Roger A. Werner and John D. Wolter

Glenn Research Center, Cleveland, Ohio

Calibration for Thrust and Airfl ow Measurements in 

the CE-22 Advanced Nozzle Test Facility

NASA/TM—2010-216771

November 2010
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Roger A. Werner and John D. Wolter

Glenn Research Center, Cleveland, Ohio

Calibration for Thrust and Airfl ow Measurements in 

the CE-22 Advanced Nozzle Test Facility

NASA/TM—2010-216771

November 2010

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

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Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2010-216771 1 

Calibration for Thrust and Airflow Measurements in the 

CE-22 Advanced Nozzle Test Facility 

Roger A. Werner and John D. Wolter 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Summary 

CE-22 facility procedures and measurements for thrust and airflow calibration obtained with 

choked-flow ASME nozzles are presented. Six calibration nozzles are used at an inlet total 

pressure from 20 to 48 psia. Throat areas are from 9.9986 to 39.986 in.2

. Throat Reynolds 

number varies from 1.8 to 7.9 million. Nozzle gross thrust coefficient (CFG) uncertainty is 0.25 

to 0.75 percent, with smaller uncertainly generally for larger nozzles and higher inlet total 

pressure. Nozzle discharge coefficient (CDN) uncertainty is 0.15 percent or less for all the data. 

ASME nozzle calibrations need to be done before and after research model testing to achieve 

these uncertainties. In addition, facility capability in terms of nozzle pressure ratio (NPR) and 

nozzle airflow are determined. Nozzle pressure ratio of 50 or more is obtainable at 40 psia for 

throat areas between 20 and 30 in.2

. Also presented are results for two of the ASME nozzles 

vectored at 10, a dead-weight check of the vertical (perpendicular to the jet axis) force 

measurement, a calibration of load cell forces for the effects of facility tank deflection with tank 

pressure, and the calibration of the metric-break labyrinth seal. 

Nomenclature 

CDN Nozzle Discharge Coefficient 

CFG Nozzle Gross Thrust Coefficient 

ERB Engine Research Building 

ESP Electronically Scanned Pressure 

NPR Nozzle Pressure Ratio 

WP Primary Weight Flow (lbm/sec) 

Introduction 

Procedures used to calibrate the CE-22 Advanced Nozzle Test Facility for nozzle model 

thrust and airflow are presented along with calibration measurements. Multiple calibration steps 

are performed, each building upon the previous. For the final calibration, choked-flow ASME 

nozzles are used. The calibration data will provide a data base to which future calibrations in the 

facility can be compared. The ASME nozzle data is processed with the calibration coefficients 

and compared to the ASME nozzle reference values for determination of the measurement 

uncertainty. Nozzle pressure ratio (NPR) limits of the facility were also determined. The 

information presented in this report will provide guidance to facility users in the selection of 

model sizing, instrumentation, and test conditions. 
NASA/TM—2010-216771 2 

Figure 1.—CE-22 Advanced Nozzle Test Facility. 

Facility 

The CE-22 Advanced Nozzle Test Facility (Fig. 1) is one of the seven Flow Physics Labs in 

the Engine Research Building (ERB) at the NASA Glenn Research Center. The CE-22 facility 

provides economical testing of 1/4-scale models incorporating advanced nozzle concepts. 

Model throat Reynolds numbers can range between 1.8 and 7.9 million at inlet pressures of 20 

to 48 psia. The NPR range is from about 1.2 to 60. The facility can measure forces and 

moments in all three axes. The test chamber pressure can be controlled to simulate altitude 

conditions. The primary air can be heated to 370 F. Secondary air at 40, 125, or 450 psig is 

available and can be heated to 250 F. Unheated air temperature for primary and secondary 

flow is 65 to 85 F depending on ambient conditions. The facility also has an inlet vane device 

for primary air swirl and a color Schlieren system for quantitative nozzle exit airflow analysis. 

Detailed descriptions of the facility are given in References 1 to 3 and a description of the sixcomponent thrust stand and force interaction calibration is given in Reference 3. Appendix A 

lists all of the constants, averages, and calculations used for facility data reduction including the 

calibrations. 

A 49-in. long, 28-in. inside diameter cylindrical altitude exhaust collector is used for this 

calibration program. Inlet duct length from the thrust stand mount to the ASME nozzle inlet is 

24.75 in. The collector and inlet configurations remained the same throughout the program. 

Instrumentation in the primary flow stream as well as calculated variables based on this 

instrumentation are organized by station, illustrated in Figure 2, and named according to the 

convention shown in Figure 3. 
NASA/TM—2010-216771 3 

Primary airflow is measured using total-to-static differential pressure transducers between 

stations 2 and 5 three transducer ranges are used in the facility—1, 2, and 5 psid. Four 

transducers at a time are installed for each range; but of these, one 1-psid, one 2-psid, and 

three 5-psid transducers were not included in the data reduction because of a large 

disagreement with each other and with separate measurement of static and total pressure by 

the electronically scanned pressure (ESP) system. A description of the ESP system is given in 

Reference 4. 

Figure 3.—Measurement variable naming convention. 

TTS[NN] 

TT = Variable Type 

common examples: 

 “PT” – Total Pressure 

 “PS” – Static Pressure 

 “TT” – Total Temperature 

 “TS” – Static Temperature 

 “M” – Mach Number 

S = Station (see Fig. 2) 

NN = Number (when multiple 

measurements exist) 

Total Pressure 

Static Pressure 

Total Temperature

Station 1 Stations 2,5 Station 3 Station 6

Station 1 

Station 2 

Station 3 Station 5

Airflow 

Station 6 

Total 

Pressure 

Station 8

Throat 

Station 9

Exit 

Station 7 

Nozzle 

Inlet 

Station 4 

Figure 2.—Station designations in primary air stream. 
NASA/TM—2010-216771 4 

Maximum Nozzle Pressure Ratio 

The ASME flow calibrations were done in October and November of 2005. The NPR limits 

for each nozzle with inlet pressure are empirically determined and are shown on Figure 4 versus 

primary airflow. NPR as high as 60 is measured. The limits of the total-to-static differential 

pressure transducer ranges used at station 5 are also shown in Figure 4. 

Six-Component Thrust Stand 

Figure 5 depicts the thrust stand including force and moment sign convention. Reference 3 

gives a detailed description of the thrust stand and the in-stand calibration procedure. The thrust 

stand is a redundant system having a total of eight reaction load cells—two axial, two lateral, 

and four vertical. The redundancy is resolved by summing the two axial load cells together and 

combining the four vertical load cell together two different ways (front-back and right-left). The 

axial load cells can be summed because of an elastic hinge feature in the stand design. Two 

5x5 matrices are generated and are transformed into the interaction coefficients. The interaction 

coefficients and the reaction load cell measurement combinations are then used to calculate the 

test stand forces and moments. Load cell sizes are 4000 lbf for both axial cells, 2000 lbf for the 

forward lateral, 4000 lbf for the aft lateral, and 2000 lbf for the four vertical load cells. 

Reference 3 Errata 

Five typographic errors can be found on page 8 of Reference 3. In Table III, row two and 

column two, replace FZ with FX; and for paragraph four, lines five and six, replace (CX1 and 

CX2) and (CX3 and CX4) with (CZ1 and CZ2) and (CZ3 and CZ4).

Figure 4.—NASA CE-22 facility nozzle pressure ratio NPR versus primary airflow. 

Nov, 2005

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Wp, lbm/sec

 NPR Limits for ASME Nozzles

Primary Total 

Pressure 

48 psia

40 psia

30 psia

20 psia

10 psia

46 psia

42 psia

10

15.4

20 23.8

30

Nozzle throat 40

area, in2

1.0

2.0

5.0

Airflow DP25, psid
NASA/TM—2010-216771 5 

Figure 5.—Six component thrust stand. 

Load Cell Installation Procedures 

Load cells are calibrated in a calibration laboratory. Before installation in the thrust stand, 

the load cells are laid inside the CE-22 test cell and wired to the signal conditioners using the 

normal connections. The excitation voltage is applied and the load cells are allowed to “cook” for 

about 48 hr. Venting of the reaction load cells is then verified by closing the tank, electronically 

zeroing and spanning the loadcells (using the knobless conversion command of the data 

acquisition system, hereafter referred to as a “knobless calibration” of the load cells), and 

evacuating the chamber to vacuum exhaust conditions; vented load cells should not have any 

zero shifts with altitude exhaust pressure variation. Any preservative gel inside the load cells 

must be removed to prevent clogging the vent holes. The load cells are now mounted in the 

thrust stand. 

Interaction Coefficients 

Before each set of force or moment calibration loadings, a knobless calibration is performed. 

