2. Abstract
The study focuses on the type of propellants used on the Saturn V first stage.
Apollo 16 was used as the reference mission for Saturn V data. A trajectory code was
developed in order to replicate the performance characteristics of the original vehicle
launch up to the burnout of the first stage. A chemical equilibrium analysis was used
with input parameters of an F1 class engine in order to get propellant performance data
for subcooled propane. Propane performance data was used in the validated trajectory
code in order to get performance parameters for comparison to the original Apollo 16
Saturn V vehicle. For one propane case, the fuel and oxidizer tanks were left the same
size and an appropriate mixture ratio was found. For a second propane case, the fuel
and oxidizer tanks were resized to match the initial weight of the Apollo 16 Saturn V and
ice on the tanks was considered. For a third propane case, the tanks were once again
resized to match liftoff weight, but the mixture ratio was altered to achieve maximum
thrust. In the final propane case, the tanks were resized to match liftoff weight of the
original Saturn V, but the mixture ratio was altered to achieve as close as possible to
the highest Isp we could achieve without altering the exterior dimensions of the Saturn V.
As a proof of theory, a propanefueled SIC vehicle was treated in a rocket equation
analysis and its performance found to surpass that of a traditional, RP1 fueled SIC.
This comparison provided a classical proof of the benefits of propane over RP1.
2
6. Introduction
Faced with the task of lifting large payloads through Earth’s substantial gravity
well, launch vehicles call, first and foremost, for a staged architecture, the first stage of
which typically utilizes a high energy density hydrocarbon fuel and thus low structural
mass ratios. RP1 (Rocket Propellant1), a highly refined form of kerosene, has
traditionally served this purpose well, and as a result boasts a great deal of proven
hardware and processes built around it. Propane (C3H8), however, a hydrocarbon very
similar to RP1, exhibits potentially greater energy densities, and thus the opportunity
for increased performance over the historically successful fuel. Energy density,
expressed by a propellant’s impulse density, considers both bulk density and specific
impulse of combustion products. While a subcooled volume of propane has a lower
density than RP1 and would require more tankage for an equal amount of propellant
mass, its projected higher values of specific impulse would compensate for the slightly
larger structural masses required to carry it. Moreover, subcooled propane and oxygen,
for a range of 7° Rankine, share a liquid state, and could be stored together with a
common bulkhead. Mass savings in propane tankage, then, could possibly make up for
the increased structural weight required to keep the fuel subcooled, allowing for higher
payloadtoorbit opportunities than possible with RP1 for an equivalent liftoff mass.
6
7. Description of CEA Code
In order to perform the necessary propellant information and combustion
calculations, NASA’s CEA Code was used. Chemical Equilibrium with Applications was
produced in its present form by Glenn Research Center in 1994.
The code takes inputs relevant to both propellant and rocket parameters such as
chamber pressures, chamber temperatures, expansion ratios, fuel selection, oxidizer
selection, ambient pressure, and much more, depending upon the purpose and scope
of the run.
For the purposes of this project, the code was run as a rocket problem with RP1
and LOX or with propane and LOX.
7
8. Considered Oxidizer to Fuel Ratios
Case 1: Tanks Filled
Setting out to compare the performance of RP1 as a fuel to that of subcooled
propane, an SIC booster stage identical to that of SIC11 was considered, i.e. without
tanks resized to accommodate propane fuel. This would provide a straightforward
metric of comparison, from which further analysis could be conducted. A configuration
was desired that maximized propellant weight, or filled the SIC11 propellant tanks. To
this end, the density of RP1 and SIC11’s mass thereof were used to calculate a
maximum allowable volume available for fuel.
Multiplying this allowable fuel volume by the density of propane yields a mass of
propane to fill SIC11’s tanks.
In accordance with intuition, the fuel tank weighs less when full of propane than with
RP1, assuming that no extra structure is applied to keep the propane subcooled.
Keeping the same amount of LOX in the stage, the mixture ratio is calculated as follows:
8
9.
Case 2: Tanks Resized
Through the process of simply filling up the Saturn V tanks with propane and
excluding any icing weight, a total weight of 6,375,810 lb is calculated for time at
ignition. The difference between this weight and the Saturn V weight of 6,537,238 lb [1]
gives a value of 161,428 lb. To determine the maximum O/F ratio possible, through this
limited allowable weight gain, we can consider all of this weight being added to just the
oxidizer propellant and tank. Calculating the weight of the ice, considering it covering
just the surface area of the fuel tank with a thickness of 0.25 inches and a density of
57.74 lb/ft3
, gives a value of 7,544.87 lb. Thus, the true extra weight needed to add to
the oxidizer propellent and tank is just 153,883.1 lb.
