%Calculate the Static Stability Params for the %Navion General Aviation A/C % 16.333 % Adapted from Nelson, page 57 %clear all W=2750 %lb V=176 % ft/sec X_cg=0.295 %cbar h=0.295 S=184 % ft^2 b=33.4 % ft cbar = 5.7 % ft S_t=43 %ft^2 l_t=16 %ft h_t=l_t/cbar+h % Wing C_m_ac_w=-0.116 C_l_alp_w=0.097 %/deg alp_0_L=-5 % deg X_ac=0.25 %cbar h_nbar=0.25 i_w=1 %deg %Tail C_l_alp_t=0.088 %/deg C_m_ac_t=0 %i_t=-1% deg eta=1; b_t=2.2/5.5*b; V_H=l_t*S_t/cbar/S AR=b^2/S AR_t=b_t^2/S_t d2r=180/pi; % convert wing section lifts to 3D wing C_L_alp_w=C_l_alp_w*d2r/(1+C_l_alp_w*d2r/(pi*AR)) C_L_alp_t=C_l_alp_t*d2r/(1+C_l_alp_t*d2r/(pi*AR_t)) % Wing contribution % from 2-4 % C_m_cg_w=C_L_w(h-h_nbar)+C_m_ac_w; % % with C_L_w=C_L_0_w + C_L_alp_w alp_w % where C_L_0_w = lift coeff at zero angle of attack C_L_0_w = C_L_alp_w * abs(alp_0_L/d2r) % C_m_cg_0_w=C_L_0_w*(h-h_nbar)+C_m_ac_w C_m_cg_alp_w=C_L_alp_w*(h-h_nbar) % for downwash % eps = eps_0 + eps_alp alp_w eps_0=2*C_L_0_w/pi/AR eps_alp=2*C_L_alp_w/pi/AR % Tail from 2-8 C_m_cg_0_t=eta*V_H*C_L_alp_t*(eps_0+i_w/d2r-i_t/d2r) C_m_cg_alp_t=-eta*V_H*C_L_alp_t*(1-eps_alp) % total C_m_cg_0=C_m_cg_0_w+C_m_cg_0_t C_m_cg_alp=C_m_cg_alp_w+C_m_cg_alp_t figure(1);clf alp=[0:1:12]'; plot(alp,C_m_cg_0_w+C_m_cg_alp_w*alp/d2r,'LineWidth',2) hold on plot(alp,C_m_cg_0_t+C_m_cg_alp_t*alp/d2r,'m--','LineWidth',2) plot(alp,C_m_cg_0+C_m_cg_alp*alp/d2r,'r:','LineWidth',2) plot([0 12],[0 0],'k','LineWidth',2) legend('Wing','Tail','Total') %hold off xlabel('\alpha (deg)') ylabel('C_{m_{cg}}') % neutral point C_L_alp_T=C_L_alp_w+eta*S_t/S*C_L_alp_t*(1-eps_alp) gamma=C_L_alp_T/C_L_alp_w hnp=(h_nbar+(gamma-1)*h_t)/gamma return clear all Hnp=[];kk=0;CMT=[];CMt=[];CMw=[]; for i_t=[-2:1] kk=kk+1; navion_1 Hnp=[Hnp hnp] CMw=[CMw C_m_cg_0_w+C_m_cg_alp_w*alp/d2r]; CMt=[CMt C_m_cg_0_t+C_m_cg_alp_t*alp/d2r]; CMT=[CMT C_m_cg_0+C_m_cg_alp*alp/d2r]; hold on end figure(2);clf plot(alp,CMw,'LineWidth',2) hold on plot(alp,CMt,'--','LineWidth',2) plot(alp,CMT,'r:','LineWidth',2) legend('Wing','Tail','Total') plot([0 12],[0 0],'k','LineWidth',2) hold off xlabel('\alpha (deg)') ylabel('C_{m_{cg}}')