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Design of a Robust High Altitude Rocket Motor Igniter

Kimberly Norrie1 and Michael D. Judge2 Bristol Aerospace Limited, Rockwood Propellant Plant, Winnipeg, Manitoba, Canada

Kevin P. Ford, P.O. Curran and Alice I. Atwood China Lake Naval Air Warfare Centre, California, U.S.A.

In order to ensure reliable high altitude ignition of the improved Black Brant Mk 1 sounding rocket, a new igniter was designed and tested. Since traditional theoretical methods for calculating the required igniter charge size gave widely varying requirements, an empirical method was instead utilized. Various igniter models were fired in an enclosed chamber and heat flux and pressure outputs were measured. These data were compared to laser ignitability results obtained for the Black Brant solid propellant to ensure that sufficient igniter output was provided. A static test and flight test demonstrated that the redesigned igniter performed well to ignite the rocket under near vacuum conditions.

I. Introduction The Black Brant rocket motor is a high altitude sounding rocket which has been utilized by a number of research

agencies worldwide including NASA, the Canadian Space Agency and the Swedish Space Corporation. The Black Brant rocket motor has been in production since 1962 and has a 98.5% reliability rate. In 1998, the Black Brant rocket motor was redesigned to incorporate a newer, industry-standard solid propellant formulation as well as a new insulation system and igniter design; this variant of the rocket was named the Black Brant Mk1. The Black Brant Mk1 propellant formulation is based on ammonium perchlorate and a hydroxy-terminated polybutadiene binder with aluminum powder added for increased impulse. The propellant does not contain a burn rate catalyst.

In 2006, following a flight anomaly that was attributed to the new composite basket igniter, it was determined

that a more robust igniter design was required for the Black Brant Mk1 motor to ensure reliable ignition. This paper details the design and proofing of this improved igniter.

II. Experimental Work, Results and Discussions

A. Propellant Ignitability Characterization

As an initial step to designing the improved igniter, the ignition parameters of the propellant were fully characterized in order to determine the required output parameters for the new igniter. In order to model the ignition requirements for a given propellant, it is necessary to ascertain what level of heat flux must be applied for what duration, at a given pressure, to reliably induce self-sustaining combustion of the propellant.

Laser ignitability testing of the propellant was performed at Naval Air Warfare Centre, Weapons Division, China

Lake, California. A Photon Sources Model 300 CO2 laser with a wavelength of 10.6 µm was used, narrowed and focused through a set of optics, allowing various heat flux exposures. Exposure time of the sample to the laser beam was set through the use of a pulse control sequencer. Precut propellant samples were positioned in a chamber which could be pressurized or held under vacuum, equipped with a zinc selenide window to allow ingress of the laser

1Corresponding Author, Senior Rocket Systems Engineer, Bristol Aerospace Limited, Rockwood Propellant Plant, P.O. Box 874, 660 Berry St., Winnipeg, MB, Canada, R3C 2S4, kimberly.norrie@magellan.aero. 2Corresponding Author, Senior Chemist, Bristol Aerospace Limited, Rockwood Propellant Plant, michael.judge@magellan.aero.

44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit21 - 23 July 2008, Hartford, CT

AIAA 2008-4785

Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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beam. Optics were adjusted to obtain the desired input flux level from the beam prior to each firing, using the beam’s “hot spot” as the measurement standard for flux level. Flux level was calibrated using a Vatell Thermogage Circular Foil heat flux transducer. For each combination of heat flux and pressure, both a first light and a no/no-go (complete ignition) value of exposure time to the laser beam were obtained. A Motorola MRD 300 light sensing phototransistor was used to record the first appearance of light from the sample. An oscilloscope recorded the length of the laser pulse and the first light or thermogage output. Once the general ignition region for the propellant was established, a go/no-go Bruceton type analysis was performed, usually requiring 17 data points.

Propellant samples were obtained from a block of propellant cast from a full scale production batch of Black

Brant Mk1 propellant mixed at the Bristol Rockwood Plant. The propellant was tested at 2.4 psia, ambient pressure (13.6 psia), 30, 50 and 100 psia. For pressures of 50 and 100 psia, a 5.2 cubic feet per minute flow meter operating with a 10 percent nitrogen flow rate was used. At 30 psia, the flow rate was below 10 percent. Both cut and uncut propellant samples were tested in order to ascertain any variations in ignitability between the two. The uncut surfaces were those formed by contact of the propellant with the mold interior walls and exhibited a thin, glossy “resin rich” surface with no exposed ammonium perchlorate and represented a worst case ignition scenario where an as-cast propellant bore is being ignited. For samples that required a cut surface, the propellant was cut before each test to expose a fresh sample to the laser and all samples were coated with a zirconium carbide powder prior to testing, in order to enhance the first light signal. Flux levels of 50, 80 and 150 cal/cm2-s were applied.

The data obtained are summarized in Tables 1 and 2.