Coefficients from laboratory calibration are used with the knobless measurements to determine 

load cell slopes for converting output electrical signals into lbf units. The in-stand calibration is 

performed as outlined in Reference 3. In-stand calibration results are shown on nine figures in 

Appendix B. These results are very good with all of the reactions being linear and having no 

slope changes through the zero load point. The slope values are used to determine the 

interaction matrix coefficients. 
NASA/TM—2010-216771 6 

Dead Weight Check 

After the interaction matrix coefficients are set as constants in the data reduction program, 

the vertical downward (positive) force measurement is checked with dead weights. A fixture for 

hanging the weights is mounted on the airflow supply duct of the thrust stand. Weights are 

applied in steps of 50 lbm up to a total of 250 lb. The fixture has a slot allowing a 5-in forward-aft 

movement of the weight loading. Also, two duct pieces with a total length of 15 in. are installed 

between the stand and the fixture for additional axial locations for applying the weights loadings. 

The 9.625-in. distance to the centroid is obtained by putting weights directly on the aft portion of 

the thrust stand. Vertical force measurement results are shown in Figure 6. 

Vertical force measurements are within 1 lbf of the weights for lengths of 9.625, 35.125, and 

40.125 in. Measurement differences are greater than 1 lbf for weights of 100 lb and higher at 

50.125 and 55.125-in. lengths. The effect of this distance is illustrated by replotting the vertical 

force measurements against axial length (Fig. 7). Dial indicators were placed between the live 

and the ground frames of the thrust stand and no deflections were observed during loading of 

the weights. An inclinometer was also located on the calibration fixture, and the deflection angle 

measurements are given in Figure 8. Deflection angle increased with length and loading. A 

maximum of 0.065 for downward deflection of the fixture was measured. These two results 

indicate that the angular deflection with weight is caused by a deflection of the tank, which 

supports the entire thrust stand structure, rather than a deflection between the live and ground 

frames of the thrust stand. 

Correction for the dead weight check is not made in the data reduction program. For flow 

vectored at 10 at 40 in. from the thrust stand centroid, a correction of the force vector angle 

would be less than 0.1. The effects of the dead weight check on the other measured forces and 

moments are shown on five figures in Appendix C. 

Figure 6.—Vertical force FZ resulting from a dead weight check. Axial distance aft of the x-y centroid 

of the thrust stand is varied from 9.625 to 55.125 in. 

Dead Weight Check 

-4

-2

0

2

4

0 50 100 150 200 250

Weight, lb

FZ - Weight, lbf

 9.625 in

35.125

40.125

50.125

55.125
NASA/TM—2010-216771 7 

Figure 7.—Vertical force FZ resulting from a dead weight check versus distance to the thrust stand centroid. 

Figure 8.—Angular deflection measurement of the dead weight check fixture with vertical load. 

Dead Weight Cal

-4

-2

0

2

4

0 10 20 30 40 50 60

Distance to Trust Stand Centroid, LX, in

FZ - Weight, lbf

 0 lbf

 50

100

150

200

250

Dead Weight Cal

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 10 20 30 40 50 60

Distance to Thrust Stand Centroid, LX, in

Deflection Angle, deg

 50 lbf

100

150

200

250
NASA/TM—2010-216771 8 

Test Chamber Pressure Effects 

Reaction load cell loadings as caused by evacuating the test chamber to vacuum pressure 

conditions are shown in Figure 9 and the effects of pressure on combinations of load cells are 

shown in Figure 10. These figures show typical responses of the vented load cells in the CE-22 

facility. The loadings are caused by test chamber deflections. The load cell reactions are most 

significant in the vertical (z) direction. Consequently, the corrections for these forces, developed 

in the next paragraphs, will be greatest in the z direction. The thrust bed is “exercised” and a 

knobless load cell calibration is applied before decreasing the test cell pressure, P0. 

Figure 9.—Reaction load cell response to altitude exhaust pressure. 

Figure 10.—Response of combinations of reaction load cells to altitude exhaust pressure. 

21 Oct, 2005

-40

-30

-20

-10

0

10

0 2 4 6 8 10 12 14 16

Alitude Exhaust Pressure, P0, psia

Reaction Load Cells, lbf

RX1

RX2

RY1

RY2

RZ1

RZ2

RZ3

RZ4

21 Oct, 2005

-10

-5

0

5

10

0 2 4 6 8 10 12 14 16

Alitude Exhaust Pressure, P0, psia

Reaction Load Cell Combinations for 

Transformation, lbf

RX2-RX1

RY1

RY2

RZ3-RZ1

RZ2-RZ4

RZ2-RZ1

RZ3-RZ4
NASA/TM—2010-216771 9 

The forces and moments produced by P0 effects are given in Figures 11 and 12. The 

equations for the data reduction corrections of the exhaust pressure effects are shown in the 

figures. Slopes of the linear curve fits are used. P0KNOB is a recording of the P0 chamber 

pressure when a knobless calibration of the load cells is performed. These corrections (FXP0, 

FYP0, etc.) are subtractions in the calculations (Equations F051 to F054, Appendix A). There is 

no difference whether the calibration (and knobless) begins at sea level pressure and goes to 

altitude or starts at altitude exhaust pressure and goes to sea level. 

Figure 11.—Thrust stand force corrections for altitude exhaust effects. 

Figure 12.—Thrust stand moment corrections for altitude exhaust effects. 

21 Oct, 2005

y = -0.0595x + 1.3275

y = -0.2132x + 3.2355

y = -0.0871x + 1.6998

-3

-2

-1

0

1

2

3

0 2 4 6 8 10 12 14 16

Alitude Exhaust Pressure, P0, psia

Forces, lbf

FX

FY

FZ

FXP0 = (P0 - P0KNOB) * (-0.0595)

FYP0 = (P0 - P0KNOB) * (-0.2132)

FZP0 = (P0 - P0KNOB) * (-0.0871)

21 Oct, 2005

y = -8.8182x + 143.3

y = -1.0324x + 15.528

y = 2.3569x - 42.182

-50

0

50

100

150

0 2 4 6 8 10 12 14 16

Alitude Exhaust Pressure, P0, psia

Moments, in-lbf

MX

MY

MZ

MXP0 = (P0 - P0KNOB) * (-8.818)

MYP0 = (P0 - P0KNOB) * (-1.032)

MZP0 = (P0 - P0KNOB) * (2.357)
NASA/TM—2010-216771 10 

Labyrinth Seal Force Calibration 

The labyrinth seal force calibration, which is also called the AP calibration or the blank-off 

plate calibration, results in the FTARE term in the axial force summation (calculation F052 in 

Appendix A). This calibration is achieved by blanking off the primary airflow duct and 

maintaining constant pressure in the duct while increasing the altitude exhaust pressure from 

the vacuum tare condition. This calibration is another area-delta-pressure term in the force 

equation and is used to balance out the pressure-area forces with the load cell forces at static 

conditions. The calibration calculation is given by Equations F069 and F070 in Appendix A. The 

same fixture used for the dead weight check is used to blank off the duct. 

A knobless load cell calibration is recorded at vacuum conditions and then the duct is 

pressurized to a desired level (PT5). Altitude exhaust pressure is then increased with duct 

pressure held constant, and data is recorded at various PS3/P0 ratios. PS3 is the pressure 

inside the seal cavity upstream of the labyrinth seal. Since a small amount of airflow goes 

through the seal, PS3 will read slightly lower than pressures inside the primary airflow duct. 

After completing a PS3/P0 sweep, the conditions are returned to vacuum; a knobless calibration 

is recorded; and the procedure is repeated for another PT5 pressure level. With the blank-off 

plate installed, a zero pressure differential across the plate at vacuum tare is very hard to 

achieve for a knobless calibration. Therefore an additional term, FXKNOB, is included in the 

calculations to cancel out the small axial force loading from the pressure differential during the 

knobless calibration. Calibration results for the seal are shown in Figure 13 in the form of 

measured effective labyrinth seal area (ALS3M) as a function of the pressure ratio PS3/P0. 

Figure 13.—Labyrinth seal calibration. 

Oct 2005

-1.530

 2.308E-03x3 - 6.927E-02x2 + 6.841E-01x - 3.777

2.766E-02x3 - 2.703E-01x2 + 7.768E-01x - 2.388

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0 5 10 15 20 25

PS3 / P0

ALS3M, in2

40 psia PT5

30 psia 

20 psia 

30 psia (repeat)

14.5 psia 

If PT5 < 21 psia: ALS3 = ALS3[30-40 psia] + 0.0493*PT5 - 1.0345
NASA/TM—2010-216771 11 

Figure 13 shows that the 30 and 40-psia PT5 data as well as a repeat 30-psia calibration all 

fall on the same curve. This curve is divided into three segments for the curve fits, and the 

resulting equations are shown on the figure. This same curve but with an intercept adjustments 

is used for the 20 and 14.5 psia data. A second curve fit is done for the intercepts (plot not 

included) and the resulting equation for duct pressures below 21 psia is also included in 

Figure 13. 