This produces a new fuel weight equal to the old value of 1,278,466 lb [1] and a
new oxidizer weight of 3,463,363 lb. This gives the maximum O/F possible of 2.709.
Case 3: Maximum Thrust
Through the use of CEA, we were able to determine the mass ratio that would
produce the maximum thrust available. This was found by producing a graph of the
thrust coefficient times the effective exhaust velocity, the momentum thrust per mass
flow rate, vs O/F. This produced a polynomial with one maximum at a mass ratio value
of 2.66 as can be seen in Figure 1.
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11. Description of Trajectory Code
To simulate the flight of the Saturn V first stage, a trajectory code had to be
generated. This trajectory code had to account for key aspects of the flight, including
range, altitude, velocity, dynamic pressure, initial vehicle weight and weight of the
vehicle at burnout. Given that the key element of our design task was to compare the
performance characteristics of the Saturn V fueled by RP1/LOX and propane/LOX, the
code had to be sensitive to a number of various inputs related to the mass of the
vehicle, the thrust generation for various propellants, and aerodynamic effects due to
drag and gravity.
The program rested on an assortment of variables and calculations, as well as
constants and characteristics of past Apollo missions, specifically the Apollo 16 mission,
which was chosen as a baseline comparison for the code and all generated results
obtained from the simulations. These constants included gravitational acceleration, as
well as the universal gas constant, for use when calculating the Mach number during
flight. Various initial conditions were also defined. Examples of these are velocity,
acceleration, mach, range, altitude, dynamic pressure, etc. Each of these was set to
zero as their initial conditions. General characteristics regarding the Saturn V body were
also defined, including the crosssectional area of the first stage [1] and the exit area of
the F1 engine [3]. The value for these are listed below:
Table 1: Critical Area Figures
Crosssectional Area (Stage 1) 855.30 ft2
Exit Area (Single F1) 89.36 ft2
11
12.
The event times from the Apollo 16 mission were used in various aspects of the
program. The times for ignition, holddown arm release, center engine cutoff, and end of
burn were used to simulate the flight with as much accuracy as possible [1]. These
values are listed in the table below.
Table 2: Launch Sequence Event Times
Event Time (s)
Ignition 6.4
Holddown Arm Release 0.3
Center Engine Cutoff 137.9
End of Burn 161.8
Separation 163.5
Another key component of the program was the commanded pitch angle. The program
was written such that at certain times of flight, the pitch angle would adjust to place the
launch vehicle on a correct trajectory with respect to the actual Apollo missions. These
pitch angles are listed in the table below [4].
Table 3: Trajectory Control Sequence
Time (s) Pitch Degrees (deg) Pitch Rate (deg/s)
0.3 to 30 0 0
30 to 80 0 to 37.40 0.7280000
80 to 135 37.40 to 62.23 0.4696364
135 to 165 62.23 to 71.14 0.2970000
12
13.
The program required various inputs from the user based on the propellant type being
used:
1. Input stage 1 masses, including structural mass, payload mass, and propellant
mass (appendix A). These were summed up to acquire the total vehicle weight.
2. F1 class chamber conditions based on the propellant type and mixture ratio.
These values included chamber pressure and temperature, exit pressure and
temperature, and specific heat. All data was gathered from CEA runs and input
into the program.
The basis of the program consisted of simple numerical integrations over time
step loops using equations of motion based around Newtons Second Law. The goal
was to calculate three main forces acting on the rocket: thrust, drag, and gravity.
Calculating these through multiple iterations while also calculating the change in mass
of the vehicle would give the acceleration of the vehicle, which could then give the
velocity and displacement per time step.
Atmospheric Calculations
The program began its computing iterations by calculating the change in pitch
angle based on the current time of flight. Next, it calculated the drag coefficient based
on current Mach number. Finally, atmospheric properties were calculated. Density was
calculated using the exponential equation below:
13
14.
where a and b are defined according to the units desired [5]. Pressure and temperature
were calculated using the atmospheric model included in Matlab’s aerospace toolbox.
This atmospheric model was based on the U.S. Standard Atmosphere, 1976.
Thrust
The next step in the computational process was determining the mass flow rate
based on time of flight. This was done using the graph shown below [1,54].
