A.4.2.4.1
pg. 1
A.4.2.4.1 Pressure – fed Propellant System
Propellant feed systems account for a large portion of the mass and cost of an engine for
a launch vehicle. Historically, smaller rockets tend to use pressure fed propellant feed
systems due to their simplicity and cost.1 Pressure-fed systems require an extra tank and
gaseous pressurant. This adds more mass but is necessary for the fuel to overcome the
adverse pressure gradient and enter the chamber.
Pressure-fed systems require the selection of a pressurant and two options commonly
used and closely investigated are nitrogen and helium. Nitrogen is less expensive at
$0.50/kg than helium at $20/kg.2 Hydrogen also has the disadvantage of being a very
small diatomic molecule. Should our tanks be constructed our of a very porous material,
the hydrogen molecules could leak through the material and render the feed system
useless. Even with a small amount leakage, additional helium would need to be stored in
the tanks for balloon launch due to the long ascent. Some materials are capable of
containing helium, but using these materials and specially manufacturing all tanks to be
able to hold helium would significantly increase costs. Pressurant will eventually enter
all tanks therefore all tanks must be designed to contain helium as well as fuel or
oxidizer. Our conclusion is to use nitrogen because of pricing, molecule size, and more
frequent use in rocketry history.
In order to calculate the proper mass of the pressurant first we must know the final
temperature of the pressurant in the tanks. For this we assume isentropic expansion with
constant γ and use the following equation:
 pf 

T f  Ti 
p
 i 
 1

(A.4.2.4.1)
where Tf is the final temperature, Ti is the initial temperature of the propellant, pf is the final pressure of the
pressurant, pi is the initial pressure of the propellant, and  is the ratio of specific heats.
The initial temperature is considered to be ambient temperature, the final pressure must
be greater than the chamber pressure, the initial pressure is to be arbitrarily chosen so as
to minimize the added inert mass but still maintain a pressure high enough to keep
Author: Nicole Wilcox
A.4.2.4.1
pg. 2
temperatures reasonable. After the final temperature is found, one can use the following
equation to find the mass of the propellant:
m press 
V press p f
(A.4.2.4.2)
RT f
where Tf is the final temperature, pf is the final pressure of the pressurant, mpress is the mass of pressurant
required, and Vpress is the final volume that the pressurant must fill at the final pressure.
To find the volume of the tank that the pressurant will initially be held in, one can simply
rearrange the previous equation and use initial values for pressure and temperature rather
than final. In the previous formula, the initial volume is simply the volume of the
pressurant tank itself, but the final volume is the volume of the pressurant tank as well as
all other liquid propellant tanks, fuel and oxidizer. An iterative solution was not used due
to the assumption that the pressurant volume would be low in comparison with the
oxidizer and fuel tanks. This proved to be true as in all cases the volume added by the
pressurant tank was no more than 2.86% of the summed tank volume. Using the previous
formulae, the below values were found for all three vehicles:
Table A.9.2.3.1 Pressurant Mass and Cost per Launch Vehicle a
Payload
200 g
1 kg
5 kg
a
Pressurant Mass (kg)
59.0
38.2
166.3
Pressurant Volume (m3)
0.1158
0.0751
0.3266
numbers based on initial pressure of 12 MPa
In the final design, pressurant is only located in the first stage of each rocket due to the
use of hybrid engines for those stages. There is liquid injection thrust vector control
(LITVC) on the second stage, but that consist of a self-pressurized tank.
Spin
stabilization is used on the third stage so neither pressurant or LITVC is necessary.
Pressurant only accounts for a small portion of the total mass of the first stage in each
rocket, but without pressurant, the oxidizer would simply not feed into the chamber at all
due to an adverse pressure gradient because of the high chamber pressure.
Author: Nicole Wilcox
A.4.2.4.1
1
pg. 3
Humble, R. W., Henry, G. N., Larson, W. J., Space Propulsion Analysis and Design, McGraw-Hill, New
York, NY, 1995.
2
“Missile Fuels Standard Prices Effective Oct 1, 2007.”, Defense Energy Support Center, Fort Belvoir,
Virginia, July 2007. [http://www.desc.dla.mil/DCM/Files/MFSPFY08_071107.pdf. Accessed 1/15/08.]
3
Sutton, G., Biblarz, O., Rocket Propulsion Elements, John Wiley & Sons, Inc., New York, NY, 2001.
Author: Nicole Wilcox