47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition AIAA 2009-1099

5 - 8 January 2009, Orlando, Florida

The Design of Optimized 3D Tip-to-tail Scramjet Engines

Frederick Ferguson,1 Nasstaja Dasque2, and Yesuenyeagbe Fiagbe3
North Carolina A&T State University

Abstract
Worldwide, significant research efforts are in progress towards the development of scramjet
engines. These efforts are primarily focused on the integration of the scramjet to either ‘a blended body’
or ‘a waverider derived’ hypersonic vehicle configurations; one of which may become the candidate for
the first access to space air vehicle. The design of the scramjet is a complicated process due to many
technical constraints, such as, aerothermodynamics, materials and mechanical. Examples of aerodynamic
constraints include inlet-unstarts, mass capture, isolator characteristics, boundary layer separation, and
constraints on combustor entrance flow profiles and operating temperatures. Examples of mechanical
constraints include variable geometry flexibility and cooling system limits. All in all, the design of the
scramjet is influenced greatly by its flight constraints. If the flight conditions were fixed, then the scramjet
design problem became deterministic. As such, with a few assumptions, the engine configuration that will
produce minimum drag and maximum thrust may be determined directly. However, the design problem
under consideration for many practical applications requires extensive variability in altitude and Mach
number, and as such, its solution can only be obtained through an optimization process. Additionally, this
analysis assumed that the scramjet powered vehicle or missile is launched with an external propulsion
source to some ‘pre-determined’ Mach number and altitude. At that point, the scramjet engine is started
and propels the system until freestream flight conditions once again preclude further operation of the
engine. The research efforts described in this paper focused on the design of an optimized scramjet
configurations that are decouple for the hypersonic vehicle. Efforts are focused on the derivation of
efficient compression forebodies, isolators, combustion chambers, and nozzle after-bodies and their
integration into optimized scramjet configurations.

Nomenclature
= angle of attack
= shock wave angle
Cf = skin friction coefficient
Cp = pressure coefficient
D = Drag, force component parallel to the freestream velocity
= specific heats ratio
M = Mach number
= wedge angle
P = pressure
u = velocity component parallel to the freestream velocity
S = Surface area
T = temperature
OOP = Object Oriented Programming

1
Professor & Director, Center for Aerospace Research, and AIAA Senior Member.
2
Graduate Student, Center for Aerospace Research, and AIAA Member.
3
Graduate Student, Center for Aerospace Research, and AIAA Member.

Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
 I. Introduction
A. Background
Aircraft designers of the 21st century are focusing on a revolutionary engine technology that is
capable of not only propelling vehicles to hypersonic speeds, but also one that can facilitate integrated air-
to-space operations. The SCRAMJET, abbreviated from the words; Supersonic Combustion Ramjet, is
the latest evolution of the jet engine family. The scramjet, like its predecessor, the ramjet, is a natural
extension of the jet engine concept. However, unlike the ramjet, the scramjet uses no rotating parts.
Scramjets will enable three categories of hypersonic craft; namely, weapons, such as cruise missiles;
aircraft, such as those designed for global strike and reconnaissance missions; and space-access vehicles
that will take off and land like conventional airliners1.
While the physical concepts behind the scramjet are very simple, the practical ramifications of
constructing such an engine are quite formidable. A few of the challenges are supersonic fuel-air mixing,
the heat dissipation both from the air friction and the internal combustion, and the engine operating
temperatures. Consequently, the flow path of the incoming air needs to be extremely precise to minimize
hot spots. However, by far, the biggest challenges arise from the intense operational temperatures. Since
the air entering the engine is already heated by friction with the engine walls, combustion chamber
temperatures could exceed 5000 degrees Fahrenheit, if left unchecked1-2. At these temperatures most
metals melt, and air and fuel become ionized, and the physics of their behavior becomes unpredictable.
The objective of this paper is to identify the preliminary design variables of an idealized ram-scramjet
engine under optimum conditions.

