>> >> -------------------------------------------------- >> From: <cas...@mminternet.com> >> Sent: Wednesday, March 30, 2011 3:57 PM >> To: "FlightGear developers discussions" >> <flightgear-devel@lists.sourceforge.net> >> Subject: [Flightgear-devel] Calculating free stick position and forces >> >>> Ok, here are a couple of thoughts on improving the elevator model; as >>> always comments and suggestions are welcome, flames will be ignored >>> >>> @ line 220 or so of FGAerodynamics add: >>> >>> alphat = alpha + tailincidence - downwash; // alpha fro the tail >>> >>> for now we'll assume no flying tails just a normal hinged elevator, so >>> the >>> incidence is fixed and specified in the aircraft xml file. To >>> calculate >>> the downwash we use the following formula >>> >>> downwash = 2 * CL(wing) / (pi * AR) >>> >>> where AR is the aspect ratio of (cbar*cbar)/Sw, but cbar is actually a >>> variable dependent on the wing/flap configuration; so we need to >>> recalculate cbar whenever the configuration changes and, at some point, >>> we'll need to consider any delta cbar as a time dependent variable >>> based >>> on flap extension/retraction rates. >>> >>> Obtaining CL and pi is trivial, so the task at hand is the best way to >>> calculate the aspect ratio - something that only has to happen when the >>> wing configuration changes. >>> >>> So once we have the alpha at the tail and assuming a trim tab set to >>> some >>> value the stick free elevator (aka floating) becomes >>> >>> elev_float = - ((b1*alphat + b3*trim)/b2*elevator) * alphat >>> >>> where b1 = (partial) Ch with respect to (partial) alphat >>> and >>> b2 = (partial) Ch with respect to (partial) elevator >>> and >>> b3 = partial Ch with respect to (partial) trim >>> >>> All that remains is to calculate the elevator balance position where Cm >>> = >>> 0; i.e., steady state flight aka a trimmed aircraft or >>> >>> elev_float = elev_balance >>> >>> I'll stop here for now. The next set of calcs would be to determine >>> the >>> control force gradient to apply to the stick as it is moved from the >>> neutral (or zero stick force location). >>> >>> Regards >>> John >> >> >> I applaud what you are trying to do but would caution at using such a >> gross >> simplification for downwash, which is a very complicated thing to >> estimate. >> (see the literature) > > please cite a source rather than a general statement. see > > http://adg.stanford.edu/aa241/stability/staticstability.html > > and citing from the paper > > "The value of the downwash at the tail is affected by fuselage geometry, > flap angle wing planform, and tail position. It is best determined by > measurement in a wind tunnel, but lacking that, lifting surface computer > programs do an acceptable job. For advanced design purposes it is often > possible to approximate the downwash at the tail by the downwash far > behind an elliptically-loaded wing" > > and > http://www.scribd.com/doc/51685604/16/Designing-the-Horizontal-Tail > > and a similar cite > > " ε = ε0 + dε/dαw * αw > > where ε0 is the downwash at zero angle of attack > > The downwash behind a wing can be derived from the finite-wing theory and > shown to be related to the wing lift coefficient and aspect ratio: > > ε= 2CLw/π ARw > > The rate of change of downwash angle with angle of attack is determined by > taking derivative of the equation" > > Granted it's an approximation, but I don't have a wind tunnel or a large > CFD program handy... ;-) This is a first step, we can do any refinements > as desired and/or required once a working model is in place > >> Perhaps downwash and hinge force calculations should be the subject of a >> section in the xml aerodynamics file so that they can be tailored on a >> per-aircraft basis. >> > > the xml files should be used to load the respective aircraft data for aero > coefficients, tail geometry, and metrics. For speed and efficiency the > actual calculations should reside in the JSBSim code > > John > Ooops, the equations got trashed by the email server. you'll have to go to the cited docs.
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