Choked-Flow ASME Nozzle Calibration 

The CE-22 facility airflow and inlet momentum are measured at station 5, and the respective 

calibration coefficients are determined using choked-flow ASME nozzles for the airflow and 

thrust calibration values. The ASME equations are based on Reference 5 and are given in 

Appendix A, calculations F071 to F077. The CV velocity coefficient calculation is modified to use 

an industry recommendation of 0.109 instead of 0.107 for a constant in the equation. 

ASME Nozzle Description 

The calibration nozzles are ASME long-radius flow nozzles as shown in Reference 6, 

page 217. The smallest of the nozzles (9.9986 in.2

) is a low β nozzle having a throat-to-inlet 

diameter ratio of 0.408. The other five nozzles are high β nozzles with β ranging from 0.506 to 

0.815. A schematic of the 19.990-in.2

 nozzle is given in Figure 14; this figure also shows a 

modification at the nozzle outlet. The nozzle exit contour goes radial outward and then forward 

(upstream) in 1/8-in. steps and then angles forward at 45. The modification is an industry 

recommendation that improves thrust calibration. 

Figure 14.—Cross section of 19.990-in.2 ASME nozzle. 

 

0

1

2

3

4

5

6

7

-1 0 1 2 3 4 5 6 7 8

X, in

Y (RADIUS), in

20 ASME

Nozzle center line

Ref (X = 0.000)

I.D. = 5.045 in 
NASA/TM—2010-216771 12 

ASME Nozzle Calibration Procedure 

On each day prior to a run, the thrust stand load cells are exercised in all three axes with 

force loadings from the in-stand calibration system. The test chamber is taken to minimum 

exhaust pressure for the vacuum tare; a knobless calibration is taken and a data point is 

recorded. The inlet pressure is set to a desired level after which the exhaust pressure is 

increased until the first NPR value is obtained. The first NPR will be the highest of an NPR 

sequence. NPR is reduced by increasing the exhaust pressure until the sequence is completed. 

Standard deviations of online averages of test conditions and force measurements are 

monitored until an acceptable low deviation is observed and then a data point is recorded. Upon 

completion of an NPR sequence, the facility is returned to the vacuum tare condition and a data 

point is recorded; the force and airflow values (load cells and transducers) are reviewed for zero 

shifts. This procedure, beginning with a knobless calibration at vacuum, is repeated for 

subsequent NPR sequences at other total pressure levels. This same procedure is used during 

research model testing. 

Hysteresis error is eliminated by always reducing NPR—if a point is missed the sequence is 

continued without reversing direction. The ASME force and airflow values will calibrate out the 

nonlinearity of the load cells and pressure transducers. If a load cell is replaced during a test 

program, then a complete calibration including the force interaction coefficients, lab seal, and 

ASME has to be redone. A pressure transducer replacement would only require a repeat of the 

ASME nozzle calibration or a reprocessing of the original data with a new DP25 average. 

ASME Calibration Results 

Figures 15 to 17 give the results of the momentum station CF5 calibrations for 1.0-, 2.0-, 

and 5.0-psid DP25 differential pressure transducers. Data taken at 3, 4.5, and 6 NPR is 

averaged together to reduce data scatter. These points for averaging are purely arbitrary and 

other averages better suited for the research tests could be used—perhaps 3 or more points at 

2.0 NPR, etc. The DP25 transducer data was reviewed during data processing for inconsistent 

trends, etc. For this report, one each of the 1.0- and 2.0-psid transducers were removed from 

the calculations and three of the four 5.0-psid transducers were not used. This is an important 

step to reduce CF5 fluctuations in the plots and improve the calibration. The CF5 data is plotted 

against the ideal Mach number at station 5, M5ID. M5ID is primarily a function of nozzle throat 

area. 

Figures 18 to 20 show NPR corrections that are applied to the CF5 averages. A limited 

amount of data was taken for NPR above 7.5; therefore, the repeat set of nozzle data taken with 

2.0-psid DP25 transducers was included to better define the 2.0-psid NPR corrections. ASME 

nozzle calibrations should duplicate all the NPR values of the research test plan to correctly 

calibrate the facility. These corrections will vary depending on what averages are used for the 

for the CF5 plots. If the research model has screens at the model inlet, then PT5/P0 should be 

used instead of NPR. 

Figures 21 to 23 present the CD5 airflow calibrations for the three transducer ranges. CD5 

does not vary with NPR and averages for CD5 and M5ID using all the choked-flow NPR data 

can be used. 

 
NASA/TM—2010-216771 13 

Figure 15.—Station 5 force coefficient CF5 calibrations, 1-psid DP25 transducers. 

Figure 16.—Station 5 force coefficient CF5 calibrations, 2-psid DP25 transducers. 

1 psid DP25, Oct-Nov 2005 

0.99

1.00

1.01

1.02

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

M5ID

CF5C

48 psia

40 psia

30 psia

20 psia

AVERAGE, 3-6 NPR

 2 psid DP25, Oct-Nov 2005

0.99

1.00

1.01

1.02

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

M5ID

CF5C

48 psia

40 psia

30 psia

20 psia

AVERAGE, 3-6 NPR
NASA/TM—2010-216771 14 

Figure 17.—Station 5 force coefficient CF5 calibrations, 5-psid DP25 transducers. 

Figure 18.—CF5 correction for NPR effects, 1-psid DP25 transducers. 

 5 psid DP25, Oct-Nov 2005

0.99

1.00

1.01

1.02

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

M5ID

CF5C

48 psia

46 psia

40 psia

30 psia

20 psia

AVERAGE, 3-6 NPR

1 psid DP25, 2005

y = 0.00067x + 0.9970

y = 1.00165

y = -0.000033x + 0.9989

y = -0.000033x + 1.0010

y = -0.000033x + 1.00005

y = 1.00115

y = -0.000033x + 1.0011

0.997

0.998

0.999

1.000

1.001

1.002

1.003

1.004

0 10 20 30 40 50 60

NPR

CF5C / CF5C(avg, 3-6 NPR)

9.9986 in2

15.392

19.990

23.758

40 psia - BLUE

30 psia - RED

20 psia - GREEN
NASA/TM—2010-216771 15 

Figure 19.—CF5 correction for NPR effects, 2-psid DP25 transducers. 

Figure 20.—CF5 correction for NPR effects, 5-psid DP25 transducers. 

2 psid DP25, 2005

y = 0.00067x + 0.9970

y = 1.0016

y = 1.0007

y = -0.000039x + 1.0007

y = -0.000039x + 1.0014

0.997

0.998

0.999

1.000

1.001

1.002

1.003

1.004

0 10 20 30 40 50 60

NPR

CF5C / CF5C(avg, 3-6 NPR)

9.9986 in2

15.392

19.990

23.758

30.009

40 psia - BLUE

30 psia - RED

20 psia - GREEN

SOLID - REPEAT 

5 psid DP25, 2005

y = 1.0004

y = -0.000025x + 0.9996

y = 0.00067x + 0.9970

y = 1.00195

y = -0.000025x + 1.0001

y = 1.0026

0.997

0.998

0.999

1.000

1.001

1.002

1.003

1.004

0 10 20 30 40 50 60

NPR

CF5C / CF5C(avg, 3-6 NPR)

19.990 in2

23.758

30.009

39.986

40 psia - BLUE

30 psia - RED

20 psia - GREEN
NASA/TM—2010-216771 16 

Figure 21.—Station 5 airflow coefficient CD5 calibrations, 1-psid DP25 transducers. 

Figure 22.—Station 5 airflow coefficient CD5 calibrations, 2-psid DP25 transducers. 

 1 psid DP25, Oct-Nov 2005

0.99

1.00

1.01

1.02

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

M5ID

CD5C

48 psia

40 psia

30 psia

20 psia

 2 psid DP25, Oct-Nov 2005

0.99

1.00

1.01

1.02

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

M5ID

CD5C

48 psia

40 psia

30 psia

20 psia
NASA/TM—2010-216771 17 

Figure 23.—Station 5 airflow coefficient CD5 calibrations, 5-psid DP25 transducers. 

Thrust and Airflow Uncertainty 

Thrust and airflow as represented by nozzle gross thrust coefficient CFGmeas and nozzle flow 

coefficient CDNmeas (calculations F057.1 and F038, Appendix A) are calculated for the ASME 

nozzles using facility measurements and the CF5 and CD5 calibrations. The percent difference 

to ASME predictions of CFGasme and CDNasme (CFGP, calculation F077, and CDP, calculation 

F071, Appendix A) is plotted versus NPR and presented in Appendix D. The percent difference 

in the nozzle performance coefficients for all throat areas and DP25 transducers is less than 

0.25 for most of the force measurements and less than 0.13 percent for all of the airflow 

measurements. 

At the end of the calibration program, repeat data was taken with 2.0-psid transducers and 

nozzle throat areas of 15.392-, 19.990-, and 23.758-in.2

—the most used transducer range and 

nozzle areas for the facility. The thrust and flow coefficients are processed as above using only 

the first set of 2.0-psid calibrations. Results are presented in Figures 24 and 25 that show a 

percent difference comparison as high as 1.1 percent for thrust and 0.23 percent for airflow. 

