NASA/TM-2005-213670

Local Flow Conditions for Proplusion 

Experiments on the F-15B Propulsion Flight 

Test Fixture

Michael J. Vachon, Timothy R. Moes, Stephen Corda

NASA Dryden Flight Research Center

Edwards, California

November 2005
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NASA/TM-2005-213670

Local Flow Conditions for Proplusion 

Experiments on the F-15B Propulsion Flight 

Test Fixture

Michael J. Vachon, Timothy R. Moes, Stephen Corda

NASA Dryden Flight Research Center

Edwards, California

November 2005

National Aeronautics and

Space Administration

Dryden Flight Research Center

Edwards, California 93523-0273
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ABSTRACT

Local flow conditions were measured underneath the National Aeronautics and Space 

Administration F-15B airplane to support development of future experiments on the Propulsion 

Flight Test Fixture (PFTF). The local Mach number and flow angles were measured using a 

conventional air data boom on a cone-cylinder mounted under the PFTF and compared with the 

airplane air data nose boom measurements. At subsonic flight speeds, the airplane and PFTF Mach 

numbers were approximately equal. Transonic Mach number values were up to 0.1 greater at 

the PFTF than the airplane, which is a counterintuitive result. The PFTF local supersonic Mach 

numbers were as much as 0.46 less than the airplane values. The maximum local Mach number at 

the PFTF was approximately 1.6 at an airplane Mach number near 2.0. The PFTF local angle of 

attack was negative at all Mach numbers, ranging from –3 to –8 degrees. When the airplane angle 

of sideslip was zero, the PFTF local value was zero between Mach 0.8 and Mach 1.1, –2 degrees 

between Mach 1.1 and Mach 1.5, and increased from zero to 1 degree from Mach 1.5 to Mach 

2.0. Airplane inlet shock waves crossed the aerodynamic interface plane between Mach 1.85 and 

Mach 1.90.

NOMENCLATURE

ax longitudinal acceleration, ft/s2

az vertical acceleration, ft/s2

AFTF Aerodynamic Flight Test Fixture

D drag, lbf

g acceleration due to gravity, ft/s2

h pressure altitude, ft

Mi indicated Mach number obtained from the airplane air data nose boom

Mi,PFTF PFTF local Mach number calculated using the cone-cylinder air data boom

MPC indicated Mach number corrected for static pressure position error

MPFTF local PFTF Mach number calculated using the airplane air data nose boom

NACA National Advisory Committee for Aeronautics

NASA National Aeronautics and Space Administration

PS specific excess power, ft/s

pi,nb airplane air data nose boom static pressure, uncorrected for static pressure 

position error, lbf/ft2

pT total pressure, lbf/ft2

PFTF Propulsion Flight Test Fixture

t time, sec
T thrust, lbf or temperature, °R

V velocity, ft/s

W weight, lbf

ΔMPC Mach number static pressure position error

INTRODUCTION

The NASA F-15B research test bed airplane has a unique capability to flight test propulsion 

devices, utilizing a Propulsion Flight Test Fixture (PFTF) that is hung underneath the airplane 

centerline (refs. 1 and 2). The PFTF provides a relatively inexpensive and efficient way to develop 

and flight test a wide range of propulsion devices and components. Propulsion hardware can be 

mounted to a six-component force balance underneath the fixture. The PFTF provides the support 

structure and volume for required propulsion systems, for example, propellant feed systems, control 

systems, and instrumentation. Subsonic, transonic, and supersonic flight data can be obtained up to 

airplane free-stream conditions of approximately Mach 2.0 and dynamic pressure of 1,100 lbf/ft2

(52.67 kPa).

Knowledge of the local flow conditions upstream of the propulsive device is critical to the 

determination of performance and operability. The current flight tests obtained local flow conditions 

including Mach number, angle of attack, angle of sideslip, total pressure, static pressure, and shock 

wave location at the anticipated aerodynamic interface plane of a propulsive device mounted under 

the PFTF. Local conditions were compared to the airplane flow conditions.

AIRPLANE AND EXPERIMENT DESCRIPTIONS

The NASA F-15B is a platform uniquely qualified to support these flight tests. This highperformance research airplane is capable of accomplishing all desired test points while providing 

instrumentation recording, data telemetry, and real-time video. The PFTF utilized during this 

experiment was designed specifically for the NASA F-15B airplane. Flight test conditions and 

maneuvers were chosen based upon expected requirements for future experiments to be carried on 

the PFTF.

Airplane Description

The F-15B airplane is a two-seat trainer–fighter version of the F-15A high-performance, airsuperiority fighter airplane built by McDonnell Aircraft Company (now The Boeing Company), 

St. Louis, Missouri. The F-15B airplane has a length of 63.7 ft (excluding the air data nose boom), 

a wingspan of 42.8 ft, and a height of 18.7 ft. The airplane is characterized by a shoulder-mounted 

main wing with a modified delta shape, twin vertical tails, all-moving horizontal stabilators, two 

engines mounted close together in the fuselage, and an elevated cockpit to enhance visibility. 

Primary flight control surfaces are controlled by a hydromechanical system and an electrical control 

augmentation system (CAS).
The F-15B airplane is powered by two Pratt & Whitney (West Palm Beach, Florida) F100‐PW‐100 

turbofan engines that each produce an uninstalled, sea level static thrust of approximately 23,500 

lbf in full afterburner. With these powerplants, the airplane is capable of dash speeds in excess 

of Mach 2.0 at altitudes of 40,000 to 60,000 ft. The airplane has a full-fuel takeoff weight of 

approximately 42,000 pounds and a landing weight of approximately 32,000 pounds. It has aerial 

refueling capability for extended-duration research missions.

The inlet system of the F-15B airplane consists of two two-dimensional, external compression, 

horizontal ramp inlets. Each inlet has three horizontal ramps mounted at the top of the inlet duct. 

The first ramp and upper cowl assembly rotate about a transverse hinge point at the lower cowl 

lip. Separate cowl and diffuser ramp actuators provide independent control of the first and third 

ramps, respectively. The second ramp position is dependent upon the first and third ramp positions. 

The second and third ramps, along with the side plates, are designed with porous bleed holes to 

remove the lower energy boundary layer flow. A fixed bypass bleed exit and a variable bypass 

door are provided for engine–inlet performance matching. At supersonic speeds, the bypass 

door is modulated to maintain the proper inlet throat Mach number. The system provides for a 

variable capture area that optimizes inlet performance, minimizes spillage drag, and maximizes 

inlet stability. The inlet system can be controlled automatically by the air inlet controller or, in an 

emergency, manually by the pilot.

The NASA F-15B airplane has been converted from an air-superiority fighter to a supersonic 

research test bed. Airplane modifications include the installation of research systems for the 

purposes of instrumentation, digital recording, telemetry, in-flight video, and global positioning 

system (GPS) navigation. A significant feature of the research capability of this airplane is the 

ability of the airplane to carry large experiment test fixtures on the lower fuselage centerline pylon. 

The fixtures installations are similar to the installation of a centerline fuel tank.

Experiment Description

The PFTF is a third generation research fixture that builds upon heritage from the development 

of the first and second generation Aerodynamic Flight Test Fixtures (AFTF), flown on NASA F‐104 

and F-15B airplanes, respectively (refs. 3 and 4). The PFTF complements the current inventory 

of F-15B airplane experiment flight test fixtures, the AFTF and the Centerline Instrumented Pylon 

(CLIP). The CLIP is a new fixture designed to accommodate larger span models underneath the 

airplane.

