{
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 7 : Rocket propulsion"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.1 page : 21"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"\t\t\t\t\n",
"#Input data\n",
"mp = 12. \t\t\t\t#flow rate in kg/s\n",
"Ae = 335.*10**-4 \t\t\t\t#exit area in m**2\n",
"Ce = 2000. \t\t\t\t#exhaust velocity in m/s\n",
"h = 10. \t\t\t\t#altitude in km\n",
"Pe = 1.*10**5 \t\t\t\t#exhaust pressure in Pa\n",
"P0 = 1.*10**5 \t\t\t\t#p0 = atomspheric pressure in Pa at h = 0.\n",
"P10 = 0.25*10**5 \t\t\t\t#atmospheric pressure in Pa umath.sing gas tables\n",
"\n",
"\t\t\t\t\n",
"#Calculations\n",
"Fs = mp*Ce*10**-3 \t\t\t\t#thrust of motor at sea level math.since pe = p0 in kN\n",
"F10 = ((mp*Ce) + Ae*(Pe-P10))*10**-3 \t\t\t\t#thrust of motor at altitude of 10km in kN\n",
"\n",
"\t\t\t\t\n",
"#Output\n",
"print 'A)thrust of motor at sea level is %3i kN upwards \\\n",
"\\nB)thrust of motor at an altitude 10km is %3.4f kN'%(Fs,F10)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"A)thrust of motor at sea level is 24 kN upwards \n",
"B)thrust of motor at an altitude 10km is 26.5125 kN\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.2 page : 22"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"\t\t\t\t\n",
"#Input data\n",
"P0 = 38*10**5 \t\t\t\t#combustion chamber pressure in Pa\n",
"T0 = 3500 \t\t\t\t#combustion chamber temperature in K\n",
"ma = 41.67 \t\t\t\t#oxidizer flow rate in kg/s\n",
"MR = 5 \t\t\t\t#mixture ratio\n",
"k = 1.3 \t\t\t\t#adiabatic consmath.tant\n",
"R = 287 \t\t\t\t#gas consmath.tant in J/kg-K\n",
"Pamb = 0.0582*10**5 \t\t\t\t#ambient pressure in Pa\n",
"Pe = Pamb \t\t\t\t#exhaust pressure at sea level in Pa\n",
"\n",
"\t\t\t\t\n",
"#Calculation \n",
"mf = ma/MR \t\t\t\t#mass flow of fuel in kg/s \n",
"mp = mf+ma \t\t\t\t#propellant mass flow in kg/s\n",
"Cp = (k*R)/(k-1) \t\t\t\t#specific heat at consmath.tant pressure in J/kg-k\n",
"p = P0/Pe \t\t\t\t#ratio of pressures at combustion chamber and exhaust \n",
"Me = ((((p**((k-1)/k))-1)*2)/(k-1))**0.5 \t\t\t\t#Mach number\n",
"t = 1/(1+(((k-1)/2)*Me**2)) \t\t\t\t#ratio of exhaust temperature to combustion temperature\n",
"Te = t*T0 \t\t\t\t#exhaust temperature in Kelvin\n",
"a = (1/Me)*(((2/(k+1))+(((k-1)/(k+1))*Me**2))**((k+1)/(2*(k-1)))) \t\t\t\t#ratio of areas at exit section and throat section of the nozzle\n",
"Ce = (k*R*Te)**0.5*Me \t\t\t\t#exit velocity in the exhaust in m/s\n",
"Cj = Ce \t\t\t\t#average effective jet velocity in m/s, math.since Pe = Pamb\n",
"P1 = P0*(2/(k+1))**(k/(k-1)) \t\t\t\t#pressure at throat section in Pa\n",
"T1 = T0*(2/(k+1)) \t\t\t\t#temperature at throat section in K\n",
"d1 = P1/(R*T1) \t\t\t\t#density of fuel at throat section in kg/m**3\n",
"C1 = (k*R*T1)**0.5 \t\t\t\t#velocity at throat section in m/s\n",
"A1 = (mp/(d1*C1))*10**4 \t\t\t\t#nozzle throat area in cm**2\n",
"Ae = a*A1 \t\t\t\t#exit area in cm**2\n",
"F = (mp*Ce)*10**-3 \t\t\t\t#thrust in kN\n",
"Cmax1 = (2*Cp*T0)**0.5 \t\t\t\t#maximum possible velocity in m/s\n",
"Cf = (F*10**3)/(P0*A1*10**-4) \t\t\t\t#thrust coefficient, F in kN and A1 in m**2\n",
