishes:

A black cowling absorbs 6.4× more solar energy than bare polished aluminum. If you have a white plane, the solar correction is small and you can safely leave the default or switch to the white option. If you have a dark blue Cessna, the default is already correct.

The solar factor

Solar radiation from Open-Meteo (in watts per square meter) is converted into a temperature contribution through a chain of unit conversions and scaling factors. The result is a single number — the solar factor — in units of °F per W/m². Each hourly solar reading is multiplied by this factor to get the solar temperature delta added to the ambient temperature before the cooling step runs.

The solar factor connects the incoming power (watts per square meter of cowling) to a steady-state temperature lift. The τ/C ratio represents how effectively the engine retains the solar energy — engines with high thermal capacity (large C) show less solar heating because they absorb the same power across more mass.

Effective solar area

The physical cowling on a GA aircraft might present 0.3–0.7 m² to the sun. But not all absorbed heat reaches the engine core. Most is re-radiated from the cowling surface, and only a fraction penetrates to the cylinders and oil. The model uses an effective area of 0.10 m² for the reference O-320 — roughly 20% of the physical cowl area. This was calibrated to produce approximately a 10°F solar lift on a clear winter day (600 W/m²) with a dark blue cowling, which matches pilot reports.

For other engines, the effective area scales with the surface area factor:

For the O-320 with dark blue paint at 600 W/m² (typical clear winter sun):

When solar is applied

Open-Meteo provides hourly shortwave radiation values. At night, this is zero — the solar term vanishes automatically, so the model is identical to the pure cooling model from sunset to sunrise. No additional logic is needed to "turn off" solar; a zero solar reading simply produces a zero delta.

5. Frost Risk Model

Why frost point, not dewpoint

Dewpoint is the temperature at which air is saturated with respect to liquid water. Below freezing, the relevant threshold is the frost point — the temperature at which air is saturated with respect to ice. Because ice has a lower saturation vapor pressure than supercooled liquid water at the same temperature, the frost point is always slightly higher than the dewpoint when temperatures are below 0°C. If you're checking whether ice will form on your wings, the frost point is the correct threshold.

Magnus formula for frost point

Starting from the dewpoint (in °F, converted to °C), the model computes the actual vapor pressure using the Magnus formula, then inverts a modified Magnus formula calibrated for ice saturation to find the frost point:

Example: dewpoint of 20°F (−6.7°C) gives a frost point of about 21.4°F — slightly higher, because ice needs less moisture to saturate than liquid water does at the same temperature.

Radiative cooling: nighttime vs. daytime

On a clear, calm night, aircraft surfaces cool below the ambient air temperature through radiative emission to the sky. Thin aluminum wing skin has very low thermal mass — it sheds stored heat rapidly, and surface temperatures can drop 3-8°F below ambient. The model uses 5°F as the nighttime radiative cooling estimate, in the middle of observed values.

During daytime, the physics change fundamentally. Even under heavy overcast, the atmosphere radiates longwave (thermal infrared) energy back toward the surface — clouds act as a thermal blanket. This is why frost overwhelmingly forms on clear nights: overcast skies prevent the radiative heat loss that drives surface temperatures below ambient. During the day, surfaces stay within about 1°F of ambient temperature regardless of cloud cover.

The distinction matters because low shortwave radiation means different things at different times. At night, 0 W/m² is simply the absence of sunlight — clear or cloudy, there's no solar input. During the day, low shortwave (50-100 W/m²) means heavy overcast — and those same clouds that block the sun are radiating longwave energy back, suppressing radiative cooling.

The dual frost condition

Frost is flagged when two conditions are both met:

Both conditions must be true. If the surface is at 30°F but the frost point is only 20°F, there is not enough moisture in the air to deposit ice — no frost warning. If the frost point is 28°F and the estimated surface is 29°F, ice won't form either, because the surface is above the frost point. Ice forms only when the surface is cold enough to freeze and the air has enough moisture to deposit.

