How much do aileron on a commercial airliner move for manoeuvring and trim?

Question

I recently flew on an MD88 and had a good view of the aircraft's wing from my seat (read: I sat right next to the toilet). During the flight I noticed a couple odd things about the ailerons on the left wing. First, the middle one (there are three that I could see) was constantly pitched up by about an inch. Second, none of the ailerons seemed to move more than a couple millimeters during even the fastest banks (in fact, it was only that second aileron which I observed moving at all).

My questions are:

1. Was the second aileron being constantly pitched up for some reason? Or was it a trim issue?
2. How much do the ailerons even need to move to bank the aircraft? Would a couple millimeters do the job, or should I have seen more movement?

Edit: After taking some of the comments and searching around some more I found this diagram which seems to indicate what I was observing was not an aileron, but the outboard flap. Also this answer details why outboard ailerons are often locked in high-speed flight. But that still leaves the question of why the flap was constantly pitched up throughout the flight.

Answer 1

1. I have never flown an aircraft, only flew in them, but I am studying aerospace engineering. If ailerons were deflected the whole time, I would say that it was a trim issue. Note that the MD-88 are old aircraft (introduced at 1980 and production stopped at 1999, source: Wiki page on MD80 series), so having some idiosyncrasies such as some roll instability or drift is to be expected. I have not studied the degradation of aircraft over time, but it makes sense. I had to mention that since stackexchange does not like people sharing opinions.

2. This question is more interesting for me since we can do some back of the envelope calculations to establish some simple facts. Lets approximate how much force would be required to get an angular acceleration of say 5 degrees per second squared, a very extreme case. Gradual turns are initiated with angular accelerations of about 2 degree per second squared; that way a 30 degree bank takes about 15 seconds to enter.

   The most relevant thing that would be required is an estimate of the mass moment of inertia (MMOI) of the aircraft along its X axis (which is an axis pointing in the flight direction).

   First the Maximum takeoff weight (MTOW) is taken from data (MD88 mass data) and the dimensions are approximated from drawings and data (MD88 dimension data)

   Than the aircraft is modeled as a filled cylinder with the wings as two cuboid. The mass of these 3 sections are approximated from the mass fraction as found in this article. Crunching up all the numbers leads to an approximate $I_x$ for the MD-88 as $3350 \times 10^3$ $kg$ $m^2$.

   We know that $M = I \alpha$, where $M$ is the rolling moment, $I$ is the MMOI and $\alpha$ is the angular acceleration. 5 degrees per seconds squared is about 0.09 radians per seconds squared. And $M = Fl$, where $F$ is the force from the aileron and $l$ is the moment arm. The moment arm is about 16 $m$ since the half wing span is about 17.9 $m$. So we have $F = \frac{I \alpha}{l}$. This leads to a requirement of 19000 N of force from both ailerons, and about 9500 N from each aileron.

   In normal flight (at approximately MTOW) the wings are producing about 600 $kN$ of force to keep the aircraft in air. For this rather extreme banking maneuver the ailerons need to create a 10 $kN$ difference in lift (which is about 2% of the total lift).

   Lets estimate the required change in lift coefficient for this change in lift. Assuming one aileron influences 15% of the wing surface, a flight at an altitude of 10 km, and a airspeed of 230 m/s, we find that each aileron should cause a 0.05 change in the lift coefficient of the wing segment. Have a look at the image below for an idea of about how much the lift coefficient changes with flap deflection. It seems evident that about a 5 degree deflection is required to get to the required order of magnitude of change in the lift coefficient.

_{(source: stanford.edu)}

Now that we have some idea about the order of magnitudes, we can talk about the aileron deflection question. Using information from the aileron sizing documentation, we can think about the moment caused by your specific question. If we imagine a deflection of 5 mm (seems ok for stabilization but a little too low for control), we can approximate a aileron deflection of about 0.7 degree (assuming a $c_a/c$ of 0.25 and chord length of 1.5 $m$). Hence, I do not think deflections of a few mm are enough to roll the aircraft as would be required during landing maneuvers around an airport. Thus I think the aileron you saw that was trimmed is doing the heavy lifting for the rolling.

There are further subtleties introduced into the required magnitude of deflection of the ailerons due to other design parameters such as the incidence angle of the wing and the specific nature of the airfoil in the wing extremities. The former introduces a differential in how much the left and right ailerons need deflecting and the latter may cause the sections with the ailerons to have inherently higher lift in order to get a better lift distribution over the wing. These two are just to mention two of many things that interact to determine the rolling dynamics of the aircraft.

I wanted to include more sources for my work, but apparently I can only include two links; so I removed all of my supporting material and left only the image for consideration. If you want sources for my analysis, send me a message.