1. Embry-Riddle Aeronautical University 1
RS-68 Engine on Delta IV Heavy for EFT-1
Jack H. Taylor1
Embry-Riddle Aeronautical University, Daytona Beach, FL, 32114
Nomenclature
Ae /A*
= Nozzle exit area to throat area ratio
Ae = Area of nozzle exit
A*
= Nozzle throat area
𝐶"#$%&'
= Ideal coefficient of thrust
𝐶"(%&'
= Real coefficient of thrust
c*
= Characteristic velocity
DCBC = Diameter of Common Booster Core (CBC)
De = Diameter of RS-160 nozzle
ge = Gravity of Earth
hb = Burnout height
hmax = Maximum height
Isp = Specific impulse
Me = Mach at nozzle exit
𝑚 = Mass flow rate
𝑚* = Gross mass of EFT-1 configuration
𝑚+ = Burnout (dry) mass of EFT-1 configuration
𝑚*,-,
= Total mass of CBC
𝑚+,-,
= Burnout mass or dry mass of CBC
𝑚. = Mass of Payload (Orion Capsule + Launch Escape System)
𝑚/ = Mass of propellant of CBC
P/P0 = Static pressure over total pressure ratio
Pa = Atmospheric pressure
P0 = Combustion chamber pressure
Pe = Pressure at nozzle exit
ℛ = Mass Ratio
Th = Engine thrust
Thcone = Engine thrust with cone nozzle
tb = Burn time
ue = Nozzle exhaust velocity
ueq = Effective exhaust velocity
𝛼 = Conical nozzle half-angle
∆𝑢 = Vehicle total velocity change
λ = Conical nozzle thrust reduction factor
γ = Specific heat
1
Aerospace Engineering, 600 S. Clyde Morris Blvd.

2. Embry-Riddle Aeronautical University 2
I. Abstract
HIS report will analyze and reverse engineer certain characteristics of the Pratt & Whitney Rocketdyne RS-68
rocket engine. Engine properties such as thrust, thrust coefficients, and chamber pressure will be reverse
engineered using a mixture of assumed values and engine data. Bell vs. cone nozzle design will also be explored.
Expanding on this base, the reverse engineered RS-68 engine will be used to estimate flight speed and maximum
height of NASA’s EFT-1 mission. The assumptions made cause the reverse engineered engine to have a slightly higher
combustion pressure, a higher Isp, and moderately lower thrust than the actual engine. Despite the engine
discrepancies, the predicted mission analysis was significantly close to the actual launch.
II. Introduction
The RS-68 is a LOX/LH2 liquid rocket engine. Developed by Rockedyne and Pratt & Witney in the 1990s, this
engine is used solely on the first stage of United Launch Alliance’s Delta IV rocket and its subsequent configurations
the Delta IV Medium+, and the Delta IV Heavy. The engine is incorporated into a modular first stage design called
the Common Booster Core (CBC). One CBC is used for the Delta IV and Medium+ variants while three CBCs are
used together to make the more powerful Delta IV Heavy.
The Delta IV heavy is the most powerful rocket in use today. It
was the only launch vehicle capable of carrying NASA’s new Orion
capsule into orbit. The mission, called Experimental Flight Test 1
(EFT-1), launched on December 5th
2015 at 7:05 am EST from Cape
Canaveral Air Space Launch Complex-37B. The mission lasted four
and a half hours and brought the Orion capsule into two orbits. The
Delta IV’s first stage delivered Orion to a low earth orbit (LEO) also
known as a parking orbit. After one orbit at LEO, the second stage
ignited and burned to a much higher higher second orbit1,2
.
Figure 1 demonstrates the ignition of the RS-68 engines in the
Heavy configuration. The clear exhaust is due to the liquid hydrogen
and liquid oxygen fuel. Although using the same fuel as the Space
Shuttle Main Engines, it produces an orange color rather than the
distinguishing blue. The orange comes from the burning of ablative
cooling material that lines the inside of the nozzle1
.
