Rocket Motor Performance Analysis: Thrust, Flow, Impulse, & Specific Impulse Measurements, Study Guides, Projects, Research of Mechanical Engineering

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MAE 4223

Aerospace Engineering Laboratory

Solid Rocket Motor Performance

DATE DUE: 2-15-2001 BY: Charles O’Neill

TABLE OF CONTENTS

Page

ABSTRACT ii

LIST OF FIGURES iii

LIST OF TABLES iv

INTRODUCTION 1

EQUIPMENT 1

PROCEDURE 2

THEORY 2

RESULTS 3

CONCLUSIONS AND RECOMMENDATIONS 8

REFERENCES 9

APPENDICES 10

SAMPLE CALCULATIONS 11

SPREADSHEET TABLES 12

DATA SHEETS 18

iii

LIST OF FIGURES

Figure Title Page

1 Rocket Test Equipment 1

2 F22-7K Calibration 3

3 G33-7J Calibration 4

4 F22-7J Factory Data: Thrust versus Time 5

5 G33-7J Factory Data: Thrust versus Time 5

6 F22-7J Experimental Thrust Time History 6

7 F22-7J Experimental Flow Rate 6

8 G33-7J Experimental Thrust Time History 7

9 G33-7J Experimental Flow Rate 8

INTRODUCTION

Two small rocket motors are tested to determine their performance

characteristics. The motors are National Association of Rocketry (NAR) F and G

classified motors manufactured by Aerotech Inc. A moment-arm load cell with a strain

gage transducer system connected to an oscilloscope will record the time history of the

rocket burns. Motor thrust and propellant properties will be recorded and discussed.

EQUIPMENT

The equipment required for the experiment consisted of rocket motors and the

measurement/test equipment.

Two solid propellant rocket motors were tested. Both motors were in the Aerotech

RMS 29/40-120 family. Both the F22-7J and the G33-7J used the same reusable casing.

The F22 grain was one piece whereas the G33 consisted of two axially connected grains.

The rocket nozzle was of a converging-diverging type; however, a quick inspection

indicated that the nozzle was probably not shaped to take advantage of the diverging

portion. Both motors used the proprietary Aerotech Black Jack propellant. Containing

less than 4 ounces of propellant, both motors are legal for general use by non-rated

civilians.

The rocket test equipment consisted of three systems: measurement, firing and

display. A schematic drawing is given in Figure 1. The battery, indicator and oscilloscope

were moved away from the rocket firing area.

Figure 1. Rocket Test Equipment

The measurement system was a moment-arm load cell. The rocket motor fired

upwards at the end of the 8.5 in moment arm. The root end of the moment arm was

connected to the base through a group of strain gages.

The firing system was electrical. An electrically activated igniter was installed in

the motor. Battery power was routed to the igniter with a human activated switch

installed for precise control of the firing.

The measurement system consisted of a strain gage, indicator and oscilloscope.

The strain gage measured the strain induced into the load cell due to the weight acting at

the end of the moment arm. The strain gage indicator consisted of a Wheatstone bridge

advantage of being easy to implement with irregularly stepped data and of being first

order accurate. Integration was performed by multiplying the time step with the average

value of the two nearest data points. This method is mathematically described as,

∫ ∑^ (^ )

t t

x x

y y

I yx

0

2 1

2 1

As seen above, this method is easy to implement with the obtained rocket data. As

expected, the total number of regions is one less than the number of points. The accuracy

of this method is sufficient with small time steps.

RESULTS

Calibration was performed as described above. For the F22 motor, a linear best-fit line is

shown in Figure 2.

F22-7J Calibration

Weight = 3.8082 mV + 174. R^2 = 0. 0

Transducer Output [mV]

Calibration Weight [grams]

Figure 2. F22-7K Calibration

As discussed in the theory, only the slope of the best-fit line is needed. Thus, the

relationship between a change in applied weight and transducer output is determined to

be,

∆ W = 3. 8082 ⋅∆ V

Similarly for the G33 motor, the best-fit line is shown in Figure 3. The

relationship between a change in applied weight and the transducer output is determined

to be,

∆ W = 4. 2629 ⋅∆ V

G33-7J Calibration

Weight = 4.2629 mV - 142. R^2 = 0.