"Cch1 = Cj/Cf \t\t\t\t#characteristic velocity in m/s\n",
"\n",
"\t\t\t\t\n",
"#Output\n",
"print 'A)nozzle throat area is %3.2f cm**2 \\\n",
"\\nB)thrust is %3.1f kN \\\n",
"\\nC)thrust coefficient is %3.2f \\\n",
"\\nD)characteristic velocity is %3i m/s \\\n",
"\\nE)exit velocity in exhaust is %3i m/s \\\n",
"\\nF)maximum possible exhaust velocity is %3i m/s'%(A1,F,Cf,Cch1,Ce,Cmax1)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"A)nozzle throat area is 197.65 cm**2 \n",
"B)thrust is 130.0 kN \n",
"C)thrust coefficient is 1.73 \n",
"D)characteristic velocity is 1502 m/s \n",
"E)exit velocity in exhaust is 2599 m/s \n",
"F)maximum possible exhaust velocity is 2950 m/s\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.3 page : 23"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"\t\t\t\t\n",
"#Input data\n",
"a = 3. \t\t\t\t#exit area to throat area ratio\n",
"T0 = 2973. \t\t\t\t#combustion chamber temperature in K\n",
"P0 = 20.*10**5 \t\t\t\t#combustion chamber pressure in Pa\n",
"k = 1.3 \t\t\t\t#adiabatic consmath.tant\n",
"R = 248. \t\t\t\t#gas consmath.tant in J/kg-K\n",
"Pamb = 1.*10**5 \t\t\t\t#ambient pressure in Pa\n",
"Me = 2.52 \t\t\t\t#mach number for k = 1.3 and a = 3 umath.sing gas tables \n",
"g = 9.81 \t\t\t\t#acceleration due to gravity in m/s**2\n",
"\n",
"\t\t\t\t\n",
"#Calculation\n",
"p = 1/((1+(((k-1)/2)*Me**2))**(k/(k-1))) \t\t\t\t#ratio of pressures at exhaust and combustion chamber \n",
"Pe = p*P0 \t\t\t\t#exhaust pressure in Pa\n",
"t = 1/(1+(((k-1)/2)*Me**2)) \t\t\t\t#ratio of exhaust temperature to combustion temperature\n",
"Te = t*T0 \t\t\t\t#exhaust temperature in Kelvin\n",
"Ce = (k*R*Te)**0.5*Me \t\t\t\t#exit velocity in the exhaust in m/s\n",
"M = (Pe*Ce)/(R*Te) \t\t\t\t#propellant mass flow per unit area of exit in kg/m**2-s\n",
"Fa = ((M*Ce)+(Pe-Pamb))*10**-3 \t\t\t\t#thrust per unit area of exit in N/m**2\n",
"Is = (Fa*10**3)/(M*g) \t\t\t\t#specific impulse in sec\n",
"\n",
"\t\t\t\t\n",
"#Output\n",
"print 'A)thrust per unit area of exit is %3.2f kN/m**2 \\\n",
"\\nB)specific impulse is %3.2f sec'%(Fa,Is)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"A)thrust per unit area of exit is 918.93 kN/m**2 \n",
"B)specific impulse is 181.98 sec\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.4 page : 24"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"\t\t\t\t\n",
"#Input data\n",
"mp = 5. \t\t\t\t#propellent flow rate in kg/s (mismath.sing data)\n",
"de = 0.10 \t\t\t\t#nozzle exit diameter in m\n",
"Pe = 1.02*10**5 \t\t\t\t#nozzle exit pressure in Pa\n",
"Pamb = 1.013*10**5 \t\t\t\t#ambient pressure in Pa\n",
"P0 = 20. \t\t\t\t#thrust chamber pressure in Pa\n",
"F = 7000. \t\t\t\t#thrust in N\n",
"u = 1000. \t\t\t\t#rocket speed in m/s\n",
"g = 9.81 \t\t\t\t#acceleration due to gravity in m/s**2\n",
"\n",
"\t\t\t\t\n",
"#Calculation\n",
"Cj = F/mp \t\t\t\t#effective jet velocity in m/s\n",
"Ca = Cj-u \t\t\t\t#absolute jet velocity in m/s\n",
"wp = mp*g \t\t\t\t#weight flow rate of propellent in N/s\n",
"Is = F/(wp) \t\t\t\t#specific impulse in sec\n",
"SPC = 1/Is \t\t\t\t#specific propellent consumption in sec**-1\n",
"\n",
"\t\t\t\t\n",
