An Integrated, Modular Simulation System for Education ... - Cal Poly

original published values were sea level, 176.4 ft/sec, and 0.0023769 slugs/ft^3. The finalvalues established for trimming the model are: 2.153 ft, 175.215 ft/sec , and 0.00237254slugs/ft^3. The atmosphere was trimmed rather than the controls as the model is assumedto have the controls trimmed for the condition. Before the trim of the model was refinedthe initial conditions perturbed the model enough to excite the phugoid mode at the startof a simulation. For a man in the loop simulation the small perturbation was notdistinguishable, however the motion was significant in batch simulations duringvalidation of the model.The second change from the most basic model is to correct for the assumption thatthe aircraft body axis is the same as the airpath axis (the difference between the directionthe aircraft is pointed and the direction it is actually going). Originally the model was toonly map the lift and drag forces to the body axis [Ref. 32]. After referencing the PhEagleI c++ code, the PhEagle II S-function included the side forces [Fy] to the coordinatetransform. The transform was done in two stages from airpath axis through the angle betaalong the airpath z axis (equation 7.). Then through the angle alpha along the beta y axisEquation 7 Wind to β⎛ cos( β) sin( β)0⎞⎛ DragWind⎞⎛ Fxα⎞⎜−sin( β) cos( β) 0⎟* ⎜ FyWind ⎟ α⎜⎟ ⎜ ⎟ = ⎜ Fy ⎟⎜ ⎟⎝ 0 0 1⎠⎝ LiftWind ⎠ ⎝ Fzα⎠Equation 8 β to Aircraft Body⎛cos( α) 0 sin( α)⎞ ⎛ Fxα⎞⎛ FxBody⎞⎜ 0 1 0 ⎟ * ⎜ Fyα⎟⎜⎟ ⎜ ⎟ = ⎜ FyBody⎟⎜ ⎟⎝ sin( α) 0 cos( α)⎠ ⎝ Fzα⎠⎝ FzBody⎠to the aircraft body axis (equation 8.). Thetransform were multiplied together thenmultiplied by the force vector to obtain thefinal transform matrix (equation 9). TheEquation 9 Total Transform⎛cos( α) 0 sin( α)⎞ ⎛ cos( β) sin( β)0⎞⎛cos( α)cos( β) − cos( α)sin( β) sin( α)⎞ ⎛ DragWind⎞⎜ 0 1 0 ⎟ * ⎜−sin( β) cos( β)0⎟sin( β) cos( β)0 *⎜⎟ ⎜⎟ = ⎜⎟ ⎜ FyWind ⎟⎜⎟ ⎜ ⎟⎝ sin( α) 0 cos( α)⎠ ⎝ 0 0 1⎠⎝ sin( α)cos( β) −sin( α)sin( β) cos( α)⎠ ⎝ LiftWind ⎠55