Primary Reflected Isolator Diffuser Combustor Nozzle

Shock Shock Zone Zone Zone Zone
Zone Zone

A B C D E F G

Fig. 1: Illustration of the Cross Section of the Scramjet

Fig. 2: Illustration of A Typical 4-Pts Scramjet with Square Combustor C-Sections

B. Highlights of Proposed Paper

In this effort, the scramjet configuration design process is developed in two parts. First, a
representative centerline cross-sectional 2D geometry of the scramjet is developed. Refer to Figure 1.
Second, the cross-sectional 2D geometry is transformed into 3D configurations and analyzed. Refer to
Figure 2.
The scramjet construction process is accomplished through the use of specially developed
subroutines, programmed in FORTRAN, to manipulate and assemble elementary configurations into
completed engine concepts. The elementary shapes of interest to this study include the star-shaped
leading edges, the caret-shaped inlets, and cylindrical combustors, convergent and divergent nozzles, and
plug nozzle after-bodies. This research effort is built on Ref. 3-8, and is based on the design, construction,
analysis and integration of elementary aerodynamic shapes into complete hypersonic vehicle and
propulsion systems configurations. As its output, the design code generates the engine configuration and
analyzes its aerodynamic and thrust performance. Further, the algorithms used to evaluate the resulting
engine performance characteristics, such as the Isp, the thrust, and maximum operating temperatures, are
based on empirical engineering correlations and strict geometric principles.

II. Scramjet Configuration Design

A. 2D Forebody Configuration Design
The two most important schematics representing the basic geometry of the scramjet are shown in
Figure 1 and Fig. 2. These two Figures illustrate the 2D and 3D dimensional natures of this concept,
whereas, the 2D baseline geometry serves as the basis upon which 3D shapes are constructed. The design
illustration provided in Figure 3 shows the nose section of the scramjet, which directs the attached planar
shock to the nacelle inlet “lip” when operating at some design altitude and Mach number. The captured
flow is then pushed through the isolator ducts and through a transition section, before being mixed with
fuel, burned and later expelled through the nozzle.

Fig. 3. Scramjet Inlets for the Ram-Scramjet Concept.

Using the notations provided in Figure 3, the aerodynamic parameters, such as, density, pressure,
temperature and velocity can be computed as prescribed in Ref . 9. For instance, with a known cruise
Mach number, M and a prescribed shock angle, 1 , the initial shape of the forebody lower surface
angle, 1 , and the Mach number behind the shock, M1 , are determined by using the oblique shock
relations given in equations (1) and (2);
M 2 sin 2 1 1
tan = 2 cot (1)
M 2( + cos 2 1 ) + 2
1 1

and
M n,1
M1 = (2)
sin ( 1 )
Where the symbol, , is a constant equals to 1.4, and the symbols, M n,1 and M n, , are defined as
follows,
1 + [( 1) 2] M n2,
M n2,1 = (3)
M n2, ( 1) 2
and
M n, = M sin( 1) (4)
 It is of interest to note that the value of 2 is dictated by the cowl location and a fixed point on the
forebody. When the results of 1 and M1 are coupled to an appropriate value for 2 , the flow properties
at the cowl inlet can be calculated using equations (1) and (2) in which the values of M 2 and 1 are
replaced with those of M1 and 2 .

Fig. 4: Star-Shaped Inlets for the Ramjet-to-Scramjet Concept.

B. 2D Isolator Configuration Design

Once the flow is captured, it enters the isolator duct. The behavior of the isolator is critical to the
design of the dual mode ram-scramjet, since the isolator may either be comprised of a system of normal
or oblique shocks, refer to Figure 4. Typically, the isolator will generate an exit static pressure somewhere
above the range of its inlet pressure, P2, and that corresponding to a normal shock at the inlet conditions,
Pn2. Any back pressure greater that the pressure behind the normal shock will cause the isolator to
‘unstart’. In this analysis, the isolator is considered to be a constant area duct in which friction and heat
transfer are neglected. Under these conditions, if the value of the static pressure ratio, p3/p2, is assumed in
the appropriate range, then the system of 1D conservation laws will result in the following expression for
the isolator exit Mach number10-13;

[ ]
1

M 22 1 + (( 1) 2 )M 22
2
2
1
M3 = (5)
(1 M 22 P3 P2 )
2 2

Similarly, with the exit Mach number known, the length of the isolator can be evaluated based on the
following experimental relationship developed in Ref 11:

L
=
H {50((P
3 P2 ) + 1) + 170((P3 P2 ) 1)2 } (6)
(Re )
1
H 4 M 22 1
where Re is the inlet Reynolds number based on the momentum thickness, , and H is the height of the
isolator duct.