The second set of data (post cal) was processed for CF5 and CD5 calibration values and 

these are shown in Figures 26 and 27 along with the original calibration (pre cal). The lines in 

these figures are for the average of the two calibrations. All the 2-psid data for the three nozzles 

was processed again using the average calibration coefficients, and results versus NPR are 

given in Figures 28 and 29. 

5 psid DP25, Oct-Nov 2005

0.99

1.00

1.01

1.02

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

M5ID

CD5C

48 psia

46 psia

40 psia

30 psia

20 psia
NASA/TM—2010-216771 18 

Figure 24.—ASME nozzle gross thrust coefficient CFG uncertainty of repeat data using pre-run CF5 calibrations. 

Figure 25.—ASME nozzle gross flow coefficient CDN uncertainty of repeat data using pre-run CD5 calibrations. 

Repeat Data, 2 psid DP25

-0.75%

-0.50%

-0.25%

0.00%

0.25%

0.50%

0.75%

1.00%

1.25%

0 10 20 30 40 50 60

NPR

(CFG meas - CFG asme)/CFG asme, %

15.392 in2

19.990 in2

23.758 in2

40 psia - BLUE

30 psia - RED

20 psia - GREEN

Repeat Data, 2 psid DP25

-1.00%

-0.75%

-0.50%

-0.25%

0.00%

0.25%

0.50%

0.75%

1.00%

0 10 20 30 40 50 60

NPR

(CDN meas - CDN asme)/CDN asme, %

15.392 in2

19.990 in2

23.758 in2

40 psia - BLUE

30 psia - RED

20 psia - GREEN
NASA/TM—2010-216771 19 

Figure 26.—Average of station 5 force coefficient CF5 pre and post calibrations, 2-psid DP25 transducers. 

Figure 27.—Average of station 5 flow coefficient CD5 pre and post calibrations, 2-psid DP25 transducers. 

 2 psid DP25, Oct-Nov 2005

0.99

1.00

1.01

0.15 0.20 0.25

M5ID

CF5C

48 psia

40 psia

30 psia

20 psia

OPEN - PRE CAL

SOLID - POST CAL

LINE - AVG

AEVERAGE, 2-6 NPR

2 psid DP25, Oct-Nov 2005

0.99

1.00

1.01

0.15 0.20 0.25

M5ID

CD5C

48 psia

40 psia

30 psia

20 psia

OPEN - PRE CAL

SOLID - POST CAL

LINE - AVG
NASA/TM—2010-216771 20 

Figure 28.—ASME nozzle gross thrust coefficient CFG uncertainty of all data using average of pre 

and post CF5 calibrations, 2-psid DP25 transducers. 

Figure 29.—ASME nozzle flow coefficient CDN uncertainty of all data using average of pre and post 

CD5 calibrations, 2-psid DP25 transducers. 

Average Calibration Data, 2 psid DP25

-1.00%

-0.75%

-0.50%

-0.25%

0.00%

0.25%

0.50%

0.75%

1.00%

0 10 20 30 40 50 60

NPR

(CFG meas - CFG asme)/CFG asme, %

15.392 in2

19.990 in2

23.758 in2

40 psia - BLUE

30 psia - RED

20 psia - GREEN

SOLID - REPEAT

Average Calibration Data, 2 psid DP25

-1.00%

-0.75%

-0.50%

-0.25%

0.00%

0.25%

0.50%

0.75%

1.00%

0 10 20 30 40 50 60

NPR

(CDN meas - CDN asme)/CDN asme, %

15.392 in2

19.990 in2

23.758 in2

40 psia - BLUE

30 psia - RED

20 psia - GREEN

SOLID - REPEAT
NASA/TM—2010-216771 21 

Figure 30.—ASME nozzle gross thrust CFG uncertainty using the average CF5 calibrations for each 

ASME nozzle area, 2-psid DP25 transducers. 

Figure 28 gives 0.75-percent agreement with ASME predictions for thrust and Figure 29 

have 0.13-percent agreement for airflow. The thrust data from Figure 28 are shown versus 

nozzle throat area in Figure 30. Here, there is 0.25-percent agreement for all pressures at 

23.758 in.2

, 0.50-percent agreement at 19.990 in.2 and 0.75-percent agreement at 15.392 in.2. 

Except for two points, the 40 psia data is in agreement with the ASME values for all areas and 

the 20 psia data is also within 0.25-percent agreement at 19.990 in.2

. Total time duration of two 

weeks was between the two sets of 2-psid DP25 data. Between these tests the 5.0-psid 

calibrations were done, and then the 2.0-psid transducers were reinstalled. 

Research Model Testing 

For best results, a research model should have the same throat area has one of the ASME 

nozzles. Also, an ASME nozzle calibration needs to be done upon completion of a research 

program and averaged with the pre-run calibration for final data processing. Six weeks of 

research testing would be about an ideal time period. Research programs lasting much longer 

than 2 months should consider having an ASME nozzle calibration near the middle of testing. 

Future programs will determine the time between calibrations and if only the calibration 

coefficient values are required or if the NPR effects also need to be recalibrated. 

Research nozzles with area expansion will produce thrust somewhere between the ASME 

force and the nozzle exit ideal force (calculation F039, Appendix A). Figure 31 shows the forces 

for the maximum NPR points at 30 and 40 psia. As the nozzle throat area is increased, the 

thrust stand FX force decreases while the ASME force increases. Also shown is the maximum 

nozzle force at each nozzle area for ideal expansion. The station 5 ideal momentum force F5ID 

increases slightly with the increase in airflow. Figure 32 gives the percent increase expected for 

the load cell measurements with the ideal expansion. At a nozzle area of 40 in.2

, the axial load 

cell measurement force increases up to 30 percent of its ASME value. Axial load cell 

nonlinearity may affect the nozzle thrust measurement uncertainty since the area expansion 

2 psid DP25, 2-max NPR

-1.00%

-0.75%

-0.50%

-0.25%

0.00%

0.25%

0.50%

0.75%

1.00%

15 20 25

Throat Area, in2

(CFG meas - CFG asme)/CFG asme, %

40 psia

30 psia

20 psia

40 psia, repeat

30 psia, repeat

20 psia, repeat
NASA/TM—2010-216771 22 

Figure 31.—Comparison of forces at maximum NPR, 30 and 40 psia. 

Figure 32.—Axial thrust stand force (FX) increase with ideal area expansion 

ratio, percent of ASME axial load cell force, 30 and 40 psia. 

force measurements are above those for the ASME nozzle calibration. This effect may be small 

as the axial force increase is only 4.6 percent of full scale load cell range at 40 psia and 

3.3 percent at 30 psia. Two 4000-lbf load cells are used. A maximum force of 2693 lbf was 

measured for the summation of axial load cells at 10 in.2

 and 49 psia; therefore, using 2000-lbf 

load cells might be considered for use in the future. Area sizing of a research model has to 

consider the higher ASME nozzle calibration force with larger throat area against the lower load 

cell force measurements and increases of area expansion effects. 

 

MAX NPR

0

500

1000

1500

2000

2500

3000

3500

5 10 15 20 25 30 35 40 45

Nozzle Throat Area, A8, in2

Forces, lbf

40 psia, FX

40 psia, F5ID

40 psia, FASME

40 psia, F9ID

30 psia, FX

30 psia, F5ID

30 psia, FASME

30 psia, F9ID

MAX NPR

0%

5%

10%

15%

20%

25%

30%

35%

5 10 15 20 25 30 35 40 45

Nozzle Throat Area, A8, in2

FX increase / FXASME, %

40 psia

30 psia
NASA/TM—2010-216771 23 

Thrust and Airflow Measurements at 1.5 NPR 

Measurements were taken at 1.5 NPR with 20 psia for various ASME nozzles, and the 

results are presented in Table I using the CDN and CFG coefficients. Comparisons are shown 

with the choked-flow ASME predictions and with Fluidyne predictions from the aero propulsion 

industry. Measured CDN at 1.5 NPR is up to 0.5 percent less than the Fluidyne predictions for 

1-psid data with nozzle areas of 19.990 in.2

 and larger and for all the data using larger 

transducers. Measured CFG at 1.5 NPR compares quite well with Fluidyne values having a 

0.25-percent agreement except for 1-psid data at 9.9986 in.2

 and 2-psid data at 15.392 in.2 and 

19.990 in.2

; the respective differences are 0.6, 0.8, and 0.3 percent. 