Fig. 2 Mass Flow Rate vs. Range Time
14
15. A general equation was developed using various points on the graph to mimic the
increase in mass flow rate that occurs approximately at a range time of 80 seconds.
Next, the exit velocity of the F1 class engine needed to be calculated. The exit
velocity depended on three variables that were acquired from CEA: specific pressure,
chamber temperature, and exit temperature. These were input into the equation below:
The thrust could then be derived using the mass flow rate, exit velocity, exit pressure
(from the CEA run using whichever propellant type and mixture ratio was chosen) and
the ambient pressure via the following equation:
Drag
Drag was calculated using the drag equation below.
The drag coefficient was calculated using a series of equations retrieved by recreating
the drag coefficient data found on the Saturn V Launch Simulation website [4]. Then,
the data was split into five sections at the inflection points to generate equations for
each Mach number section. This data is the accumulation of multiple sources of
experimental data of the Saturn V in flight combined with that of the MercuryAtlas
rocket, which is similar enough to a Saturn to achieve a similar drag coefficient curve
and is very detailed. This was done because the information required for the Saturn V
is incomplete. This method produced the follow set of equations:
15
16.
which can be visualized below [4]:
Fig. 3 Drag Coefficient vs. Mach Number
Gravity
The gravitational force exerted on the vehicle was calculated using the standard
gravitational acceleration value of 32.17 ft/s2
and then multiplying it by the mass of the
vehicle at that particular point in time.
Equations of Motion
After all the forces were calculated, they were broken up into x and y
components based on the pitch angle of the rocket. These force components were then
16
17. divided by the total mass of the vehicle at that particular time and then multiplied by the
time step. This resulted in a change in velocity for the x and y direction. To find the
total velocity of the vehicle, these were added to the last recorded velocity in the
iteration process. The same process was done to find the range and altitude of the
launch vehicle by simply multiplying the current velocity by the time step and adding it to
the last recorded value for the range or altitude.
The final step in the loop was to calculate the change in mass of the vehicle from
propellant expelled through the engines.
Program Configuration
The program consisted of two loops that were set to run a designated number of
times. The first loop was for the powered ascent. This loop ran from ignition of the
vehicle at t = 6.4 s to end of the burntime at t = 161.8 s. The second loop was for the
period of coasting between the end of the burntime and separation between stage 1 and
stage 2. This ran for 1.7 s and ended immediately before the separation occurred. The
time step used in the program was 0.1 seconds.
17
18. Results and Discussion
The Original Apollo 16
Based on data gathered from references [1] and [2], data with regards to the
launch of Apollo 16 are summarized below:
Table 4: Original SIC Tank Data
RP1 Oxidiser
Tank Height (feet) 44 64
Tank Diameter (feet) 33 33
Propellent Weight (lb) 1,439,871 3,311,226
Tank Weight (lb) 24,000 38,000
Table 5: Original Saturn V Mass Ratio Data
Stage 1 Stage 2 Stage 3
Structural Mass (lb) 303,367 90,360 31,394
Propellant Mass (lb) 4,751,097 1,005,757 238,949
Payload Mass (lb) 1,482,774 386,657 116,314
Total Mass (lb) 6,537,238 1,482,774 386,657
Payload Ratio, λ 0.293 0.353 0.430
Structural Ratio, ε 0.060 0.082 0.116
18
19. Using the data above with the trajectory code discussed earlier, as well as CEA runs
using RP1/LOX propellant combo with a mixture ratio of 2.27, simulation data was
calculated, along with various graphs comparing the simulation data to that of the actual
Apollo 16 flight, as shown below.
Table 6: Comparison of Simulation Output vs Apollo 16 Data
Output Data Apollo 16 Data
Percent
Difference (%)
Max range: 60.25 miles 59.76 miles 0.83
Max altitude: 41.72 miles 42.07 miles 0.83
Max velocity: 7,702.65 ft/s 7,767.80 ft/s 0.84
Max Q: 728.28 psi 726.81 psf 0.20
Burnout vehicle mass: 1,877,301.15 lbs 1,857,487 lbs 0.80
Fig. 4 Apollo 16 Flight Profile
19
22. Fig. 9 Apollo 16 Velocity vs Time
As can be seen in the Table and various graphs above, the trajectory code is validated
by matching the Apollo 16 flight within 1% in all 5 categories compared: altitude, range,
velocity, max dynamic pressure, and weight of the vehicle at burnout.
