Load factor in a turn
Bank the glider and the wing has to work harder, because the lift is no longer pointing straight up but still has to carry the whole weight. That extra work is the load factor, and the number that matters to you is not really the g — it is what the g does to your stall speed. In a 60° turn your stall speed is 41% higher than it is wings level, and that is often above the speed people actually thermal at.
Degrees, either side of level. A left turn and a right turn load the wing identically, so the sign is ignored.
Glider, pilot, parachute, water. The unit button only changes the label — the answer is your number multiplied by the load factor, so it comes back in whatever you put in. Leave it blank to hide that panel.
From your own flight manual, at the mass you are flying at today — not from a type page. Same story with the unit: the multiplier does not care which one you use.
Load factor at of bank
Extra over 1g
Stall speed ×
Effective weight
Stall speed here
Wings level you stall at . Here you stall at — more.
There is no level turn here
The curve is flat, and then it is not
Load factor against bank angle. Everything a glider pilot does routinely lives in the left two thirds of this picture.
The angles pilots actually use
Every row here is computed from n = 1/cos(bank) when the page loads, so it cannot drift away from the formula it is illustrating.
| Bank | Load factor | Extra g | Stall speed × | Stall speed up | Yours |
|---|---|---|---|---|---|
The first five columns are the same for every glider ever built — they are trigonometry, not aerodynamics. The last column is the only one that is about your aircraft, and it comes from the stall speed you typed in.
Go the other way
Given a load factor, which bank angle produces it in a level turn? bank = arccos(1/n). If your flight manual gives a manoeuvring limit load factor, this is the bank angle that reaches it — in a level, coordinated, constant-speed turn and in no other circumstance.
Where your stall speed catches you
This is the version of the question that has an answer you can fly with. Tell it the speed you actually thermal at, and it will tell you the bank angle at which your stall speed has climbed to meet it.
That is the angle at which the margin reaches zero, not the angle at which it becomes uncomfortable. It goes long before that, and it goes at a shallower bank still if you are turning in the rough air near a thermal's edge, or if the turn is not balanced.
Why 45 degrees is the everyday number and 60 is not
The cosine is nearly flat near zero and falls off a cliff near 90, so 1/cos does the opposite: it barely moves at first, then runs away. The two ends of that are worth putting side by side.
Rolling from wings level to — a third of the way to vertical — costs you . Thirty degrees of bank for about a sixth of a g. Going from to — ten degrees, a third of the roll and something you could do without noticing — costs . Same wing, same aeroplane: six times the g for a third of the roll, which is about eighteen times the price per degree.
That is why 45° sits where it does in ordinary soaring practice. At 45° you are pulling 1.41g and your stall speed is up 19%, which most gliders and most pilots carry comfortably while still turning tightly enough to stay in a thermal core. Push on to 60° and you have doubled the load and put the stall speed up 41% for another 15° of bank. Sixty is a perfectly flyable angle — instructors demonstrate steep turns for exactly this reason — but it is the angle at which the arithmetic stops being generous, and it wants deliberate speed and a deliberate lookout rather than drifting into it while staring at the vario.
Note what the curve does not say. It says nothing about what your glider is allowed to carry, because that is a number in your flight manual for your airframe and I do not know it. It says only what a level turn at a given bank demands.
The spiral dive: how these numbers run away from you
A spiral dive is not a manoeuvre anybody chooses. It is a steep turn that got away, and it gets away because each step in it makes the next step more likely. The chain is short and it is worth being able to recite:
- The bank increases. Perhaps a wing drops in rough air near the core, perhaps you tighten to stay centred, perhaps you are looking at the vario rather than the horizon.
- Load factor increases as 1/cos, and by now you are on the steep part of the curve, so a small increase in bank is a large increase in g.
- Stall speed increases with the square root of that, so the margin you had a moment ago has shrunk. Either the nose drops of its own accord or you lower it to keep flying.
- The nose is down and steeply banked, so speed builds — fast, because a glider pointing downhill has very little drag to stop it.
- The nose keeps going down, so the natural reaction is to pull. And this is the step that closes the loop: pulling with the bank still on does not raise the nose, it tightens the turn. The lift is pointing mostly sideways, so almost all of the extra you pull goes into turning harder, not into climbing.