C. Basic geometry: Diffuser-Combustor-Nozzle Configuration

Consider the development of the combined Diffuser-Combustor-Nozzle Elements of the Scramjet, as
illustrated in the second half of the schematic presented in Figure 1, and as depicted in Figure 5. It is of
interest to note that the design points, D, E, F and G, are calculated in a manner similar to the one
described above to result in the scramjet burner depicted in Figure 5. By choosing the design points, A –
G, in the form of design parameters and independent of each other, the resulting integrated configuration
can have its E-point beyond its F-point location with respect to the x-axis. This approach provides a great
deal of flexibility in arriving at a class of configurations with desirable aerodynamic characteristics. When
the configurations illustrated in Figures 4 and 5 are coupled, the centerline cross section of the scramjet is
formed. A typical 2D centerline cross section of the scramjet derived from this study is illustrated in
Figure 6.

Fig. 5: Illustration of the 2D Combustor Nozzle Concept

Fig. 6: Illustration of Ramjet Derived from a 4-Point Star-Shaped Fore-body

D. Transformations of 2D C-Sections into 3D Configurations

For illustrative purposes, consider the 2D cross-sectional concept illustrated in Figure 7a 4, which
is also the nose of the 2D scramjet configuration. As recalled, this 2D geometry is developed through the
use the oblique planar shock. These relationships are also used to evaluate the defining dimensions of the
‘star-shaped’ prism. Once the 2D shape is realized, using the ‘waverider’ methodology, Ref 7, appropriate
3D stream surfaces are constructed. In a similar manner, these surfaces are pieced together to form the
‘four-point-star-shaped’ prism illustrated in Figure 7b. The transformation process is illustrated in Figures
7a and 7b.
Stream tubes are also constructed from the stream surfaces by piecing appropriate surfaces
together. Finally, stream tubes are pieced together to generate a combined 3D forebody, inlet and isolator
configuration as illustrated in Figures 8. Using this technique ‘completed forebody inlet isolator
configurations’ can be derived by piecing together the appropriate numbers of stream tubes to result in 3-,
4-, 5- 6-, 7- and 8-points star-shaped configurations, respectively. In the case of a ‘four-point star-shaped
forebody inlet isolator configuration’, four tubes are pieced together to generate the final configuration
illustrated in Figure 8.

Fig. 7a: 2D Forebody C-Section Fig. 7b: 3D Forebody Configuration

Fig. 8: Forebody-Isolator Element Fig. 9: Combustor-Nozzle Element

Now, consider a typical transition, combustion and nozzle combination of scramjet elements as
illustrated in Figure 9. A close look at Figure 9, indicates that the transition and combustor elements are
depicted with their external surfaces removed. This is done to highlight the geometry of the inner tube.
The aero thermodynamic evaluation of this part of the scramjet involves the quasi 1D calculations of the
flow field variables at each station in the length-wise direction of the duct illustrated in Figure 9. This task
is accomplished through the application of the appropriate conservation laws at the inlet and exit of each
element making up the scramjet, as described below:
( U A)inlet + m& f = ( U A)exit (7)

(u 2
A + pdA )
Inlet (
+ m& f + Fvis )Ductt = (u 2
A + pdA )
Exit (8)

$ V ! Vf $ V !
"( VA) h + + m& f h f + + Q& = "( VA) h + (9)
# 2 Inlet 2 # 2 Exit

The symbols, m& f hf and Q& , in equations (7) – (9) represent the rate of fuel added to the mass capture as it
travels through the combustor, hf, represents the enthalpy of the fuel and Q& represents the heat generated
in the combustor.
It is of interest to note that by choosing the design points, A – G, in the form of design parameters and
independent of each other, the resulting integrated configuration can have its E-point beyond its F-point
location with respect to the x-axis. This approach provides a great deal of flexibility in arriving at
scramjet candidates with desirable aerodynamic and thrust characteristics. In addition, when generating
the 3D configurations, the choice of the forebody is of great importance, since it provides the geometric
information needed for the third dimension. In this research, star-shaped, forebodies are generated with
the number of blades ranging from three to eight, with either circular or rectangular combustor c-sections,
as illustrated in Figures 1 and 10.