The thrust and chamber pressure of the RS-68 will be the two key
parameters to reverse engineer and comparing those results to the real
values will serve as the measure of accuracy. Using the thrust value,
the ideal and actual thrust coefficients CT will be found then the bell
style nozzle will be assumed to be conical and the nozzle thrust
reduction factor λ will be calculated. The chamber pressure value will
be used to plot the pressure difference across the nozzle as the rocket
ascends and the perfectly expanded altitude will be calculated.
The second half of the analysis will use the previous values to
roughly calculate the maximum height and ∆𝑢 that can be achieved
by a Delta IV Heavy carrying the Orion crew capsule as performed
during EFT-1. Only the speed and altitude of first orbit will be
considered as that was the orbit established by the first stage RS-68
engines. Therefore this analysis will consider the Delta IV Heavy as
a single stage rocket with the payload as the Orion upper stage
combined with the emergency launch escape system.
T
Figure 1. Delta IV Heavy with three
RS-68 engines. Remote camera shot of
the three RS-68 engines at liftoff. Mach
diamonds form behind the nozzle as the
over-expanded exhaust leaves the engine
and compresses, forming oblique shock
waves and bright heat concentrations.

3. Embry-Riddle Aeronautical University 3
III. Knowns and Assumptions
A. Knowns
For the RS-68 engine the knowns used were accessed by a RS-68 data sheet provided by ULA1
and an EFT-1 data
sheet also provided by NASA2
and ULA:
1) tb = 367 s
2) 𝑚*,-,
= 226,000 𝑘𝑔
3) DCBC = 5.1 m
4) 𝑚+,-,
= 24,494 𝑘𝑔
5) 𝑚. = 35,384 𝑘𝑔
B. Assumptions
The LOX/LH2 fuel of the engine allowed for several reasonable assumptions. Assuming these values made it
possible to solve for combustion chamber pressure and thrust. Typical specific impulse and characteristic velocity
values for liquid oxygen-liquid hydrogen systems from Rocketdyne4
are as follows:
1) Isp = 455 s
2) c*
= 2386 m/s
The most important factor to consider to make a reasonable Ae /A*
assumption is the altitude for which this engine
operates. As a first stage engine, it can be expected to have a relatively low Ae /A*
compared to engines designed for
vacuum only operation. Therefore Ae /A*
should be at least less than 30. A useful example chart in the textbook4
characterized an engine with Ae /A*
= 20. This seemed to be a reasonable assumption and choosing this value would
further aid in the analysis allowing for the use of the chart to confirm values. Therefore:
1) Ae /A*
= 20
Other reasonable assumptions can be made to simply the situation. For this reason, the specific heat of the exhaust
is treated the same as air such that:
1) γ = 1.4
Another assumptions are that the engine is burning fuel at a constant rate, friction loses and drag are neglected, the
flow inside the nozzle is isentropic, and gravity can be assumed constant 9.81 m/s2
. Gravity is considered constant
because the highest orbit achieved will be LEO which is not high enough to have a significant reduction of g.
IV. Methodology
A. Nozzle Diameter
To find the diameter of the nozzle, imagery of the engine was examined in Photoshop. With the known diameter
of the CBC at 5.1m across, pixel count to length (m) could be established. In the particular image used, see Fig. 2, the
diameter of the CBC was 430 pixels wide.
𝐷BCB
𝑃𝑖𝑥𝑒𝑙 𝐶𝑜𝑢𝑛𝑡
=
5.1𝑚
430 𝑝𝑖𝑥𝑒𝑙𝑠
= 0.01186
m
px
Using this relationship, the nozzle diameter De could be found. The pixel count across the nozzle in the same image
was 206px, which yields a De = 2.44 m and an Ae = 4.67 m2
.
The same image was used to find an approximate nozzle half-angle. This will be useful later when assuming a
conical nozzle geometry. From Photoshop, 𝛼 = 15°.

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B. Mass Flow Rate
The known 𝑚*,-,
and
𝑚+,-,
will be used to
calculate 𝑚/,-,
. Simply
subtracting 𝑚+,-,
from
𝑚*,-,
will give
𝑚/,-,
= 201,500 𝑘𝑔.
