Quantitative analysis · version 1.1 · 10 August 2026
Contrails are water vapour. Arithmetic settles the rest.
This site does not argue about photographs of the sky. It takes the claim “those are not condensation trails but deliberate spraying” and treats it seriously — as an engineering programme that somebody would have to design, fund, staff and keep secret. Then it works out what that costs in tonnes, in people and in probability.
The answer cuts both ways: contrail physics was described and used operationally half a century before this theory appeared, and a programme on the required scale would break, on average, after 107 days.
When an engine draws a line across the sky
The condition for a contrail is a thermodynamic inequality with four quantities in it. You can work it out on paper — and that is exactly how it was done in 1953.
A jet engine throws hot, moist exhaust into air at about −55 °C. The plume mixes with its surroundings: it cools and is diluted at the same time. The question is whether, on the way, it reaches supersaturation with respect to water — because then the vapour condenses onto soot particles and freezes instantly.
The key quantity is the slope of the mixing line: how much the partial pressure of water vapour in the plume rises for every kelvin by which the plume cools.
A contrail forms if and only if a line of that slope touches the saturation curve over water. Below the threshold it always forms — regardless of who is at the controls or what they think of the government. Above the threshold it will not form, even if the aircraft passes right overhead.
The claim
“Aircraft never used to leave trails, and now they do — something has changed.”
What the record shows
Contrails were photographed en masse over Europe during the Second World War, and in 1953 Herbert Appleman published a nomogram for forecasting them which the US Air Force used operationally[Appleman 1953]. The military forecast contrails because a contrail gives away a bomber's position. That physics was already half a century old when the word “chemtrails” appeared in the 1990s.
Two things did change: the number of flights (from a few million a year to 35.3 m) and the engines — modern high-bypass designs have a higher propulsion efficiency η, which raises the temperature threshold and makes contrails form across a wider range of conditions.
What actually comes out of the engine
The mass balance closes and can be checked independently: this much fuel goes in, that much product comes out.
Jet kerosene is a hydrocarbon mixture close to C₁₂H₂₃. Burning a kilogram yields about 3.16 kg of CO₂ and 1.24 kg of water. In 2023 the world fleet burned 348.75 billion litres of fuel[ATAG], that is 280 Mt.
That gives a consistency check which cannot be dodged: CO₂ computed from stoichiometry comes to 886 Mt, while the industry reports 882 Mt. Agreement to 100.5 %. If the carbon balance closes, so does the hydrogen balance — and that one says those engines released 348 Mt of water vapour. Which is exactly what you can see in the sky.
Jet fuel is not an arbitrary liquid. The ASTM D1655 / DEF STAN 91-091 standard lists the permitted additives: antioxidants, metal deactivators, corrosion inhibitors, static dissipators and anti-icing additives[ASTM]. In that standard metals are a limited contaminant, not an ingredient — because copper or zinc ruin the thermal stability of the fuel and deposit in the fuel nozzles. A jet engine is an exceptionally expensive and exceptionally sensitive machine; deliberately feeding metal oxides into it would destroy the turbine blades faster than any effect appeared in the sky.
“But soil tests show aluminium, barium and strontium”
They do. They would have done so in 1850 as well. These are the most common elements in the Earth's crust.
Aluminium makes up 8.23 % of the mass of the continental crust — the third most abundant element after oxygen and silicon[Rudnick & Gao]. Clay, road dust, ash, the dust in your flat — all of it contains aluminium in percentages, not in traces. “Aluminium detected in soil” carries about as much information as “water detected in a river”.
Two mistakes recur in the “laboratory reports” that circulate:
| Mistake | What it consists of |
|---|---|
| Swapped units | A soil result in mg/kg (milligrams per kilogram) is compared with a drinking-water limit in µg/l. That is three orders of magnitude and an entirely different matrix. A water limit is not a soil limit — nobody drinks soil. |
| No background, no blank | One sample is taken after rain and announced as an anomaly, without measuring the same spot before the rain or a control site. Without a geochemical background every result is “elevated” relative to a zero that never existed. |
The real test is different and perfectly feasible: if aircraft were the source of the metals, their concentration would have to fall with distance from flight corridors and rise with traffic density. Nobody has demonstrated that relationship. The relationship the data do show is proximity to roads, smelters and mines, and the type of underlying geology.
Suppose it were true. How much would it take?
Here the theory stops being a matter of opinion. Aerosol has mass, mass has to be produced, and raw-material output is counted to the tonne.
There is peer-reviewed literature on how much material you must disperse to change the climate. Smith and Wagner costed a programme with a modest goal: halving the increase in radiative forcing. In its fifteenth year it needs 3.0 Mt of SO₂ a year, released at an altitude of 20 km[Smith & Wagner].
