True airspeed
Your airspeed indicator does not measure speed. It measures dynamic pressure and labels it in knots, which is the right thing for it to do — the wing cares about dynamic pressure too, so the stall and the polar stay put on the dial. But the air, the ground and the clock all care about how fast you are actually going. In wave at FL180 that is roughly a third more than the needle says.
This is the cruise-at-altitude half of the problem. The density altitude calculator is the other half — what a hot afternoon does to your field, your tug and your ground roll. Same physics, different day.
Altitude
What the altimeter reads with 1013 hPa (29.92 inHg) wound in — a flight level, in other words.
What the altimeter reads with the setting below wound in. Density does not care what your subscale says, so this converts before it does anything else.
True airspeed
Correction
Density ratio σ
Pressure altitude
ISA deviation
The working
Density falls with altitude and rises as air gets colder, and the two effects are separate. Pressure gives you one ratio, absolute temperature gives you the other, and dividing one by the other gives σ, the density ratio against sea level standard. True airspeed is calibrated airspeed divided by its square root, because dynamic pressure goes as density times speed squared.
Density altitude is a readout here, not a step on the way: it is worked out backwards from σ rather than σ being worked out from it. Both routes are in the tests. Near the ground, in air within 15 °C of standard, they agree to a tenth of a percent. The gap opens up with cold and with height — about six tenths of a percent at FL300 in air 30 °C below standard, which is an ordinary wave day. That is the straight line drifting off the curve, not this.
You are above the tropopause. The atmosphere stops cooling at about 36,000 ft and this page switches to the isothermal formula there, which is why the pressure ratio keeps falling while the standard temperature does not.
Against the two-percent rule
The shortcut everyone is taught is to add 2% per 1,000 ft. It is a good shortcut and you should keep it — it is doing mental arithmetic in a cockpit, which this page is not. But it is a straight line drawn through a curve, so it is worth knowing which way it is wrong.
Exact
2% per 1,000 ft
The shortcut is out by
Where the shortcut drifts
Against density altitude, so the comparison is like for like. Apply the rule to an indicated altitude on a warm day and you carry a second error on top of this one, in the same direction.
| Density altitude | Exact | Rule | Rule is out by |
|---|---|---|---|
The shortcut is generous through the middle of the band, worst at around 12,500 ft where it overstates true airspeed by about 3%, and it crosses over at roughly 26,000 ft — above that it starts understating. Three percent of 60 kt is under two knots, which is why the rule survives: it is wrong by less than you can hold an airspeed.
What it does to a turn
A turn is geometry, and geometry runs on true airspeed. At the same indicated speed and the same bank, the radius grows as 1/σ — the square of the correction, not the correction itself. This is the part that surprises people who have only ever thermalled low down.
Radius down low
Radius up here
Bigger by
Same aircraft, same indicated speed, same bank angle, same feel through the stick. The circle on the ground is a different size. A rotor core or a wave bar that you could work at circuit height may simply not fit inside your turn at altitude, and the answer is more bank rather than more back stick — the stall still happens at the indicated speed it always did.
What this assumes, and what it can't know
The number you typed is treated as calibrated airspeed, and this page cannot make it so. Getting from indicated to calibrated is a position-error correction: it depends on where the static ports sit on that particular fuselage, on the probe, on the tape over the wrong hole. It is tabulated per type in the flight manual and there is no general formula for it. At normal cruise it is usually a knot or two; near the stall, and with the airbrakes out, it is larger and it is not always in the same direction. If your manual has the table, apply it first and put the calibrated figure in the box.
The standard atmosphere arithmetic is exact. Pressure ratio, temperature ratio, density ratio and the square root: there is nothing fitted or estimated in the correction factor. What is estimated is your inputs — an outside air temperature probe in the sun, or read through a canopy that has been baking, is the usual source of error here, and 5 °C is worth about 1% on the answer.
Compressibility is ignored, and at ordinary glider speeds it is small. Strictly, TAS = EAS/√σ, and calibrated airspeed only equals equivalent airspeed while the air is not compressing against the pitot. At 100 kt at FL180 the difference is about a third of a knot — smaller than the position error you already cannot correct for. But it grows roughly as the cube of the speed, and it grows with height: at 175 kt at FL300 it is five and a half knots, and the figure above reads high by that much. It is not applied, because applying it would imply a precision that the uncorrected position error does not support. It is named here, with its size, because leaving it out silently would be worse.
Humidity is ignored. Moist air is slightly less dense than dry air, so a humid day gives marginally more true airspeed than this shows. The effect is small beside temperature and pressure and it is conventionally left out.
Above about 36,000 ft the standard atmosphere changes shape and this page changes with it, through the isothermal layer and the warming layer above 20 km. The equivalent density altitude shown in the working is a formal extrapolation of the low-level curve up there and drifts from the geometric answer; σ is the number doing the work and σ is right.
No red-line, no Vne, no placard. Flutter margins are set in true airspeed, which is why manuals reduce the indicated red-line with altitude — but that reduction is specific to the airframe and belongs to your flight manual, not to a web page. Read the table in your own manual before you fly fast up high.
Not yet checked by anyone but me. If you instruct, or one of these assumptions is wrong, I would genuinely rather hear it than not — tell me and I will credit you here. This is ground school, not a flight computer, and not an authority on your aircraft. Fly the numbers in your own flight manual and the instruments in front of you.
