How these are worked out — the equations behind this sheet, their sources, and what each one assumes.
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.
| Bank | Load factor | Airspeed | Sink rate | Radius | Time 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.