TABLE I.—CDN AND CFG AT 2.0 AND 1.5 NPR 

DP25 A8 PT NPR CDN CDN CDN CFG CFG CFG 

 Meas. ASME ASME Meas. ASME ASME 

 choked Fluidyne choked Fluidyne 

 cal. pred. cal. pred. 

psid in2 psia 

1 9.9986 20.07 2.07 0.991 0.990 0.992 0.990 0.994 0.996 

1 9.9986 20.06 1.58 0.991 --- 0.992 0.989 --- 0.995 

1 15.392 20.09 2.05 0.990 0.990 0.992 0.994 0.994 0.996 

1 15.392 20.05 1.51 0.990 --- 0.992 0.993 --- 0.995 

1 19.990 20.07 2.06 0.991 0.990 0.992 0.995 0.994 0.996 

1 19.990 20.03 1.58 0.988 --- 0.992 0.994 --- 0.995 

1 23.758 19.94 2.08 0.991 0.991 0.992 0.996 0.994 0.996 

1 23.758 20.08 1.56 0.988 --- 0.992 0.996 --- 0.995 

2 15.392 20.02 2.08 0.989 0.990 0.992 0.995 0.994 0.996 

2 15.392 20.02 1.48 0.988 --- 0.992 0.986 --- 0.994 

2 19.990 19.98 2.06 0.989 0.990 0.992 0.994 0.994 0.996 

2 19.990 20.01 1.60 0.987 --- 0.992 0.998 --- 0.995 

2 23.758 20.09 2.09 0.989 0.991 0.992 0.995 0.994 0.996 

2 23.758 20.06 1.56 0.986 --- 0.992 0.993 --- 0.995 

5 23.758 20.09 2.07 0.992 0.991 0.992 0.994 0.994 0.996 

5 23.758 20.00 1.58 0.989 --- 0.992 0.993 --- 0.995 

ASME Nozzle Vectoring 

The 15.392-in.2 and the 19.990-in.2 throat area ASME nozzles were mounted to the facility 

supply duct with choke plates at the nozzle inlet and wedges for 10 of turning. These were 

used to check the vectoring measurement system in four directions (left and right yaw, up and 

down pitch). Pressures of 40, 30, and 20 psia were set in the nozzle; this required station 6 

pressures to be approximately 12 percent higher for the 15.392-in.2

 nozzle and 20 percent 

higher for the 19.990-in.2

 to obtain the same nozzle pressure ratio. Nozzle total pressure was 

determined from the throat static-pressure taps. The 15.392-in.2

 nozzle used the 1.0-psid DP25 

transducers and calibration coefficients while the 19.990-in.2

 nozzle used the 2.0-psid 

transducers and calibration coefficient averages. Measured axial force included linear 

interpolations of M5ID and PT5 (instead of PT) for CF5; NPR corrections for CF5 were 

approximated using PT5/P0 instead of NPR. 
NASA/TM—2010-216771 24 

Vectoring results are shown in Figures 33 and 34. The negative angles (yaw right and pitch 

up) are plotted as positive angles for better comparisons. The data comparisons are slightly 

larger for the smaller nozzle; there is a 0.4-degree spread between the two sets of pitch-up 

runs. Both figures show non-symmetry for vectoring and a facility bias might be present. The 

data should be corrected for a zero-angle offset to have symmetry for positive and negative 

vector angles. 

Figure 33.—10 vectoring with the 15.392-in.2 throat ASME nozzle, 1-psid DP25 transducers. 

Figure 34.—10 vectoring with the 19.990-in.2 throat ASME nozzle, 2-psid DP25 transducers. 

15.392 in2 (choke plate), 1 psid

0

2

4

6

8

10

12

0 5 10 15 20 25 30 35

Nozzle Pressure Ratio, NPR

Force Vector Angle, deg

40 psia, Yaw Flow Left 

30 psia, Yaw Flow Left

20 psia, Yaw Flow Left

30 psia, Yaw Flow Right

30 psia, Pitch Flow Up

30 psia, Pitch Flow Up (repeat)

19.990 in2 (choke plate), 2 psid

0

2

4

6

8

10

12

0 5 10 15 20 25 30 35

Nozzle Pressure Ratio, NPR

Force Vector Angle, deg

40 psia, Yaw Flow Left 

30 psia, Yaw Flow Left

20 psia, Yaw Flow Left

30 psia, Yaw Flow Right

30 psia, Pitch Flow Up

30 psia, Pitch Flow Down
NASA/TM—2010-216771 25 

Nozzle Inlet Total-Pressure Profiles 

Total pressure profiles are included to show the quality of the nozzle inlet conditions. 

Figure 35 shows the variation of the station 6 pressure profiles for all the ASME nozzles. As flow 

at station 6 increases with the increase of throat area, the pressure profile exhibits more 

distortion. The low pressure at the center is caused by the wake of an upstream temperature 

measurement rake. The temperature rake crosses the pressure rake at 90 and is also 

upstream of the flow straightening screen; the total-pressure rake is downstream of the screens. 

Figure 36 gives inlet pressure profiles when the temperature measurement rake is out. The 

pressure is higher in the center when compared to the profile of the previous figure. The three 

pressure levels have identical profiles. 

Figure 35.—Inlet total-pressure profiles for all the ASME nozzle throat areas, 30 psia, inlet 

temperature rake installed. 

30 psia, choked nozzle

-100

-50

0

50

100

0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.02

P(i) / PT6

% Area

9.9986 in2

15.392

19.990

23.758

30.009

39.983
NASA/TM—2010-216771 26 

Figure 36.—Inlet total-pressure profiles for three inlet pressures at an ASME nozzle throat area of 

30.009-in.2

, no inlet temperature rake. 

References 

1. Beltran, Luis; Del Roso, Richard L.; and Del Rosario, Ruben: Advanced Nozzle and 

Engine Components Test Facility. NASA TM 103684, 1992. 

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19920007841_1992007841.pdf 

2. Kerl, Joyel M.; Severt, Gwynn A.; and Loos, Kurt: Advanced Nozzle Test Facility at 

NASA Glenn Research Center. AIAA–2002–3245, June 2002. 

Available from http://www.aiaa.org/content.cfm?pageid=2 

3. Wong, Kin C.: Derivation of the Data Reduction Equations for the Calibration of the SixComponent Thrust Stand in the CE-22 Advanced Nozzle Test Facility. NASA/TM—2003-

212326, 2003. 

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20030054464_2003060401.pdf 

4. Panek, Joseph W.: Verifying Data Integrity of Electronically Scanned Pressure Systems 

at the NASA Glenn Research Center. NASA/TM—2001-211155, 2001. 

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20020013986_2002000087.pdf 

5. Siegfried, R.G.; and Kuchar, A.P.: A Standard for Exhaust Nozzle Tests. General 

Electric ESAD Technical Brief 71006, April 6, 1971. 

6. Application, Part II of Fluid Meters, 6th Edition 1971: Interim Supplement 19.5 on 

Instruments and Apparatus. ASME, New York, 1972. 

T-rake out, 30-in2, Oct 91

-100

-50

0

50

100

0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.02

P(i) / PT6

% AREA

40 psia

30

20
NASA/TM—2010-216771 27 

Appendix A.—Abridged and Revised Facility Calculations 

Constants: 

CONF = input Configuration number 

NOZZ = input Nozzle designation (in CONF) 

A8 = input Throat area of ASME nozzle, in2 (in CONF) 

A9_A8 = input Nozzle area expansion ratio (in CONF) 

A5 = 56.745 Station 5 flow area, in2 

ALS1 = 14.137 Labyrinth seal face area, in2 

ANGE = input Nozzle mounting angle (vector calibration), deg 

FXKNOB = input ADP cal FX Offset (=FXKNOBM at vac tare), lbf 

P0KNOB = input Value of P0 at time of the most recent KNOB, psia 

SFXP0 = input Slope for P0 effect on FX, in2 

SFYP0 = input Slope for P0 effect on FY, in2 

SFZP0 = input Slope for P0 effect on FZ, in2 

SMXP0 = input Slope for P0 effect on MX, in3 

SMYP0 = input Slope for P0 effect on MY, in3 

SMZP0 = input Slope for P0 effect on MZ, in3 

BETAZ = input Yaw angle zero correction from vectored ASME, deg 

ALPHAZ = input Pitch angle zero correction from vectored ASME, deg 

Sij = 25 inputs, (i=1-5, j=1-5) load cell interaction coefficients from in-stand 

 calibration, set equal to SDUM (i, j) in calculations 

Uij = 25 inputs, (i=1-5, j=1-5) load cell interaction coefficients from in-stand 

 calibration, set equal to UDUM (i, j) in calculations

PI = 3.141592654 

RG = 53.352 ft-lbf / lbm-R 

GAM = 1.4 specific heat ratio 

GC = 32.174 lbm-ft / sec2-lbf 

PSTS = 14.696 / sqrt (518.67) lbf/in2 / sqrt R 

Averages: 