"#Output\n",
"print 'A)effective jet velocity is %3i m/s \\\n",
"\\nB)specific impulse is %3.2f sec \\\n",
"\\nC)specific propellent consumption is %3.3f s**-1 \\\n",
"\\nD)absolute jet velocity is %3i m/s'%(Cj,Is,SPC,Ca)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"A)effective jet velocity is 1400 m/s \n",
"B)specific impulse is 142.71 sec \n",
"C)specific propellent consumption is 0.007 s**-1 \n",
"D)absolute jet velocity is 400 m/s\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.5 page: 24"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"\t\t\t\t\n",
"#Input data \n",
"Cj = 2700. \t\t\t\t#average effective jet velocity in m/s\n",
"u = 1350. \t\t\t\t#forward flight velocity in m/s\n",
"mp = 78.6 \t\t\t\t#propellant mass flow in kg/s\n",
"\n",
"\t\t\t\t\n",
"#Calculation\n",
"s = u/Cj \t\t\t\t#effective jet speed ratio\n",
"np = (2*s)/(1+s**2) \t\t\t\t#propulsive efficiency\n",
"F = Cj*mp*10**-3 \t\t\t\t#thrust in kN\n",
"Pt = F*u*10**-3 \t\t\t\t#Thrust power in MW, F in N\n",
"\n",
"\t\t\t\t\n",
"#Output\n",
"print 'A)thrust is %3.2f kN \\\n",
"\\nB)Thrust power is %3.3f MW \\\n",
"\\nC)propulsive efficiency is %3.1f'%(F,Pt,np)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"A)thrust is 212.22 kN \n",
"B)Thrust power is 286.497 MW \n",
"C)propulsive efficiency is 0.8\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.6 page : 24"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from scipy.integrate import quad \n",
"\n",
"\t\t\t\t\n",
"#Input data\n",
"mi = 15000. \t\t\t\t#mass of the rocket in kg\n",
"mp = 125. \t\t\t\t#propellant mass flow in kg/s\n",
"Cj = 2000. \t\t\t\t#velocity of gases coming out in m/s\n",
"t = 70. \t\t\t\t#time interval in sec\n",
"t0 = 0. \t\t\t\t#lower limit in integration in sec\n",
"t1 = 70. \t\t\t\t#upper limit in integration in sec\n",
"g = 9.81 \t\t\t\t#acceleration due to gravity in m/s**2\n",
"\n",
"\t\t\t\t\n",
"#Calculation\n",
"u = (-Cj*(math.log(1-((mp*t)/mi))))-(g*t) \t\t\t\t#velocity attained in 70 sec in m/s\n",
"\n",
"def f0(t): \n",
"\t return ((-2000*(math.log(1-((125*t)/15000))))-(g*t))\n",
"\n",
"h1 = ( quad(f0,t0,t1))[0]\n",
"\n",
"h2 = (u**2/(2*g))*10**-3 \t\t\t\t#Distance reached after fuel last i.e. after 70 sec due to kinetic energy by umath.sing KE = PE in km\n",
"h = h1+h2 \t\t\t\t#maximum height the rocket will reach in km\n",
"\n",
"\t\t\t\t\n",
"#Output\n",
"print 'A)velocity attained in %i sec is %3.2f m/s \\\n",
"\\nB)maximum height the rocket will reach is %3.3f km'%(t,u,h)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"A)velocity attained in 70 sec is 1064.24 m/s \n",
"B)maximum height the rocket will reach is 28476.353 km\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.7 page : 25"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"\t\t\t\t\n",
"#Input data\n",
"A1 = 18.*10**-4 \t\t\t\t#throat area in m**2\n",
"P0 = 25.*10**5 \t\t\t\t#combustion chamber pressure in Pa\n",
"Is = 127.42 \t\t\t\t#specific impulse in sec\n",
"wp = 44.145 \t\t\t\t#weight flow rate of propellent in N/s\n",
"g = 9.81 \t\t\t\t#acceleration due to kravity in m/s**2\n",
"\n",
"\t\t\t\t\n",
"#Calculation\n",