Assuming a constant
fuel mass flow, i.e.
TU
TV
= 0 then 𝑚 = 𝑚/,-,
/𝑡+
which then yields an
𝑚 = 550 𝑘𝑔/𝑠.
C. Throat Area (A*
)
The throat area of the
Converging-Diverging (CD)
nozzle is easily found with
the assumed value of Ae/A*
and the calculated Ae. Divide
Ae by the throat to exit ratio to
obtain A*
. In this case,
A*
= 0.1220 m.
D. Exit Mach number
Due to the assumption the
flow is isentropic, finding
Mach number is fairly
straightforward. With the
assumed Ae/A*
and the
calculated Ae from Fig 2, the
following isentropic equation
can be used to determine exit Mach Me. Remembering 𝛾 = 1.4,
𝐴Z
𝐴∗
=
𝛾 + 1
2
]
^_`
a(^]`)
∗
1 +
𝛾 − 1
2
𝑀a
𝑀
^_`
a(^]`)
Solving this equation for M yields the exit Mach number, Me = 4.725.
E. Reservoir (chamber) Pressure
Obtaining the stagnation pressure inside the combustion chamber P0 will be a vital step to calculating the thrust of
the engine. The characteristic velocity c*
was assumed because of the fuel type of engine. The mass flow rate 𝑚 was
calculated in part one of this section and A*
was calculated in part C. There is now enough data to calculate P0 with
this equation.
𝑃* =
𝐶∗
𝑚
𝐴∗
This yields a 𝑃* = 10.74 𝑀𝑃𝑎.
Figure 2. Close-up of RS-68 engines. The blue line across the center CBC was
430px long and a known distance of 5.1m. The red line across the nozzle was 206px
long, yielding a De = 2.44m. The smaller blue lines were aligned to the edge of the
nozzle and the center line to approximate the nozzle half angle 𝛼 which was almost
150
exactly.

5. Embry-Riddle Aeronautical University 5
F. Nozzle Exit Flow Pressure
Another step required in order to calculate engine thrust is finding the pressure in the flow as it leaves the nozzle.
This step requires knowing the stagnation pressure of the flow and the Mach number at the exit. Both of these values
are now known. The exit pressure Pe can be calculated by this isentropic equation,
𝑃Z
𝑃*
= 1 +
𝛾 − 1
2
𝑀a
]
^
^]`
This gives a
h%
hi
= 0.002619 which makes 𝑃Z = 28.12 𝑘𝑃𝑎.
G. Calculating Engine Thrust
The engine Isp was assumed to be around 455 s and ge is taken as 9.81 m/s2
. Isp can be written as,
𝐼k/ =
𝑢Zl
𝑔Z
Therefore effective exhaust velocity ueq = 4464 m/s. Effective exhaust velocity is related to exhaust velocity, exit
pressure, mass flow rate, and exit area by this equation, assuming Pa = 101 kPa at sea level,
𝑢Z = 𝑢Zl −
𝑃Z − 𝑃m
𝑚
𝐴Z
Exhaust velocity 𝑢Z = 5087𝑚/𝑠. Now we are ready to use the rocket thrust equation to calculate the thrust produced
by the RS-68 engine.
𝑇ℎ = 𝑚𝑢Z + 𝑃Z − 𝑃m 𝐴Z
Which yields 𝑇ℎkp = 2,451 𝑘𝑁 and 𝑇ℎrms = 2,793 𝑘𝑁.
H. Coefficient of Thrust
Now that the thrust is calculated, the coefficient of thrust the real engine can be calculated.
𝐶"_uZmp =
𝑇ℎ
𝑃* 𝐴∗
The real coefficient of thrust is therefore, 𝐶"_uZmp = 1.871, while the ideal coefficient of thrust is,
𝐶"v$%&'
=
2𝛾a
𝛾 − 1
2
𝛾 + 1
^_` ^]`
∗ 1 −
𝑃Z
𝑃*
^]`
^
+
𝑃Z − 𝑃m
𝑃*
𝐴Z
𝐴∗
Which yields a 𝐶"v$%&'
= 1.645.