Figure 10: Illustration of ‘Four-Point Star-shaped Scramjet’ with Square Combustor C-Sections
 III. Scramjet Configuration Design
A. Ramjet-Scramjet Analysis
The analysis of the scramjet system consists of the evaluation of the following six major
components; namely, the primary shock zone, the inlet, the isolator, the diffuser and mixing region
(transition element), the combustor and the nozzle. The evaluation of the primary shock zone, the inlet
and the nozzle is straight forward and is conducted in accordance with Ref. 3-4, 10. However, the
evaluation of the flowfield parameters in the transition, combustion and nozzle elements are somewhat
complicated and are conducted in accordance with the quasi 1D influence coefficients method described
in Ref. 14-16.

B.: Scramjet Basic Assumptions

The framework for the scramjet model has been established in the form of predictive relationships
which are suitable for appropriate integration into the quasi 1D equation equations with design parameters
for optimization. In addition, the working fluid is air, and it has been modeled using the thermally perfect
gas law, as such the equation of state holds. The additional assumptions are as follows:
B.1: Fuel Injection Model
In this study and as in Ref. 15, the fuel is assumed to be hydrogen, and it is injected into the
combustor at an angle of 45o in order to achieve adequate mixing with the air. Fuel injection conditions
are set to the following: M H 2 = 1.0, T H 2 = 600 K , PH 2 = 101325 N / m 2 and H = 1.4. The heat of reaction
for hydrogen and the stoichiometric fuel/air ratio are, respectively, H r = 119,954 kJ kg and f st = 0.0294 .
The fuel to air ratio for the hydrogen-air mixture is determined from the chemical equation describing the
ideal combustion of hydrogen and air.
B.2: Chemical Energy Release
The combustion chamber is model in two parts: the first part consists of a constant cross sectional
area, while the second part allows for variation in its cross sectional area. It can be shown that for 1D
theory, the energy released due to the combustion of fuel, dm& , can be expressed in the form of
incremental total temperature ratio, dT0 T0 , as follows20:
%Q dH 0 1 dT0
= 1+ M2 (10)
c pT 2 T0
where the chemical energy, %Q , is defined as, %Q = &H r dm & m& , and the symbols, Hr and &b, represent
the fuel heating value and the burning efficiency, respectively. In addition, the incremental change in the
(
total energy of the mixture, dH 0 , is evaluated as follows: dH 0 = H a ,0 H f , 0 dm )
& m& , where the
20
symbols, H a ,0 and H f ,0 , represents the total enthalpy of the air and fuel, respectively .

C: Numerical Integration of the Scramjet Flowfield parameters

The flowfield variables, p, , u and T, in the transition, combustor and nozzle sections of the ram-
scramjet engine, illustrated in Figures 1 and 10, are modeled using the quasi-one-dimensional analysis
relationships14-16. The parameters influencing the quasi-one-dimensional flow through these sections
include the area variation, dA A , the skin friction coefficient, 4 C f dx D , the chemical heat release,
(%Q dH 0 ) c p T , and fuel mass injection, dm& m& . The heating parameters are activated only within the
combustor element. Consequently, an explicit integration scheme based on a system of ordinary
differential equations can be designed to update the following three thermodynamic parameters as
follows:
dT0
Titotal
+1 = Titotal 1.0 + (11)
T0 i
 dM
M itotal
+1 = M itotal 1.0 + (12)
M i

dp
pitotal
+1 = pitotal 1.0 + (13)
p i

where the following incremental properties are evaluated as follows:

dT0 1 %Q dH 0
= (14)
T0 i
C1 c pT
dM dA dT0 2C f dx dm& dWM d
= C2 + C3 + C4 + C5 + C6 + C7 (15)
M i A i T0 i
D i
m& i WM i i

dp dA dT0 2C f dx dm& dWM d

= C8 + C9 + C10 + C11 + C12 + C13 (16)
p i
A i T0 i
D i
m& i WM i i

Where the coefficients, C1 through C13, are evaluated at each spatial step in accordance Ref. 14-16.

D: Scramjet Performance Parameters

Once the flowfield solutions are obtained in the transition, combustor and nozzle elements; the
thrust of the engine is calculated as the difference between the impulse function at the combustor exit and
the isolator entrance20:
T = I Po int G I Po int C (17)

(
where, the impulse function, I, is defined as, I = pA 1 + M 2 . , and the points, C and G, are described in )
Figure 1. In a similar manner the drag force, Fx, generated by the combined forebody, inlet and isolator
elements are computed. The performance parameters of this interest to this study are the net thrust, Tnet =
T – Fx, and the Thrust to Drag ratio, TD, where TD is defined as T/D.