"F = Is*wp \t\t\t\t#thrust in N\n",
"mp = wp/g \t\t\t\t#propellant mass flow in kg/s\n",
"Cj = F/mp \t\t\t\t#average effective jet velocity in m/s\n",
"Cf = F/(P0*A1) \t\t\t\t#thrust coefficient\n",
"Cw = wp/(P0*A1)/10**-3 \t\t\t\t#propellent weight flow coefficent *10**-3\n",
"SPC = (wp/F)/10**-3 \t\t\t\t#specific propellent consumption in sec**-1 *10**-3\n",
"Cch1 = Cj/Cf \t\t\t\t#characteristic velocity in m/s\n",
"\n",
"\t\t\t\t\n",
"#Output\n",
"print 'A)thrust coefficient is %3.2f \\\n",
"\\nB)propellent weight flow coefficent is %3.2f*10**-3 \\\n",
"\\nC)specific propellent consumption is %3.2f*10**-3 s**-1 \\\n",
"\\nD)characteristic velocity is %3.0f m/s'%(Cf,Cw,SPC,Cch1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"A)thrust coefficient is 1.25 \n",
"B)propellent weight flow coefficent is 9.81*10**-3 \n",
"C)specific propellent consumption is 7.85*10**-3 s**-1 \n",
"D)characteristic velocity is 1000 m/s\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.8 page : 26"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"\t\t\t\t\n",
"#Input data\n",
"m1 = 200. \t\t\t\t#internal mass in kg\n",
"m2 = 130. \t\t\t\t#mass after rocket operation in kg\n",
"m3 = 110. \t\t\t\t#payload,non-propulsive structure, etc in kg\n",
"tp = 3. \t\t\t\t#rocket operation duration in sec\n",
"Is = 240. \t\t\t\t#specific impulse in sec\n",
"g = 9.81 \t\t\t\t#acceleration due to kravity in m/s**2\n",
"\n",
"\t\t\t\t\n",
"#Calculation\n",
"MR = m2/m1 \t\t\t\t#mass ratio\n",
"Mp = m1-m2 \t\t\t\t#mass of propellant in kg\n",
"mp = Mp/tp \t\t\t\t#propellent flow rate in kg/s\n",
"wp = mp*g \t\t\t\t#weight flow rate of propellent in N/s\n",
"IMF = (m2-m3)/(m1-m3) \t\t\t\t#initial mass fraction\n",
"PMF = 1-IMF \t\t\t\t#propellant mass fraction\n",
"F = Is*wp \t\t\t\t#thrust in N\n",
"TWRi = F/(m1*g) \t\t\t\t#initial thrust to weight ratio \n",
"TWRf = F/(m2*g) \t\t\t\t#final thrust to weight ratio\n",
"av = F/m2 \t\t\t\t#Maximum accelaration of the vechicle in m/s**2\n",
"Cj = Is*g \t\t\t\t#effective exhaust velocity in m/s\n",
"It = Is*Mp*g*10**-3 \t\t\t\t#total impulse in kN-s, units of the answer given in the book is wrong\n",
"IWR = (It*10**3)/((m1-m3)*g) \t\t\t\t#impulse to weighr ratio, It in N-s\n",
"\n",
"\t\t\t\t\n",
"#Output\n",
"print 'A)mass ratio is %3.2f \\\n",
"\\nB)propellent mass fraction is %3.3f \\\n",
"\\nC)propellent flow rate is %3.1f kg/s \\\n",
"\\nD)thrust is %3.1f N \\\n",
"\\nE)thrust to weight ratio is %3.2f intial) and %3.2f final) \\\n",
"\\nF)accelaration of the vechicle is %3.2f m/s**2 \\\n",
"\\nG)effective exhaust velocity is %3.1f m/s \\\n",
"\\nH)total impulse is %3.3f kN-s \\\n",
"\\nI)impulse to weighr ratio is %3.2f'%(MR,PMF,mp,F,TWRi,TWRf,av,Cj,It,IWR)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"A)mass ratio is 0.65 \n",
"B)propellent mass fraction is 0.778 \n",
"C)propellent flow rate is 23.3 kg/s \n",
"D)thrust is 54936.0 N \n",
"E)thrust to weight ratio is 28.00 intial) and 43.08 final) \n",
"F)accelaration of the vechicle is 422.58 m/s**2 \n",
"G)effective exhaust velocity is 2354.4 m/s \n",
"H)total impulse is 164.808 kN-s \n",