And here comes the problem that no argument about a conspiracy of silence can get around: airliners do not fly in the stratosphere. They fly at 9–12 km, in the troposphere — the layer that contains the weather, the clouds and the rain. Aerosol released at that height is washed out within days to weeks. In the stratosphere it persists for about 22 months[Toohey et al.].
To get the same effect from cruising altitude you have to make up in mass flow what you lose in lifetime — roughly 22 times more material per year. That comes to 66 Mt a year, or 1.87 t on each of the 35.3 m flights.
This figure is a lower bound. It assumes a one-month aerosol lifetime in the troposphere, where the literature says days to weeks, and it ignores the fact that aerosol at 10 km is less effective radiatively than at 20 km. We took the variants most favourable to the theory.
| Material | World production | Programme needs |
|---|---|---|
| Primary aluminium | 72 Mt/yr | 0.48× |
| Barite (source of barium) | 8.2 Mt/yr | 13.7× |
| Strontium (in ore) | 0.51 Mt/yr | 129× |
| All anthropogenic SO₂ emissions worldwide | 73.5 Mt/yr | 90 % |
That last row is the important one. A programme of this size would be comparable to the entire industrial sulphur load of the planet — and that is a quantity measured every year, country by country, by ground networks and satellites, and published in open databases. You cannot add the same amount again and fail to show up in that data.
On top of that comes an account that would kill the programme in the books before it killed it in the atmosphere. Carrying 1.87 t of extra payload on every flight costs fuel:
How many people would have to be in on it
An aircraft is not one person. It is a chain of people, each of whom touches the machine or the cargo — and every one of them would have to stay quiet.
The world has 29,039 commercial aircraft in service, 1,138 airlines and 4,072 airports with scheduled traffic[ATAG]. We count people, not shifts: one pilot flies hundreds of flights a year, so the number of insiders is far smaller than the number of flights. The staffing ratios are taken from the low end of the industry range.
| Role | People |
|---|---|
| Mechanics and maintenance≈12 technicians per aircraft; line checks see every installation | 348,468 |
| Pilots≈9 pilots per aircraft (daily crewing × reserves, leave, training) | 261,351 |
| Ground handling and refuelling≈4 people per aircraft topping up the substance tank | 116,156 |
| Chemical production and logistics1 job per 1,000 t of annual output | 66,000 |
| Engineers and installation certification≈30 aircraft types × a design and certification team | 20,000 |
| Scientists suppressing measurementsIAGOS/CARIBIC operations, satellite retrievals, air quality laboratories | 10,000 |
| Airline boards5 people per airline; someone signs off a foreign installation in their own fleet | 5,690 |
| Government and military coordinationprogramme staff across dozens of states | 5,000 |
| Aviation authorities approving the modification≈50 people × ≈50 civil aviation authorities | 2,500 |
| Total, baseline variant | 835,165 |
What has deliberately been left out
Cabin crew (696,936 people — they would see the installations in the holds), air traffic controllers, customs officers, insurers, airline auditors, the makers of the tanks and pumps, tanker drivers, and the medical staff who would have to treat the consequences. Each of those groups raises the figure; none of them lowers it.
Work it out yourself
Change the assumptions. The model recomputes live — with the same formulas as the model described in the methodology.
The mathematics of keeping it quiet
A secret is not a state. It is a decay process — and it has a decay constant, which can be measured on the scandals that did come out.
David Grimes set this out in a model published in PLOS ONE[Grimes 2016]. If every participant has an independent probability p in a given year of talking — deliberately, while drunk, on their deathbed or through carelessness — then the chance that the secret still holds after t years is:
For 835,165 insiders and the most forgiving p:
| Expected time to the first leak | 107 days |
| Time after which the odds fall to 50 % | 74 days |
| Chance of surviving one year | 3.3 % |
| Chance of surviving 30 years | 10-45 |
| How many could know to give this a 5 % chance over 30 years | 24,415 |
Twenty-four thousand people is roughly the payroll of one large airline. They will not run 96,646 flights a day across six continents.
The limits of this model — honestly
The Grimes model has been criticised, among others by the philosopher M. Dentith[Dentith]: the choice of calibration cases is arbitrary (it takes the ones that came out), and assuming a single shared p for every participant is a simplification. Those are fair objections.
They do not rescue the conclusion, because the margin is far too large. For a programme with 835,165 participants to have even one chance in a hundred, p would have to be about 10⁻¹⁰ — one leak per ten billion person-years. Humanity has not a single example of discipline like that, and the result does not depend on whether p is out by an order of magnitude or two.