0

Transducer Output [mV]

Calibration Weight [grams]

Figure 3. G33-7J Calibration

Experimental uncertainty is estimated by considering the uncertainty in the

measurements. For the F22-7J rocket motor, the calibration related thrust and voltage.

From above, the thrust is given by,

T = 3. 808 mV

The transducer output voltage is assumed to be known within ±0.001 Volt and the

calibration weights are known to ±1 gram. Thus, the worst-case estimates of the thrust

are,

T = 3. 808 ( V ± 1 mV ) ± 1 gram

At 1 second, the F22-7J rocket has a transducer output of 426.868 mV. The minimum

thrust estimate as determined by uncertainty analysis is,

( )

T lbf

T gram

T gram

Likewise, the minimum thrust estimate is,

( )

T lbf

T gram

T gram

Thus, the estimated thrust for the F22-7J at 1 second considering the uncertainty of

measurement and calibration is,

T = 3. 58 ± 0. 01 lbf

The uncertainty estimate of less than one quarter of one percent is acceptable for this

experiment.

Factory performance characteristics of both the F22 and G33 motors were

determined from charts given by Aerotech [1] [2] and included in Data Sheet 3 and 4 in

the Appendix. The F22 motor reaches a maximum thrust of just over 6 pounds at ¼ of a

second into the burn. The burn is slightly regressive until 2 seconds. After 2 seconds, the

Aerotech F22 and G33 motors were experimentally tested as described above.

The F22 motor burn history was recorded without errors; however, the G33 motor burn

history was not properly captured by the oscilloscope. This improper capture meant that

the total propulsive performance is not available for the G33.

The F22-7J motor was tested and the thrust-time history is given in Table 4. The

thrust-time history is plotted in Figure 6.

0.000 1.000 2.000 3.000 4.000 5. Time [sec]

Thrust [lbf]

Figure 6. F22-7J Experimental Thrust Time History

The flow rate through the F22 motor is given in Figure 7.

0.000 1.000 2.000 3.000 4.000 5. Time [sec]

Flow Rate [lbf/s]

Figure 7. F22-7J Experimental Flow Rate

The total impulse delivered by the F22 motor was 14.2 lb-sec as given in Table 4 and

Data Sheet 1 in the Appendix. The propellant specific impulse is 129 seconds.

As compared to the factory data, the experimental data shows significantly less

thrust. Where the factory was easily exceeding 6 lbs of thrust, the experiment slowly

worked up to 4.5 lbs of thrust. Additionally, the factory data shows a neutral burn rate;

however, the experimental thrust increases up to 2 seconds. The F22 grain has an axial

slot. From [3], slots are neutral burning as determined from both the experimental and

factory data. The total impulse provided by the motor was slightly over 14 lb-sec for both

the factory and experimental data.

The experimental specific impulse was lower than the factory advertised.

Aerotech’s data was calculated to give a 143 second specific impulse; however, the

experiment only achieved a 129 second specific impulse. This may indicate weak or old

propellant.

Because the day was cold, the propellant burn rate could have been affected. Also,

the moisture content was high, so it may be possible that the motor had absorbed some

water between the unpacking time and the firing time. In any case, the F22 motor only

provided 75% of the rated and advertised thrust.

The G33-7J motor was tested and the data given in Table 5 and Data Sheet 2 in

the Appendix. A thrust-time plot of the G33 motor’s burn is given in Figure 8. A plot of

flow rate versus time is given in Figure 9.

0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4. Time [sec]

Thrust [lbf]

Figure 8. G33-7J Experimental Thrust Time History

REFERENCES

1. Aerotech Inc, http://www.aerotech-rocketry.com/customersite/products/motors/

RMSreloads/hobbyreloads/E23F22F52graph.GIF, 2001.