"I)impulse to weighr ratio is 186.67\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.9 page : 27"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"\t\t\t\t\n",
"#Input data\n",
"u = 2800. \t\t\t\t#rocket speed in m/s\n",
"Cj = 1400. \t\t\t\t#effective exhaust velocity in m/s\n",
"mp = 5. \t\t\t\t#propellent flow rate in kg/s\n",
"q = 6500. \t\t\t\t#heat of propellent per kg of propellant mixture in kJ/kg\n",
"\n",
"\t\t\t\t\n",
"#Calculation\n",
"s = u/Cj \t\t\t\t#effective jet speed ratio\n",
"np = (2*s)/(1+s**2) \t\t\t\t#propulsive efficiency\n",
"F = Cj*mp*10**-3 \t\t\t\t#thrust in kN\n",
"Pt = F*10**3*u*10**-6 \t\t\t\t#Thrust power in MW, F in N\n",
"Pe = Pt/np \t\t\t\t#engine outputin MW\n",
"nth = Pe*10**3/(mp*q) \t\t\t\t#thermal efficiency, Pe in kW\n",
"no = np*nth \t\t\t\t#overall efficiency\n",
"\n",
"\t\t\t\t\n",
"#Output\n",
"print 'A)propulsive efficiency is %3.1f \\\n",
"\\nB)propulsive power is %3.1f MW \\\n",
"\\nC)engine outut is %3.1f MW \\\n",
"\\nD)thermal efficiency is %3.4f \\\n",
"\\nE)overall efficiency is %3.3f'%(np,Pt,Pe,nth,no)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"A)propulsive efficiency is 0.8 \n",
"B)propulsive power is 19.6 MW \n",
"C)engine outut is 24.5 MW \n",
"D)thermal efficiency is 0.7538 \n",
"E)overall efficiency is 0.603\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.10 page : 27"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"\t\t\t\t\n",
"#Input data\n",
"Cj = 1250. \t\t\t\t#effective exhaust velocity in m/s\n",
"s = 0.8 \t\t\t\t#effective jet speed ratio i.e. flight to jet speed ratio\n",
"ma = 3.5 \t\t\t\t#oxidizer flow rate in kg/s\n",
"mf = 1. \t\t\t\t#fuel flow rate in kg/s\n",
"g = 9.81 \t\t\t\t#acceleration due to gravity in m/s**2\n",
"q = 2500.*10**3 \t\t\t\t#heat of propellent per kg of propellant mixture in J/kg\n",
"\n",
"\t\t\t\t\n",
"#Calculation\n",
"u = s*Cj \t\t\t\t#flight velocity in m/s\n",
"mp = ma+mf \t\t\t\t#propellant mass flow in kg/s\n",
"F = Cj*mp*10**-3 \t\t\t\t#thrust in kN\n",
"wp = mp*g \t\t\t\t#weight flow rate of propellent in N/s\n",
"Is = (F*10**3)/(wp) \t\t\t\t#specific impulse in sec,F in N\n",
"np = (2*s)/(1+s**2) \t\t\t\t#propulsive efficiency\n",
"nth = 0.5*mp*((Cj**2+u**2)/(mp*q)) \t\t\t\t#thermal efficiency\n",
"no = np*nth \t\t\t\t#overall efficiency\n",
"\n",
"\t\t\t\t\n",
"#Output\n",
"print 'A)thrust is %3.3f kN \\\n",
"\\nB)specific impulse is %3.2f sec \\\n",
"\\nC)propulsive efficiency is %3.4f \\\n",
"\\nD)thermal efficiency is %3.4f \\\n",
"\\nE)overall efficiency is %3.1f'%(F,Is,np,nth,no)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"A)thrust is 5.625 kN \n",
"B)specific impulse is 127.42 sec \n",
"C)propulsive efficiency is 0.9756 \n",
"D)thermal efficiency is 0.5125 \n",
"E)overall efficiency is 0.5\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.11 page : 28"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"\t\t\t\t\n",
"#Input data\n",
"mp = 193. \t\t\t\t#propellent flow rate in kg/s\n",
"P1 = 27.*10**5 \t\t\t\t#pressure at throat section in Pa\n",
"T1 = 3000. \t\t\t\t#temperature at throat section in K\n",
"de = 0.6 \t\t\t\t#nozzle exit diameter in m\n",