The PFTF is designed to be a flying engine test stand from which propulsion data can be obtained 

in the real flight environment. Advanced and prototype engines and propulsion technology can be 

carried and flight tested on the PFTF. The PFTF structure contains volume for propulsion system 

components such as fuel tanks, fluid systems, instrumentation, controllers, and other articles. A 

unique capability of the PFTF is the integral, six-component force balance. The balance permits 

the in-flight measurement of aerodynamic and propulsive forces.

The current flight test configuration is similar to that previously flown for the PFTF Cone-Drag 

Experiment (ref. 2), in which a cylinder with a conical nose and blunt base was carried below the 
PFTF. Figure 1 shows the NASA F-15B airplane with the PFTF local flow experiment, in flight. 

The cylinder, including the conical nose, was 68 in. long with a diameter of 10 in. The conical nose 

was 13.5 in. long with a semi-apex angle of 20 deg. The PFTF and cone-cylinder weighed 868.3 

lbs. Figure 2 shows the PFTF and cone-cylinder arrangement.

An attempt was made to mount the cylinder such that the local angle of attack and angle of 

sideslip were zero at a flight condition of Mach 1.5. This Mach number was selected based on 

the design point of several prospective experiments of interest at the time. Zero local angle of 

sideslip was set with respect to the airplane centerline. Zero local angle of attack was estimated 

by using local flow angle data from NASA F-15B/AFTF flight test data (ref. 4). While the AFTF 

configuration was considerably different from the current PFTF configuration, the AFTF data 

provided the best possible estimate. Based on the AFTF data, the PFTF cylinder angle of incidence 

was set at 2.5 deg nose up, with respect to the airplane air data nose boom centerline.

Instrumentation

Standard NACA air data nose booms built by SpaceAge Control, Inc. (Palmdale, California) 

were mounted on the NASA F-15B airplane nose and on the front of the cone-cylinder. Each air 

data boom measured the local total pressure, static pressure, angle of attack, and angle of sideslip. 

The air data boom contained two sets of static pressure ports separated by 0.75 in. The aft set 

of static pressure ports on the cone-cylinder air data boom were aligned with the aerodynamic 

interface plane. The measurements from the two sets of static pressure ports were averaged to 

obtain Mach number and altitude. The cone-cylinder air data boom was mounted with the angle of 

sideslip vane on the top side of the boom, contrary to standard air data boom installations that place 

the angle of sideslip vane on the bottom of the boom.

Conventional flow angle vanes, for measurement of angle of attack and angle of sideslip, were 

mounted downstream of the static pressure ports. Note that flow angle at the aerodynamic interface 

plane could not be measured with this configuration. The angle of attack and the angle of sideslip 

vanes were located 14.25 in. and 18.25 in., respectively, aft of the aerodynamic interface plane.

Three axis forces and moments were measured on the cone-cylinder using the integral PFTF 

force balance. Total temperature was measured by probes mounted on both the airplane and on the 

aft right side of the PFTF. Accelerometers were mounted on the fore and aft end of the cylinder 

to measure the cone-cylinder lateral and vertical accelerations. Other airplane measurements 

included linear and angular accelerations. All data were digitally recorded onboard the airplane and 

telemetered to ground-based recorders and control room displays in real time. Two video cameras, 

one facing forward and once facing aft, were mounted on the lower left of the airplane fuselage, 

aimed at the PFTF, and monitored in the aft cockpit and in the control room.

Flight Test Conditions and Maneuvers

Data were collected continuously from takeoff to landing. Maximum-power level accelerations 

were performed at pressure altitudes of 30,000 ft and 40,000 ft. The level accelerations were started 

at approximately Mach 0.8 and terminated at the maximum Mach number corresponding to the 
1,100-psf dynamic pressure limit of the PFTF. Figure 3 shows the flight test points within the 

NASA F 15B/PFTF flight envelope. Only one level acceleration to maximum Mach number could 

be completed per flight because of airplane fuel limitations.

After reaching the maximum Mach number, level decelerations were performed at each altitude. 

Steady heading sideslips were performed at discrete Mach numbers during the decelerations to 

collect local sideslip data. 

Two data flights were flown; one level acceleration at an altitude of 40,000 ft and one at an 

altitude of 30,000 ft. The flight test conditions for the two flights are shown in table 1. The actual 

deviations in the pressure altitude during the level accelerations were +0/–500 ft for the 40,000-ft 

altitude maneuver and +40/–600 ft for the 30,000-ft altitude maneuver.

Table 1. The NASA F-15B Propulsion Flight Test Fixture local flow flight test conditions.

Flight

number

Mach

number,

start – end of 

level 

acceleration

Pressure

altitude,

ft (m)

Maximum 

dynamic

pressure,

lbf/ft2 (N/m2)

Pressure,

lbf/ft2 (N/m2)

Temperature,

°R (°K)

261 0.8 – 1.975 40,000

(12,192)

1069.5 

(51,208)

391.7

(18,755)

390.0

(216.7)

262 0.8 – 1.55 30,000

(9,144)

1056.9 

(50,605)

628.4

(30,088)

411.7

(228.7)

RESULTS AND DISCUSSION

Results are presented and discussed for the local flow conditions; Mach number, angle of 

attack, and angle of sideslip. Force balance and specific excess power data are also presented 

and discussed. In general, the local flow conditions are plotted as compared with the free-stream 

Mach number (MPFTF). The free-stream Mach number is defined as the Mach number in the same 

vertical plane as the airplane air data nose boom but at the same altitude as the PFTF air data boom 

(see figure 2). Detailed tabular local flow data are contained in appendix A. This data may by used 

to aid in the planning of prospective propulsion experiments on the NASA F-15B/PFTF.

Local Mach Number

The local and free-stream Mach numbers are calculated from the total and static pressure 

measured by the cone-cylinder air data boom and airplane air data nose boom, respectively. The 

details of the Mach number calculation are given in appendix B.
Free-stream Mach number time histories for the 40,000-ft altitude and 30,000-ft altitude level 

acceleration or deceleration are shown in figures 4(a) and 4(b), respectively. The 40,000-ft altitude 

level acceleration was started at approximately Mach 0.84 and reached a maximum Mach number of 

1.98. The 30,000-ft altitude level acceleration was started at approximately Mach 0.8 and reached a 

maximum of Mach 1.58. The acceleration of the airplane decreased with increasing Mach number, 

indicated by the continuous decrease in the slope of the lines in figures 4(a) and 4(b). Note that the 

acceleration remains positive at the end of the maneuver.

The PFTF local Mach number is compared with the free-stream Mach number in figures 5(a) and 

5(b) for the 40,000-ft altitude and 30,000-ft altitude level acceleration or deceleration. A diagonal, 

dashed straight line drawn in each plot connects the points at which the free-stream and PFTF 

local Mach numbers are equal. As expected, the plots are similar for the two altitudes since the 

Reynolds numbers are similar. For the 30,000-ft altitude data, the Reynolds number range is from 

2.278 × 106/ft to 4.414 × 106/ft. For the 40,000-ft altitude data, the Reynolds number range is from 

1.526 × 106/ft to 3.768 × 106/ft.