IV. Optimization of the Scramjet Configuration

A. Ramjet-Scramjet Optimization Algorithm
The scramjet design process described in this paper is mapped to the following nonlinear
optimization problem is the following form;
maxize F ( x)
(18)
Subjected To G ( x) ' 0

where x = x1, x2, …, x10 is the vector of scramjet design variables, F(x) is the scalar cost function,
that represents either the thrust or the thrust to drag ratio, and G(x) is a vector-valued set of nonlinear
constraints, that represents the aerodynamic and geometric constraints, such as, the nozzle to inlet area
ratio, the isolator back pressure ratio and the combustion chamber maximum temperature. In general, the
function, F(x), is the fitness function characterizing how much the shape suits the optimization problem.
G(x) represents all the constraints of the problem. The design variables xi represent the geometric
parameters that control the general locations of points; A – G, that defines the 2D cross sectional
geometry illustrated in Figures 2 and 11. The goal of this optimization problem is to identify the ideal set
of geometric parameters that define the scramjet geometry, subsystems shape and aerodynamic
constraints for which the maximum thrust characteristic is observed.
Fig. 11: Scramjet 2D Cross Section with Optimization Design Parameters Highlighted.

In general, there are two families of optimization algorithms; namely a first family of ‘local
minimum solution’ based algorithms such as gradient methods, and a second family of ‘global minimum
solution’ based algorithms such as the genetic algorithm (GA), and simulated annealing (SA). In this
research effort, the optimization of the 3D scramjet configuration is conducted through the use of a
genetic algorithm. Starting from an initial scramjet configuration, the genetic algorithm is able to quickly
find an optimum. The method used is based on an OOP Fortran code.

V: Results and Conclusion

A: Preliminary Results
Two samples, one from each of the two classes of configurations that were developed as part of this
study, are illustrated in Figures 1 and 10. As can be observed in these Figures, a variety of shapes can be
generated by manipulating the design points A through G, in any manner of combination. In addition,
configurations with rectangular or circular cross sections can be constructed and analyze at will. The
results presented in this section highlight the performance of the two main parts of the scramjet; namely,
the forebody-isolator configuration and the combustor-nozzle configuration. These results are described
in the following two subsections of this paper.

Z ZoneD

ZoneC

ZoneB

ZoneA

Fig. 11: Isolator Shear stress Distribution Fig. 12: Isolator C-Section Pressure Distribution

Fig. 13: Isolator Internal Mach Number Fig. 14: Isolator Internal Pressure Distribution
Distribution
A.1: Preliminary Forebody-Isolator configuration Results
Figure 11 illustrates the shear stress distribution on the surface of the forebody-isolator element. In
Figure 11 the outer surface to the isolator is removed to reveal the shear stress distribution on the internal
surfaces of the isolator. Figure 12, on the other hand, shows the pressure distribution at cross-sections
located at stations, A, B, C and D, of the forebody-isolator element. These results indicated that the
pressures are constant at each location, however, the magnitude of the pressures increases as expected,
and are predicted as expected from the results illustrated in Ref. 3-4, 7-10. Attempts were made to
independently validate the forebody-isolator performance using CFD Euler and Navier –Stokes Solvers.
Preliminary results, indicating the Mach numbers and pressure behavior within the forebody-isolator
system from the Euler solutions for the 3D Mach 5 configurations, are illustrated in Figures 13 and 14.
In an effort to identify the design parameters necessary for optimization, the overall performance of
the forebody-isolator configuration was studied as a function of its geometric and freestream input
parameters. The captured mass flow rates, the Mach numbers at the exit of the isolator, the forebody-
isolator drag and the non-dimensional drag ratios were observed as the freestream mach number and the
wedge angle were allowed to vary. The Mach number was allowed to vary in the range of 2 to 12 while
the wedge was kept at 12 degrees. On the other hand, the wedge angle varied from 8 to 16 degrees, while
the freestream Mach number was fixed at 5. The results from these studies are illustrated in Figures 15
through 20.

