Saqr ConsultingDesign sheets
Saqr Consulting

Glide & Sink Polar

Best glide · minimum sink · the speed to fly · the cost of a turn
A file you keep, not an account. Nothing is stored on this site.
The aircraft
g
dm²
Weight does not change the glide ratio at all — it changes the speed at which you get it, and it raises the sink rate. That is why glider pilots carry water ballast on a strong day and dump it on a weak one.
mm
CL
Span sets the induced drag and so sets the whole right-hand half of the polar. Maximum lift sets where the polar stops: below the stall there is no curve, only a spin.
CD0
e
From Sheet 07 and Sheet 04. On a glide, parasite drag and induced drag are equal at the best-glide speed — that equality is the best-glide condition, and it is the one fact on this sheet worth memorising.
The flight
m/s
m
The height you are at when the motor stops, or the height of the launch. A headwind does not only shorten the glide — it moves the speed you should fly at.
m/s
Leave it at zero and this sheet is about gliding down, which is what most of it is for. Put a number in and it becomes a cross-country sheet: the faster you expect to climb, the faster it pays to fly between climbs, and the speed that gets you furthest per metre of height stops being the speed that gets you there soonest. This is MacCready's construction, and the number is a forecast rather than a measurement — it is what you think the next thermal will give you.
°
Circling to stay in a thermal, or turning back to the field. The load factor is 1/cos of this, and both the speed and the sink rate rise with its square root.
m ASL
°C
% RH
Thin air moves the whole polar to the right and down: the same glide ratio, reached faster, losing height faster. The ratio itself does not care about density.
Sink rate against airspeed — the glide polar Sink increases downwards. The tangent from the origin touches the curve at the best glide speed; the lowest point of the curve is minimum sink.
Where people go wrong

The errors this method actually invites, and what it does about each. Every one of them is already a warning somewhere — in a note that appears when your own figures trip it, in the scope statement, or in the equations behind the page. Collected here so you can read them before you need them.

Expecting weight to change the glide ratio. It does not. Weight appears in neither lift coefficient, so it changes both speeds and the sink rate as the square root of weight and leaves the ratio alone. Double the weight and the aeroplane glides just as far, arrives sooner, and cannot stay up in weak lift — which is the entire case for water ballast.

Flying at minimum sink. Minimum sink asks for √3 times the best-glide lift coefficient, and on a draggy short-span model that is often above the wing's maximum. The default trainer here is such an aircraft: it stalls before it reaches the bottom of its own polar.

Slowing down into wind. The optimum moves the other way. Into wind the tangent starts upwind of the origin and touches the polar further right, so the speed to fly is higher, not lower.

Trusting the left-hand end of the curve. The drag rise approaching the stall is not in the polar, and CD0 is held constant as the aircraft slows even though it rises at low Reynolds number. Both make the slow end optimistic.

Using the constant-speed turn penalty. At a constant lift coefficient — which is how anyone actually circles — the sink penalty is √n, not n^1.5. Seven per cent at 30° of bank and 41% at 60°, where the stall speed has gone up 41% as well.

Setting the MacCready to the climb you just had. It is the climb you expect next. Setting it from the thermal behind you makes you push hard into air that has not agreed to pay for it, and the height you spend arrives at a weaker climb than the one you priced. The setting is a forecast, and a pessimistic forecast costs far less than an optimistic one.

What a turn costs, at the speed that sinks least
BankLoad factorAirspeed Sink rateRadiusTime for a circle

The polar is the parabolic drag model, which is good in the middle and optimistic at both ends: it does not know about the drag rise near the stall, and at model Reynolds numbers the real CD0 rises as the aircraft slows.