Differences are seen between the acceleration and deceleration data, especially at transonic Mach 

numbers (approximately Mach 0.95 to Mach 1.2) and at Mach numbers between approximately 

Mach 1.47 and Mach 1.7 (at an altitude of 40,000 ft only). This may be due to hysteresis in the 

shock wave development or movement in shock location due to inlet spillage during deceleration. 

The largest differences occur at transonic speeds and at high Mach numbers when the F-15B 

airplane inlet shocks are approaching and then impinging upon the PFTF air data boom.

Figures 6(a) and 6(b) show the difference between the PFTF local Mach number and the freestream Mach number. In general, the PFTF local Mach number is lower than the free-stream Mach 

number except in the transonic region between approximately Mach 0.995 and Mach 1.15. At 

subsonic speeds, the difference between the PFTF local and airplane Mach numbers is small.

For the level acceleration at an altitude of 40,000 ft, figure 6(a), the difference between the 

PFTF local Mach number and the airplane Mach number is increasingly negative. Subsonically, 

this reduction in Mach number ranged from approximately –0.02 at Mach 0.84 to a maximum of 

approximately –0.05 near Mach 1.0. The difference transitions dramatically very near Mach 1.0 

such that the PFTF local Mach number is greater than the free-stream value until approximately 

Mach 1.15. Between free-stream Mach numbers of 1.15 and 1.86, the difference between PFTF 

local Mach number and the free-stream value becomes increasingly negative, differing from 

0 to approximately –0.45. Beginning at Mach 1.86, the PFTF local Mach number increases 

discontinuously from approximately Mach 1.4 to Mach 1.55. This increase is likely caused by the 

passage of the F-15B airplane inlet shock across the cone-cylinder air data boom static pressure 

ports. The maximum free-stream Mach number of 1.978 corresponds to a PFTF local Mach number 

of 1.58.

The same trends in the Mach number differences are seen in the 30,000-ft altitude data, figure 

6(b), although the absolute values are slightly different. The maximum Mach number achieved 

at an altitude of 30,000 ft was limited by the dynamic pressure limit imposed on the airplane to 

protect the PFTF force balance from potentially excessive side loads. The transition at which the 
PFTF local Mach number is greater than the free-stream value is slightly longer at this altitude, 

lasting until a free-stream value of Mach 1.25. As tested at an altitude of 30,000 ft, the maximum 

free-stream Mach number of 1.55 corresponds to a PFTF local Mach number of 1.4.

Local Angle of Attack

The airplane air data nose boom and PFTF local angles of attack are plotted as a function of the 

airplane free-stream Mach number in figures 7(a) and 7(b) for the 40,000-ft altitude and 30,000-ft 

altitude test points. The PFTF local angle of attack is several degrees lower than the airplane angle 

of attack for all Mach numbers, indicating a local downwash flow field beneath the airplane. The 

PFTF local angle of attack is always negative for all Mach numbers, while the airplane angle of 

attack is always positive at all speeds at an altitude of 40,000 ft and up to Mach 1.35 at an altitude 

of 30,000 ft.

For the 40,000-ft altitude data, shown in figure 7(a), the PFTF local angle of attack has a roughly 

constant value of –2 to –4 deg between Mach 0.85 and Mach 1.3. At higher supersonic Mach 

numbers, the PFTF local angle of attack decreases almost linearly from approximately –2.5 deg at 

Mach 1.3 to –7.8 deg at Mach 1.98. Note that the airplane angle of attack decreases approximately 

linearly from Mach 0.85 to Mach 1.5, then remains constant at zero from Mach 1.5 to Mach 1.98.

The 30,000-ft altitude data, presented in figure 7(b), shows trends similar to the 40,000-ft 

altitude data of figure 7(a). The PFTF local angle of attack is fairly constant at –3 to –4 deg over the 

Mach number range from Mach 0.8 to approximately Mach 1.3. Above Mach 1.3, the PFTF local 

angle of attack shows a linear decrease. The airplane angle of attack shows a continual decrease 

throughout the Mach number range.

Local Angle of Sideslip

Angle of sideslip flight data are shown in figures 8(a) and 8(b) for an altitude of 40,000 ft, and in 

figures 9(a) and 9(b) for an altitude of 30,000 ft. The PFTF local angle of sideslip and the airplane 

air data nose boom angle of sideslip are shown plotted as compared with the free-stream Mach 

number. Figures 8(a) and 9(a) show airplane and local PFTF sideslip angles during constant-altitude 

accelerations for altitudes of 40,000 ft and 30,000 ft, respectively. No intentional sideslip was 

induced by pilot rudder input during these accelerations. Three steady heading sideslip maneuvers 

were performed as the airplane decelerated at constant altitude. These data are shown in figures 

8(b) and 9(b) for the 40,000-ft altitude and 30,000-ft altitude level decelerations, respectively.

All of the PFTF local angle of sideslip data appear to be noisier than the airplane free-stream 

data. This noise may be caused by lateral vibration of the cone-cylinder assembly. However, the 

PFTF local angle of attack data did not show the same degree of unsteadiness.

During the level accelerations at both altitudes, the airplane angle of sideslip is benign, 

remaining within one degree of zero. Between approximately Mach 1.1 and Mach 1.5, the PFTF 

local angle of sideslip indicates approximately –2 deg (nose right) while the airplane measured 

angle of sideslip is near zero. Supersonically, from Mach 1.3 to Mach 2.0, the airplane angle of 
sideslip is near zero. The PFTF local angle of sideslip changes dramatically from –2 deg to 0 deg 

at approximately Mach 1.5. Above approximately Mach 1.55, the local angle of sideslip increases 

from 0 to 1 deg (nose left).

During installation, the cone-cylinder air data boom was carefully aligned with the airplane 

air data nose boom for these tests, so it is not believed that the local sideslip was induced by 

misalignment of the cone-cylinder hardware. The phenomenon is believed to be a result of an 

airplane asymmetry and not a local fixture asymmetry because this mismatch in airplane and local 

angle of sideslip has been noted in subsequent flight tests with the AFTF mounted in place of the 

PFTF. Slight differences in the scheduling of the right and left F-15B airplane inlet ramps could 

cause this induced sideslip. 

There are two principal differences between the PFTF and AFTF air data probe configurations. 

The PFTF air data boom is mounted at a 2.5-deg nose-up angle, and the angle of sideslip vane is 

situated on top of the boom. This positions the trailing edge of the vane within 10 in. of the leading 

edge of the PFTF pylon, and aerodynamic interaction with the detached pylon bow shock may be 

occurring at low supersonic speeds. For flight tests with the AFTF, the air data boom is always 

aligned with the F-15B airplane waterline and the angle of sideslip vane is mounted on the bottom 

of the boom, avoiding any potential aerodynamic influences.

Steady heading sideslips sweeps were performed at approximately Mach numbers 1.2, 1.4, and 

1.8 during the 40,000-ft altitude level deceleration shown in figure 8(b) and at Mach numbers 1.1, 

1.25, and 1.4 during the 30,000-ft altitude level deceleration shown in figure 9(b). Figures 8(b) 

and 9(b) compare the PFTF local flow sideslip angle obtained from the sideslip sweeps with the 

free-stream sideslip angle. The airplane sideslip input was a maximum of approximately 1.5 to 

2 deg. The measured change in the local sideslip angle caused by the airplane sideslip input was 

approximately 0.5 to 1 deg less than input.

