# Simple Examples¶

RocketCEA always begins with an import statement and an instance of a CEA_obj:

```from rocketcea.cea_obj import CEA_Obj
C = CEA_Obj( oxName='LOX', fuelName='LH2')
```

If the above is done at a command prompt, we can query the CEA_Obj as shown below:

```>>> from rocketcea.cea_obj import CEA_Obj
>>> C = CEA_Obj( oxName='LOX', fuelName='LH2')
>>> C.get_Isp(Pc=100.0, MR=1.0, eps=40.0)
374.3036176557629
>>> C.get_Isp(Pc=100.0, MR=6.0, eps=40.0)
448.190232998362
```

Note that the number of significant figures in the Isp above are much higher than in the standard CEA output.

While there is likely no physical significance to this, it can sometimes be useful numerically in computations that take derivatives of Isp with respect to a design variable. (for example optimizers.)

## Simple SI Units Example¶

By importing CEA_Obj from cea_obj_w_units instead of cea_obj, all of the I/O units can be changed from the default units (i.e. ft, lbm, BTU, degR, etc.).

The above example in English units is recreated below with SI units(chamber pressure input in MPa). Notice that CEA_Obj is created with pressure_units=’MPa’ as an input parameter. (For ease of comparison, the 100 psia input value of Pc from above is converted to MPa as 100/145.037738.):

```>>> from rocketcea.cea_obj_w_units import CEA_Obj
>>> C = CEA_Obj( oxName='LOX', fuelName='LH2', pressure_units='MPa')
>>> C.get_Isp(Pc=100.0 /145.037738, MR=1.0, eps=40.0)
374.30361765576265
>>> C.get_Isp(Pc=100.0 /145.037738, MR=6.0, eps=40.0)
448.1902329983554
```

All of the units may be specified by changing the CEA_Obj inputs from the defaults given below, to the desired units shown as comments. Simply include an input parameter in the creation of CEA_Obj as shown above with pressure_units.:

```isp_units            = 'sec',         # N-s/kg, m/s, km/s
cstar_units          = 'ft/sec',      # m/s
pressure_units       = 'psia',        # MPa, KPa, Pa, Bar, Atm, Torr
temperature_units    = 'degR',        # K, C, F
sonic_velocity_units = 'ft/sec',      # m/s
enthalpy_units       = 'BTU/lbm',     # J/g, kJ/kg, J/kg, kcal/kg, cal/g
density_units        = 'lbm/cuft',    # g/cc, sg, kg/m^3
specific_heat_units  = 'BTU/lbm degR' # kJ/kg-K, cal/g-C, J/kg-K
viscosity_units      = 'millipoise'   # lbf-sec/sqin, lbf-sec/sqft, lbm/ft-sec, poise, centipoise
thermal_cond_units   = 'mcal/cm-K-s'  # millical/cm-degK-sec, BTU/hr-ft-degF, BTU/s-in-degF,
#  cal/s-cm-degC, W/cm-degC
```

Note

If the units you desire are not shown above, your units may be added by importing add_user_units from rocketcea.units and calling it prior to creating CEA_Obj. For example MPa was added with the line.

add_user_units(‘psia’, ‘MPa’, 0.00689475729) # multiplier = user units / default units

## N2O4/MMH Performance¶

Successive queries of the CEA_Obj can be made to create tables of information. The script below will make a table of N2O4/MMH performance data.

```from rocketcea.cea_obj import CEA_Obj

C = CEA_Obj( oxName='N2O4', fuelName='MMH')

def show_perf( Pc=100.0, eps=10.0, MR=1.0 ):

IspVac, Cstar, Tc, MW, gamma = C.get_IvacCstrTc_ChmMwGam(Pc=Pc, MR=MR, eps=eps)

print( '%8.1f %8.1f   %8.1f       %8.1f      %8.1f    %8.1f %8.2f  %8.4f '%\
(Pc, eps, MR, IspVac, Cstar, Tc, MW, gamma))

print(' Pc(psia) AreaRatio  MixtureRatio   IspVac(sec)  Cstar(ft/sec) Tc(degR)  MolWt    gamma')

Pc = 250.0
eps = 50.0
for MR in [1.0 + i*0.1 for i in range(20)]:
show_perf( Pc=Pc, eps=eps, MR=MR )

