%program to make the P-V diagram of Otto cycle
clear all % clear all the variables from workspace
close all % close all the figures
clc % clears the command window
%input variables already known
T1=500; % temperature at state 1
P1=101325; % pressure at state 1
gamma=1.4; % adiabatic constant for air
T3=2000; % temperature at state 3
%engine geometric parameters
bore=0.1; % bore diameter
stroke=0.1; % stroke
con_rod=0.15; % connecting rod length
cr=12; % compression ratio
%calculating the swept and clearance volume
v_swept=(pi/4)*bore^2*stroke; % swept volume
v_clearance=v_swept/(cr-1); % clearance volume
%calculating the volume of state 1 and state 2
V1=v_swept+v_clearance; % volume at state 1 (i.e swept vol + clearance vol)
V2=v_clearance; % volume at state 2 (i.e clearance volume)
%calculating the state variables of state 2
P2=P1*cr^gamma; % using adiabatic eq.|(p1*v1^gamma)=(p2*v2^gamma)
T2=(P2*T1*V2)/(P1*V1); % using ideal gas eq.| (P1*V1)/T1=(P2*V2)/T2
%volume and pressure trace during compression
constant_c = P1*V1^gamma; % constant value using adiabatic equation | PV^gamma=c
V_compression = kinematics_of_engine(bore, stroke, con_rod, cr,180,0) % function to calculate the volume trace during compression
P_compression = constant_c./V_compression.^gamma; % tracing the pressure during compression
%calculating the state variables of state 3
V3=V2; % constant volume heat addition
P3=T3*P2/T2; % using ideal gas equation for constant volume |(P2/T2)=(P3/T3)
%volume and pressure trace during expansion
constant_c = P3*V3^gamma; % constant value using adiabatic equation | PV^gamma=c
V_expansion = kinematics_of_engine(bore, stroke, con_rod, cr,0,180) % function to calculate the volume trace during expansion
P_expansion = constant_c./V_expansion.^gamma; % tracing the pressure during compression
%calculating the state variables of state 4
V4=V1; % constatnt volume heat rejection
P4=P3*(V3/V4)^gamma; % using adiabatic eq.|p3*v3^gamma=p4*v4^gamma
%plotting of exact otto cycle
figure(1) % figure to show the correct otto cycle
hold on % hold all the plots
plot(V1,P1,'*','color','r') % plot coordinates of state 1
plot(V_compression, P_compression) % plotting the trace of Volume and pressure during compression
plot(V2,P2,'*','color','r') % plot coordinates of state 2
plot( [V2,V3],[P2,P3],'color','r') % join the state 2 and 3 by straight line
plot(V3,P3,'*','color','r') % plot coordinates of state 3
plot(V_expansion, P_expansion) % plotting the trace of volume and pressure during expansion
plot(V4,P4,'*','color','r') % plot coordinates of state 4
plot([V4,V1],[P4,P1]) % join the state 4 and 1 by straight line
%plotting of another straight line otto cycle for comparison
figure(2) % figure to show the wrong otto cycle
plot([V1 V2 V3 V4],[P1,P2,P3,P4],'color','b') % join all the coordinates of states by straight line
%calculation of the thermal efficiency of the engine
eff_term=cr^(gamma-1) % term to store the value of cr^(gamma-1)
therm_eff=1-(1/eff_term) % thermal efficiency of engine
%% errors faced and how did they overcome
%error 1: unrecognized variable or function 'v_comprseesion'
%solution_1: 'V_compression' is written by replacing 'v_comprseesion'
%error 2: expansion adiabatic graph not drawn
%solution 2: in line 65, 'plot(V_compression, P_compression)' is replaced
%by plot(V_expansion, P_expansion)
%error 3: incorrect dimension for raising matrix to a power
%solution 3:in kinematics_of_engine , line 20, element wise operator was put
%errors graphs and output graphs are attached