Carburettor ice is made by the fuel, not the venturi

Not half a venturi takes apart the favourite wrong explanation of lift — the wing as half a venturi — and finds every step of the story true and the whole of it no explanation. The carburettor is the machine the venturi story is literally about, and it carries a second version of the same problem. Every pilot of a piston aircraft is taught that a carburettor can ice in clear air on a mild day, and the usual reason given is the venturi: the air speeds up through the throat, its pressure falls, and air whose pressure falls cools.

Each clause is true. The air does speed up, its pressure does fall, and it does cool. The question is by how much, compared with what else is going on in the throat, and whether the cooling reaches the surfaces the ice actually grows on. The answer is that the venturi is a minor contributor, that the cold is the fuel’s, and that the icing is decided by the water in the air.

Three things change the temperature #

Three processes change the temperature in a carburettor throat, and they are worth separating before any one of them is blamed.

The air expands. Accelerated adiabatically to a speed $V$, air drops its static temperature by $V^2/2c_p$. That is a statement of energy conservation — Bernoulli’s energy form for a compressible gas — and it is exact.

The fuel evaporates. Petrol sprayed into the throat takes its latent heat of vaporisation from the air around it. At an air–fuel ratio $A$, with a fraction $\varphi$ of the fuel evaporating, each kilogram of air loses $\varphi\,h_{fg}/A$.

The water condenses. Humid air cooled below its dew point can no longer hold its vapour, and the excess condenses — as liquid above freezing and as ice below it — releasing its latent heat back into the mixture.

What the venturi does, and what the metal feels #

A carburettor’s venturi at full throttle accelerates the air to something like a hundred metres a second. The expansion cools the moving air by $100^2/(2 \times 1005)$ = 4.98 kelvin. At twice the speed it would be twenty.

Ice does not form in the moving air, though; it forms on metal — the venturi’s walls, the fuel nozzle, the throttle plate. And a surface in a moving gas does not sit at the gas’s static temperature. The gas brought to rest against it in its boundary layer recovers most of its kinetic energy as heat, and an uncooled surface settles at the recovery temperature, $T + rV^2/2c_p$, with a recovery factor $r$ of about 0.89 for a turbulent layer. So the metal sits only $(1 - r)V^2/2c_p$ below the incoming air’s temperature: 0.55 kelvin at a hundred metres a second, 2.2 at two hundred.

The same arithmetic explains why a thermometer on an aircraft reads warm, why a wall in a fast flow heats itself, and why the venturi cannot be the main source of carburettor ice. The throat’s expansion is a real cooling of the moving gas and a trivial cooling of anything the gas flows over. Even at the throttle plate at part throttle, where the air squeezing past the plate’s edge can approach the speed of sound and its static temperature can dip by forty-eight kelvin, the plate itself — at the recovery temperature — is cooled by about five. That is enough to matter on a day within a few degrees of freezing, and the icing literature does name it, as throttle ice, a part-throttle form separate from the fuel’s; it is the one place the expansion earns a share.

What the fuel does #

Petrol has a latent heat of vaporisation of about 350 kilojoules a kilogram, and a carburettor mixes it with air at about one part in twelve and a half by mass for the rich mixture engines run at high power. If all of it evaporates, each kilogram of air gives up $350\,000/12.5$ joules, and its temperature falls by $28\,000/1005$ = 27.9 kelvin. If half evaporates in the throat and the rest later, 13.9.

Either figure dwarfs the venturi’s. And unlike the expansion, the evaporation’s cooling is not recovered at the walls: fuel that lands on metal and evaporates there chills the metal directly, and fuel evaporating in the stream cools the gas that then flows over the metal. The fuel’s cooling is where carburettor ice gets its cold.

The strongest evidence for this is a comparison of engines rather than a calculation. A fuel-injected engine has a throttle body with the same kind of restriction and the same expansion, but its fuel is injected downstream, near the cylinders. It keeps the venturi’s cooling and loses the fuel’s, and it is far less prone to induction icing — which is how aviation authorities explain the difference. If the venturi were the cause, the throttle body would ice just as often.

What the water does #

Cold alone does not make ice; water does, and here the humidity of the day enters twice. It supplies the water that can freeze, and in condensing, it heats the mixture.