Note that at both altitudes, during the accelerations and decelerations, there is a repeatable 

double-spike in the PFTF local angle of sideslip just below an F-15B airplane free-stream Mach 

number of 1.1, but it is not reflected in the airplane sideslip data. The local angle of sideslip 

increases to as high as 2 deg and decreases to as low as –3 deg while the airplane sideslip remains 

constant. These spikes are believed to be a transonic phenomenon, possibly shock development 

or interaction with the sideslip vane; the airplane inlet asymmetry mentioned previously may be 

a contributing factor. These spikes in angle of sideslip have also been observed when flying the 

AFTF at similar Mach numbers.

Force Balance Data

PFTF force balance data was obtained for the cone-cylinder. The highest loads measured during 

the flight tests were with the airplane nose wheel landing gear extended. Previously collected 

vibration flight data have identified a low frequency vortex shedding from the nose wheel landing 

gear door that may be the cause of these higher loads (ref. 5). The force balance measured sinusoidal 

oscillations with a frequency of approximately 1 Hz during the level acceleration and deceleration 

maneuvers.
Specific Excess Power

Figures 10(a) and 10(b) show specific excess power (

!

PS) as a function of Mach number for 

the NASA F-15B airplane with the PFTF and cone-cylinder configuration for the 40,000-ft 

altitude and 30,000-ft altitude level accelerations. The specific excess power, shown in equation 

(1), was calculated using accelerometer data for the longitudinal acceleration (ax) and the vertical 

acceleration (az).

For both altitudes, the specific excess power remains positive at the completion of the level 

accelerations. The specific excess power increases subsonically to a maximum value, decreases 

transonically until past the transonic drag rise, then increases slightly until continually decreasing 

supersonically. At an altitude of 40,000 ft, the rise in 

!

PS beginning at Mach 1.5 is a result of the 

higher efficiency obtained from the F-15B airplane variable geometry inlet as the inlet third ramp 

begins to schedule.

The specific excess power data shows that the F-15B airplane is aerodynamically capable of 

accelerating to higher Mach numbers, if needed, for future test points with the PFTF at an altitude 

of 40,000 ft, but has reached the limit of available power at an altitude of 30,000 ft.

CONCLUDING REMARKS

Flight tests were conducted to characterize the local flow underneath the NASA F-15B test 

bed research airplane in a region in which potential propulsion experiments could be carried. The 

Propulsion Flight Test Fixture (PFTF) with a cone-cylinder assembly was mounted underneath 

the F-15B airplane fuselage centerline. The cone-cylinder assembly is a dimensionally crude 

representation of a propulsion-type experiment. The local Mach number, angle of attack, and angle 

of sideslip data were compared between the airplane and the PFTF local flow. Maximum power, 

level accelerations were flown at pressure altitudes of 30,000 and 40,000 ft. Characteristics of the 

PFTF local flow are discussed below.

Local Mach Number

In subsonic flight, the PFTF local Mach number and airplane Mach number are approximately 

the same. In transonic flight, the PFTF local Mach number is approximately 0.1 greater than the 

airplane Mach number, which is a counterintuitive result. Above an airplane Mach number of 1.2, 

the difference between the airplane and PFTF local Mach numbers increases from 0.0 to 0.46 at 

an airplane Mach number of 1.86. The inlet shock wave crosses the PFTF cone-cylinder air data 

boom pressure ports at approximately Mach 1.86. At an airplane Mach number of 2.0, this shock 

passage results in a PFTF local Mach number of approximately 1.6. The F-15B airplane was 

!

PS = T " D

W

#

$

% &

'

(V = dh

dt

+

V

g

dV

dt = az)t +

V

g

ax (1)
10

shown to have specific excess power at 40,000 ft for accelerating to higher Mach numbers.

Local Angle of Attack

The PFTF local angle of attack was negative at all Mach numbers, indicating a local downwash 

underneath the airplane. The PFTF local angle of attack was several degrees less than the airplane 

angle of attack at all Mach numbers, ranging from –3 to –8 deg.

Local Angle of Sideslip

The airplane angle of sideslip was essentially zero from subsonic Mach numbers to Mach 2.0. 

The PFTF local angle of sideslip averaged 0 deg from Mach 0.8 to Mach 1.1, approximately –2 deg 

(nose right) between Mach 1.1 and Mach 1.5, and up to +1 degree (nose left) above Mach 1.5.

These local flow measurements are for a specific configuration flown on the Propulsion Flight 

Test Fixture underneath the NASA F-15B airplane. They provide useful guidance in designing 

potential propulsion experiments for the NASA F-15B test bed airplane and valuable data for 

making preflight predictions.

Dryden Flight Research Center

National Aeronautics and Space Administration

Edwards, California, August 25, 2005
11

REFERENCES

1. Corda, Stephen, M. Jake Vachon, Nathan Palumbo, Corey Diebler, Ting Tseng, Anthony Ginn,

 and David Richwine, The F-15B Propulsion Flight Test Fixture: A New Flight 

 Facility for Propulsion Research, NASA/TM-2001-210395, 2001.

2. Palumbo, Nathan, Timothy R. Moes, and M. Jake Vachon, Initial Flight Tests of the F-15B

 Propulsion Flight Test Fixture, NASA/TM-2002-210736, 2002.

3.Meyer, Robert R. Jr., A Unique Flight Test Facility: Description and Results, 

 NASA TM‐84900, 1982.

4. Richwine, David M., F-15B/Flight Test Fixture II: A Test Bed for Flight Research, 

 NASA Technical Memorandum 4782, 1996.

5. Corda, Stephen, Russel J. Franz, James N. Blanton, M. Jake Vachon, and James B. DeBoer, 

 In-Flight Vibration Environment of the NASA F-15B Flight Test Fixture, 

 NASA/TM-2002-210719, 2002.

6. Ehernberger, L. J., Edward A. Haering, Jr., Mary G. Lockhart, and Edward H. Teets, 

 “Atmospheric Analysis for Airdata Calibration on Research Aircraft,” AIAA-92-0293, 

 January 1992. 

7. Shapiro, Ascher H., The Dynamics and Thermodynamics of Compressible Fluid Flow, 

 Volume 1, The Ronald Press Company, New York, 1953.
12

APPENDIX A

LOCAL FLOW DATA

FL GI HT

261

Freestream

Mach

Number, M ni f T mi e, t

Altitude,

h

Dynam ci

Pressure,

q

Longitud ni al

Acce el rat oi n,

ax

Vert ci al

Acce el rat oi n,

az

Freestream

Total

Pressure,

pT, ni f

Freestream

Stat ci

Pressure,

ps, ni f

Local

Total

Pressure,

pT, ol cal

Local

Stat ci

Pressure,

ps, ol cal

Freestream

Ang el of

Attack, anb

Local Ang el

of Attack,

a ol cal

Freestream

Ang el of

S di esl pi , bnb

Local Ang el

of S di esl pi ,

b ol cal

ACCEL sec ft bl /ft2 g s' g s' bl / ni 2 bl / ni 2 bl / ni 2 bl / ni 2 deg deg deg deg

0 8. 5 0 0. 39996 198 3. 0 1. 54 0 9. 56 4 3. 7 2 7. 8 4 5. 2 2 8. 9 3 9. 9 -0 1. 6 -0 4. 3 -0 4. 1

