Reading a glider polar

What the curve actually is

For every airspeed you could fly at, the polar records how fast you descend. That is all it is. Speed along the bottom, sink down the side, one point per speed.

The shape is not arbitrary. Fly slowly and induced drag dominates, so sink is high. Fly fast and profile drag dominates, so sink is high again. Somewhere between the two there is a minimum, and the curve is roughly a parabola around it. That is why a quadratic — sink = aV² + bV + c — fits a real glider well enough to be useful, and it is also why it stops being useful outside the range it was fitted over. More on that failure below, because it fails in a specific direction.

Two points on the curve get names in training and both are found the same way: by drawing a straight line and seeing where it touches.

Best glide is a tangent from the origin

Glide ratio is distance over height, which is airspeed over sink rate. On the chart, that ratio is the slope of a line from the origin out to a point on the curve. Shallow line, good glide.

So the best glide you can achieve is the shallowest such line that still touches the curve — the tangent from the origin. Where it touches is your best-glide speed, and the slope of that line is your glide ratio.

Minimum sink is simpler and is a different point entirely: the bottom of the curve. It is slower than best glide, and it is the speed to fly when you want to stay up rather than go anywhere — thermalling, or waiting for something to happen.

Speed to fly is the same tangent, moved

Here is the idea that makes the whole thing click, and it is one picture.

Cross-country speed is not glide performance. It is the average of gliding and climbing: you cover distance while descending, then stop and climb back up. Flying faster covers ground faster but costs more height, so it costs more climbing time. There is an optimum, and MacCready's insight was that it depends on how good the next climb will be.

Geometrically: instead of drawing the tangent from the origin, you draw it from a point offset by the climb you expect. If you expect 2 m/s, you anchor the line 2 m/s above the zero-sink line — at a climb — and draw the tangent from there. Where it touches the curve is your speed to fly.

Wind moves the same anchor sideways. A headwind of 10 m/s shifts it 10 m/s to the right, and the tangent from the new position touches further along the curve: fly faster into wind. A tailwind shifts it left and you slow down. Sinking air moves the anchor down, which is why you push forward in sink — the tool treats airmass sink and MacCready as the same kind of quantity, because geometrically they are.

The interactive polar draws exactly this and lets you drag the anchor point. It is worth thirty seconds of dragging, because the relationship between wind, expected climb and speed becomes obvious in a way no formula makes it.

The thing about MacCready that gets misremembered

The setting is the average climb you expect in the next thermal, as your averager will read it. Not the one you just left. Not the best of the day. Not the instantaneous vario.

This matters because the two common errors run in opposite directions and both cost you. Setting MacCready to the climb you just had, on a day that is dying, makes you fly too fast into weakening conditions. Setting it to zero all day because you are nervous makes you slow, which is safe and is also why you land out at four o'clock having covered very little.

There is a deeper point that experienced pilots make and that the theory does not contain: the classical model assumes the next climb is there. It has no concept of not finding one. That is why real cross-country flying is generally conducted below the MacCready optimum — the arithmetic maximises average speed, and the pilot is also managing the risk of the arithmetic being wrong.

Ballast: the result that surprises people

Adding water does not improve your glide ratio. Not by a little — not at all.

Scaling a glider's mass by a factor μ scales the whole polar in a particular way: every speed multiplies by k = √μ, and every sink rate multiplies by the same k. Since glide ratio is speed divided by sink, both scale together and the ratio is exactly unchanged. What changes is the speed at which you achieve it, which goes up by k.

So a ballasted glider gets the same glide ratio, faster. On a polar chart the curve simply slides right and down along itself. And because the MacCready tangent then touches further along, the ballasted ship's speed to fly is higher at every positive MacCready setting.

From the polar alone, therefore, water is free and you should always carry it — which is obviously wrong, and the fact that the polar says so is the most important thing this page can tell you about the polar's limits.

Altitude: the correction that is usually skipped

A published polar is a sea-level curve. Fly the same indicated speeds at 8,000 ft density altitude and the true airspeeds and true sink rates are both higher, by the same factor 1/√σ, where σ is the density ratio.