The mixture’s temperature is the solution of an energy balance: the air’s heat capacity times its cooling equals the fuel’s latent heat taken, less the latent heat released by whatever water condenses. Water condenses only when the cooled mixture is below its dew point at the carburettor’s pressure — reduced below the day’s by the throttle — and the saturation vapour pressure is taken from Magnus’ formula, over liquid water above freezing and over ice below it. The balance is solved by bisection and closes to a part in $10^{16}$.

Dry air on a 20 °C day cools to −7.9 °C. The same air at 90 per cent humidity cools only to +6.8 °C: the water it drops as it cools past its dew point gives back fourteen and a half kelvin of heat. Humid air cannot be cooled as far as dry air by the same fuel, because some of the fuel’s work goes into condensing the water rather than into cooling the air.

That is the reason carburettor ice has such a peculiar dependence on the weather. A humid day supplies more water to freeze and also resists being cooled to freezing, and the two effects pull against each other.

Where the mixture freezes with water to freeze #

The map shows where the mixture ends up below freezing. In dry air the fuel’s cooling alone takes the mixture below zero on days up to 25 °C. As the humidity rises the boundary retreats, because condensation holds the mixture up, and at 90 per cent humidity the mixture freezes only on days of 15 °C and below. With half the fuel evaporating in the throat the whole region shrinks by about fourteen degrees.

Being below freezing is not enough for ice; there must also be water that condenses. Cold dry air has almost none — at −10 °C and 90 per cent humidity it holds under one and a half grams of vapour per kilogram of air — so it freezes readily and leaves little to freeze.

Put the two conditions together and the amount of ice a kilogram of air can leave in the throat — its condensate, while the mixture is below freezing — peaks sharply. At 90 per cent humidity it is 1.3 grams per kilogram at −10 °C, rises to 5.0 at 15 °C, and falls to nothing a few degrees warmer, where condensation starts to keep the mixture above zero. The worst day for carburettor ice is a mild, humid one. It is exactly the day pilots are taught to fear, and the arithmetic says why: cold enough for the fuel’s cooling to reach freezing, and warm enough to be carrying plenty of water.

How much ice, and how fast #

The severity figure is per kilogram of air, and an engine breathes a great deal of air. A 180-horsepower aircraft engine at full power burns about thirty-four kilograms of fuel an hour, and at an air–fuel ratio of twelve and a half draws about 0.12 kilograms of air a second through its carburettor. On the worst day of the figure, five grams of water per kilogram of that air condense below freezing: 0.6 grams a second, thirty-five grams a minute.

Most of that water leaves as droplets or snow in the mixture and is swallowed by the engine. The part that matters is the part that sticks, and it does not have to be much. A throat five centimetres across and five long has a wall area of about eighty square centimetres, and a layer of ice two millimetres thick over it weighs fifteen grams. If a tenth of the condensate deposits, that layer builds in about four minutes; if one per cent, in about forty — the range between a sudden loss of power and a slow one that a pilot might not notice until it has gone far.

The consequence is the one the story of the venturi gets right. A throat narrowed by ice passes less air at the same pressure drop, and since the carburettor meters fuel by that drop, the mixture richens as the power falls. An engine icing in cruise loses power slowly and runs roughly — which a pilot will first notice as a gradual fall in engine speed or manifold pressure — and ice at the throttle plate can eventually jam it. A venturi’s throat is a sensitive place to put an obstruction, because the flow through it is decided there.

Why the story blamed the venturi #

The venturi is the part of a carburettor a diagram shows, and the principle it demonstrates — faster air, lower pressure — is the one every account of carburettors starts from. Lower pressure and lower temperature go together in an expanding gas, so the cooling seems to come free with the explanation of how the device works. Nothing in that chain is false; what fails is the proportion, and the proportion is invisible in a diagram.

The same slip appears wherever a temperature is quoted without saying which one. The static temperature of the moving air, the temperature of a surface in it and the total temperature of the stream are three different numbers, and three readings of one flow can disagree by exactly the kinetic energy’s worth. The venturi story quotes the first and applies it to the second. The fuel’s cooling, by contrast, is the same in all three, because it removes heat rather than converting it into motion.

