Wind Correction & True Airspeed
A round trip in wind loses exactly (Vw/TAS) squared — the tailwind home never makes up for the headwind out. Plus the E6B rules, checked.
The 1-in-60 rule against arcsine
What a round trip really averages
True airspeed: the 2% rule against the density ratio
A round trip in wind loses exactly (Vw/TAS)²
This is the one people argue about: the tailwind home does not make up for the headwind out. You spend longer in the headwind than in the tailwind, so the average is the harmonic mean rather than the arithmetic one — and the loss comes out as exactly the square of the wind-to-airspeed ratio. Twenty knots on a hundred-knot aeroplane costs 4% of the round trip; forty knots costs 16%.
And even a pure crosswind costs, because you crab into it both ways. Forty knots abeam a hundred-knot aeroplane gives 91.65 kt of groundspeed — an 8.35% loss with no headwind at all. There is no wind direction that's free: the best case is calm, and every wind is a tax.
The 1-in-60 rule for wind correction is exact at 30°, which is a genuine accident worth knowing. It uses 60 where the small-angle constant is really 180/π = 57.30 — a +4.72% bias — but arcsine curves upward, and the two errors cancel exactly at a ratio of 0.5. Below 30° the rule always reads high (crabbing slightly too much, the forgiving direction); above it, the rule collapses — at a 0.8 ratio it says 48° where the truth is 53.
And the "add 2% per 1,000 ft" true airspeed rule runs high — in the unsafe direction. TAS is indicated over √σ, and the rule reads 3.2% high at 12,000 ft. The best-fit constant to that altitude is 1.63% per thousand. Overestimating true airspeed means underestimating time en route, which means planning less fuel than the flight needs.
- Wind aloft is not the wind on the ground. Surface friction slows and backs it, so a forecast 2,000 ft wind is typically 20–40° veered and half again as strong as the windsock shows. Planning from the surface wind understates both drift and time.
- When the numbers are tight, plan on the headwind leg alone. Treat the tailwind as a bonus rather than an average — the leg that takes longer is the one you're wrong about for longer.
- The wind can simply win. If the crosswind component exceeds your true airspeed, no heading holds the track at all. That's a real situation in a slow aeroplane and a strong jet.
- Groundspeed is what fuel planning cares about; true airspeed is what the aeroplane does. The gap is entirely wind, and it's asymmetric in a way that flatters optimism.
How to use
- Work the crosswind component first, then the correction angle from it.
- Plan a round trip on the harmonic mean, not the average of the two legs.
- Use the density ratio for true airspeed rather than the 2 per cent rule.
- Plan from winds aloft, not from the surface wind.
Frequently asked questions
Does a tailwind home make up for a headwind out?
No, and the shortfall is exactly the square of the wind-to-airspeed ratio. You spend longer flying into the headwind than you do riding the tailwind, so the round trip averages the harmonic mean rather than the arithmetic one. Twenty knots of wind on a hundred-knot aeroplane costs four per cent of the round trip, and forty knots costs sixteen. Wind never helps over an out-and-back.
Why does wind always cost time on a round trip?
Because the slow leg lasts longer than the fast one. If you fly out at eighty knots and back at a hundred and twenty, you spend three-fifths of the total time on the slow leg and only two-fifths on the fast one, so the average works out below a hundred. The arithmetic mean of the two groundspeeds is exactly your true airspeed, which is precisely the intuition that misleads.
Does a pure crosswind slow you down?
Yes, because you have to crab into it in both directions and that turns some of your airspeed sideways. Forty knots directly abeam a hundred-knot aeroplane leaves 91.65 knots along the course, an 8.35 per cent loss with no headwind component at all. There is no wind direction that is free — the best case is calm and every wind is a tax.
What is the 1-in-60 rule for wind correction?
Take the crosswind component, divide by true airspeed, and multiply by sixty to get the correction angle in degrees. Ten knots of crosswind on a hundred-knot aeroplane gives six degrees. It is a linear stand-in for the arcsine and it is accurate enough to do in your head, which is the entire point of it.
How accurate is the 1-in-60 rule?
Exact at thirty degrees, which is a genuine accident. It uses sixty where the small-angle constant is really 180 over pi, or 57.30 — a 4.72 per cent bias — but arcsine curves upward as the angle grows, and the two errors cancel precisely at a ratio of one half. Below thirty degrees it reads high by at most 4.72 per cent; above, it collapses, reading 48 degrees where the truth is 53.
Is it safer for the 1-in-60 rule to read high or low?
High, which is what it does in the range people actually use. Reading high means crabbing slightly more than needed, so you drift very slightly upwind and notice it — an error you correct without consequence. Reading low leaves you downwind of the intended track, which compounds over a leg. That the rule errs in the forgiving direction below thirty degrees is a large part of why it has lasted.
How do I convert indicated airspeed to true airspeed?
Divide indicated by the square root of the density ratio. At eight thousand feet on a standard day the density ratio is about 0.786, so the square root is 0.887 and true airspeed is about thirteen per cent above indicated. Temperature matters too — a hot day is less dense, so the same indicated airspeed gives a higher true airspeed than the altitude alone suggests.
Is the "add 2 per cent per thousand feet" rule accurate?
It runs high, and in the unsafe direction. Against the exact density ratio it reads about one per cent high at two thousand feet and 3.2 per cent high at twelve thousand. The best-fit constant to that altitude is 1.63 per cent per thousand feet, which fits to under half a per cent. Overestimating true airspeed means underestimating time en route, and so planning less fuel than the flight needs.
What is the difference between groundspeed and true airspeed?
True airspeed is how fast the aeroplane moves through the air and groundspeed is how fast it moves over the ground. The difference is entirely wind. Fuel planning cares about groundspeed, because that determines how long the flight takes, while the aeroplane performance charts are written in true airspeed. The gap is asymmetric in a way that flatters optimism.
Can the wind be too strong to hold a track?
Yes. If the crosswind component exceeds your true airspeed there is no heading that makes good the course at all — the arcsine has no solution because the ratio is greater than one. It is a real situation in a slow aeroplane meeting a strong jet, and the answer is a different route or a different altitude rather than a different heading.
Should I plan from the surface wind or winds aloft?
Winds aloft, and the difference is bigger than most people allow for. Surface friction both slows the wind and backs it, so a forecast two-thousand-foot wind is typically twenty to forty degrees veered from the surface and half again as strong. Planning a cross-country from the windsock understates the drift and the time, usually in the direction that matters.
How should I plan fuel when the wind is uncertain?
On the headwind leg alone, treating any tailwind as a bonus rather than as part of an average. The round-trip arithmetic already says the wind costs you rather than cancelling out, and forecast winds have real error bars. The leg that takes longer is the one you are wrong about for longer, so it deserves the pessimistic assumption.
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