"Pe = 1.1*10**5 \t\t\t\t#exhaust pressure in Pa\n",
"Pamb = 1.013*10**5 \t\t\t\t#ambient pressure in Pa\n",
"F = 380*10**3 \t\t\t\t#thrust of motor in N\n",
"u = 694.44 \t\t\t\t#flight velocity in m/s\n",
"g = 9.81 \t\t\t\t#acceleration due to gravity in m/s**2\n",
"q = 6500*10**3 \t\t\t\t#heat of propellent per kg of propellant mixture in J/kg\n",
"\n",
"\t\t\t\t\n",
"#Calculation\n",
"Ae = (math.pi*0.6**2)/4 \t\t\t\t#exit area in m**2\n",
"Cj = F/mp \t\t\t\t#average effective jet velocity in m/s\n",
"Ce = (F-((Pe-Pamb)*Ae))/mp \t\t\t\t#exhaust velocity in m/s, wrong answer in textbook\n",
"wp = mp*g \t\t\t\t#weight flow rate of propellent in N/s\n",
"Is = (F)/(wp) \t\t\t\t#specific impulse in sec\n",
"SPC = (wp/F)/10**-3 \t\t\t\t#specific propellent consumption in sec**-1 *10**-3\n",
"Pt = F*u*10**-6 \t\t\t\t#Thrust power in MW\n",
"Pl = (0.5*mp*((Cj-u)**2))*10**-6 \t\t\t\t#Power loss in exhaust in MW\n",
"Pe = Pt+Pl \t\t\t\t#engine output in MW\n",
"np = Pt/Pe \t\t\t\t#propulsive efficiency\n",
"nth = Pe*10**3/(mp*q*10**-3) \t\t\t\t#thermal efficiency and Pe,q in kW\n",
"no = np*nth \t\t\t\t#overall efficiency\n",
"\n",
"\t\t\t\t\n",
"#Output\n",
"print 'A)effective jet velocity is %3.4f m/s \\\n",
"\\nB)Actual jet velocity is %3.4f m/s \\\n",
"\\nC)specific impulse is %3.1f sec \\\n",
"\\nD)specific propellent consumption is %3.4f*10**-3 sec**-1 \\\n",
"\\nE)propulsive efficiency is %3.5f \\\n",
"\\nD)thermal efficiency is %3.3f \\\n",
"\\nE)overall efficiency is %3.5f'%(Cj,Ce,Is,SPC,np,nth,no)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"A)effective jet velocity is 1968.9119 m/s \n",
"B)Actual jet velocity is 1956.1665 m/s \n",
"C)specific impulse is 200.7 sec \n",
"D)specific propellent consumption is 4.9824*10**-3 sec**-1 \n",
"E)propulsive efficiency is 0.62736 \n",
"D)thermal efficiency is 0.335 \n",
"E)overall efficiency is 0.21035\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.12 page : 29"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"\t\t\t\t\n",
"#Input data\n",
"m1 = 3600. \t\t\t\t#internal mass in kg\n",
"Cj = 2070. \t\t\t\t#average effective jet velocity in m/s\n",
"tp = 80. \t\t\t\t#rocket operation duration in sec\n",
"g = 9.81 \t\t\t\t#acceleration due to gravity in m/s**2\n",
"\n",
"\t\t\t\t\n",
"#Calculation\n",
"up = 2*Cj \t\t\t\t#flight velocity in m/s\n",
"MR = 1/math.exp((up+(g*tp))/Cj) \t\t\t\t#mass ratio\n",
"m2 = MR*m1 \t\t\t\t#mass after rocket operation in kg\n",
"PMF = 1-MR \t\t\t\t#propellant mass fraction\n",
"Mp = m1-m2 \t\t\t\t#mass of propellant in kg\n",
"mp = Mp/tp \t\t\t\t#propellent flow rate in kg/s\n",
"F = Cj*mp*10**-3 \t\t\t\t#thrust in kN\n",
"Zp = (((1+((1-(1/PMF))*math.log(1/MR)))*Cj*tp)-(0.5*g*tp**2))*10**-3 \t\t\t\t#powered altitude gain in km\n",
"Zc = ((0.5*up**2)/g)*10**-3 \t\t\t\t#coasting altitude gain in km\n",
"Z = Zp+Zc \t\t\t\t#maximum altitude in km\n",
"\n",
"\t\t\t\t\n",
"#Output\n",
"print 'A)flow rate of propellent is %3.2f kg/s \\\n",
"\\nB)thrust developed is %3.3f kN \\\n",
"\\nC)altitude gains during powered and coasting flights are %3.3f km and %3.3f km respectively'%(mp,F,Zp,Zc)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"A)flow rate of propellent is 40.83 kg/s \n",