```

The resulting table is shown below:

```Pc(psia) AreaRatio  MixtureRatio   IspVac(sec)  Cstar(ft/sec) Tc(degR)  MolWt    gamma
250.0     50.0        1.0          306.1        5378.5      4243.4    16.73    1.2539
250.0     50.0        1.1          311.6        5476.1      4532.8    17.39    1.2377
250.0     50.0        1.2          316.7        5554.9      4791.1    18.03    1.2216
250.0     50.0        1.3          321.4        5617.1      5018.0    18.63    1.2062
250.0     50.0        1.4          325.6        5664.5      5214.0    19.21    1.1918
250.0     50.0        1.5          329.3        5698.4      5379.7    19.75    1.1786
250.0     50.0        1.6          332.4        5719.6      5515.7    20.26    1.1668
250.0     50.0        1.7          335.1        5728.7      5623.4    20.74    1.1569
250.0     50.0        1.8          337.4        5726.4      5704.9    21.19    1.1489
250.0     50.0        1.9          339.3        5713.9      5763.2    21.60    1.1428
250.0     50.0        2.0          340.8        5692.9      5801.9    21.99    1.1384
250.0     50.0        2.1          341.9        5665.4      5824.6    22.34    1.1353
250.0     50.0        2.2          342.7        5633.5      5834.8    22.67    1.1333
250.0     50.0        2.3          343.0        5598.6      5835.2    22.98    1.1319
250.0     50.0        2.4          342.8        5562.1      5828.0    23.27    1.1311
250.0     50.0        2.5          341.6        5524.8      5814.9    23.54    1.1307
250.0     50.0        2.6          338.7        5487.2      5797.4    23.79    1.1305
250.0     50.0        2.7          335.5        5449.7      5776.3    24.03    1.1306
250.0     50.0        2.8          332.4        5412.5      5752.5    24.25    1.1308
250.0     50.0        2.9          329.3        5375.8      5726.4    24.47    1.1311
```

## LOX/LH2 Delta V¶

Conducting an analysis with RocketCEA is much easier than the standard approach to running CEA and reviewing the pages of CEA output (as we did in the LOX/LH2 example from Standard Examples)

We can query the CEA_Obj instance repeatedly for specific information, as opposed to simply printing a page of CEA output.

If we wanted to run some deltaV calculations on a LOX/LH2 stage to see what impact changing the engine’s area ratio would have, we might do the following.

```from math import log
from rocketcea.cea_obj import CEA_Obj

C = CEA_Obj( oxName='LOX', fuelName='LH2')

Wstg = 5106.0 # lbm
Wpropellant = 45920.0 # lbm

Winit = Wstg + Wpropellant + Wpayload
Wfinal = Winit - Wpropellant

def show_deltaV( Pc=475.0, eps=84.0, MR=5.88 ):
IspVac = C.get_Isp(Pc=Pc, MR=MR, eps=eps)
IspDel = 0.969 * IspVac
deltaV = 32.174 * IspDel * log( Winit / Wfinal ) # ft/sec
print( '%8.1f %8.1f    %8.2f    %8.1f     %8.1f        %8.1f     '%(Pc, eps, MR, IspVac, IspDel, deltaV))

print(' Pc(psia) AreaRatio  MixtureRatio   IspVac(sec)  IspDel(sec)   deltaV(ft/sec)')
show_deltaV( Pc=475.0, eps=84.0 )

for eps in range(100, 251, 50):
show_deltaV( Pc=475.0, eps=eps )

show_deltaV( Pc=475.0, eps=280.0 )
```

The script above calls RocketCEA for a number of area ratio values to get ideal vacuum Isp. An efficiency is applied to that ideal Isp to arrive at a delivered Isp. The delivered Isp is then used to calculate a stage deltaV.

The script gives the following output:

```Pc(psia) AreaRatio  MixtureRatio   IspVac(sec)  IspDel(sec)   deltaV(ft/sec)
475.0     84.0        5.88       464.9        450.5         21392.5
475.0    100.0        5.88       467.7        453.2         21518.6
475.0    150.0        5.88       473.5        458.8         21785.7
475.0    200.0        5.88       477.1        462.3         21954.9
475.0    250.0        5.88       479.8        464.9         22075.5
475.0    280.0        5.88       481.0        466.1         22133.4
```