0 9. 0 19 4. 40001 222 2. 0 1. 37 1 0. 09 4 6. 0 2 7. 9 4 7. 4 2 8. 8 3 3. 1 -0 4. 5 -0 6. 2 -0 4. 4

0 9. 5 30 8. 39995 247 1. 0 2. 79 0 9. 56 4 8. 6 2 8. 1 5 0. 2 2 9. 1 2 4. 8 -0 6. 5 -0 7. 4 0 1. 2

1 0. 0 39 6. 39957 275 0. 0 2. 10 0 9. 34 5 1. 6 2 8. 6 5 3. 3 2 6. 4 2 6. 4 -0 3. 9 -0 6. 2 0 4. 8

1 0. 5 49 6. 39941 303 4. 0 2. 28 0 9. 34 5 4. 8 2 7. 3 5 6. 6 2 7. 4 2 6. 2 -1 0. 4 -0 6. 8 -0 4. 4

1 1. 0 58 4. 39931 333 2. 0 2. 37 0 9. 45 5 8. 3 2 7. 4 6 0. 0 2 6. 9 2 3. 5 -0 6. 5 -0 5. 9 0 2. 5

1 1. 5 67 8. 39926 364 1. 0 2. 16 0 9. 50 6 1. 9 2 7. 4 6 3. 5 2 7. 6 2 0. 6 -0 3. 9 -0 5. 3 -0 9. 0

1 2. 0 77 8. 39918 396 5. 0 2. 06 0 9. 98 6 5. 8 2 7. 4 6 7. 5 2 8. 4 1 9. 3 -0 2. 9 -0 1. 9 -1 3. 0

1 2. 5 87 6. 39919 430 4. 0 1. 84 0 8. 92 6 9. 9 2 7. 4 7 1. 5 2 8. 6 1 4. 3 -0 9. 7 -0 1. 3 -1 6. 3

1 3. 0 98 0. 39918 465 4. 0 1. 72 0 9. 77 7 4. 1 2 7. 4 7 6. 7 2 9. 4 1 2. 9 0 1. 6 -0 1. 6 -1 8. 9

1 3. 5 109 6. 39911 501 9. 0 1. 48 0 9. 45 7 8. 6 2 7. 4 8 1. 3 3 0. 5 1 0. 4 -0 8. 4 -0 0. 3 -1 9. 6

1 4. 0 125 2. 39897 540 2. 0 1. 44 0 9. 45 8 3. 4 2 7. 4 8 6. 7 3 2. 0 0 8. 3 -1 2. 3 0 0. 0 -1 7. 0

1 4. 5 137 8. 39824 581 6. 0 1. 27 1 0. 19 8 8. 6 2 7. 5 9 2. 9 3 3. 0 0 8. 3 -1 8. 5 0 5. 5 -1 8. 3

1 5. 0 156 0. 39749 624 3. 0 0. 95 0 9. 50 9 4. 0 2 7. 6 9 7. 2 3 4. 5 0 3. 4 -2 0. 4 0 0. 0 -2 3. 6

1 5. 5 172 2. 39648 670 2. 0 1. 09 1 0. 14 9 9. 8 2 7. 7 10 3. 5 3 5. 6 0 2. 5 -2 4. 6 0 0. 0 0 7. 5

1 6. 0 188 4. 39532 717 8. 0 1. 18 0 9. 66 10 5. 8 2 7. 8 11 1. 1 3 6. 8 0 1. 4 -3 0. 5 0 0. 3 -0 0. 1

1 6. 5 207 2. 39515 764 0. 0 1. 14 0 9. 87 11 1. 7 2 7. 8 11 5. 4 3 8. 4 0 0. 8 -3 5. 3 -0 1. 0 0 7. 5

1 7. 0 222 4. 39577 808 7. 0 0. 88 0 9. 02 11 7. 3 2 7. 7 12 4. 8 4 0. 2 -0 1. 2 -3 8. 3 -0 1. 9 0 9. 8

1 7. 5 243 0. 39598 856 1. 0 0. 88 1 0. 19 12 3. 2 2 7. 7 13 3. 3 4 2. 7 0 2. 8 -3 7. 3 -0 2. 5 0 6. 5

1 8. 0 268 6. 39576 906 5. 0 0. 80 0 9. 87 12 9. 6 2 7. 7 14 2. 4 4 5. 5 0 1. 6 -4 2. 8 -0 1. 7 0 4. 2

1 8. 5 295 6. 39752 949 9. 0 0. 84 0 9. 34 13 5. 0 2 7. 4 15 0. 8 4 8. 9 0 1. 7 -4 5. 7 -0 2. 5 1 0. 4

1 9. 0 321 2. 39977 991 3. 0 0. 67 0 9. 66 14 0. 1 2 7. 1 15 9. 8 4 4. 8 0 1. 9 -4 7. 7 -0 1. 9 0 6. 5

1 9. 5 354 8. 40215 1032 4. 0 0. 53 0 9. 34 14 5. 1 2 6. 8 16 9. 8 4 6. 2 0 2. 2 -4 8. 3 -0 1. 1 1 1. 1

1 9. 8 374 0. 40334 1055 5. 0 0. 13 0 9. 56 14 8. 0 2 6. 6 17 5. 5 4 7. 3 0 2. 3 -5 2. 5 -0 2. 5 1 3. 7
13