Frost persistence

Once frost has formed on a surface, it does not vanish the moment conditions briefly improve. If the estimated surface temperature climbs a degree or two above freezing for an hour, the frost that deposited at 7 PM is still sitting on the wing at 11 PM. The model accounts for this with a sticky frost rule: once frost is flagged, it remains flagged until the estimated surface temperature has been above 32°F for at least 1 consecutive hour.

Pilot reports and research consistently show frost clears from thin aluminum wing skin within 15-60 minutes of direct sun, or within 1-2 hours on cloudy mornings as ambient air warms above freezing. The 1-hour threshold reflects this: enough time for the metal to genuinely warm through without holding a stale frost flag into mid-morning.

6. Weather Data Sources

Open-Meteo (temperature, solar, dewpoint)

Hourly ambient temperature, shortwave solar radiation, and dewpoint are fetched from Open-Meteo using the latitude and longitude of the selected airport. The request fetches 2 days of history and 7 days of forecast, giving the thermal model a realistic running start from 48 hours of observed temperatures. The three fields requested are:

• temperature_2m — air temperature at 2 meters above ground, in °F
• shortwave_radiation — downwelling solar irradiance at surface, in W/m²
• dewpoint_2m — dewpoint at 2 meters above ground, in °F

Open-Meteo blends model output statistics with observational data to produce gridded hourly forecasts. The grid resolution is on the order of 1–11 km depending on region and model layer. Local effects — valley inversions, lake breezes, terrain shadowing — may not be captured.

AWC (METAR and airport lookup)

Airport location (latitude, longitude, elevation) is resolved through the Aviation Weather Center station info API. The tool sends the ICAO identifier you enter; if no match is found and you typed a three-letter code, it also tries prepending "K" (so "HVN" automatically tries "KHVN"). If the resolved station has no METAR available, the tool searches a 0.5° bounding box and substitutes the nearest reporting station.

The current METAR (when enabled) is fetched from the same AWC API. It is shown for situational awareness and is not directly used in the thermal model computation — the model runs on Open-Meteo data.

Airport location → weather grid

Open-Meteo is queried with the airport's exact latitude and longitude from the AWC station record. The weather forecast is therefore centered on the airport, not on the nearest city or weather station. For most GA airports, this is close enough. For airports in unusual terrain or microclimates, ground truth may differ from the gridded forecast.

7. Status Thresholds

The engine temperature estimate is classified into one of three status levels:

The real problem is not oil viscosity

The standard explanation for cold-start damage is that cold oil is thick, slow to circulate, and leaves engine parts running dry during the first seconds after startup. It's intuitive. It's also largely wrong, at least for modern engines.

Today's multigrade aviation oils — 15W-50, 20W-50 — are formulated to flow at low temperatures. Even at 0°F, these oils move adequately through the lubrication system. A pilot who watches the oil pressure gauge climb normally after a cold start concludes that everything is fine. As Mike Busch of Savvy Aviation has written, the real cause of cold-start engine damage is something most pilots never think about: differential thermal expansion of dissimilar metals.

Aluminum contracts twice as fast as steel

Aircraft piston engines are assemblies of two very different materials. The crankcase, pistons, and cylinder heads are aluminum. The crankshaft, connecting rods, cylinder barrels, and piston pins are steel. At room temperature, these components are machined to precise clearances — enough room to move freely, not so much that they slap around.

The problem is that aluminum's thermal expansion coefficient is roughly twice that of steel. As temperature drops, aluminum contracts twice as much as steel does over the same temperature change. Clearances that were designed for room temperature shrink — sometimes dramatically.

Continental specifies a minimum crankshaft bearing clearance of 0.0018 inch for its 470/520/550 series engines at room temperature. Testing conducted by Tanis Aircraft Products measured a clearance reduction of 0.002 inch at −20°F — meaning an engine assembled to minimum Continental tolerances could have zero or slightly negative bearing clearance at that temperature. The crankshaft is effectively seized before it turns a single revolution.