2. Aerotech Inc, http://www.aerotech-rocketry.com/customersite/products/motors/

RMSreloads/hobbyreloads/G33graph.GIF, 2001.

3. C.D. Brown, Spacecraft Propulsion , AIAA, 1996.

APPENDICES

SPREADSHEET TABLES

TABLE 1: F22-7J AND G33-7J CALIBRATION TABLES:

TABLE 3: G33-7J FACTORY DATA

G33-7J

quantity pixel units rate thrust cal 8 0.801 9.987516 lbs/unit time 4 2.2 1.818182 sec/unit

Propellent Weight 0.159031 lbf

Thrust Time Impulse Flow rate x y lbs sec lb-sec lb/sec

3.75 2.042 0 0 0 3.778 1.245 7.96005 0.050909 0.202619 0. 3.829 1.208 8.329588 0.143636 0.755247 0. 3.921 1.231 8.099875 0.310909 1.374101 0. 4.056 1.217 8.2397 0.556364 2.005312 0. 4.268 1.204 8.369538 0.941818 3.201053 0. 4.49 1.222 8.189763 1.345455 3.341968 0. 4.681 1.231 8.099875 1.692727 2.828473 0. 4.796 1.259 7.820225 1.901818 1.664374 0. 4.917 1.287 7.540574 2.121818 1.689688 0. 5.018 1.342 6.991261 2.305455 1.334287 0. 5.092 1.407 6.342072 2.44 0.89697 0. 5.171 1.518 5.233458 2.583636 0.831334 0. 5.259 1.713 3.285893 2.743636 0.681548 0. 5.324 1.842 1.997503 2.861818 0.312201 0. 5.403 1.944 0.978777 3.005455 0.213751 0. 5.481 2 0.419476 3.147273 0.099149 0. 5.62 2.023 0.189763 3.4 0.076986 0. 5.694 2.037 0.049938 3.534545 0.016125 0. 5.792 2.037 0.049938 3.712727 0.008898 0.

Impulse 21.

Sp Impulse 135.

TABLE 4: F22-7J EXPERIMENTAL DATA

scale change Weight y 1000.000 1.258 794.913 mv/unit before 134.000 g x 2.000 1.550 1.290 sec/unit after 84.000 g