FLIGHT

261

Freestream

Mach

Number, Minf Time, t

Altitude,

h

Dynamic

Pressure,

q

Longitudinal

Acceleration,

ax

Vertical

Acceleration,

az

Freestream

Total

Pressure,

pT,inf

Freestream

Static

Pressure,

ps,inf

Local

Total

Pressure,

pT,local

Local

Static

Pressure,

ps,local

Freestream

Angle of

Attack, anb

Local Angle

of Attack,

alocal

Freestream

Angle of

Sideslip, bnb

Local Angle

of Sideslip,

blocal

DECEL sec ft lb/ft2 g's g's lb/in2 lb/in2 lb/in2 lb/in2 deg deg deg deg

1.98 0.0 40334 1055.5 0.013 0.956 14.80 2.66 17.55 4.73 0.23 -5.25 -0.25 1.371.95 3.2 40356 1023.8 -0.520 1.019 14.39 2.66 17.52 4.64 0.22 -4.86 -0.08 1.541.90 6.0 40378 972.3 -0.510 1.009 13.74 2.66 15.80 4.38 0.09 -4.86 0.18 0.611.85 8.8 40407 920.5 -0.513 0.956 13.08 2.66 14.78 4.75 0.06 -4.47 -1.33 0.221.80 11.8 40430 869.6 -0.476 1.083 12.43 2.66 13.74 4.41 0.34 -4.28 1.71 1.241.75 14.8 40454 822.6 -0.460 0.902 11.84 2.66 12.93 4.16 -0.06 -3.99 0.89 1.111.70 18.0 40475 775.6 -0.457 0.934 11.24 2.66 12.14 3.93 -0.09 -3.47 0.41 0.781.65 21.4 40488 729.2 -0.431 0.956 10.66 2.66 11.40 3.70 -0.01 -3.57 0.13 0.121.60 25.0 40505 684.8 -0.394 0.945 10.10 2.66 10.95 3.55 0.03 -2.82 -0.03 0.251.55 28.8 40520 642.7 -0.360 0.987 9.57 2.66 10.35 3.49 0.14 -2.17 0.12 0.121.50 33.0 40549 601.9 -0.328 0.998 9.06 2.66 9.69 3.38 0.28 -1.98 0.15 -2.061.45 37.8 40562 561.0 -0.284 1.030 8.54 2.65 9.09 3.22 0.52 -1.43 0.82 -1.861.40 42.8 40582 523.2 -0.256 0.987 8.07 2.65 8.51 3.08 0.58 -1.20 -0.33 -2.551.35 48.6 40599 485.7 -0.220 0.924 7.61 2.65 8.01 2.97 0.65 -0.55 -0.13 -2.161.30 55.2 40577 450.6 -0.217 1.019 7.18 2.65 7.49 2.89 1.17 0.00 0.06 -1.831.25 61.8 40586 416.6 -0.212 0.934 6.76 2.65 7.05 2.79 1.21 -0.71 0.00 -2.191.20 68.6 40585 384.3 -0.221 0.945 6.37 2.65 6.62 2.74 1.60 -1.20 -0.74 -1.891.15 74.6 40567 352.2 -0.256 1.062 5.99 2.65 6.25 2.65 1.98 -0.26 -0.56 -1.561.10 79.8 40580 322.9 -0.215 0.977 5.65 2.65 5.88 2.55 2.06 0.07 -0.46 -0.811.05 86.0 40602 293.4 -0.204 0.924 5.30 2.65 5.52 2.47 2.09 -1.26 -0.22 -0.181.00 91.4 40482 267.7 -0.177 1.099 5.03 2.79 5.26 2.52 2.39 -0.65 -0.33 -0.010.95 100.4 40681 239.4 -0.071 1.025 4.71 2.72 4.94 2.83 2.21 -0.71 -0.39 -0.610.90 113.2 40691 214.8 -0.043 0.913 4.45 2.70 4.65 2.79 2.52 -0.84 -0.10 -0.080.85 127.8 40704 191.7 -0.007 0.977 4.22 2.68 4.44 2.79 3.50 -0.48 -0.03 -0.71
14

FL GI HT

262

Freestream

Mach

Number, M ni f T mi e, t

Altitude,

h

Dynam ci

Pressure,

q

Longitud ni al

Acce el rat oi n,

ax

Vert ci al

Acce el rat oi n,

az

Freestream

Total

Pressure,

pT, ni f

Freestream

Stat ci

Pressure,

ps, ni f

Local

Total

Pressure,

pT, ol cal

Local

Stat ci

Pressure,

ps, ol cal

Freestream

Ang el of

Attack, anb

Local Ang el

of Attack,

a ol cal

Freestream

Ang el of

S di esl pi , bnb

Local Ang el

of S di esl pi ,

b ol cal

ACCEL sec ft bl /ft2 g s' g s' bl / ni 2 bl / ni 2 bl / ni 2 bl / ni 2 deg deg deg deg

0 8. 0 0 0. 29956 282 5. 0 1. 78 0 9. 02 6 6. 7 4 4. 5 6 8. 4 4 5. 5 2 4. 7 -0 6. 1 -0 3. 7 -0 7. 7

0 8. 5 8 2. 29957 319 5. 0 3. 97 0 8. 49 7 0. 2 4 4. 6 7 2. 0 4 5. 5 1 7. 2 -0 8. 7 1 3. 5 0 7. 8

0 9. 0 12 0. 29946 357 0. 0 4. 75 1 0. 19 7 4. 0 4 4. 9 7 5. 3 4 5. 5 1 7. 2 -1 1. 0 0 2. 4 -0 1. 5

0 9. 5 15 6. 29994 398 2. 0 4. 43 0 9. 13 7 8. 1 4 5. 1 7 9. 6 4 5. 8 1 1. 5 -1 2. 0 0 4. 9 -0 1. 5

1 0. 0 20 0. 29958 441 0. 0 3. 41 1 0. 51 8 2. 8 4 5. 9 8 3. 9 4 1. 5 1 6. 9 -1 1. 3 0 4. 6 0 2. 5

1 0. 5 25 8. 29900 487 0. 0 3. 09 0 9. 56 8 8. 0 4 3. 9 8 9. 4 4 2. 8 1 5. 0 -0 9. 4 0 5. 5 0 3. 5

1 1. 0 32 0. 29882 535 5. 0 2. 63 0 9. 71 9 3. 6 4 4. 0 9 5. 1 4 2. 0 1 2. 9 -1 1. 3 0 6. 4 0 3. 5

1 1. 5 39 4. 29866 585 8. 0 2. 20 0 9. 87 9 9. 6 4 4. 0 10 0. 9 4 3. 3 0 9. 2 -0 8. 1 0 7. 0 -1 0. 4

1 2. 0 48 6. 29878 637 1. 0 1. 77 0 9. 77 10 5. 7 4 4. 0 10 7. 3 4 3. 9 0 7. 4 -1 0. 7 0 7. 9 -1 2. 3

1 2. 5 60 2. 29858 692 2. 0 1. 50 0 9. 93 11 2. 4 4 4. 1 11 4. 5 4 4. 7 0 4. 6 -0 6. 5 1 1. 6 -1 7. 0

1 3. 0 74 4. 29869 748 2. 0 1. 18 0 9. 93 11 9. 2 4 4. 1 12 2. 1 4 6. 1 0 2. 8 -0 6. 5 1 0. 7 -1 8. 3

1 3. 5 91 4. 29824 808 7. 0 1. 07 0 9. 87 12 6. 7 4 4. 1 13 0. 3 4 8. 1 0 2. 0 -0 8. 7 0 7. 3 -1 7. 3

1 4. 0 110 2. 29826 869 4. 0 1. 00 0 9. 77 13 4. 2 4 4. 1 13 8. 6 5 0. 1 -0 0. 6 -1 6. 8 0 6. 3 -1 8. 0

1 4. 5 129 8. 29815 932 8. 0 0. 78 0 8. 71 14 2. 1 4 4. 1 14 7. 9 5 2. 4 -0 4. 4 -2 1. 1 0 0. 6 -2 1. 3

1 5. 0 158 6. 29699 1003 5. 0 0. 45 0 9. 45 15 1. 0 4 4. 3 15 9. 0 5 5. 0 -0 4. 1 -2 3. 7 0 1. 7 -1 2. 3

1 5. 5 199 8. 29530 1080 1. 0 0. 42 1 0. 83 16 0. 8 4 4. 6 17 0. 1 5 6. 6 -0 4. 6 -2 7. 2 0 5. 3 0 6. 5

1 5. 5 206 0. 29555 1081 1. -0 1. 87 0 9. 66 16 0. 9 4 4. 6 17 0. 6 5 6. 7 -0 5. 2 -2 6. 6 0 4. 9 0 5. 5
15

