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%################################%@@@@@@@@ Given information @@@@@%================================

R_u= 8314; %Universal Gas Constant, J/(kmole. K)g0= 9.81; %Gravitational acceleration at sea level (m/s^2)

%#################################%@@@ The Propelllant properties @@%#################################Tc= 3370; %The Flame Temperature (chamber temperature) (K)Rho_p= 1772; %The density of propellant ( kg/m^3)M_w= 29.3; %The molecular weight (g/mole)R= 284; %The exhaust Gas Constant (J/(kg.K))Gamma= 1.17; %Specific Heats Ratios of exhaust gasesn=0.4; k=4; %Burning rate exponent and burnng rate constantC_star= 1575; %Characteristic Velocity (m/s)

%#############################################%@@@ Properties of air at altitude of 25 m @@@

%#############################################P0= 101026; %Ambient Pressure (Pa)T0 = 288.1; %Ambient Temperature (K)R_air = 286.9; %Air Gas Constant (J/kg.K)Rho_air= 1.222; %the density of air (kg/m^3)Gamma_air= 1.4; %Specific Heats Ratios of air

%############################################%@@@@ For the nozzle to be fully expanded @@@%############################################Pe = P0; %An assumption for optimal solution

%###############################################%@@@ Mission specifications and requirements @@@%###############################################M_No=0.85; %Mach NumberminVelocity= 289.15; % Minimum Velocity of flight (m/s)minRange= 60000; %Minimum target range (m)

%###############################################%@@@@@@ Design Requirements and limitations @@@%###############################################maxMass= 800; %Maximum Total mass of the missile (kg)missilelength=6.0; %Maximum length of the missile (m)% given that:

warheadMass= 150; %The mass of the warhead (kg)guidaceMass= 40; %The guidance system mass (kg)

%###########################################%@@@@@@@@@@ Methodoloy of designing @@@@@@@@%###########################################fprintf('\tNozzle Expansion Ratio Properties\n\t Me\t\t\t\t Epsilon\n');%Epsilon is the expansion ratio (Epsolon= exitAera/ throatAera)%For simplying the formulation: let:

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a=Gamma-1;b=Gamma+1;for Me=1.2:0.05:3;

Epsilon = (((1+((a/2)*Me*Me))^(b/(2*a)))*((2/b)^(b/(2*a))))/Me;fprintf('\t%0.2f \t\t\t \t%0.3f\n', Me, Epsilon);

end%####################################################%@@@@ chossing Initial value of Espilon @@@@@@@@@@@@@%####################################################

Espilon= 7.440;Me= 2.567; %Corresponding Mach number to Espilon

fprintf('\nFor Expansion Ratio = %0.3f and Exit Mach Number = %0.3f: \n',Epsilon, Me);

%########################################################################## %@@@ Calculation of chamber pressure (Pc) for Me using isentropic formula

@@@@%##########################################################################

Pc = P0*((1+(a/2)*Me*Me)^(Gamma/a));fprintf('Chamber Pressure = %0.3f Pa\n', Pc);

%############################################%@@@ Calculation of X-function @@@@@@@@%############################################X_star= sqrt(Gamma)*(2/b)^(b/(2*a));

fprintf('X-function = %0.3f \n', X_star)%#################################################

%@@@ Calculation of the coefficient of Thrust @@@@%#################################################

Cf_optimum = sqrt((2*Gamma*Gamma/a)*((2/b)^(b/a))*(1-(Pe/Pc)^(a/Gamma)));

Cf_actual = 0.9*Cf_optimum;fprintf('Thrust Coefficient = %0.3f \n', Cf_actual);

%####################################################%@@@ Calculation of Specific Impulse(Isp) @@@@@@@@@@@%####################################################Isp= (C_star * Cf_actual)/g0;

fprintf('Specific Impulse = %0.5f s\n', Isp);%##################################################%@@@ Preliminary Design of Motor Dimensions @@@@%##################################################D_motor= 0.83; %Initial assumption of motor diameter (m)L_charge= 2.63; %Initial assumption of charge length (m)t_casing_insulation= 0.025; %Initial assumption of thickness of casing andinsulation

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%charge diameter :dc= D_motor-2.0*t_casing_insulation; %Determining diameter of charge

%Calculating burn aera (A_b):A_b= 0.9*pi*dc*L_charge;

%Calculating throat aera and diameter :

A_star=((Rho_p*A_b*k*(1.0e-5)^n*sqrt(R*Tc))/(1000*X_star *(Pc)^(1-n)));D_star= sqrt(4*A_star/pi);

fprintf('Throat Area = %0.5f m^2\nThroat Diameter = %0.5f m\n', A_star,D_star);

%#############################################%@@@@ Exhaust velocity determination @@@@@@@@@%#############################################Ve = sqrt((2*Gamma*R*Tc/a)*(1-(Pe/Pc)^(a/Gamma)));fprintf('Exhaust Velocity = %0.5f m/s\n', Ve);

%###########################################%@@@@ The Thrust (Fn) calculation @@@@@@@@@%###########################################Fn= Cf_actual* Pc * A_star;

fprintf('Thrust = %0.5f N or %0.5f kN\n', Fn, Fn/1000);

%@@@@ The mass flow rate (m_dot) calculation:

m_dot = Fn/Ve;fprintf('Mass Flow Rate = %0.5f kg/s\n', m_dot);

%#######################################################%@@@@ Calculation of the propellant mass (M_p) @@@@@@@@@%#######################################################%first calculating the graing volume (V0):V0= pi*dc*dc*L_charge/4;

%Area of port (A_conduit) is to be at least four times the throat area (m^2:A_conduit = 4*A_star;D_conduit = sqrt(4*A_conduit/pi);%volume of port (V_conduit) determination:V_conduit = A_conduit*L_charge;

%The volume of grain (Vc):Vc = V0 - V_conduit;%The mass of propellant is:M_p = Rho_p*Vc;fprintf('\nPropellant volume = %0.5f m^3\n', Vc);fprintf('\nPropellant Mass = %0.5f kg\n', M_p);%######################################################################## %@@@@ The Burning rate (r_b)and burning time (t_b) calculation @@@@@@@@@%######################################################################## r_b = k*((Pc*1.0e-5)^n)/1000;

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t_b= M_p/m_dot;

fprintf('Burning Rate = %0.5f m/s\nburning time = %0.5f s\n', r_b,t_b);

%####################################################%@@@ Calculation of Total Impulse(It) @@@@@@@@@@@%####################################################It=Fn*t_b;fprintf('Total Impulse = %0.5f s\n', It);