Piston-to-cylinder dynamics add a second failure mode running in the opposite direction. After a cold start, aluminum pistons heat and expand rapidly while the steel cylinder barrels warm slowly, held back by their thermal mass and the cooling fins drawing heat away. The piston-to-cylinder clearance that started dangerously tight gets even tighter as the pistons expand faster than the barrels, risking metal-to-metal scuffing before the engine reaches operating temperature.

Why 32°F and 20°F are the breakpoints

Busch frames the threshold question in terms of severity. A cold start below 32°F is what he calls a "misdemeanor" — real risk, real wear, but the engine will probably turn. A cold start below 20°F is a "felony." The damage is cumulative, and it gets measurably worse the colder the engine gets. As he puts it: "A single cold start without proper preheating can produce more wear on your engine in less than a minute than 500 hours of normal cruise operation."

32°F is the first hard line: below freezing, bearing and piston clearances are meaningfully reduced from their design values, and every degree colder compounds the problem. 20°F is where the risk becomes severe enough to warrant treating preheat not as a recommendation but as a requirement — the clearance math at that temperature leaves little margin.

The GREEN threshold at 32°F reflects the physical reality that above freezing, aluminum and steel contraction is modest and within the design envelope of modern engines. The YELLOW band from 20°F to 32°F is the range where the risk is real but manageable with a proper preheat — strongly recommended, not optional. Below 20°F, the metal clearance problem becomes severe enough that starting without preheat is the kind of decision that shortens engine life in ways that don't show up until overhaul.

8. Assumptions and Limitations

The model is useful precisely because it's explicit about what it does and does not model. Here's what it gets right and where it falls short:

What the model captures well

• Long cold soaks (8+ hours) in steady or slowly changing ambient temperatures
• Relative differences between engines — a 550ci Continental cools differently than a 200ci Continental
• Daytime solar warming on clear days with known cowl colors
• Frost risk under clear-night radiative cooling, with daytime cloud-blanket suppression
• Overnight cool-down forecasts using weather model data

What the model does not account for

• Wind chill on the cowl. The cooling rate increases with wind speed. The model assumes still-air convection. A steady 20-knot wind across an open ramp can significantly accelerate cooling. If it's windy, treat the estimate as optimistic.
• Hangar vs. tiedown. A hangared aircraft in an unheated hangar still cools to ambient, but without wind the tau is longer than the model assumes. A heated hangar is a completely different scenario — use the Ambient Temp override.
• Recent flight heat beyond the fetch window. If the aircraft flew within the last few hours, the engine is warmer than the model's starting assumption. Use the Engine Temp override in Advanced settings to set a realistic starting point.
• Altitude and density altitude. The model uses sea-level-calibrated material properties. At altitude, thinner air reduces convective cooling somewhat, which means real-world tau may be slightly longer at mountain airports.
• Partial cowl openings. Some aircraft have cowl flaps that can be left partially open or have different effective opening areas. The cowl plug factor is binary (on or off). Reality is more variable.
• Precipitation. Rain or snow on the cowl dramatically changes the heat transfer dynamics. The model has no precipitation correction.
• Internal heat sources. A battery on trickle charge, engine pre-heater running, or a cowl cover trapping residual heat are all situations the model cannot see.
• Weather data latency. Open-Meteo forecasts update several times per day but are not real-time. The most recent hour's data may be a model estimate rather than an observation. METAR data from AWC has similar update latency.

The bottom line on accuracy

For a standard overnight cold soak on a still, clear night with no recent flights, the model is quite accurate — within a few degrees of a direct measurement. As the scenario departs from those conditions, uncertainty grows. Think of it as a well-informed starting point, not a certified reading. Your engine monitor (if equipped) or a cylinder temperature probe gives you ground truth.

9. Further Reading

• Preheating: Whys and Hows — Mike Busch at Savvy Aviation on why preheating matters, what temperature thresholds to use, and the real-world consequences of cold starts.
• FAA AC 91-74B — Pilot Guide: Flight in Icing Conditions. The current FAA advisory circular covering frost, ice, and cold weather flight operations.