"B)thrust developed is 84.521 kN \n",
"C)altitude gains during powered and coasting flights are 93.987 km and 873.578 km respectively\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.13 page : 29"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"\t\t\t\t\n",
"#Input data\n",
"s = 0.2105 \t\t\t\t#effective jet speed ratio\n",
"Is = 203.88 \t\t\t\t#specific impulse in sec\n",
"tp = 8 \t\t\t\t#rocket operation duration i.e. burn out time in sec\n",
"g = 9.81 \t\t\t\t#acceleration due to kravity in m/s**2\n",
"\n",
"\t\t\t\t\n",
"#Calculation\n",
"Cj = g*Is \t\t\t\t#average effective jet velocity in m/s\n",
"up = s*Cj \t\t\t\t#maximum flight speed in m/s\n",
"MR = 1/math.exp((up+(g*tp))/Cj) \t\t\t\t#mass ratio\n",
"PMF = 1-MR \t\t\t\t#propellant mass fraction\n",
"Zp = (((1+((1-(1/PMF))*math.log(1/MR)))*Cj*tp)-(0.5*g*tp**2))*10**-3 \t\t\t\t#powered altitude gain in km\n",
"Zc = ((0.5*up**2)/g)*10**-3 \t\t\t\t#coasting altitude gain in km\n",
"Z = Zp+Zc \t\t\t\t#maximum altitude in km\n",
"\n",
"\t\t\t\t\n",
"#Output \n",
"print 'A)effective jet velocity is %3i m/s \\\n",
"\\nB)mass ratio and propellent mass fraction are %3.2f and %3.2f respectively \\\n",
"\\nC)maximum flight speed is %3.2f m/s \\\n",
"\\nD))altitude gains during powered and coasting flights are %3.3f km and %3.3f km respectively'%(Cj,MR,PMF,up,Zp,Zc)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"A)effective jet velocity is 2000 m/s \n",
"B)mass ratio and propellent mass fraction are 0.78 and 0.22 respectively \n",
"C)maximum flight speed is 421.01 m/s \n",
"D))altitude gains during powered and coasting flights are 1.601 km and 9.034 km respectively\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.14 page : 30"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"\t\t\t\t\n",
"#Input data\n",
"R0 = 6341.6*10**3 \t\t\t\t#radius of earth at mean sea-level in m\n",
"g = 9.809 \t\t\t\t#acceleration due to gravity in m/s**2\n",
"Z1 = 0 \t\t\t\t#altitude at sea-level in m\n",
"Z2 = 300*10**3 \t\t\t\t#altitude above sea-level in m\n",
"\n",
"\t\t\t\t\n",
"#Calculation\n",
"uorb1 = R0*math.sqrt(g/(R0+Z1)) \t\t\t\t#orbit velocity of a rocket at mean sea level in m/s\n",
"uesc1 = math.sqrt(2)*uorb1 \t\t\t\t#escape velocity of a rocket at mean sea level in m/s\n",
"uorb2 = R0*math.sqrt(g/(R0+Z2)) \t\t\t\t#orbit velocity of a rocket at an altitude of 300 km in m/s\n",
"uesc2 = math.sqrt(2)*uorb2 \t\t\t\t#escape velocity of a rocket at an altitude of 300 km in m/s\n",
"\n",
"\t\t\t\t\n",
"#Output \n",
"print 'A)orbit and escape velocities of a rocket at mean sea level are %3i m/s and %3i m/s \\\n",
"\\nB)orbit and escape velocities of a rocket at an altitude of 300 km are %3.1f m/s and %3.2f m/s'%(uorb1,uesc1,uorb2,uesc2 )\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"A)orbit and escape velocities of a rocket at mean sea level are 7886 m/s and 11153 m/s \n",
"B)orbit and escape velocities of a rocket at an altitude of 300 km are 7706.8 m/s and 10899.08 m/s\n"
]
}
],
"prompt_number": 14
}
],
"metadata": {}
}
]
}