DP25 (PS2-PS5) delta-pressure transducers, psid 

P0 Altitude-exhaust pressures, psia 

PS1 Inlet duct static pressures, psia 

PS2 Inlet duct static pressures, psia 

PS3 Labyrinth seal inlet static pressures, psia 

PS5 Airflow station static pressures, psia 

PT5 Airflow station total pressure (average PS1, PS2), psia 

PS6 Model inlet static pressures, psia 

PT6 Model inlet area weighted total pressure (includes PS6), psia 

PS8 Model throat static pressures, psia 

PASME ASME nozzle throat static pressures (PS8), psia 

TT6 Model inlet total temperatures, R 

 
NASA/TM—2010-216771 28 

Equations: 

C 

C A. FACILITY CALCULATIONS

C 

C F006 NPR 

C 

 PT = PT6 

C IF ASME CHOKED-FLOW PLATE USED (VECTORED NOZZLES): 

 IF (ANGE.GT.0.) THEN 

 PT = 1.8929 * PASME 

 ENDIF 

 NPR = PT/P0 

C 

C F016 Gamma constants (sta. 5) 

C 

 GP1 = GAM + 1 

 GM1 = GAM - 1 

 G1 = GM1 / GAM 

 G2 = 2 / GP1 

 G3 = 2 / GM1 

 G4 = GP1 / (2 * GM1) 

 G5 = SQRT (GC * GAM / RG) 

 G6 = SQRT (2 * RG * GC / G1) 

 G7 = 2 / (RG * GC * G1) 

 G8 = - 2 / GAM 

C 

C F017 Ideal Mach number at sta. 5 

C 

 PR5F= (PT5 / (PT5 - DP25))**G1 

 M5ID = SQRT (G3 * (PR5F - 1)) 

C 

C F019 Sta. 5 flow coefficient (ASME nozzle choked-flow calibration) 

C 

 CD5 = curve fits from ASME calibration, fcn (M5ID) 

C 

C F020 Mass flow at sta. 5 (primary), lbm/sec 

C 

 W5ID = G5 * A5 * PT5 * M5ID / (SQRT (TT6) * PR5F**G4) 

 WP = CD5 * W5ID 

C 

C F021 Ideal momentum at sta. 5 (metric break), lbf 

C 

 MOM5ID = GAM * (PT5 - DP25) * A5 * M5ID**2 

C 

C F022 Mach number at sta. 5 

C 

 M5 = CD5 * M5ID 

C 

C F023 Corrected mass flow, lbm/sec 
NASA/TM—2010-216771 29 

C 

 WPCOR = PSTS * WP * SQRT (TT6) / PT 

C 

C F027 Differential pressures at lab seal and sta.5, psid 

C 

 DP30 = PS3 - P0 

 DP50 = (PT5 - DP25) - P0 

C 

C F028 Force on lab seal, lbf 

C 

 FLS = ALS1 * DP30 

C 

C F029 Ideal inlet force at sta. 5, lbf 

C 

 F5ID = MOM5ID + A5 * DP50 

C 

C F030 Sta. 5 force coefficient (ASME nozzle choked-flow calibration) 

C 

 CF5 = curve fits from ASME calibration, fcn (M5ID, PT, NPR, etc.)

C 

C F031 Inlet force at sta. 5, lbf 

C 

 F5 = CF5 * F5ID 

C 

C F032 Effective lab seal area from blank-off plate calibration, in2 

C 

 PS3QP0 = PS3 / P0 

 ALS3 = curve fits from AΔP calibration, fcn (PS3QP0, PT5) 

C 

C F033 Pressure tare force, lbf 

C 

 FTARE = ALS3 * DP30 

C 

C F034 NPR for 1D choked flow 

C 

 NPRC = (1 / G2)**(1/G1) 

C 

C F035 Unchoked sta. 8 ideal flow (throat), lbm/sec 

C 

 D8C = SQRT (4 * A8 / PI) !! can use hydraulic mean diameter 

C !! (D8C = 4 * A8 / wetted perimeter) 

 IF ((PT/PS8) .LE. NPRC) THEN 

 M8 = SQRT (G3 * ((PT/PS8)**G1 - 1)) 

 TS8 = TT6 / (PT/PS8)**G1 

 MU8 = 7.3025E-7 * TS8**1.5 / (TS8 + 198.72) 

 RN8 = 48 * WP / (PI * D8C * MU8) 

 W8ID = G5 * PS8 * A8 / SQRT (TS8) * M8 

 ENDIF 

C 
NASA/TM—2010-216771 30 

C F036 Choked sta. 8 ideal flow (throat), lbm/sec 

C 

 IF (NPR .GT. NPRC) THEN 

 M8 = 1 

 TS8 = TT6 * G2 

 MU8 = 7.3025E-7 * TS8**1.5 / (TS8 + 198.72) 

 RN8 = 48 * WP / (PI * D8C * MU8) 

 W8ID = G5 * PT * G2**(1/G1) * A8 / SQRT (TS8) 

 ENDIF 

C 

C F037 Ideal velocity at sta. 9 (perfect expansion), ft/sec 

C 

 VEL9 = G6 * SQRT (TT6 * 1 - (1/NPR)**G1)) 

C 

C F038 Nozzle discharge coefficient 

C 

 CDN = WP / W8ID 

C 

C F039 Ideal thrust at sta. 9, lbf 

C 

 F9ID = WP * VEL9 / GC 

C 

C Force balance, lbf: 

C X-positive forward & Y-positive right (looking upstream), Z-positive down 

C C-calibration forces, positive with X, Y, and Z 

C R-reaction forces, negative with X, Y, and Z (R positive when C negative) 

C tension load cells-positive, compression load cells-negative 

C 

C F040 Calibration load cell forces 

C 

 FCY2 = CY2 

 FCY1 = CY1 

 FCZ1 = CZ1 

 FCZ2 = CZ2 

 FCZ3 = CZ3 

 FCZ4 = CZ4 

 FCX1 = - CX1 

 FCX2 = CX2 

C 

C F041 Reaction load cell forces 

C (Un-vented load cells need to be corrected for P0 zero shift here) 

C 

 FRY2 = RY2 

 FRY1 = RY1 

 FRZ1 = - RZ1 

 FRZ2 = RZ2 

 FRZ3 = RZ3 

 FRZ4 = - RZ4 

 FRX1 = - RX1 
NASA/TM—2010-216771 31 

 FRX2 = RX2 

C 

C F042 Reaction matrices 

C 

 R(1) = FRX1 

 R(2) = FRX2 

 R(3) = FRY1 

 R(4) = FRY2 

 R(5) = FRZ1 + FRZ3 

 R(6) = FRZ2 + FRZ4 

C 

 Q(1) = R(1) 

 Q(2) = R(2) 

 Q(3) = R(3) 

 Q(4) = R(4) 

 Q(5) = FRZ1 + FRZ2 

 Q(6) = FRZ3 + FRZ4 

C 

C F044 Calibration forces for in-stand static calibration 

C 

 F(1) = FCX1 + FCX2 

 F(2) = FCY1 + FCY2 

 F(3) = FCZ1 + FCZ2 + FCZ3 + FCZ4 

C 

C F045 Reaction-Calibration force differentials for in-stand static calibration 

C 

 R1F12 = R (1) - F (1) / 2 

 R2F12 = R (2) - F (1) / 2 

 R3F22 = R (3) - F (2) / 2 

 R4F22 = R (4) - F (2) / 2 

 R5F32 = R (5) - F (3) / 2 

 R6F32 = R (6) - F (3) / 2 

 Q5F32 = Q (5) - F (3) / 2 

 Q6F32 = Q (5) - F (3) / 2 

 R5F3 = R (5) - F (3) 

 R6F3 = R (6) - F (3) 

 Q5F3 = Q (5) - F (3) 

 Q6F3 = Q (6) - F (3) 

 R3F2 = R (3) - F (2) 

 R4F2 = R (4) - F (2) 

C 

C F046 Research model forces and moments from inverse matrix, lbf and in-lbf 

C 

 DO I = 1, 5 

 FS(I) = SDUM(I,1) * R(1) + SDUM(I,1) * R(2) + SDUM(I,2) * R(3) + 

 & SDUM(I,3) * R(4) + SDUM(I,4) * R(5) + SDUM(I,5) * R(6) 

 ENDO 

 DO I = 1,5 

 FU(I) = UDUM(I,1) * R(1) + UDUM(I,1) * R(2) + UDUM(I,2) * R(3) + 
NASA/TM—2010-216771 32 

 & UDUM(I,3) * R(4) + UDUM(I,4) * R(5) + UDUM(I,5) * R(6) 

 ENDO 

C 

C F047 Force and moment corrections for P0 and secondary flow, 

C P0 corrections result from tank deflection effects on force balance 

C fcn (P0-P0KNOB), only slopes from calibration are used, linear fit, 

C Pressurized secondary line effects on force balance are calibrated with 

C the model installed and capped lines over a range of secondary 

C pressures, fcn (psec-P0), psec = PS302C, PS303C, PS123C, PS124C 

C and other line pressures 

C 

 FXP0 = SFXP0 * (P0 - P0KNOB) 

 FYP0 = SFYP0 * (P0 - P0KNOB) 

 FZP0 = SFZP0 * (P0 - P0KNOB) 

 MXP0 = SMXP0 * (P0 - P0KNOB) 

 MYP0 = SMYP0 * (P0 - P0KNOB) 

 MZP0 = SMZP0 * (P0 - P0KNOB) 

C 

C Add secondary-flow pressurized-line curve fits from calibration 

C 

 FX302 = 0. 

