What's the maximum bank angle of a glider?

Question

I know that stall speed and wing load increase with the angle of the turn and I have experienced 65 degrees turns in a glider (demonstrated by an instructor). Let's say a collision is imminent (or we are in some other emergency situation) what would be the theoretical maximum bank angle? I'll check on the placard the next time I'm in the airfield, but I don't think it's in there.

Answer 1

The bank angle ($\phi$) in a stationary turn is limited by the maximal load factor of the aircraft (or the pilot- whichever is less): $$\phi_{max}=\arccos(\frac{1}{n_{max}})$$

Utility category gliders ($n_{max}=5.3$) have a maximum bank angle of 79°. Aerobatic gliders with $n_{max}$ between 7 and 10 can fly only slightly steeper turns (82°-84°).

If you're flying with an airspeed slower than design manoeuvring speed $V_A$ the limiting factor is the maximum lift coefficient. In that case, the formula gets $$\phi_{max}=\arccos(\left(\frac{V_S}{V}\right) ^2)$$ $V_S$ is the stalling speed in the current configuration, $V$ the airspeed of the glider.

(own work)

Then, how do you get the tightest turn radius? With high speed and high bank angle or with low speed and low bank angle? Without the structural limitation the radius could become 0. With it, however, your best option to get a minimal turn radius is to fly with maneuvring speed and maximum load factor.
You can use the following diagram to calculate the minimum turn radius at any speed (just multiply the ordinate with the squared stall speed of your aircraft).

As stated in many comments, during aerobatics/dynamic manuevers you can get any bank angle for a certain (sometimes really short) period of time:

0°/180° bank angle Source

90° bank angle Source

Answer 2

Gliders do not have a technical limitation for the bank angle.

Flying with high bank angle (not turning / "knife flight") does not add any force. Therefor the main problem is to maintain enough speed to fly stable.

Depending on the aerodynamic design of the glider it might not be stable to fly at bank angles around 90 degree and fall into (steep) spin (trundle) as the speed reduces too quickly. Any glider (as any other plane) must be designed to sustain the forces appearing on a stable steep spin. Given that there is enough height recovering from (steep) spin is quite easy. Some gliders are even designed to recover themselves from the spin (e.g.: ASK-21).

So after all bank angles around 90 degree are quite safe and for some planes a stable flight is possible (for a couple of seconds).

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On the other hand: The scenario you came up with, that you have to avoid a crash into another, plane I'd do a "hard turn" (risking to over-g the plane) rather than a "roll".

Answer 3

Airplanes move in 3D, so banking to avoid a collision should be combined with a climb or a dive, depending on the relative altitude of the opposing aircraft. If you want to maximize turn rate, you would best use an instationary manoeuver anyway (instationary means that lift has not to equal weight during the maneuver).

First to the bank angle limit in stationary flight: This is given by the maximum load factor $n_{z_{max}}$ of your glider which is 6.5g in case of the ASK-21. The equation for the bank angle $\phi$ is $$\phi = arccos\left(\frac{1}{n_z}\right)$$ When we now look at the resulting turn radius $R$: $$R = \frac{\frac{n_z}{\sqrt{n^2_z - 1}}}{c_L\cdot\frac{\rho}{2}\cdot\frac{S_{ref}}{m}}$$ we see that more bank will not necessarily make the turn much tighter: You run into a limit in stationary turns where the speed increase needed to create the additional lift for turning tighter requires a bigger turn, and both effects cancel each other. A graphical explanation is given below where the little gliders show which bank angle is needed for the turn radius at which the glider sits. The red dashed line is the load factor at that radius.

Load factor over turn radius, assuming a lift coefficient $c_L$ of 1.4 and a wing loading $\frac{S_{ref}}{m}$ of 35 kg/m² (own work).

In order to avoid other traffic, it might be more advisable to sharply pull up, slowing down the aircraft in the process, and then turning vertically from that climb position when the glider is close to zero g. If you like, you may now invert the plane because there is no limit on the roll angle once you fly such dynamic maneuvers.