# What are these points in this drag curve ("Lilienthal'sches Polardiagramm")?

If it matters, this is taken from EASA PPL questions by AustroControl. So far I think the points correspond to the following situations:

• 1 Inverted Flight (confirmed)
• 2 ???
• 3 Maybe Best Gliding Angle???
• 4 ???
• 5 Slow Flight (confirmed)
• 6 Maybe Stall ???

• Look at what's unique about each point. (2) generates zero lift. (3) is the point of minimum drag. (4) is the point of maximum lift/drag ratio. (5) is the point of maximum lift. Does that steer you in the right direction? Jul 31 at 18:25
• 6 is the stall. 2 is just the zero-lift point (like NASA's zero-g Vomet Comet would want - completely unloading the wing). 4 is a very important point to understand: best glide AoA (= speed more or less)! Jul 31 at 22:04
• Right on with (5). It's the other way around with drag: parasitic drag dominates at the left side (at (2) it's all parasitic drag since there's no lift to induce any drag). Induced drag dominates to the right at high (positive or negative) AoA. Aug 1 at 6:21
• Keep in mind that each point just gives the instantaneous Cl and Cd, or in the nomenclature of the graph, Ca and Cw, of some particular Angle-of-Attack. So, point #1 could certainly be obtained in non-inverted flight, if the pilot shoved the stick forward suddenly. The G-load (basically another word for the lift vector) would be negative. This is not compatible with a steady-state condition, unless the aircraft is inverted, but that doesn't mean that the aircraft must be inverted to experience this part of the flight envelope. Aug 2 at 16:09
• Re " So, point #1 could certainly be obtained in non-inverted flight, if the pilot shoved the stick forward suddenly." -- most safely demonstrated starting from a steep climb. Just as you would demonstrate a slightly less extreme version of the maneuver, bringing the wing to the zero-lift angle-of-attack, and bringing the G-load only to zero, rather than to a - value. If you attempt to demonstrate either of these maneuvers from normal level flight, in most aircraft you will end up with the aircraft very steeply nose-down and the airspeed rapidly rising toward the red line. Now what to do? Aug 2 at 16:14

To be more exact, the above figure is taken from a question catalog for the AustroControl PPL theory exam. The catalog is based on the de-facto standard German PPL textbook Advanced PPL-Guide 2a - Aerodynamik Flugzeuge by Aircademy Ldt.

The book itself including the figure is under copyright, so it is best not to post a scan here. The original annotations for the numbers of that figure in the book (Chapter 2, "Strömung am Tragflügel", Fig. 19) are:

number original annotation (DE) translated annotation (EN)
1 Rückenflug inverted flight
2 $$c_a = 0$$, Sturzflug nose dive
3 $$c_w = min$$
4 $$\frac{c_a}{c_w} = max$$
5 $$c_a = max$$, Langsamflug slow flight
6 überzogener Flugzustand stall
• Did you provide the English translations of the annotations or are they in the original? "Nose dive" is a surprising / harsh description of zero load factor. (For that matter I'm curious about "Sturzflug": I speak German, but my flight training and experience is USA-based so I'm not sure if this really is the standard term for this scenario.) Nice answer though, +1 for identifying the source material. Aug 1 at 14:55
• The original annotations are in German („Sturzflug“, etc.). English translations my own (cross-checked at dict.cc). Aug 1 at 15:46
• @TypeIA -- echoes of my comments to the actual question-- zero lift / zero load factor/ zero G's can certainly be demonstrated or experienced in conditions other than a vertical dive, but a vertical dive ("nose-dive") is the only situation where zero lift / zero load factor/ zero G's (as registered on the G-meter which only detects the "up-and-down" component in the aircraft's normal reference frame) can be sustained in a steady-state situation. It's a bit much to expect study materials for a PPL exam to be cognizant of the differences between steady-state and transient conditions. Aug 3 at 0:23

The graph seems to make more sense for a non-symmetrical airfoil.

1 is clearly a negative angle of attack
2 is no lift but slightly more drag than 3 ... hmm
3 has lift but a little less drag. Non symmetrical airfoils can generate lift at 0 Angle of Attack, so 2 probably needs to be at a slightly negative AoA for zero lift. This accounts for the higher drag.
4 is best lift to drag ratio
5 is a higher Coefficient of Lift but proportionally higher drag, which means higher AoA to compensate for slower flight (or higher wing loading, such as in a turn). Point 5 would be at what is known as "stall speed" (really stall AoA).
6 yes, this is stalled

• Re "2 is no lift but slightly more drag than 3 ... hmm"-- yes, as you noted, this would be for a non-symmetrical (cambered) airfoil. To make zero lift, despite the cambered shape, the airfoil must be plowing along nose-down at a negative angle-of-attack-- more draggy than an A-o-A closer to zero, which would generate some mild amount of lift. PS I'm not sure what is the significance of the "Lilienthal" reference, but all his wings were highly cambered! (Very thin, with strongly concave under-surfaces.) Aug 3 at 0:56