Subcooled Propane
Case 1: O/F = 2.59
Table 7: SIC Tank Data with Propane, O/F = 2.59
Propane LOX
Tank Height (feet) 45.45 66.12
Ice Weight (lb) 7,725.24
Propellent Weight (lb) 1,278,465.57 3,260,087.21
Tank Weight (lb) 24,788.92 39,258.13
22
23.
Table 8: Saturn V Mass Ratio Data with Propane, O/F = 2.59
Stage 1 Stage 2 Stage 3
Structural Mass (lb) 313,139 90,360 31,394
Propellant Mass (lb) 4,589,691.4 1,005,757 23,8949
Payload Mass (lb) 1,482,774 386,657 116,314
Total Mass (lb) 6,537,261 1,482,774 386,657
Payload Ratio λ 0.293 0.353 0.430
Structural Ratio ε 0.062 0.082 0.116
The following table shows the simulation data output from the trajectory program after
inputting the above weights and CEA numbers discussed previously. This case used
the mixture ratio between propane and LOX of 2.59.
Table 9: Comparison of Propane/LOX (O/F = 2.59) to Apollo 16
Output Data Percent Difference (%)
Max range: 62.16 miles 4.02
Max altitude: 46.32 miles 10.11
Max velocity: 7966.10 ft/s 2.55
Max Q: 708.55 psi 2.51
Burnout vehicle mass: 1890734.73 lbs 0.09
Case 2: O/F = 2.709
23
24. Table 10: SIC Tank Data with Propane, O/F = 2.709
Propane LOX
Tank Height (feet) 44 66.94
Ice Weight (lb) 7,544.87
Propellent Weight (lb) 1,278,465.67 3,463,363.51
Tank Weight (lb) 24,000 39,745.95
Fig. 10 Tankage Comparison for Propane O/F = 2.709
Table 11: Saturn V Mass Ratio Data with Propane, O/F = 2.709
Stage 1 Stage 2 Stage 3
Structural Mass (lb) 312,668 90,360 31,394
24
25. Propellant Mass (lb) 4,741,829 1,005,757 23,8949
Payload Mass (lb) 1,482,774 386,657 116,314
Total Mass (lb) 6,537,271 1,482,774 386,657
Payload Ratio λ 0.293 0.353 0.430
Structural Ratio ε 0.0618 0.082 0.116
The following table shows the simulation data output from the trajectory program after
inputting the above weights and CEA numbers discussed previously. This case used
the mixture ratio between propane and LOX of 2.709.
Table 12: Comparison of Propane/LOX (O/F = 2.709) to Apollo 16
Output Data Percent Difference (%)
Max range: 63.56 miles 6.36
Max altitude: 48.86 miles 16.14
Max velocity: 8159.53 ft/s 5.04
Max Q: 711.88 psi 2.05
Burnout vehicle mass: 1891545.21 lbs 0.05
Case 3: O/F = 2.66
Table 13: SIC Tank Data with Propane, O/F = 2.66
Propane LOX
Tank Height (feet) 44.59 66.61
Ice Weight (lb) 7,618.1
Propellent Weight (lb) 1,295,528.33 3,446,105.37
Tank Weight (lb) 24,320.3 39,546.89
25
27. The following table shows the simulation data output from the trajectory program after
inputting the above weights and CEA numbers discussed previously. This case used
the mixture ratio between propane and LOX of 2.66.
Table 15: Comparison of Propane/LOX (O/F: 2.66) to Apollo 16
Output Data Percent Difference (%)
Max range: 64.31 miles 7.61
Max altitude: 50.43 miles 19.87
Max velocity: 8277.67 ft/s 6.56
Max Q: 714.01 psi 1.76
Burnout vehicle mass: 1891510.54 lbs 0.05
The following graphs show a comparison of all cases compared an Apollo 16 flight
simulated using the trajectory program.
27
32. Rocket Equation Analysis
Before conducting a propellant trade study, proposed trades must be examined
from a theoretical, or Rocket Equation, perspective. Tsiolkovsky’s equality, which
relates the mass ratio of a given vehicle, the exhaust velocity of its propellant, and the
velocity imparted to the vehicle, provides an orderofmagnitude approximation of
performance for a rocketbody. Typically used to calculate the required mass ratio for a
given mission, here Tsiolkovsky’s relation will be used to calculate an imparted Δv to the
Saturn V Apollo 16 first stage with the understanding that improvements in Δv may be
translated to reductions in liftoff weight or increases in payload weight. From such a
conclusion, more illustrative and descriptive means of comparing performance can be
implemented, as was done in the case of the 3DOF trajectory code.