Fig. 15: Isolator Mach Exit vs. Wedge Angle Fig. 16: Mach Exit vs. Flight Mach Number

Fig. 17: Isolator Mass Capture vs. Wedge Angle Fig. 18: Mass Capture vs. Flight Mach Number
Fig. 19: Isolator Drag Ratio vs. Wedge Angle Fig. 20: Drag Ratio vs. Flight Mach Number

A.2: Preliminary Combustor-Nozzle Configuration Results

Consider the combined Diffuser-Combustor-Nozzle configuration, as illustrated in Fig. 5. As
noted in Figures 5 and 11, the geometric points, A through G, lying on the x-axis not only define the
various components of the scramjet propulsion system, such as, it’s forebody, inlet, isolator, diffuser,
combustor and nozzle, they also serves as the key indicators for the 3D construction of these components.
For the purposes of this study a combustor-nozzle configuration of internal circular and external square
cross-sections was constructed at Mach 5. Additionally, the internal and external tubes making up this
scramjet were terminated at the same point on the x-axis. Quasi-1D analysis was then conducted on this
configuration. The results of this test are presented in the form of the velocity, pressure and total
temperature distribution along the x-axis of the scramjet in Figures 21 through 23.
Once again, the observed behaviors of the flowfield parameters are predicted as expected. As
observed, these plots illustrate the expected behavior of the thermodynamic variables associated with
heating in the combustion chamber that are consistent with either constant area, increasing area or
decreasing area ratios. Additionally, preliminary results indicated that the thrust to drag performance of
the scramjets constructed using this design approach can be as much as 100.0. A sample of the variation
of the engine Isp versus the free stream Mach number ranging from 4 to 12 is illustrated in Figure 24.

B: Conclusion
This paper gives a preliminary report on efforts to design a reconfigurable propulsion system; morphing
from ramjet to scramjet mode of operation in flight. Performance requirements will almost certainly
dictate the use of a translating center body and associated outer ‘clamshell’. The design of the forebody-
inlet-isolator was accomplish through the use of 2D planar flowfields. In addition, realistic ramjet-to-
scramjet propulsion systems were derived and analyzed from Quasi 1D flowfields. Detailed analysis of
the ‘ramjet-to-scramjet propulsion systems’ performance at various Mach numbers is of interest to this
study and will form a significant element of this research project as it develops.

C. Conclusion
In general, the code developed as part of this research effort was used to conduct the following
studies:
1. Generate propulsion systems configurations from prescribed 2-D shock waves;
2. Evaluate the resulting engine geometric characteristics;
3. Evaluate the thrust performance of the engine, and;
4. Identify the design parameters that affect the engine’s overall performance and shape; and
develop the engine ‘optimization design space’.
At this stage of its development, the optimization process outline in this paper is yet to be tested and
debugged.
 The preliminary outcomes of this research can be classified in the following two categories. First,
the propulsion system design and assembly process led to the discovery of engineering parameters that
directly influence the aerodynamic performance of the resulting configuration. These parameters were
manipulated to generate configurations with superior thrust and Isp characteristics. Second, design
information needed to develop routines for the follow-on morphing and optimization of the ‘ramjet-to-
scramjet configuration’ were generated and analyzed.

1500 1500
1.8 1.8

1.6 1.6
1400 1400
Local C-Sectional Area

Local C-Sectional Area

1.4 1.4

Local Velocity

Local Pressure
1.2 1300 1.2 1300

1 1

0.8 1200 0.8 1200

0.6 0.6
1100 1100
0.4 0.4

3 4 5 6 3 4 5 6
x Location in Scramjet x - Location in Scramjet
Fig. 21: Scramjet Area & Velocity Distribution Fig. 22: Scramjet Area & Pressure Distribution

6000
Isp

4400
1.8
4200
5500
1.6
4000
Local Total Temperature
Local C-Sectional Area

1.4
5000
3800
1.2
3600
4500
1
3400
0.8
4000
3200
0.6
3000
3500
0.4
2800
3 4 5 6 4 6 8 10 12
x - Location in Scramjet Freestream Mach Number
Fig. 23: Scramjet Area & Total Temperature
Fig. 24: Scramjet Isp vs Mach Number
Distribution

VI: Acknowledgments
This work has been partially sponsored by the following agencies; WPAB, NAVAIR, NASA Glenn
and Langley Research Centers. In addition, special appreciation is extended to Dr. Datta Gaitonde and
Mr. Donnie Saunders of the Air Vehicles Directorate at Wright Patterson Air Force Base for their
encouragement and support of this project. Appreciation is expressed to Dr. Isaiah Blankson of NASA
Glenn Research Center and Dr. Reginal Williams of the Naval Airforce Base at Patuxent River in
Maryland.
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