- Now speed and load factor are both climbing together, towards the never exceed speed and towards the limit load factor at the same time. Neither of those numbers is on this page, because both belong to your aircraft.
The way out is to break the loop at step five rather than pull harder into it: reduce the bank first, then ease out of the dive. Rolling towards level puts the lift back under you, so the pull does something useful instead of feeding the spiral. Fly the recovery your instructor taught you and your flight manual describes — the point here is only the mechanism, so that the recovery makes sense rather than being a memorised sequence.
And notice that during all of this, n = 1/cos(bank) is no longer telling you the truth. It describes a steady level turn, and a spiral dive is neither steady nor level: the aircraft is accelerating and the pilot is pulling, so the actual load factor is whatever that pull commands. It can be well above the figure this page gives for the bank angle you can see.
Where this formula stops being true
The most dangerous thing a pilot can take away from this page is “2g at 60 degrees, so 2g is about as bad as it gets.” It is not. n = 1/cos(bank) is the load factor of a level, coordinated, constant-speed turn and of nothing else. Everywhere below, load factor comes from somewhere other than bank angle, and there is no bank angle to read it off:
- A pull-up. Pull out of a dive wings level and the g is whatever your elevator and your right arm ask for. You can exceed the numbers in the table above with the wings dead level and nothing on this page will have warned you.
- A winch launch. The rotation into the climb, and any recovery from a cable break or an over-speed, all load the wing, and the launch is the phase where the airspeed is changing fastest and the margins are smallest.
- A gust. A sharp-edged vertical gust changes the angle of attack instantly and the wing responds with whatever lift that demands. This is why certification standards specify a rough-air speed and why flight manuals put a limit on speed in turbulence: the same gust makes more g the faster you meet it. Wave rotor, a thermal's edge on a strong day, and the lee of a ridge are all places to be thinking about this rather than about bank angle.
- A spiral dive, or any accelerating turn. As above: the pull sets the g, the bank only sets how much of it is wasted sideways.
- Aerobatics of any kind, and recovery from any unusual attitude.
The table on this page is the floor for a given bank angle, not the ceiling for a given flight. It tells you what a level turn must cost. It cannot tell you what your day will actually cost you.
What this assumes, and what it can't know
This is exact trigonometry for a level, coordinated, constant-speed turn, and it is true for nothing else. n = 1/cos(bank) and stall speed multiplier = √n are not approximations and carry no fudge factors — but they describe one specific flight condition. Load factor in a pull-up, on a winch launch, in a gust or in a spiral dive comes from somewhere else entirely and is routinely higher at much shallower bank angles.
There are no operating limits on this page. No limit load factors, no never exceed speed, no manoeuvring speed, no rough-air speed, no stall speeds. Those are printed in your flight manual for your airframe in its current configuration, and a number I published would be wrong for somebody's glider on some day. If you want to know the bank angle at which you would reach your manual's limit load factor, type that figure into the inverse calculator above — the answer will be your aircraft's, because the input was.
The stall speed answers are only as good as the stall speed you typed in. Stall speed scales with the square root of mass, and the figure quoted in most flight manuals is at maximum all-up mass. Flying lighter, you stall slower than the book; with water on board, you stall faster. Use the figure for the mass you are flying at today, and if in doubt use the more pessimistic one.
√n is the optimistic end of the real answer. It assumes the wing stalls at the same angle of attack it does wings level, which is close but not exact: in a turn the inner wing is flying slower than the outer one, the airspeed indicator has more position error at high angles of attack, and a slipping or skidding turn changes things again. A real turning stall tends to arrive slightly earlier than the multiplier suggests, and a skidding turn is the classic route from a thermalling turn into a spin.
Coordinated means the ball is in the middle. If it is not, some of the wing's lift is being spent sideways and the relationship between what you can see out of the canopy and what the wing is carrying comes apart.
Weight, mass and unit. The effective weight panel is a straight multiplication, so it returns whatever unit you gave it. Strictly this is weight rather than mass; nothing here depends on the distinction.
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.