If the maximum aileron deflection possible was commanded on a commercial airliner, how fast would the aircraft roll?
I don't think there's many reasons to bank a large aircraft quickly, but what I want to know is whether it's even possible to roll it at rates such as 10-15 degrees per second or more.
The achievable roll rate depends on altitude. At sea level, big aircraft have very low roll rates, because their roll damping is very high due to the large wingspan. Roll damping goes up with the square of the wingspan, whereas the aileron moment grows linearly with wingspan.
If the aircraft flies high enough, the roll rate will go up inversely to the change in density. This is because the flight speed increases inversely with the square root of density, so the same roll rate will cause less change in the local angle of attack on the outer wing (which is the mechanism which causes roll damping). Thus, in 12 km altitude the roll rate will be twice of what it is at sea level (at the same CAS). That is why large airliners have special high-speed ailerons at midspan: They suffice for control, and using the outboard ailerons would stress the wing a lot more. Also, outboard ailerons on high aspect ratio wings cause considerable torsion, such that the wing twist from aileron deflection will reduce aileron effectiveness. Inboard ailerons are much less affected by this effect.
I would wager to say that any airliner will be perfectly capable of 15°/s roll rates if you deflect the outboard ailerons (without overstressing the wings).
The high altitude research airplane Strato 2C had a roll rate during approach of only 2°/s! This was no real problem, because the large wing (56.5 m wingspan) would not be affected by gusts when the aircraft flew lower than approx. 30 m. The turbulence is so small scale close to the ground that the gusts would average out over the large wing, and the aircraft calmed down when sinking below 30 m, even in gusty weather. At 18 km altitude, however, it handled almost like a fighter aircraft.
FAA part §23.157 say that
in a takeoff configuration (flaps on takeoff landing gear retracted, speed trimmed at 1.2 $V_{S1}$ or 1.1 $V_{MC}$ whichever is greater) a roll of 30° must be reversible within 5 seconds for a plane of less than 6.000 pounds up to 10 seconds for planes over 12.500 pounds
on approach (flaps in landing position, gear extended, speed trimmed at $V_{ref}$) this is reduced to 4 seconds for planes less than 6000 pounds up to 7 for planes over 12500 pounds
This is an average roll rate of 6° per second on takeoff and 8° per second on approach on large airplanes.
§23.157 Rate of roll.
(a) Takeoff. It must be possible, using a favorable combination of controls, to roll the airplane from a steady 30-degree banked turn through an angle of 60 degrees, so as to reverse the direction of the turn within:
(1) For an airplane of 6,000 pounds or less maximum weight, 5 seconds from initiation of roll; and
(2) For an airplane of over 6,000 pounds maximum weight, $\frac{W+500}{1,300}$ seconds, but not more than 10 seconds, where W is the weight in pounds.
(b) The requirement of paragraph (a) of this section must be met when rolling the airplane in each direction with—
(1) Flaps in the takeoff position;
(2) Landing gear retracted;
(3) For a single-engine airplane, at maximum takeoff power; and for a multiengine airplane with the critical engine inoperative and the propeller in the minimum drag position, and the other engines at maximum takeoff power; and
(4) The airplane trimmed at a speed equal to the greater of $1.2 V_{S1}$ or $1.1 V_{MC}$, or as nearly as possible in trim for straight flight.
(c) Approach. It must be possible, using a favorable combination of controls, to roll the airplane from a steady 30-degree banked turn through an angle of 60 degrees, so as to reverse the direction of the turn within:
(1) For an airplane of 6,000 pounds or less maximum weight, 4 seconds from initiation of roll; and
(2) For an airplane of over 6,000 pounds maximum weight, $\frac{W+2,800}{2,200}$ seconds, but not more than 7 seconds, where W is the weight in pounds.
(d) The requirement of paragraph (c) of this section must be met when rolling the airplane in each direction in the following conditions—
(1) Flaps in the landing position(s);
(2) Landing gear extended;
(3) All engines operating at the power for a 3 degree approach; and
(4) The airplane trimmed at $V_{REF}$.
A320 has maximum rate of roll 25°/s (according to this Flight article). And note that since A320 is fly-by-wire with augmented controls, this is not maximum possible with full aileron deflection but what maximum sidestick deflection will command. Depending on speed full deflection may cause higher rate of roll so the limit is achievable across reasonable range of speeds.
There is one good reason to roll large aircraft quickly: to counter effect of turbulence. Turbulence can roll even big aircraft pretty quickly (strong turbulence may easily roll the aircraft to more than 45° under a second) and the pilots will want to return it to level quickly to avoid changing direction and loosing much altitude.
