/*************************************************************************** TITLE: c172_aero ---------------------------------------------------------------------------- FUNCTION: aerodynamics model based on constant stability derivatives ---------------------------------------------------------------------------- MODULE STATUS: developmental ---------------------------------------------------------------------------- GENEALOGY: Based on data from: Part 1 of Roskam's S&C text The FAA type certificate data sheet for the 172 Various sources on the net John D. Anderson's Intro to Flight text (NACA 2412 data) UIUC's airfoil data web site ---------------------------------------------------------------------------- DESIGNED BY: Tony Peden CODED BY: Tony Peden MAINTAINED BY: Tony Peden ---------------------------------------------------------------------------- MODIFICATION HISTORY: DATE PURPOSE BY 6/10/99 Initial test release ---------------------------------------------------------------------------- REFERENCES: Aero Coeffs: CL lift Cd drag Cm pitching moment Cy sideforce Cn yawing moment Croll,Cl rolling moment (yeah, I know. Shoot me.) Subscripts o constant i.e. not a function of alpha or beta a alpha adot d(alpha)/dt q pitch rate qdot d(q)/dt beta sideslip angle p roll rate r yaw rate da aileron deflection de elevator deflection dr rudder deflection s stability axes ---------------------------------------------------------------------------- CALLED BY: ---------------------------------------------------------------------------- CALLS TO: ---------------------------------------------------------------------------- INPUTS: ---------------------------------------------------------------------------- OUTPUTS: --------------------------------------------------------------------------*/ #include "ls_generic.h" #include "ls_cockpit.h" #include "ls_constants.h" #include "ls_types.h" #include "c172_aero.h" #include #include #define NCL 9 #define Ndf 4 #define DYN_ON_SPEED 33 /*20 knots*/ #ifdef USENZ #define NZ generic_.n_cg_body_v[2] #else #define NZ 1 #endif extern COCKPIT cockpit_; SCALAR interp(SCALAR *y_table, SCALAR *x_table, int Ntable, SCALAR x) { SCALAR slope; int i=1; float y; /* if x is outside the table, return value at x[0] or x[Ntable-1]*/ if(x <= x_table[0]) { y=y_table[0]; /* printf("x smaller than x_table[0]: %g %g\n",x,x_table[0]); */ } else if(x >= x_table[Ntable-1]) { slope=(y_table[Ntable-1]-y_table[Ntable-2])/(x_table[Ntable-1]-x_table[Ntable-2]); y=slope*(x-x_table[Ntable-1]) +y_table[Ntable-1]; /* printf("x larger than x_table[N]: %g %g %d\n",x,x_table[NCL-1],Ntable-1); */ } else /*x is within the table, interpolate linearly to find y value*/ { while(x_table[i] <= x) {i++;} slope=(y_table[i]-y_table[i-1])/(x_table[i]-x_table[i-1]); /* printf("x: %g, i: %d, cl[i]: %g, cl[i-1]: %g, slope: %g\n",x,i,y_table[i],y_table[i-1],slope); */ y=slope*(x-x_table[i-1]) +y_table[i-1]; } return y; } void aero( SCALAR