 FX303 = 0. 

 FY302 = 0. 

 FY303 = 0. 

 FZ302 = 0. 

 FZ303 = 0. 

 MX302 = 0. 

 MX303 = 0. 

 MY302 = 0. 

 MY303 = 0. 

 MZ302 = 0. 

 MZ303 = 0. 

C 

C F048 Axial force in x-axis, lbf 

C 

 FX = - FU (1) 

C 

C F049 Side force in y-axis, lbf 

C 

 FY = FU (2) 

C 

C F050 Vertical force in z-axis, lbf 

C 

 FZ = FU (3) 

C 

C F051 Moments, in-lbf 

C 

 MX = FS (4) - MXP0 - MX302 - MX303 

 MY = FU (4) - MYP0 - MY302 - MY303 
NASA/TM—2010-216771 33 

 MZ = FU (5) - MZP0 - MZ302 - MZ303 

C 

C F052 Axial net force, lbf 

C 

 FGX = F5 + FLS + FTARE - FX + FXP0 + FX302 + FX303 

C 

C F053 Side net force, lbf 

C 

 FGY = FY - FYP0 - FY302 - FY303 

C 

C F054 Vertical net force, lbf 

C 

 FGZ = FZ - FZP0 - FZ302 - FZ303 

C 

C F055 Length for center of vectored force LX to stand x-y centroid, inches 

C Negative aft of centroid, FGX force required to be on x-axis (LYFGX 

C and LZFGX = 0) 

C 

 LXFZ = - MY / FZ 

 LXFY = MZ / FY 

C 

C F056 Resultant net force, lbf 

C 

 FG = SQRT (FGX**2 + FGY**2 + FGZ**2) 

C 

C F057.1 Resultant force coefficient 

C 

 CFG = FG / F9ID 

C 

C F057.2 Axial force coefficient 

C 

 CFGX = FGX / F9ID 

C 

C F058 Side force coefficient 

C 

 CFGY = FGY / F9ID 

C 

C F059 Vertical force coefficient 

C 

 CFGZ = FGZ / F9ID 

C 

C F060 Yaw angle, degrees 

C 

 FGYX = FGY / FGX 

 IF (ABS (FGX) .LE. 0.00001) FGYX = 0.0 

 BETA = 57.2958 * ATAN (FGYX) 

 BETAC = BETA + BETAZ 

 BETAABS = ABS (BETA) 

 BETACABS = ABS (BETAC) 
NASA/TM—2010-216771 34 

C 

C F061 Pitch angle, degrees 

C 

 FGZX = FGZ / FGX 

 IF (ABS (FGX) .LE. 0.00001) FGZX = 0.0 

 ALPHA = 57.2958 * ATAN (FGZX) 

 ALPHAC = ALPHA + ALPHAZ 

 ALPHAABS = ABS (ALPHA) 

 ALPHCABS = ABS (ALPHAC) 

C 

C F062 Roll angle, degrees 

C 

 FGYZ = FGY / FGZ 

 IF (ABS (FGZ) .LE. 0.00001) FGYZ = 0.0 

 PSI = 57.2958 * ATAN (FGYZ) 

 PSIABS = ABS (PSI) 

C 

C F063 Secondary flow W307 (nozzle) calculation - equations not shown, lbm/sec 

C F064 Secondary flow W302 (venturi) calculation - equations not shown, lbm/sec 

C F065 Secondary flow W303 (venturi) calculation - equations not shown, lbm/sec 

C 

C F067 Stream thrust parameter 

C 

 FSTR = (FG + P0 * A8 * A9_A8) / (PT * A8) 

C 

C F068 Stream thrust coefficient 

C 

 CALL MACHFAR (GAM,-A9_A8, M9ID) 

 PRID = (1 + 0.5 * (GM1) * M9ID**2)**(GAM / GM1) 

 FSAR = PRID * A9_A8 / CDN * (1 + GAM * M9ID**2) 

 FSID = FSAR * PT * A8 * CDN 

 CS = (FG + P0 * A8 * A9_A8) / FSID 

C 

C F069 Measured tare force, lbf 

C 

 FXKNOBM = (PT - P0) * (ALSI + A5) !! FXKNOB param, vac, ADP cal 

 FTAREM = FX - FLS - A5 * DP50 + FXKNOB 

C 

C F070 Calculated lab-seal area, in2 

C 

 ALS3M = FTARE / DP30 
NASA/TM—2010-216771 35 

C 

C B. ASME NOZZLE PERFORMANCE FOR CHOKED FLOW CALIBRATION

C (DO ONLY IF NOZZ = “ASME”) 

C 

 IF (NOZZ .EQ. ‘ASME’) THEN 

C 

C F071 ASME throat Reynolds number and predicted flow coefficient 

C 

 RNINIT = 12 * G2 ** (1/G1) * PT *D8 * G5 / MU8 * TS8 ** 0.5) 

 CDPINIT = 1 - 0.184 * RN1 ** (-0.2) 

 RNASME = CDPINIT * RNINIT 

 CDP = 1 - 0.184 * RNASME ** (-0.2) 

C 

C F072 Predicted ASME velocity coefficient (0.109 now recommended, was 0.107) 

C 

 CVP = 1 - 0.109 * RNASME ** (-0.2) 

C 

C F073 Predicted stream thrust parameter 

C 

 IF (NPR .GE. NPRC) THEN 

 FSP = G2 ** (1/G1) * (1 + GAM * CDP * CVP) 

 ELSE 

 FSP = 1 / NPR * (1 + GAM * CDP * CVP * M8 ** 2) 

 ENDIF 

C 

C F074 Predicted ASME nozzle force, lbf 

C 

 FASME = PT * A8 * (FSP - 1/NPR) 

C 

C F075 Calculated flow coefficient at station 5 

C 

 CD5C = CDP * W8ID / W5ID 

C 

C F076 Calculated momentum coefficient at station 5 

C 

 CF5C = (FX + FASME - FLS - FTARE) / F5ID 

C 

C F077 Predicted thrust coefficient 

C 

 CFGP = FASME / (CDP * W8ID * VEL9 / GC) 

 CFGXP = CFGP * COS (ANGE * 0.017453293) 

 CFGZP = CFGP * SIN (ANGE * 0.017453293) 
 
NASA/TM—2010-216771 37 

Appendix B.—Data Plots for Thrust Stand Interaction Calibration 

These plots show loadcell reactions to forces applied using the in-stand calibration system. 

There are two sets of loadcells installed on the stand, reaction loadcells and calibration 

loadcells. There are two axial reaction loadcells (FRX1, FRX2), two lateral reaction loadcells 

(FRY1, FRY2), and four vertical reaction loadcells (FRZ1 through FRZ4). Calibration loadcells 

follow the same naming convention. Overall calibration forces (e.g., FCX) are formed by 

combining calibration loadcell forces in that particular direction. See Appendix A for equations. 

Figure B1.—Reaction load cell calibration with an applied axial force. 

Oct 2005 

-60

-40

-20

0

20

40

60

-3000 -2000 -1000 0

Axial Calibration Load, FCX, lbf

Reaction Forces, lbf

FRX1+FRX2-FCX

FRY1

FRY2

FRZ1+FRZ3

FRZ2+FRZ4

FRZ1+FRZ2

FRZ3+FRZ4
NASA/TM—2010-216771 38 

Figure B2.—Reaction load cell calibration with an applied lateral force. 

Figure B3.—Reaction load cell calibration with an applied vertical force. 

Oct 2005 

-20

-10

0

10

20

-1000 -500 0 500 1000

Lateral Calibration Load, FCY, lbf

Reaction Forces, lbf

FRX1+FRX2

FRY1-FCY/2

FRY2-FCY/2

FRZ1+FRZ3

FRZ2+FRZ4

FRZ1+FRZ2

FRZ3+FRZ4

Oct 2005 

-20

-10

0

10

20

-1000 -500 0 500 1000

Vertical Calibration Load, FCZ, lbf

Reaction Forces, lbf

FRX1+FRX2

FRY1

FRY2

FRZ1+FRZ3-FCZ/2

FRZ2+FRZ4-FCZ/2

FRZ1+FRZ2-FCZ/2

FRZ3+FRZ4-FCZ/2
NASA/TM—2010-216771 39 

Figure B4.—Reaction load cell calibration with an applied roll moment (left side). 

Figure B5.—Reaction load cell calibration with an applied roll moment (right side). 