That mechanic has a daughter
The Grimes model counts ordinary leaks. Here there is an extra variable that none of the calibration cases had: the participant is poisoning his own children.
Everyone in chapter five breathes the same air as everybody else. They have parents, children, grandchildren. With an average household of 3.5 people[UN DESA] and a close circle of about 8 (household, parents, siblings, adult children), the numbers are:
That changes the nature of the problem. PRISM required NSA employees to keep quiet about a programme that did nothing to them. Tuskegee required doctors to be indifferent about strangers. Here every participant would be knowingly and daily poisoning their own child — and doing so for thirty years, with no way to shield their family, because the air is shared.
So let us add a second, independent channel of decay: moral defection. Let q be the annual probability that a participant breaks — because their child fell ill, because they are dying and want a clean conscience, because they are divorcing and want revenge. The number of defections per year is then simply N·q:
| If one in this many broke each year | Defections a year | Chance nobody does in 30 years |
|---|---|---|
| 1,000 | 835 | 10-10,887 |
| 10,000 | 84 | 10-1,088 |
| 100,000 | 8 | 10-109 |
| 1,000,000 | 0.84 | 10-11 |
Even on an absurdly extreme assumption — that only one person in a million a year cannot bear poisoning their own family — the programme loses almost one participant a year to defection, and the chance that nobody speaks up in thirty years is of the order of one in ten billion.
And that is the heart of it: for this theory to be true you have to accept that more than 6.7 million people — pilots, mechanics, chemists, civil servants — have spent thirty years voluntarily poisoning their own children and not one of them has a problem with it. Not “failed to prove it”. Not “was silenced”. Simply: not one of them tried.
Who would see it, if it were happening
The atmosphere is arguably the best-instrumented object on this planet, and the instruments belong to far too many different owners.
The sharpest case is IAGOS-CARIBIC. It is a measurement container with about twenty instruments, carried in the hold of a Lufthansa Airbus in scheduled service. It measures around a hundred trace gases plus aerosol parameters — precisely where the spraying is supposed to happen[IAGOS]. Between 2018 and 2020 the instrument recorded and analysed more than 1,100 passes through other aircraft's plumes[IAGOS EST]. The composition of those plumes has been measured directly, by independent laboratories, on equipment carried by an airline that the theory says would be taking part in the programme.
On top of that: satellite lidars profiling aerosol, ground networks of sun photometers, thousands of radiosondes released twice a day by the meteorological services of states that do not like each other, and national air quality monitoring networks held to limits on particulates and heavy metals.
When the question was put directly to specialists — 77 atmospheric chemists and geochemists working on element deposition — 76 replied that they had encountered no evidence of a secret programme, and that the “evidence” presented is explained by known physics and chemistry[Shearer et al. 2016]. One researcher pointed to locally elevated barium in a single sample — and noted that background measurements were missing.
Something worth saying out loud
Aviation really does change the sky and the climate — just not in the way this theory says. Cirrus formed from contrails has a radiative forcing of 57.4 mW/m², which is 67 % larger than all aviation CO₂ (34.3 mW/m²)[Lee et al. 2021]. A sky hazed over with contrails does warm the planet. That finding is public, peer-reviewed, inconvenient for the industry — and nobody is hiding it. That is what a real problem looks like: it gets written up in journals, not whispered.
Specific arguments and specific answers
No dodging. Each of these objections has a checkable answer.
I have seen photographs of an aircraft interior full of tanks and pipes.
Those are photographs from flight testing. Before a new aircraft type is certified, its behaviour has to be checked at every mass distribution — from empty to maximum, with the centre of gravity pushed to the edges of the envelope. It is done with water barrels connected by pipes, because water can be pumped between tanks in flight to shift the balance smoothly. The barrels are labelled, they have sight glasses, and the same photographs show flight test engineers at instrument consoles.
The check: such interiors appear only in prototypes and test airframes. Nobody has ever photographed them in a machine that has just disembarked its passengers.
There are patents for dispersing substances from aircraft.
There are, and have been for a long time — because cloud seeding exists, as do crop spraying, firefighting drops and sorbent drops on oil spills. A patent, however, is a legal document about an idea, not proof of deployment. Patent offices grant patents on antigravity vehicles and time machines; that does not mean anyone is driving one.
Nor is a patent evidence of secrecy — it is the exact opposite. The whole point of a patent is publishing the solution in exchange for a temporary monopoly.
Some aircraft leave long trails while others fly alongside leaving nothing.
That is the best evidence that physics is at work rather than a decision. The atmosphere is layered: a difference of 300 metres in height, or a dozen kilometres sideways, can mean different humidity and a different temperature. An aircraft inside a region supersaturated with respect to ice draws a trail for hours; one a hundred metres higher, in a dry layer, leaves nothing.