dt, int Initialize ) { static int init = 0; static int flap_dir=0; static SCALAR lastFlapHandle=0; static SCALAR Ai; static SCALAR trim_inc = 0.0002; static SCALAR alpha_ind[NCL]={-0.087,0,0.14,0.21,0.24,0.26,0.28,0.31,0.35}; static SCALAR CLtable[NCL]={-0.22,0.25,1.02,1.252,1.354,1.44,1.466,1.298,0.97}; static SCALAR flap_ind[Ndf]={0,10,20,30}; static SCALAR dCLf[Ndf]={0,0.20,0.30,0.35}; static SCALAR dCdf[Ndf]={0,0.0021,0.0085,0.0191}; static SCALAR dCmf[Ndf]={0,-0.0654,-0.0981,-0.114}; static SCALAR flap_transit_rate=2.5; /* printf("Initialize= %d\n",Initialize); */ /* printf("Initializing aero model...Initialize= %d\n", Initialize); */ /*nondimensionalization quantities*/ /*units here are ft and lbs */ cbar=4.9; /*mean aero chord ft*/ b=35.8; /*wing span ft */ Sw=174; /*wing planform surface area ft^2*/ rPiARe=0.054; /*reciprocal of Pi*AR*e*/ lbare=3.682; /*elevator moment arm / MAC*/ CLadot=1.7; CLq=3.9; CLob=0; Ai=1.24; Cdob=0.036; Cda=0.13; /*Not used*/ Cdde=0.06; Cma=-1.8; Cmadot=-5.2; Cmq=-12.4; Cmob=-0.02; Cmde=-1.28; CLde=-Cmde / lbare; /* kinda backwards, huh? */ Clbeta=-0.089; Clp=-0.47; Clr=0.096; Clda=-0.09; Cldr=0.0147; Cnbeta=0.065; Cnp=-0.03; Cnr=-0.099; Cnda=-0.0053; Cndr=-0.0657; Cybeta=-0.31; Cyp=-0.037; Cyr=0.21; Cyda=0.0; Cydr=0.187; MaxTakeoffWeight=2550; EmptyWeight=1500; Zcg=0.51; /* LaRCsim uses: Cm > 0 => ANU Cl > 0 => Right wing down Cn > 0 => ANL so: elevator > 0 => AND -- aircraft nose down aileron > 0 => right wing up rudder > 0 => ANL */ /*do weight & balance here since there is no better place*/ Weight=Mass / INVG; if(Weight > 2550) { Weight=2550; } else if(Weight < 1500) { Weight=1500; } if(Dx_cg > 0.43) { Dx_cg = 0.43; } else if(Dx_cg < -0.6) { Dx_cg = -0.6; } Cg=0.25 - Dx_cg/cbar; Dz_cg=Zcg*cbar; Dy_cg=0; if(Flap_handle < flap_ind[0]) { Flap_handle=flap_ind[0]; Flap_Position=flap_ind[0]; } else if(Flap_handle > flap_ind[3]) { Flap_handle=flap_ind[3]; Flap_Position=flap_ind[3]; } else { if((Flap_handle != lastFlapHandle) && (dt > 0)) { Flaps_In_Transit=1; } else if(dt <= 0) Flap_Position=Flap_handle; lastFlapHandle=Flap_handle; if((Flaps_In_Transit) && (dt > 0)) { if(Flap_Position < 10) flap_transit_rate = 2.5; else flap_transit_rate=5; if(Flaps_In_Transit) { if(Flap_Position < Flap_handle) flap_dir=1; else flap_dir=-1; if(fabs(Flap_Position - Flap_handle) > dt*flap_transit_rate) Flap_Position+=flap_dir*flap_transit_rate*dt; if(fabs(Flap_Position - Flap_handle) < dt*flap_transit_rate) { Flaps_In_Transit=0; Flap_Position=Flap_handle; } } } } if(Aft_trim) long_trim = long_trim - trim_inc; if(Fwd_trim) long_trim = long_trim + trim_inc; /* printf("Long_control: %7.4f, long_trim: %7.4f,DEG_TO_RAD: %7.4f, RAD_TO_DEG: %7.4f\n",Long_control,long_trim,DEG_TO_RAD,RAD_TO_DEG); */ /*scale pct control to degrees deflection*/ if ((Long_control+Long_trim) <= 0) elevator=(Long_control+Long_trim)*28*DEG_TO_RAD; else elevator=(Long_control+Long_trim)*23*DEG_TO_RAD; aileron = -1*Lat_control*17.5*DEG_TO_RAD; rudder = -1*Rudder_pedal*16*DEG_TO_RAD; /* The aileron travel limits are 20 deg. TEU and 15 deg TED but since we don't distinguish between left and right we'll use the average here (17.5 deg) */ /*calculate rate derivative nondimensionalization (is that a word?) factors */ /*hack to avoid divide by zero*/ /*the dynamic terms are negligible at low ground speeds anyway*/ /* printf("Vinf: %g, Span: %g\n",V_rel_wind,b); */ if(V_rel_wind > DYN_ON_SPEED) { cbar_2V=cbar/(2*V_rel_wind); b_2V=b/(2*V_rel_wind); } else { cbar_2V=0; b_2V=0; } /*calcuate the qS nondimensionalization factors*/ qS=Dynamic_pressure*Sw; qScbar=qS*cbar; qSb=qS*b; /* printf("aero: Wb: %7.4f, Ub: %7.4f, Alpha: %7.4f, elev: %7.4f, ail: %7.4f, rud: %7.4f, long_trim: %7.4f\n",W_body,U_body,Alpha*RAD_TO_DEG,elevator*RAD_TO_DEG,aileron*RAD_TO_DEG,rudder*RAD_TO_DEG,long_trim*RAD_TO_DEG); printf("aero: Theta: %7.4f, Gamma: %7.4f, Beta: %7.4f, Phi: %7.4f, Psi: %7.4f\n",Theta*RAD_TO_DEG,Gamma_vert_rad*RAD_TO_DEG,Beta*RAD_TO_DEG,Phi*RAD_TO_DEG,Psi*RAD_TO_DEG); */ /* sum coefficients */ CLwbh = interp(CLtable,alpha_ind,NCL,Alpha); /* printf("CLwbh: %g\n",CLwbh); */ CLo = CLob + interp(dCLf,flap_ind,Ndf,Flap_Position); Cdo = Cdob + interp(dCdf,flap_ind,Ndf,Flap_Position); Cmo = Cmob + interp(dCmf,flap_ind,Ndf,Flap_Position); /* printf("FP: %g\n",Flap_Position); printf("CLo: %g\n",CLo); printf("Cdo: %g\n",Cdo); printf("Cmo: %g\n",Cmo); */ CL = CLo + CLwbh + (CLadot*Alpha_dot + CLq*Theta_dot)*cbar_2V + CLde*elevator; cd = Cdo + rPiARe*Ai*Ai*CL*CL + Cdde*elevator; cy = Cybeta*Beta + (Cyp*P_body + Cyr*R_body)*b_2V + Cyda*aileron + Cydr*rudder; cm = Cmo + Cma*Alpha + (Cmq*Q_body + Cmadot*Alpha_dot)*cbar_2V + Cmde*(elevator); cn = Cnbeta*Beta + (Cnp*P_body + Cnr*R_body)*b_2V + Cnda*aileron + Cndr*rudder; croll=Clbeta*Beta + (Clp*P_body + Clr*R_body)*b_2V + Clda*aileron + Cldr*rudder; /* printf("aero: CL: %7.4f, Cd: %7.4f, Cm: %7.4f, Cy: %7.4f, Cn: %7.4f, Cl: %7.4f\n",CL,cd,cm,cy,cn,croll); */ /*calculate wind axes forces*/ F_X_wind=-1*cd*qS; F_Y_wind=cy*qS; F_Z_wind=-1*CL*qS; /* printf("V_rel_wind: %7.4f, Fxwind: %7.4f Fywind: %7.4f Fzwind: %7.4f\n",V_rel_wind,F_X_wind,F_Y_wind,F_Z_wind); */ /*calculate moments and body axis forces */ /* requires ugly wind-axes to body-axes transform */ F_X_aero = F_X_wind*Cos_alpha*Cos_beta - F_Y_wind*Cos_alpha*Sin_beta - F_Z_wind*Sin_alpha; F_Y_aero = F_X_wind*Sin_beta + F_Y_wind*Cos_beta; F_Z_aero = F_X_wind*Sin_alpha*Cos_beta - F_Y_wind*Sin_alpha*Sin_beta + F_Z_wind*Cos_alpha; /*no axes transform here */ M_l_aero = croll*qSb; M_m_aero = cm*qScbar; M_n_aero = cn*qSb; /* printf("I_yy: %7.4f, qScbar: %7.4f, qbar: %7.4f, Sw: %7.4f, cbar: %7.4f, 0.5*rho*V^2: %7.4f\n",I_yy,qScbar,Dynamic_pressure,Sw,cbar,0.5*0.0023081*V_rel_wind*V_rel_wind); printf("Fxaero: %7.4f Fyaero: %7.4f Fzaero: %7.4f Weight: %7.4f\n",F_X_aero,F_Y_aero,F_Z_aero,Weight); printf("Maero: %7.4f Naero: %7.4f Raero: %7.4f\n",M_m_aero,M_n_aero,M_l_aero); */ }