I. Conical Nozzle Thrust
To find the thrust of an equivalent conical nozzle. The conical nozzle thrust reduction factor λ must be found. This
can be calculated with the nozzle half-angle found from the examination of the image.
𝜆 =
1 + cos 𝛼
2

6. Embry-Riddle Aeronautical University 6
Therefore the thrust reduction factor is, 𝜆 = 0.9830.
Multiplying this factor to the originally calculated
thrust (Th) will give a new thrust that accounts for the
losses of flow that is not aligned to the axis of thrust.
With an original thrust of 2450 kN for the bell shape,
ThCone = 2410 kN.
J. Maximum Height Reached
The gross weight of the Delta IV heavy is the gross
weight of the three common cores plus the payload
weight. The payload weight will be the Orion capsule,
the Orion propulsion system, and the launch escape
system. The Orion payload is a gross weight, mL =
35,384 kg.
𝑚* = 3 𝑚*,-,
+ 𝑚.
Therefore 𝑚* = 713,400 𝑘𝑔. The mass of the structure
is just the combined structure masses of the three CBCs
and the mass of the total propellant is also the sum of
the mp of each of the CBCs. This results in a 𝑚+ =
108,870 𝑘𝑔. With those two values, the Mass Ratio can
be calculated.
ℛ =
𝑀*
𝑀+
This gives a ℛ = 6.553. The Mass Fraction is then used
to calculate the target values ∆𝑢 and hmax.
∆𝑢 = 𝑢Zl ln ℛ
The total change in velocity from the first stage is ∆𝑢 =
8,391 𝑚/𝑠. This ∆𝑢 provides ample velocity to carry
the entire Orion payload into LEO such that it is setup
for a second burn with its own engine. The maximum
height the rocket can achieve is defined by this equation:
ℎUm} =
𝑢Z
a
ln ℛ a
2𝑔Z
− 𝑢Z 𝑡+
ℛ
ℛ − 1
ln ℛ − 1
Worked out, hmax = 884 km. This number is very close to the actual parking orbit achieved by EFT-1.
K. Perfectly Expanded Altitude
The altitude where the rocket is perfectly expanded is where the atmospheric pressure Pa is equal to the exit
pressure of the nozzle, Pe = Pa. The exit pressure Pe was found to equal 28.12 kPa. Therefore, the altitude which has
Pa = 28.12 kPa is the perfectly expanded altitude. Atmospheric pressure is related to altitude with this equation,
𝑃m = 𝑃m~•
∗ 𝑒]€/•***
Setting the equation to 𝑃m = 28.12 𝑘𝑃𝐴 and assuming 𝑃m~•
= 101 𝑘𝑃𝑎, solving for h will yield h = 8970 m.
Figure 3. Delta IV moments after RS-68 ignition.
The RS-68 engines make for a striking image of this
historic Delta IV launch. The Orion capsule sitting atop
the CBCs will be brought to space for the first time.

7. Embry-Riddle Aeronautical University 7
V. Results
A. Nozzle Diameter
The calculated nozzle diameter was De = 2.44 m in length. The actual nozzle diameter is extremely close at
De_actual =2.43 m. >0.5% error.
B. Mass Flow Rate
There was no readily available data on mass flow of the RS-68 to compare to. Calculating it from given thrust led
to 𝑚msV‚mp = 645 𝑘𝑔/𝑠 vs the calculated 𝑚smps‚pmVZT = 549 𝑘𝑔/𝑠. For being so far off, its surprising the effects in
subsequent calculations were not larger. 16% error.
C. Throat Area
The assumption of Ae/A*
= 20 was an extremely close assumption. The real Ae/A*
= 21.5. That is 7% error.
D. Exit Mach Number
Although this is purely a result of part C, the calculated Me = 4.725 and the actual is very close at Me_actual = 4.814.
That is 1.85% error.