If this were about spraying, the correlation would follow aircraft type or operator. It follows the air mass — which is why a trail can break off and resume during a single pass, as the machine leaves a moist layer and re-enters it.
Trails last for hours and spread across the whole sky. Water vapour does not behave like that.
It behaves exactly like that when the air is supersaturated with respect to ice. That state is entirely normal at cruising altitude: air can be unsaturated with respect to water and at the same time supersaturated with respect to ice, because ice has a lower saturation vapour pressure than supercooled water. All that is missing are nuclei.
The contrail supplies them — soot from the engine. The crystals that grow on it do not evaporate; they keep drawing moisture from their surroundings and grow. Natural cirrus works the same way and can also hang around for half a day. That very mechanism is what gives contrail cirrus the radiative forcing discussed in chapter eight.
Governments admit they are researching geoengineering. So they are doing it.
They are researching it — and publishing it in peer-reviewed journals with full costings. The Smith and Wagner paper on which chapter four rests is exactly such a document: it works out that the programme would require designing a new aircraft, 95 airframes and 60,109 flights a year in its fifteenth year, at a cost of about 2.25 billion USD a year.
The existence of such analyses is an argument against the theory, not for it. If a programme had been running for thirty years, those authors would not be working out how to build one from scratch — and would not be concluding that no existing machine reaches the required altitude.
Cloud seeding exists, after all.
It does, and entirely openly: silver iodide or dry ice, fired from the ground or dropped from small aircraft directly into a specific cloud, at a few kilometres' altitude, under licensed and publicly accounted programmes. The scale is kilograms per operation and individual valleys.
It proves the opposite of what it is cited for: when humans modify the weather, they do it locally, cheaply and openly — and even then it is hard to prove it worked.
Maybe they only do it on some flights, so all these numbers are inflated.
The calculator in chapter five lets you take the fleet fraction down to 1 %. It is worth doing, because it exposes the trap: at 1 % of the fleet the programme still involves some 40 thousand people (still above the secrecy ceiling) while dispersing a hundredth of an already impossible mass — that is, doing absolutely nothing to the sky. The smaller the programme, the easier to hide and the more pointless. There is no value at which it is both effective and concealable.
What if the participants did not know what they were doing?
This is the strongest version of the objection and deserves a serious answer. One can imagine a programme in which a mechanic tops up an “enhancing additive” without knowing what it is.
That changes chapter seven, not chapter four. You still have to produce 66 Mt of substance a year, move it by rail and tanker to 4,072 airports, account for it in chemical, customs and tax books, and write it up in safety data sheets. Somebody still has to synthesise it and know what for. And analysing such an “additive” is a routine job for any laboratory on Earth — including the airlines' own laboratories, which test the fuel from every delivery, because whether the engine keeps running over the ocean depends on its purity.
What would change my mind
An analysis that cannot be refuted is not an analysis but a profession of faith. So: here is the list.
Any of the following results would force this page to be rewritten. None of them requires access to classified documents — all are within reach of honest research:
| A spatial gradient. Aluminium, barium or strontium in deposition falling systematically with distance from flight corridors, controlled for underlying geology, wind and industrial emissions. |
| An isotopic signature. Aluminium in samples with an isotopic signature or mineral composition that does not match local rock dust but does match an industrial product. |
| A direct measurement in the plume. An excess of metals in exhaust measured in situ — for example by the same IAGOS container that today measures soot and sulphates there. A measurement available to any team with the instruments. |
| A raw-material balance. Tens of megatonnes a year have to come from somewhere. Point to the plants, the rail wagons and the invoices that do not close in the production statistics for aluminium, barite or sulphur. |
| One document and one person. Thirty years, hundreds of thousands of people — one safety data sheet would do, or one operating manual for a dispersal installation, or one mechanic with a name and a photograph of the tank in a line aircraft. |
That last item is the most interesting. Programmes orders of magnitude smaller — PRISM, Tuskegee, MKUltra, Operation Popeye — came to light in exactly that way: through one person with documents. Thirty years and 835,165 people have not produced a single such person. That is itself a measurement.
In summary
The theory does not fail because it is strange. It fails because it does not balance.
The physics of contrails is half a century older than the theory and can be worked out on paper. The mass balance demands raw materials in quantities the world does not produce. The human balance demands 835,165 people staying silent for thirty years, where the model's ceiling is 24,415. And the moral balance demands 6.7 million people being poisoned by their own families — with not one defection.
Each of these four accounts is sufficient on its own. You do not have to trust any institution to check them — a calculator and data that lie in the open will do. Every number on this page comes from a single computational model whose every assumption is stated in the methodology.