The fuel’s cooling has an exact counterpart in liquid flow. A cavitating flow draws the latent heat for its vapour from the liquid next to the cavity, and a cavity that cools the water it came from is suppressed by that cooling in hot water and in cryogenic fuels. In a carburettor the same heat of evaporation, taken from the air instead of the liquid, is what brings the throat down to freezing.

Why real carburettors ice on warmer days than this #

The icing charts pilots use, which are empirical, put the risk of serious icing up to about 30 °C on humid days, several degrees beyond the region the well-mixed calculation gives. The difference is the calculation’s own simplification, and it points at the same culprit.

The calculation mixes the fuel’s cooling uniformly through the air. A real carburettor does not. Fuel sprayed from the nozzle wets the walls and the throttle plate, and fuel evaporating from a wetted surface chills that surface far below the temperature of the gas passing over it, in the same way a wet cloth in a breeze stays colder than the air. Water vapour that reaches such a surface meets a temperature well below the mixture’s, condenses, and freezes, even when the mixture itself is above zero. The coldest metal in a carburettor is the fuel-wetted metal, and that is where ice grows first — at the throttle plate and the nozzle, not on the smooth walls of the venturi.

So the refinement moves the region the right way and for the right reason. It widens the danger by making the fuel’s cooling more concentrated, not by giving the venturi a larger role.

What carburettor heat does #

The remedy the arithmetic implies is the one used: warm the air before it reaches the carburettor. Carburettor heat draws intake air over the exhaust manifold, raising its temperature by tens of kelvin. On the worst day of the severity figure — 15 °C at 90 per cent humidity — preheating by twenty kelvin leaves the mixture at 9.3 °C after the fuel has evaporated, and by thirty at 17 °C. The water content is unchanged, but it no longer reaches its dew point cold enough to freeze.

The cost is density. Air thirty kelvin warmer is about ten per cent less dense, so the engine breathes ten per cent less mass and makes correspondingly less power, which is why carburettor heat is applied when ice threatens rather than all the time. Preheating also runs the mixture richer, since the carburettor meters fuel by the pressure drop and not by mass flow, which is a smaller effect of the same kind.

What the picture cannot show #

A well-mixed throat. All the cooling is shared uniformly with the air. Fuel-wetted surfaces are colder than the well-mixed gas, which is why real icing extends beyond the region the calculation gives.

Equilibrium. The water that should condense does, instantly, and the fuel that evaporates does so completely at the stated fraction. Real condensation needs nuclei and time, and supersaturated vapour can persist into the cold region, which again favours deposition on surfaces over condensation in the stream.

One fuel. Petrol is a blend, its lighter fractions evaporate first, and its latent heat varies by about a fifth between blends. The air–fuel ratio of 12.5 is a rich power setting; at leaner cruise settings the fuel’s cooling is smaller in proportion.

The convention the numbers depend on #

Temperatures are in degrees Celsius for the day and the mixture, and differences in kelvin. The carburettor is taken at 85 kilopascals, a part-throttle pressure, with the day’s humidity measured at sea-level pressure. The recovery factor of the metal is 0.89. “Ice available” is the water, per kilogram of dry air, that condenses while the mixture is below freezing.

Who found it, and when #

Induction icing was recognised as a cause of engine failures in the 1920s and 1930s, as aircraft began to fly routinely in cloud and humid air. The systematic studies were the United States National Advisory Committee for Aeronautics’ in the 1940s, which measured icing in instrumented induction systems and established that fuel evaporation, not the venturi’s expansion, supplied most of the cooling, and that throttle plates and fuel nozzles iced first. The empirical charts pilots use today descend from that work and from later measurements by aviation authorities.

Still open: the temperature of a wetted plate #

The calculation’s biggest simplification is also its most interesting correction. A fuel-wetted surface in the air stream reaches a temperature set by a balance between the heat the stream brings to it and the heat its evaporating fuel takes away — a wet-bulb temperature for petrol rather than for water. It depends on the fuel’s vapour pressure, which for petrol’s volatile fractions is large, and on the ratio of heat to mass transfer in the boundary layer, which Reynolds’ analogy supplies. The calculation that follows computes that surface temperature for a representative blend and asks how far above the well-mixed boundary it moves the icing region — whether it accounts for the charts’ extension to 30 °C, or whether something else, such as the throttle plate’s own heat conduction from the engine, has to be added.