FLIGHT

262

Freestream

Mach

Number, Minf Time, t

Altitude,

h

Dynamic

Pressure,

q

Longitudinal

Acceleration,

ax

Vertical

Acceleration,

az

Freestream

Total

Pressure,

pT,inf

Freestream

Static

Pressure,

ps,inf

Local

Total

Pressure,

pT,local

Local

Static

Pressure,

ps,local

Freestream

Angle of

Attack, anb

Local Angle

of Attack,

alocal

Freestream

Angle of

Sideslip, bnb

Local Angle

of Sideslip,

blocal

DECEL sec ft lb/ft2 g's g's lb/in2 lb/in2 lb/in2 lb/in2 deg deg deg deg

1.55 0.0 29499 1083.6 -0.218 0.998 16.13 4.47 17.16 5.69 -0.35 -2.95 0.43 0.35

1.55 0.2 29497 1082.5 -0.198 0.902 16.11 4.47 17.18 5.72 -0.56 -2.88 0.27 0.05

1.50 1.0 29492 1014.9 -0.528 0.966 15.27 4.48 16.16 5.63 -0.63 -2.59 0.33 -1.14

1.45 4.2 29478 949.2 -0.482 0.945 14.45 4.48 15.11 5.35 -0.55 -2.62 1.38 -1.10

1.40 2.0 29453 884.8 -0.426 0.908 13.65 4.49 14.28 5.14 -0.40 -1.49 -0.74 -2.29

1.35 6.0 29410 822.9 -0.376 1.216 12.89 4.50 13.38 4.94 0.20 -1.07 0.82 -1.63

1.30 3.0 29439 762.3 -0.334 0.902 12.14 4.49 12.52 4.71 0.06 -0.52 0.90 -1.73

1.25 7.8 29480 704.5 -0.269 1.030 11.43 4.48 11.77 4.60 0.35 -0.42 -0.37 -1.83

1.20 4.0 29523 647.3 -0.221 0.998 10.74 4.47 11.01 4.46 0.55 -0.84 0.13 -1.86

1.15 1.0 29579 593.2 -0.160 0.940 10.08 4.46 10.32 4.36 0.74 -0.65 0.09 -0.84

1.10 10.4 29695 539.6 -0.108 0.934 9.44 4.44 9.69 4.20 1.03 -0.84 -1.23 -1.00

1.05 2.0 29837 488.5 -0.170 0.966 8.83 4.41 9.03 4.06 1.09 -0.81 0.21 0.45

1.00 7.0 29740 446.5 -0.276 1.104 8.37 4.64 8.61 4.09 1.49 -1.39 0.61 -0.05

0.95 3.0 29957 398.1 -0.075 1.014 7.82 4.52 8.04 4.65 1.23 -1.17 0.79 0.35

0.90 18.2 29937 357.3 -0.073 0.987 7.40 4.49 7.62 4.52 1.27 -1.30 0.67 -0.11

0.85 4.0 29922 318.9 -0.119 0.982 7.02 4.47 7.26 4.50 1.46 -0.91 0.98 0.09

0.80 15.2 29940 282.4 -0.045 0.961 6.67 4.45 6.89 4.54 2.22 -0.81 0.30 0.25
16

APPENDIX B

MACH NUMBER CALCULATION

The airplane freestream Mach number corrected for static pressure position error, MPC, is given 

by equation (B.1), where Mi is the indicated Mach number obtained from the airplane air data nose 

boom and ΔMPC is the Mach number static pressure position error.

Note that the airplane nose boom indicated Mach number is not the cockpit indicated Mach 

number. The cockpit indicated Mach number is obtained from the production air data system of the 

F-15B airplane and incorporates a production static pressure position error correction.

Airplane Air Data Nose Boom Indicated Mach Number

The radar-rawinsonde method of reference 6 is used to calculate the indicated Mach number. The 

static pressure is assumed to be a function of geometric altitude and is obtained from rawinsonde 

data gathered on the day of the flight test. The F-15B airplane indicated Mach number is calculated 

from the airplane air data nose boom total and static pressures and , respectively, using 

the appropriate relationships for subsonic and supersonic flow.

Subsonic flow, M < 1.0:

For subsonic flow, the Mach number is calculated from the isentropic relationship for the 

total‐to-static pressure ratio shown in equation (B.2), where γ is the ratio of specific heats (for air, 

γ = 1.4).

Equation (B.2) can be solved directly for the indicated Mach number as shown in equation (B.3).

Supersonic flow, M > 1.0:

For supersonic flow, a normal shock wave is assumed to be positioned ahead of the mouth of the 

air data boom. Therefore, the Rayleigh pitot tube formula for inviscid, adiabatic, supersonic flow 

is utilized as shown in equation (B.4):

!

MPC = Mi + "MPC (B.1)

(B.3)

!

pT

pi,nb

= 1+ " #1

2

Mind

2 $

%

& '

(

)

"

" #1 (B.2)

!

Mind = 2

" #1

pT

pi,nb

$

%

&

&

'

(

)

)

" #1

"

$

%

&

'

(

)

#1

$

%

&

&

&

&

'

(

)

)

)

)

*

+

,

,

,

,

-

.

/

/

/

/

0.5

pT pi,nb
17

!

Mind =

1.4285 " 0.357143x " 0.0625x

2 " 0.25x3 " 0.012617x4 " 0.00715x5 " 0.004358x6 " 0.0087725x9 ( )

x

#

$

%

%

&

'

(

(

0.5

!

x = 1.83937

pT pi,nb

In equation (B.4), is the total pressure downstream of the shock wave and is the static 

pressure upstream of the shock wave. The air data boom measures total and static pressures 

downstream of the shock wave. Experimental data indicates that if the static pressure measurement 

tap on the air data probe is placed at least ten probe diameters downstream of the probe nose, the 

static pressure measurement is a close approximation to the static pressure upstream of the shock 

wave (ref. 7). Therefore, the static pressure, , in equation (B.4) is equal to the air data probe static 

pressure, .

Since the Rayleigh pitot tube formula cannot be solved directly for Mach number, a polynomial 

curve fit to equation (B.4) is used to calculate Mach number as shown in equation (B.5).

where

!

pT

ps

=

1+ " #1

2

Mind

2 $

%

& '

(

)

"

" #1

2"

" +1

Mind

2 " #1

" +1

$

%

& '

(

)

1

" #1

(B.4)

(B.5)

(B.6)

pT ps

ps

pi,nb
18

Figure B.1 shows a comparison of the curve fit [equation (B.5)] with Rayleigh pitot tube formula 

[equation (B.4)].

1.00 1.25 1.50 1.75 2.00 2.25 2.50

Mach number

Total-to-static pressure ratio 5

6

7

8

9

4

3

2

1

050556

Rayleigh pitot tube formula

Curve fit

Mach Number Static Pressure Position Error

The F-15B airplane ΔMPC has been obtained through flight comparison of the air data nose boom 

Mach number with a true Mach number that is independent of position error. The true Mach number 

is calculated from global positioning system (GPS) flight data combined with weather balloon data. 

The difference between the true and indicated Mach number is defined as ΔMPC. F‐15B airplane 

flight tests have been performed to determine this correction as a function of indicated Mach 

number, as shown in table B.1.
19

Table B.1. The F-15B airplane Mach number static pressure position error.

F-15B Indicated 

Mach number,

Mi

Mach number 

static pressure 

position error, 

ΔMPC

0.000 0.0000

0.300 0.0045

0.400 0.0068

0.500 0.0091

0.600 0.0116

0.700 0.0146

0.800 0.0188

0.850 0.0217

0.900 0.0260

0.930 0.0296

0.950 0.0360

0.965 0.0500

1.015 0.0020

1.200 0.0028

1.400 0.0032

1.600 0.0032

2.000 0.0000

2.100 0.0000

Free-stream Conditions

The MPC is calculated using equation (B.1) as the sum of Mi, calculated from equation (B.2) or 

(B.3), and ΔMPC, from table B.1. After MPC has been calculated, a free-stream static pressure, is 

calculated from equation (B.2) or (B.3), assuming the has not changed, that is, that the total 

pressure position error is zero. Altitude and dynamic pressure are calculated from the free-stream 

static pressure.

pT

! !,
20

FIGURES

Figure 1. The NASA F-15B airplane with the Propulsion Flight Test Fixture local flow 

experiment, in flight.