Two consequences, and they point in different directions:

• Your glide ratio is unaffected. Both axes scale together, so the ratio does not move. The picture stretches; it does not tilt.
• Your speed to fly and your sink rate at cruise are affected. They are true airspeeds and true sink rates, and both are larger. At around 6,000 ft density altitude σ is about 0.83, so true speeds run roughly 10% above the sea-level figures.

If you fly somewhere high, this is not a rounding error. Our density altitude calculator gives you σ for the day, and the polar tool takes it as an input.

Why we do not publish a database of polars

It would be an obvious thing to build and we deliberately have not, for a reason that is checkable in about a minute.

Given minimum sink, the speed it occurs at, and best-glide speed, the glide ratio is not a free parameter — it is determined by the other three. If V_ms is minimum-sink speed and V_bg best-glide speed, then

L/D_max = 1 ÷ [ 2a(V_bg − V_ms) ],   where   a = s_ms ÷ (V_bg² − V_ms²)

Now try it on a well-known aircraft. The Standard Discus is published with a minimum sink of 0.59 m/s at 78 km/h and its best glide at 100 km/h. Put those three numbers in and the implied best glide is about 41.9. The published figure is 45.

That is a 7% disagreement inside one manufacturer's own specification, and there is no way from outside to know which of the three numbers is the one to distrust. It is not a criticism of Schempp-Hirth in particular — the same exercise misbehaves across the industry, because headline glide ratios are measured under favourable conditions and quoted generously, while a polar is a curve somebody had to fly.

So a database assembled from published headline figures would contain curves that contradict their own sources. Worse, mixing manufacturer figures with flight-test figures — Dick Johnson's measured polars in Soaring, say — produces comparisons where the ranking is driven by who measured it rather than by the aircraft, because the manufacturer-versus-measured gap is usually bigger than the difference between two similar ships.

The tool therefore asks you for your own aircraft's numbers, out of your own flight manual, the same way the cockpit load tool asks you to read your own placard. And when you enter the four published figures, it tells you whether they agree with each other. That check is more useful than any database we could have shipped.

Where the model breaks, and which way

A quadratic is a fit to measured points, not a law of nature, and it fails outside the range it was fitted over. The important thing is that both failures run the same way.

• Above the fitted range, real drag rise outruns a parabola, so the curve under-predicts sink. Your glider is worse than the model says.
• Below the fitted range, the curve carries on smoothly downward toward a finite value at zero airspeed. It is perfectly well behaved and completely wrong, because it knows nothing whatever about the stall.

Both errors flatter the glider. That is the dangerous direction, which is why the interactive version draws extrapolated sections dashed and labels any answer that falls outside the fit. It still gives you the answer — MacCready 4 into a strong headwind lands outside almost any published fit, and that is exactly the day someone wants the number — but it says what it is.

Bugs, rain and the honest caveat

Contamination is usually modelled as one multiplier applied to the whole curve, and ours is no exception. It is crude, and it is worth knowing which way it is wrong.

Scaling all three coefficients together leaves best-glide speed unchanged, because that speed depends on a ratio the scaling cancels out of. Real contamination raises profile drag, which hurts the fast end more than the slow end, and would therefore lower your best-glide speed as well as your glide ratio.

The practical consequence: with the bugs slider up, the modelled speed to fly is faster than reality, and any height requirement you derive from it is lower than reality. Both errors are optimistic. If you are flying a contaminated wing, add margin beyond what the model gives you — and remember it also says nothing about rain raising your stall speed.

What to do with all this

Three things, in order of how much they will change your flying:

1. Learn the two tangents. Origin for best glide, offset anchor for speed to fly. Once you can see it, every speed-to-fly rule of thumb you have been told becomes obvious rather than memorised.
2. Put your own aircraft's numbers in once and see whether they are self-consistent. It takes thirty seconds and it tells you how much to trust the brochure.
3. Stop treating the polar as the whole story. It cannot see the climb, so it cannot price ballast, and it cannot see the day, so it cannot price the risk of not finding the next thermal. Those are the two things good cross-country pilots are actually deciding.