What runs on indicated, and what runs on true
Split everything you do in the cockpit into two lists. On the indicated side goes anything the wing decides: the stall, the approach speed, the manoeuvring speed, the polar in the back of your flight manual, and therefore speed-to-fly. The wing responds to dynamic pressure, the ASI measures dynamic pressure, and at 18,000 ft an aerofoil at 55 kt indicated is doing exactly what it does at 55 kt indicated over the airfield. Your stalling speed on the dial does not move.
On the true side goes anything the air or the ground decides: groundspeed, track, time to the next turning point, turn radius, the rate at which you close on another aircraft, and the true rate at which you are descending. These all run on true airspeed, and at wave heights they are running a third faster than the instrument in front of you.
The trap sits exactly on the boundary. Your polar is plotted against indicated (strictly, equivalent) airspeed and it stays valid at altitude — fly the indicated speed the polar says and the aerodynamics are unchanged. But both axes scale together. At σ = 0.56 your true speed along the glide is up by a third and so is your true rate of descent. Convert one axis and not the other — take your true airspeed and pair it with the sink rate printed on the chart — and you will credit yourself with a third more glide than you have. In still air the glide angle is untouched. It is the arithmetic that goes wrong, not the aeroplane.
Wind is the honest exception. A 25 kt headwind takes a much smaller bite out of a cruise at 80 kt true than out of the same cruise at 60 kt, so the distance you make good over the ground per foot of height really does change with altitude — not because the glide angle moved, but because you are covering the air distance in less time and the wind has less time to work on you. That is the calculation the final glide tool is doing.
Wave, where the gap becomes the point
Down in the thermals the correction is a rounding error you can safely ignore: at 4,000 ft on a warm day it is about 7%, and 7% of 50 kt is three and a half knots. Nobody flies more precisely than that. In wave it stops being ignorable. At FL180 the correction is around a third, and at FL300 it is roughly two thirds — the same needle position, two thirds more speed.
Three things follow, and all three have bitten people. First, navigation: at 80 kt true into a 30 kt wind you are making 50 over the ground, and at 80 kt true with it behind you it is 110. Airspace boundaries, controlled airspace and the distance back to the airfield are all measured over the ground, and the difference between those two numbers is more than a factor of two in how long anything takes.
Second, turn radius, as the calculator above shows: it grows as 1/σ, so at FL180 the same indicated speed and bank puts you in a circle of nearly twice the radius — and therefore more than three times the area, because area goes as the square of it. Working a narrow wave bar or a rotor core is a different job up there.
Third, descent. Coming down from a wave climb, your true rate of descent is up by the same factor as your speed, so the height comes off faster than the polar's printed sink rate suggests even though the glide angle is unchanged. Combine that with the cold-soaked airframe, the oxygen system and the airspace clock and you get the standard advice for a wave descent: start earlier than feels necessary, and plan it in true terms.
At the extreme end, the same arithmetic explains the Perlan project's stratospheric flights: at the 76,000 ft they reached in 2018, σ has fallen so far that true airspeed is nearly five times indicated. It is a little over four times at 70,000 ft and still climbing. The wing still stalls at the indicated speed it always did, and the red-line has come down to meet it. That gap between the two is why this page bothers with three atmospheric layers rather than one.
Why the red line moves with altitude
Flutter is the one place where the wing does not simply care about dynamic pressure. It is a resonance between a structure's stiffness and the aerodynamic forces feeding it, and the aerodynamic damping that puts the energy back depends on how fast the air is actually moving over the surface — on true airspeed, not indicated. That is why a never-exceed speed set at sea level is not a safe never-exceed speed at 20,000 ft: the same needle reading is a much higher true speed, and the flutter margin it was chosen to protect has quietly shrunk.
Manufacturers deal with this by tabulating a reduced indicated red-line against altitude in the flight manual, sometimes as a table and sometimes as a placard on the panel. The reduction begins lower than most pilots expect and it is specific to the type, the serial block and the modification state.
This site does not publish that table for your aircraft, and it never will. Every operating limit on GliderOps is one you have read off your own paperwork — a number that is right for one glider on one day and wrong for the next one is worse than no number at all. What this page can tell you is the true airspeed you are actually doing. What your manual has to tell you is what the limit is.
Indicated, calibrated, equivalent, true
Four names, applied in order, and it is worth knowing which step this page does.
- Indicated is what the needle says. It contains the instrument's own error and the position error of the static source on that airframe.
- Calibrated is indicated with the position error taken out, from the table in your flight manual. This page cannot do this step for you and assumes you have already done it. For most gliders at cruise the difference is a knot or two; near the stall, in a slip, or with the brakes out it can be several, and glider static sources are more exposed to those effects than most.
- Equivalent is calibrated with compressibility taken out. How big that step is depends on height as well as speed, which is easy to forget: at 100 kt at FL180 it is about a third of a knot, but at 175 kt at FL300 it is five and a half. This page treats calibrated and equivalent as the same thing, which is fair at the speeds a glider normally cruises and costs you a few knots only if you are both fast and high.
- True is equivalent divided by √σ. That is the step this page does, and it is the big one.
If you want the same arithmetic pointed at the ground rather than at cruise — what a hot afternoon is doing to your launch, your tug and your ground roll — that is the density altitude calculator. It works from field elevation and an altimeter setting and answers a different question with the same σ.