E. Reservoir (chamber) Pressure
The calculated 𝑃* was, 𝑃* = 10.74 𝑀𝑃𝑎. The actual was slightly lower at, 𝑃*&ƒ„…&'
= 10.26 𝑀𝑃𝑎. 4.67% error.
F. Nozzle Exit Flow Pressure
This is again related to the change in Mach number at the exit. It does however, have an additional error due to the
slightly high 𝑃* calculated earlier. The calculated value of 𝑃Z = 28.12 𝑘𝑃𝑎 while the actual value
𝑃Z&ƒ„…&'
= 24.171 𝑘𝑃𝑎. That is close to 14% error.
G. Engine Thrust
Calculated thrust was lower than the actual thrust. In a vacuum: 𝑇ℎsmps‚pmVZT = 2,793 𝑘𝑁 while 𝑇ℎmsV‚mp =
2,950 𝑘𝑁. 5.3% error. At sea level: 𝑇ℎsmps‚pmVZT = 2,450 𝑘𝑁 and 𝑇ℎmsV‚mp = 2,482 𝑘𝑁. 1.3% error.
H. Coefficients of Thrust
Ideal coefficients of thrust are still lower than Real cases. The actual values are much higher than the originally
calculated. This is due to the increase in the actual thrust value.
𝐶"€v$%&',&'ƒ…'&„%$
= 1.645
𝐶"€v$%&'†ƒ„…&'
= 2.093
𝐶"€‡%&',&'ƒ…'&„%$
= 1.871
𝐶"€‡%&'†ƒ„…&'
= 2.643
I. Conical Nozzle Thrust
The same thrust reduction value is applied, just to the actual thrust value.
J. Maximum Height
Maximum height of the actual vs calculated engine remains unchanged as all the values used in its equation are
independent. The apogee of the parking orbit established by EFT-13
was 888 km. The calculated max height was hmax
= 884 km. That is less than 0.5% error.
Delta u was also accurate. Sanity check: ∆𝑢 = 8,391 𝑚/𝑠. This is a very reasonable number because the minimum
orbital velocity for LEO is 7800 m/s. This will ensure orbit is achieved with fuel to spare.
K. Perfectly Expanded Altitude
The calculated perfectly expanded altitude was, h = 8970 m, while hactual = 10,030 m. That is 10.6% error.

8. Embry-Riddle Aeronautical University 8
VI. Conclusion
The assumptions made purely based on the LOX/LH2 fuel proved to be significantly accurate. Most calculations
were between 1% and 5% error. Although some were up to 10% and 20%, they were in the minority. The predicted
orbital height and speed were nearly exact to the real life scenario.
VII. References
1
United Launch Alliance, LLC, “Delta IV Launch Services User’s Guide,” http://www.ulalaunch.com/ Available:
http://www.ulalaunch.com/uploads/docs/launch_vehicles/delta_iv_users_guide_june_2013.pdf.
2
“Orion Flight Test Exploration Flight Test-1,” http://www.nasa.gov/, Nov. 2014.
3
Graham, W., “EFT-1 Orion completes historic mission,” nasaspaceflight.com, Dec. 2014.
4
Hill, P. G., and Peterson, C. R., Mechanics and thermodynamics of propulsion, Reading, MA: Addison-Wesley Pub. Co.,
1992. Table 11.1
Figure 4. Thrust vs Altitude, Pa vs Altitude, and Pa-Pe vs Altitude. This plot shows the increase in thrust as the
engine climbs out of the atmosphere. The increase in thrust is due to the increase in the pressure term as the atmosphere
becomes a vacuum. The drop is pressure is shown by the blue Pressure vs altitude curve. The difference between Pa
and Pe is shown by the orange curve. When that curve is above 0, the flow is over-expanded, when it intersects 0, the
flow is perfectly expanded, and when it is below 0, the flow is under-expanded.
2200
2300
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0
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38000
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Thrust (kN)
Pressure (kPa)
Altitude (m)
Thrust, Pa, Pa-Pe
Pressure (Pa) Pa-Pe Thrust