In order to provide a controlled comparison of performance, an RP1 fueled
vehicle and propane fueled vehicle were treated in a nongravitational vacuum field,
ignoring gravity and drag losses and stating all specific impulses as in vacuo. For a
preliminary comparison, a nominal tank size, both tanks full (Case 2, above), was
considered first. Using Apollo 16 Flight Data for mass flow rates and time of significant
flight events, mass properties were calculated and the rocket equation utilized to
measure the performance of SIC fueled by propane. One particularly limiting
assumption was made with regards to this comparison: that there currently exists a
viable propanefueled rocket engine, or even so much as consensus in the rocket
industry to create one. While thrust is only of importance when launching from the
ground, and of no concern to a rocket equationbased comparison, the very existence of
32
33. a propane engine was first assumed when CEA was used to calculate specific impulses
for a propane/LOX propellant mixture. Another assumption, described earlier, leaves the
original SIC fuel tank alone, and simply presumes the presence of insulating ice around
the outside of the rocket that preserves the subcooled state of the propane, considering
the weight of the ice added to the effective structural weight of the rocket.
All rocket launches come with losses, especially those associated with imperfect
propellant management, that cannot be ignored if meaningful results are to be
obtained. Propellant masses on the order of thousands of pounds have to be ignored in
some cases due to vehicle “holddown” and residuals left in the pipes. In the case of a
Saturn V first stage, powered by five F1 engines, holddown losses can be quite large
despite the fact that vehicle holddown only lasts a fraction of a second past the point of
allenginesrunning status because of the immense mass flow rates the stage produces.
With the help of reference [1], significant trajectory event times were used in conjunction
with measured mass flow rates and mixture ratios to solve for propaneequivalent
holddown losses and residuals, and thus effective liftoff and burnout weights (Appendix
A). Table n presents the mass properties of a propaneburning SIC vehicle as well as
Isp and Δv imparted. What is found is a slight improvement over a RP1 burning SIC,
which imparted by a similar analysis 12,546 ft/s to its payload. Although the
improvement is small, only 144 ft/s, it was developed through the use of an unaltered
(save for the addition of ice) SIC, whose tanks were designed for an optimal RP1/LOX
propellant combination. Any improvement at all, even a small one, in this case, hints to
33
34. the greater advantages that may be gained by designing a stage for Propane/LOX
consumption.
Table 16: Mass and Performance Properties of a Propanefueled SIC (MR = 2.59)
This may be illustrated by repeating the previous procedure for a range of mixture
ratios, with more fuelrich configurations necessitating the offloading of liquid oxygen
and oxygenrich the opposite. Using MATLAB to plot the results shown in figures 12
through 15, one can see that while Isp, also sensitive to engine mixture ratio, is
maximized at a value of 2.8, performance remains optimal for this scenario at 2.59, or
tanksfull. The size of the SIC tanks constrain the fuel’s potential; were a
34
35. propanepowered stage’s tanks designed for a mixture ratio of 2.8, performance could
be improved further.
Figure 18: Mixture Ratio vs. Δv
Figure 19: Mixture Ratio vs. Isp
35
37. Conclusion
The propane/LOX combination has been tested against RP1/LOX in various
ways and outperforms the RP1 every time. In various configurations the propane
imparts greater ⃤v , higher burnout altitude, lower max Q, or creates any number of
desirable effects.
Though it may at first glance seem like a better choice than RP1, propane does
not come without issues. Most notably, this project assumes that there is in existence
an engine, similar to the F1, and that it is capable of producing the thrust, Isp, and
efficiency considered in the previous pages. While this does pose a problem, along with
other factors like tank sizing, turbopump power, and many more, the gains to be had by
propane cannot be ignored. Even if some of these factors caused the great minds of
the 1960’s to disregard propane, it seems clear that with modern advances in material
sciences, manufacturing, and rocket development, propane will outperform RP1 in a
groundup rocket design.
Though some may argue that the addition structure and support systems needed
to contain and maintain subcooled propane outweigh the benefits, it is clear to see that
with such large systems at stake, even a 1% difference in mass to burnout is huge
advancement and propane provides even better than that. For this reason it is deemed
that a subcooled propane/LOX propellant combination is not only feasible, but a better
choice than RP1/LOX.
37