EC04 0176‐06
21

Figure 2. The Propulsion Flight Test Fixture and cone-cylinder arrangement on the NASA 

F‐15B airplane.

0.5 1.0 1.5 2.0

Free-stream Mach number

Altitude limit

Mach

limit

Dynamic

pressure

limit

40,000 ft level acceleration

30,000 ft level acceleration

Altitude, ft

0

1

2

3

4

5

6

7 x 104

050460

PFTF design

 envelope

Figure 3. The NASA F-15B/PFTF flight envelope and flight test points.
22

0 100 200 300 400 500 600

Time, s

F-15B

Mach number 2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

050461

(a) Level acceleration and deceleration at an altitude of 40,000 feet.

(b) Level acceleration and deceleration at an altitude of 30,000 feet.

Figure 4. The NASA F-15B airplane free-stream Mach number time histories.

0 50 100 150 200 250 300 350 400

Time, s

F-15B

Mach number 2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

050462
23

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

F-15B free-stream Mach number

PFTF Mach number 1.8

1.7

1.6

1.5

1.2

1.3

1.4

1.1

0.9

1.0

0.8

050463

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

F-15B free-stream Mach number

PFTF Mach number 1.8

1.7

1.6

1.5

1.2

1.3

1.4

1.1

0.9

1.0

0.8

050464

(a) Level acceleration and deceleration at an altitude of 40,000 feet.

(b) Level acceleration and deceleration at an altitude of 30,000 feet.

Figure 5. The NASA F/15B/PFTF local Mach number as compared with free-stream 

Mach number.
24

(a) Level acceleration at an altitude of 40,000 feet.

(b) Level acceleration at an altitude of 30,000 feet. 

Figure 6. The difference between the NASA F-15B/PFTF local Mach number and the free-stream 

Mach number.

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

F-15B Mach number

PFTF Mach number – F-15B

Mach number

0.2

0.1

0

–0.2

–0.1

–0.3

–0.4

–0.5

050465

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

F-15B Mach number

PFTF Mach number – F-15B

Mach number

0.2

0.1

0

–0.2

–0.1

–0.3

–0.4

–0.5

050466
25

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

F-15B free-stream Mach number

PFTF local angle of attack

F-15B angle of attack

Angle of attack, deg

6

4

2

–2

0

–4

–6

–8

050467

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

F-15B free-stream Mach number

PFTF local angle of attack

F-15B angle of attack

Angle of attack, deg

6

4

2

–2

0

–4

–6

–8

050468

(a) Level acceleration at an altitude of 40,000 feet.

(b) Level acceleration at an altitude of 30,000 feet.

Figure 7. The local angle of attack as compared with the free-stream Mach number.
26

(a) Level acceleration.

(b) Level deceleration.

Figure 8. The local angle of sideslip as compared with the free-stream Mach number at an altitude 

of 40,000 ft.

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

F-15B free-stream Mach number

PFTF local angle of sideslip

F-15B angle of sideslip

Angle of sideslip, deg

4

3

2

1

–1

0

–2

–3

–4

050469

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

F-15B free-stream Mach number

PFTF local angle of sideslip

F-15B angle of sideslip

Angle of sideslip, deg

4

3

2

1

–1

0

–2

–3

–4

050470
27

(a) Level acceleration.

(b) Level deceleration.

Figure 9. The local angle of sideslip as compared with the free-stream Mach number at an altitude 

of 30,000 ft.

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

F-15B free-stream Mach number

PFTF local angle of sideslip

F-15B angle of sideslip

Angle of sideslip, deg

4

3

2

1

–1

0

–2

–3

–4

050471

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

F-15B free-stream Mach number

PFTF local angle of sideslip

F-15B angle of sideslip

Angle of sideslip, deg

4

3

2

1

–1

0

–2

–3

–4

050472
28

(a) Level acceleration at an altitude of 40,000 feet.

(b) Level acceleration at an altitude of 30,000 feet.

Figure 10. The NASA F-15B/PFTF local flow experiment specific excess power. 

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

Mach number, M

Specific excess power, P

S/PS, max0.8

0.9

1.0

0.7

0.6

0.5

0.3

0.4

0.2

0.1

0

050473

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

Mach number, M

0.8

0.9

1.0

0.7

0.6

0.5

0.3

0.4

0.2

0.1

0

050474

Specific excess power, P

S/PS, max
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

1. REPORT DATE (DD-MM-YYYY)

25-11-2005

2. REPORT TYPE 

Technical Memorandum

 4. TITLE AND SUBTITLE

Local Flow Conditions for Propulsion Experiments

on the NASA F-15B Propulsion Flight Test Fixture

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Michael Jacob Vachon, Timothy R. Moes, and Stephen Corda

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Dryden Flight Research Center

P.O. Box 273

Edwards, California 93523-0273

 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-001

 8. PERFORMING ORGANIZATION

 REPORT NUMBER

H-2625

10. SPONSORING/MONITOR'S ACRONYM(S)

NASA

13. SUPPLEMENTARY NOTES

An electronic version can be found at the NASA Dryden Flight Research Center Web site, under Technical Reports.

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified -- Unlimited

Subject Category -- 02, 05, 07 Availability: NASA CASI (310) 621-0390 Distribution: Standard

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email: help@sti.nasa.gov)

14. ABSTRACT

Local flow conditions were measured underneath the National Aeronautics and Space Administration F-15B airplane to support development of 

future experiments on the Propulsion Flight Test Fixture (PFTF). The local Mach number and flow angles were measured using a conventional air 

data boom on a cone-cylinder mounted under the PFTF and compared with the airplane air data nose boom measurements. At subsonic flight 

speeds, the airplane and PFTF Mach numbers were approximately equal. Transonic Mach number values were up to 0.1 greater at the PFTF than 

the airplane, which is a counterintuitive result. The PFTF local supersonic Mach numbers were as much as 0.46 less than the airplane values. The 

maximum local Mach number at the PFTF was approximately 1.6 at an airplane Mach number near 2.0. The PFTF local angle of attack was 

negative at all Mach numbers, ranging from -3 to -8 degrees. When the airplane angle of sideslip was zero, the PFTF local value was zero between 

Mach 0.8 and Mach 1.1, -2 degrees between Mach 1.1 and Mach 1.5, and increased from zero to 1 degree from Mach 1.5 to Mach 2.0. Airplane 

inlet shock waves crossed the aerodynamic interface plane between Mach 1.85 and Mach 1.90.

15. SUBJECT TERMS

Advanced propulsion systems, Air breathing engines, F-15 aircraft, Flight test fixture, Flight tests, Flow characteristics, Inlet flow, 

Inlet nozzles, Nozzle flow, Rocket-based combined-cycle engines, Testbed

18. NUMBER

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33

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(310) 621-0390

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5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

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5e. TASK NUMBER

5f. WORK UNIT NUMBER

24-723-01-000-AAA

11. SPONSORING/MONITORING

 REPORT NUMBER

NASA/TM-2005-213670

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