Oct 2005 

-20

-10

0

10

20

-500 -250 0 250 500

Vertical Calibration Load (CZ1+CZ3) for MX Rolling Moment, FCZ, lbf

Reaction Forces, lbf

FRX1+FRX2

FRY1

FRY2

FRZ1+FRZ3-FCZ

FRZ2+FRZ4

Oct 2005 

-20

-10

0

10

20

-500 -250 0 250 500

Vertical Calibration Load (CZ2+CZ4) for MX Rolling Moment, FCZ, lbf

Reaction Forces, lbf

FRX1+FRX2

FRY1

FRY2

FRZ1+FRZ3

FRZ2+FRZ4-FCZ
NASA/TM—2010-216771 40 

Figure B6.—Reaction load cell calibration with an applied pitch moment (front). 

Figure B7.—Reaction load cell calibration with an applied pitch moment (aft). 

Oct 2005 

-20

-10

0

10

20

-500 -250 0 250 500

Vertical Calibration Load (CZ1+CZ2) for MY Pitching Moment, FCZ, lbf

Reaction Forces, lbf

FRX1+FRX2

FRY1

FRY2

FRZ1+FRZ2-FCZ

FRZ3+FRZ4

Oct 2005 

-20

-10

0

10

20

-500 -250 0 250 500

Vertical Calibration Load (CZ3+CZ4) for MY Pitching Moment, FCZ, lbf

Reaction Forces, lbf

FRX1+FRX2

FRY1

FRY2

FRZ1+FRZ2

FRZ3+FRZ4-FCZ
NASA/TM—2010-216771 41 

Figure B8.—Reaction load cell calibration with an applied yaw moment (front). 

Figure B9.—Reaction load cell calibration with an applied yaw moment (aft). 

Oct 2005 

-20

-10

0

10

20

-500 -250 0 250 500

Lateral Calibration Load (CY2) for MZ Yawing Moment, FCY, lbf

Reaction Forces, lbf

FRX1+FRX2

FRY1

FRY2-FCY

FRZ1+FRZ3

FRZ2+FRZ4

FRZ1+FRZ2

FRZ3+FRZ4

Oct 2005 

-20

-10

0

10

20

-500 -250 0 250 500

Lateral Calibration Load (CY1) for MZ Yawing Moment, FCY, lbf

Reaction Forces, lbf

FRX1+FRX2

FRY1-FCY

FRY2

FRZ1+FRZ3

FRZ2+FRZ4

FRZ1+FRZ2

FRZ3+FRZ4
 
NASA/TM—2010-216771 43 

Appendix C.—Force Interactions for Dead Weight Check 

Figure C1.—Axial force FX for dead weight check. 

Figure C2.—Lateral force FY for dead weight check. 

Dead Weight Cal

-4

-2

0

2

4

0 10 20 30 40 50 60

Distance to Thrust Stand Centroid, LX, in

FX, lbf 

 0 lbf

 50 

100

150

200

250

Dead Weight Cal

-4

-2

0

2

4

0 10 20 30 40 50 60

Distance to Thrust Stand Centroid, LX, in

FY, lbf 

 0 lbf

 50 

100

150

200

250
NASA/TM—2010-216771 44 

Figure C3.—Roll moment MX for dead weight check. 

Figure C4.—Pitch moment MY for dead weight check. 

Dead Weight Cal

-100

-50

0

50

100

0 10 20 30 40 50 60

Distance to Thrust Stand Centroid, LX, in

MX, in-lbf 

 0 lbf

 50

100

150

200

250

Dead Weight Cal

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 10 20 30 40 50 60

Distance to Thrust Stand Centroid, LX, in

(MY - LX * Weight) / (LX * Weight)

 50 lbf

100

150

200

250
NASA/TM—2010-216771 45 

Figure C5.—Yaw moment MZ for dead weight check. 

Dead Weight Cal

-100

-50

0

50

100

0 10 20 30 40 50 60

Distance to Thrust Stand Centroid, LX, in

MZ, in-lbf 

 0 lbf

 50

100

150

200

250
 
NASA/TM—2010-216771 47 

Appendix D.—Nozzle Gross Thrust and Flow Coefficients 

Using Pre-Calibrations 

Figure D1.—ASME nozzle gross thrust coefficient CFG from pre-run CF5 calibrations, 1-psid 

DP25 transducers. 

Figure D2.—ASME nozzle gross thrust coefficient CFG from pre-run CF5 calibrations, 2-psid 

DP25 transducers. 

1 psid DP25

-1.00%

-0.75%

-0.50%

-0.25%

0.00%

0.25%

0.50%

0.75%

1.00%

0 10 20 30 40 50 60

NPR

(CFG meas - CFG asme)/CFG asme, %

9.9986 in2

15.392 in2

19.990 in2

23.758 in2

40 psia - BLUE

30 psia - RED

20 psia - GREEN

2 psid DP25

-1.00%

-0.75%

-0.50%

-0.25%

0.00%

0.25%

0.50%

0.75%

1.00%

0 10 20 30 40 50 60

NPR

(CFG meas - CFG asme)/CFG asme, %

9.9986 in2

15.392 in2

19.990 in2

23.758 in2

30.009 in2

40 psia - BLUE

30 psia - RED

20 psia - GREEN
NASA/TM—2010-216771 48 

Figure D3.—ASME nozzle gross thrust coefficient CFG from pre-run CF5 calibrations, 5-psid 

DP25 transducers. 

Figure D4.—ASME nozzle flow coefficient CDN from pre-run CD5 calibrations, 1-psid DP25 transducers. 

5 psid DP25

-1.00%

-0.75%

-0.50%

-0.25%

0.00%

0.25%

0.50%

0.75%

1.00%

0 10 20 30 40 50 60

NPR

(CFG meas - CFG asme)/CFG asme, %

19.990 in2

23.758 in2

30.009 in2

39.986 in2

40 psia - BLUE

30 psia - RED

20 psia - GREEN

1 psid DP25

-1.00%

-0.75%

-0.50%

-0.25%

0.00%

0.25%

0.50%

0.75%

1.00%

0 10 20 30 40 50 60

NPR

(CDN meas - CDN asme)/CDN asme, %

9.9986 in2

15.392 in2

19.990 in2

23.758 in2

40 psia - BLUE

30 psia - RED

20 psia - GREEN
NASA/TM—2010-216771 49 

Figure D5.—ASME nozzle flow coefficient CDN from pre-run CD5 calibrations, 2-psid DP25 transducers. 

Figure D6.—ASME nozzle flow coefficient CDN uncertainty from pre-run CD5 calibrations, 5-psid 

DP25 transducers. 

2 psid DP25

-1.00%

-0.75%

-0.50%

-0.25%

0.00%

0.25%

0.50%

0.75%

1.00%

0 10 20 30 40 50 60

NPR

(CDN meas - CDN asme)/CDN asme, %

9.9986 in2

15.392 in2

19.990 in2

23.758 in2

30.009 in2

40 psia - BLUE

30 psia - RED

20 psia - GREEN

5 psid DP25

-1.00%

-0.75%

-0.50%

-0.25%

0.00%

0.25%

0.50%

0.75%

1.00%

0 10 20 30 40 50 60

NPR

(CDN meas - CDN asme)/CDN asme, %

19.990 in2

23.758 in2

30.009 in2

39.986 in2

40 psia - BLUE

30 psia - RED

30 psia - GREEN
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3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Calibration for Thrust and Airflow Measurements in the CE-22 Advanced Nozzle Test 

Facility 

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Werner, Roger, A.; Wolter, John, D. 

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

WBS 561581.02.10.03.15 

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

National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

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E-17398 

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Subject Categories: 07 and 09 

Available electronically at http://gltrs.grc.nasa.gov 

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

CE-22 facility procedures and measurements for thrust and airflow calibration obtained with choked-flow ASME nozzles are presented. Six 

calibration nozzles are used at an inlet total pressure from 20 to 48 psia. Throat areas are from 9.9986 to 39.986 in.2. Throat Reynolds 

number varies from 1.8 to 7.9 million. Nozzle gross thrust coefficient (CFG) uncertainty is 0.25 to 0.75 percent, with smaller uncertainly 

generally for larger nozzles and higher inlet total pressure. Nozzle discharge coefficient (CDN) uncertainty is 0.15 percent or less for all the 

data. ASME nozzle calibrations need to be done before and after research model testing to achieve these uncertainties. In addition, facility 

capability in terms of nozzle pressure ratio (NPR) and nozzle airflow are determined. Nozzle pressure ratio of 50 or more is obtainable at 40 

psia for throat areas between 20 and 30 in.2. Also presented are results for two of the ASME nozzles vectored at 10°, a dead-weight check of 

the vertical (perpendicular to the jet axis) force measurement, a calibration of load cell forces for the effects of facility tank deflection with 

tank pressure, and the calibration of the metric-break labyrinth seal.

15. SUBJECT TERMS

Test facilities; Test chambers; Calibrating; Nozzle thrust coefficients; Thrust; Nozzle flow; Air flow; Flow coefficients; Loads 

(forces); Thrust measurement; Data reduction 

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