Looking for techniques to model resistance to roll rotation in a very simple, force-based flight model

Question

I'm new to flight dynamics programming and am curious to know how people model an aircraft's resistance to rolling in very simple force-based flight models (not CFD, etc.). For example, after a full deflection of the ailerons, the stick is returned to center and the aircraft will stop rolling.

I assume I should be looking at factors including dynamic pressure, wing area, and a center of pressure for the wing. I'm just not sure if I should just be modeling the "wing pushing against the air that it is rolling into" or if there are other more significant physical principles at play.

Essentially I am trying to create a model in which I can tune maximum roll rates against an aircraft's tendency to want to stop rolling.

Thanks, and sorry in advance if this is too vague, but any info will certainly be appreciated and will help steer me.

Answer 1

The way this is commonly done in simulators is using linearized stability derivatives. For your example, one could calculate the rolling moment on the aircraft as the sum of such terms as: rolling moment due to aileron deflection angle, rolling moment due to roll rate (roll damping), roll moment due to side slip angle, roll moment due to yaw rate, roll moment due to rudder. For doing simulation each of these coefficients can be precalculated based on flight testing or CFD and then during simulation lookup tables can be used to find the current value. My suggestion is that you take a look at JSBSim which is a cross platform opensource flight dynamics model that is used by FlightGear for example. JSBSim allows one to build an aircraft model by defining the values in an XML file. The website includes documentation, some links to papers and books, and example aircraft that are very useful.

Answer 2

This is far from a complete answer, but I want to point out that you need to recognize that the motion of any given part (e.g. molecule) of the aircraft through the airmass creates an apparent wind or "relative wind" in the opposite direction. If an aircraft is changing bank angle (rolling), the "relative wind" actually becomes "twisted" into a corkscrew-like shape. For example, the wingtip that is rising will feel a downward component in the relative wind, while the wingtip that is descending will feel an upward component in the relative wind.

This link should be of some interest -- note that the green arrows labelled "motion" are not both pointing in the same direction, and thus the direction of the local relative wind (which is opposite to the direction of the "motion" arrows) is not the same at each wingtip, and thus the angle-of-attack of each wing cannot be the same. The angle-of-attack of the rising wing has been decreased (or in extreme cases, has actually become negative), and the angle-of-attack of the descending wing has been increased. This creates the "roll damping" phenomenon-- a roll torque acting to slow the roll rate-- which can be loosely described as an inherent aerodynamic "resistance" to rolling. This phenomenon is central to the dynamics that you are trying to model.

From the phrasing of the question, it seems that you already understand much of this, but I just thought that this answer might put it into a slightly different perspective that might be helpful.

PS the link noted above leads to a discussion of yaw dynamics (adverse yaw), but that's not really what I'm trying to focus on here. I'm just using it as a useful illustration of the "twist" in the relative wind due to rolling, and the resulting "roll damping" or "resistance" to rolling, regardless of whether "adverse yaw" is also entering the picture in a significant way or not.