Week 2 Air standard Cycle

# Problem for the engine kinematics

# importing modules
import math
import matplotlib.pyplot as plt

# Definig a function to calculate the various pressure and volume.
def engine_kinematics(bore, stroke, con_rod,cr, start_crank, end_crank):

	#geometric parametrics
	a = stroke/2
	R = con_rod/a

	# Initialising stroke and clear volume
	V_s = math.pi*(1/4)*pow(bore,2)*stroke
	V_c = V_s/(cr-1)

	# converting the both starting and ending angles to radians
	sc = math.radians(start_crank)
	ec = math.radians(end_crank)

	# iteration value
	num_values = 50

	dtheta = (ec-sc)/(num_values-1)  # setting up the equal intervals between the angles
	V =[]                            # empty array for the calculation of volume


	# 'for' loop for calculation of V value for each angle 
	for i in range(0,num_values):
		theta = sc + i*dtheta                               # Splitting the terms and calculating seperately V
		term1 = 0.5 * (cr-1)
		term2 = R + 1 - math.cos(theta)
		term3 = pow(pow(R,2)-pow(math.sin(theta),2),0.5)	

		V.append((1 + term1*(term2 - term3))* V_c)			# appending the value  of V to store all the vlaues in to the empty array
	
	return V						# returning the vlaue of V 


# Initial parameters for the calculation
p1 = 101325
t1 = 500
gamma = 1.4
t3 = 2300
bore = 0.1
stroke = 0.1
con_rod = 0.15
cr = 6

V_s = math.pi*(1/4)*pow(bore,2)*stroke
V_c = V_s/(cr-1)

# Calculation of the pressure, temperature and volume at point 1 of PV diagram
v1 = V_c + V_s

rhs = p1*v1/ t1

# Calculation of the pressure, temperature and volume at point 2 of PV diagram
v2 = V_c
p2 = p1 * pow(v1,gamma)/pow(v2,gamma)
t2 = p2*v2/rhs

V_compression = engine_kinematics(bore, stroke, con_rod,cr, 180,0)		# calling the function to claculate non linear volume for the adiabatic heat addition

# Calculating corresponding pressure(compression) using another 'for' loop
constant = p1*pow(v1,gamma)
p_compression = []
for v in V_compression:
	p_compression.append(constant/pow(v,gamma))
	


# Calculation of the pressure, temperature and volume at point 3 of PV diagram
v3 = v2
p3 = rhs * t3/v3

# calling the function to claculate non linear volume for the adiabatic heat rejection
V_expansion = engine_kinematics(bore,stroke,con_rod,cr,0,180)
constant = p3*pow(v3,gamma)

# Calculating corresponding pressure(expansion) using anothe 'for' loop
P_expansion=[]
for v in V_expansion:
	P_expansion.append(constant/pow(v,gamma))


# Calculation of the pressure, temperature and volume at point 4 of PV diagram
v4 = v1
p4 = p3*pow(v3,gamma)/pow(v4,gamma)
t4 = p4*v4/rhs


# plotting the PV daigram using matplotlib.py
plt.figure()
plt.plot([v2, v3],[ p2, p3])             
plt.plot(V_compression,p_compression)		# plotting compression cycle
plt.plot(V_expansion,P_expansion)			# plotting expansion cycle
plt.plot([v4, v1],[p4, p1])					
plt.savefig('engine_kinematics')
plt.show()

I explained the problem using the comments in the code.