• F22-7J J - 0 37. grams mV grams mV - 0 -25 500 143. - 500 93.75 707 206. - 707 150 1000 243.
  • 1000 187.5
  • 1500 312.5 1813 481.
  • 1813 443.8
  • 2313 568.8 2813 718.
  • 2813 687.5 3313 843.
  • 3313 831.2 4079 968.
  • 3927 987.5
• thrust cal 8 0.801 9. quantity pixel units rate
• time 4 2.2 1. - 3.76 2.038 x y lbs sec lb-sec lb/sec
  • 3.795 1.625 4.124844 0.0636364 0.131245 0.
    • 3.84 1.483 5.543071 0.1454545 0.395506 0.
  • 3.885 1.427 6.102372 0.2272727 0.476404 0.
  • 3.969 1.413 6.242197 0.38 0.942676 0.
  • 4.094 1.427 6.102372 0.6072727 1.402792 0.
  • 4.236 1.427 6.102372 0.8654545 1.575522 0.
  • 4.382 1.441 5.962547 1.1309091 1.601344 0.
  • 4.521 1.455 5.822722 1.3836364 1.489229 0.
    • 4.66 1.483 5.543071 1.6363636 1.436223 0.
  • 4.774 1.514 5.233458 1.8436364 1.11684 0.
    • 4.92 1.556 4.813983 2.1090909 1.333569 0.
  • 5.052 1.635 4.024969 2.3490909 1.060674 0.
    • 5.16 1.75 2.876404 2.5454545 0.677589 0.
  • 5.229 1.816 2.217228 2.6709091 0.31951 0.
  • 5.295 1.889 1.48814 2.7909091 0.222322 0.
  • 5.406 1.972 0.659176 2.9927273 0.216684 0.
  • 5.545 2.01 0.27965 3.2454545 0.118634 0.
  • 5.677 2.038 0 3.4854545 0.033558
  • 5.785 2.038 0 3.6818182 - Impulse 14. - Sp Impulse 142.
• F22-J
• Thrust = 3.808 mV + 174.850 Weff 0. Weff 50.000 g
  • Reference 0.750 1.900 0.000 0.000 0.000 0.000 0. x y mV Thrust [g] Thrust [lb] sec Impulse Flow Rate
    • 0.796 1.848 41.335 157.414 0.347 0.059 0.010 0.
    • 0.817 1.423 379.173 1443.968 3.181 0.086 0.048 0.
    • 0.881 1.288 486.486 1852.638 4.081 0.169 0.300 0.
    • 0.931 1.273 498.410 1898.046 4.181 0.234 0.266 0.
    • 1.027 1.273 498.410 1898.046 4.181 0.357 0.518 0.
    • 1.138 1.273 498.410 1898.046 4.181 0.501 0.599 0.
    • 1.213 1.256 511.924 1949.508 4.294 0.597 0.410 0.
    • 1.310 1.258 510.334 1943.453 4.281 0.723 0.537 0.
    • 1.358 1.231 531.797 2025.187 4.461 0.785 0.271 0.
    • 1.440 1.240 524.642 1997.943 4.401 0.890 0.469 0.
    • 1.519 1.202 554.849 2112.976 4.654 0.992 0.462 0.
    • 1.658 1.221 539.746 2055.459 4.527 1.172 0.823 0.
    • 1.777 1.219 541.335 2061.514 4.541 1.325 0.696 0.
    • 1.860 1.217 542.925 2067.568 4.554 1.432 0.487 0.
    • 1.952 1.223 538.156 2049.405 4.514 1.551 0.538 0.
    • 2.054 1.219 541.335 2061.514 4.541 1.683 0.596 0.
    • 2.154 1.208 550.079 2094.813 4.614 1.812 0.591 0.
    • 2.260 1.248 518.283 1973.725 4.347 1.948 0.613 0.
    • 2.371 1.252 515.103 1961.617 4.321 2.092 0.621 0.
    • 2.479 1.283 490.461 1867.774 4.114 2.231 0.588 0.
    • 2.579 1.290 484.897 1846.583 4.067 2.360 0.528 0.
    • 2.633 1.277 495.231 1885.937 4.154 2.430 0.286 0.
    • 2.731 1.306 472.178 1798.148 3.961 2.556 0.513 0.
    • 2.835 1.390 405.405 1543.865 3.401 2.690 0.494 0.
    • 2.919 1.398 399.046 1519.647 3.347 2.799 0.366 0.
    • 3.008 1.431 372.814 1419.750 3.127 2.914 0.372 0.
    • 3.102 1.490 325.914 1241.146 2.734 3.035 0.355 0.
    • 3.196 1.533 291.733 1110.977 2.447 3.156 0.314 0.
    • 3.308 1.583 251.987 959.618 2.114 3.301 0.330 0.
    • 3.423 1.648 200.318 762.851 1.680 3.449 0.281 0.
    • 3.502 1.665 186.804 711.389 1.567 3.551 0.166 0.
    • 3.615 1.715 147.059 560.029 1.234 3.697 0.204 0.
    • 3.738 1.765 107.313 408.670 0.900 3.855 0.169 0.
    • 3.867 1.792 85.851 326.936 0.720 4.022 0.135 0.
    • 3.965 1.806 74.722 284.555 0.627 4.148 0.085 0.
    • 4.058 1.790 87.440 332.990 0.733 4.268 0.082 0.
    • 4.219 1.848 41.335 157.414 0.347 4.476 0.112 0. - Ib 14.
      • Ieff 129.