Table 1. Black Brant Mk1 Propellant Ignitability Data (Cut Surface)

Pressure (psia)

50 cal/cm2-s Flux

First Light (ms)

50 cal/cm2-s Flux

Go/No Go (ms)

80 cal/cm2-s Flux

First Light (ms)

80 cal/cm2-s Flux

Go/No Go (ms)

150 cal/cm2-s Flux

First Light (ms)

150 cal/cm2-s Flux

Go/No Go (ms)

2.4 122 No ignition 30.6 No ignition 4.9 No ignition

13.6 91.28 ± 25.247�

206.25 ± 8.606

24.98 ± 10.235

151.25 ± 10.058

6.31 ± 1.852 712.50 ± 32.855

30 130.73 ± 22.892

186.25 ± 11.509

33.51 ± 7.874

82.50 ± 6.611

8.23 ± 1.43 55.00 ± 2.507

50 117.09 ± 17.28

153.75 ± 23.12

26.81 ± 6.364

50.00 ± 10.239

8.03 ± 1.675 32.00 ± 2.935

100 75.40 ± 9.48 92.50 ± 6.611

26.95 ± 5.191

40.63 ± 2.507

9.78 ± 2.514 18.36 ± 0.694

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Table 2. Black Brant Mk1 Propellant Ignitability Data (Uncut Surface)

Pressure (psia)

50 cal/cm2-s Flux

First Light (ms)

50 cal/cm2-s Flux

Go/No Go (ms)

80 cal/cm2-s Flux

First Light (ms)

80 cal/cm2-s Flux

Go/No Go (ms)

150 cal/cm2-s Flux

First Light (ms)

150 cal/cm2-s Flux

Go/No Go (ms)

2.4 179.70 No ignition 49.80 No ignition 12.20 No ignition

13.6 132.04 ± 37.396�

240.00 ± 10.239

34.99 ± 6.597

155.83 ± 48.733

8.42 ± 2.57 82.50 ± 4.516

30 167.82 ± 37.425

210.00 ± 21.85

31.67 ± 10.4 91.75 ± 5.01 7.49 ± 1.274 46.25 ± 3.305

50 176.61 ± 17.034

193.75 ± 5.704

27.70 ± 6.65 77.50 ± 6.61 7.73 ± 1.233 39.25 ± 1.721

100 118.93 ± 13.45

149.29 ± 23.185

27.48 ± 7.05 63.75 ± 5.014

9.60 ± 2.15 33.25 ± 1.141

The data point for the cut sample at 150 cal/cm2-sec and 13.6 psi appears somewhat anomalous. This test was

repeated at China Lake and, on the repeated test, the propellant failed to ignite, which supports the very long ignition time found in the original test series. The origin of this effect is not known at present, but it is possible that this is a case of “overdriven combustion” in which the high heat flux artificially induces a level of combustion which cannot be sustained following the abrupt cessation of the irradiation. This phenomena has been documented prior in the literature, albeit for double base propellants, and has been compared to the extinguishment of propellants via rapid depressurization.i A detailed analysis of this phenomenon in composite propellants has also been carried out.ii These studies indicated that applied laser energy can result in combustion extinction of composite propellants. However, this effect was only seen at sub-atmospheric pressures, becoming almost non-existent at pressures above 30-50 kPa. This suggests that the exceedingly long ignition delay seen in the anomalous data point for Mk 1 propellant can be attributed to the low ambient pressure applied during this test. This extinction phenomenon is not anticipated to occur at higher pressures, regardless of applied flux.

As anticipated, the data indicate that the cut surface is more readily ignited, and this surface was assumed for

subsequent calculations. In general, it can also be seen that increasing either the pressure or the heat flux shortens the time required for ignition of the propellant, which is in keeping with data reported in the literature for similar testing on other propellants.

In order to ensure reliable motor ignition, a required flux duration consisting of the average duration plus three

standard deviations was therefore calculated for each test point. These new go/no go durations are given in Table 3 below. The durations in Table 3 can be considered, with a relatively high level of confidence, to be the durations for which the application of the corresponding pressure and heat flux will produce reliable ignition of the propellant.

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Table 3. Summary of Go/No Go Durations with 3 Standard Deviations Added, Mk 1 Cut Surface

P (psia) Duration @ 50 cal/cm2-s (msec)

80 cal/cm2-s 150 cal/cm2-s

15 232.068 181.424 811.065

30 220.777 111.333 62.521

50 223.11 80.717 40.805

100 112.333 48.146 20.439

It was necessary to both interpolate and extrapolate the above data in order to determine suitable durations of

heat application at other possible values of heat flux. Several sources in the literature state that a simplified form of the basic mathematical relationship between induction time to ignition of a material and applied heat flux can be given by equation 1 below.

ti = Aq-m [1]

Here ti is the induction period, q is the applied heat flux, A is an experimentally derived factor and m is an exponent which theoretically should equal 2 for opaque materials.iii The above neglects factors such as absorption coefficient and reflectivity of the material being heated, but appears to still be suitable as a first approximation of the relationship between induction time and heat flux. This suggests that any plot of log ignition delay against log applied flux should describe a straight line with the slope of that line being –2 and, in practice, it is normally observed that, for propellants, plots of time to first light against applied heat flux obey this law fairly well. However, plots of go/no go times against flux deviate from this ideal relationship with values of m normally between 1 and 2. That is, for a given set of conditions, the go/no go times determined for a propellant will normally be greater than the first light times, the difference between these two times corresponding to the time required for degradation gases to achieve a suitable concentration and reaction rate to feed heat into the solid surface. In addition, log-log plots of go/no go duration and flux data often deviate from the predicted linear form as higher heat fluxes are applied, especially in cases where the ambient pressure to which the propellant is exposed is relatively low, such that the time to ignition ceases to decrease on increasing flux. This phenomenon has been attributed to various effects including the existence of a certain minimum required flux application time, regardless of flux power, which makes the application of higher fluxes appear less efficient.iv The deviation of the go/no go line from the first light line is typically decreased as ambient pressure is increased.

The first light data derived from analysis of the Mk1 propellant, cut surface, is shown in Figure 1. A power line

is fitted to each series of data. The R squared values and calculated exponent for each data set are given in Table 4.

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Figure 1. Time to First Light vs Heat Flux and Pressure, Mk1 Cut Surface

1

10

100

1000

10 100 1000

Flux (cal/cm2-sec)

Firs

t Lig

ht D

elay

(mse

c)

15 psia30 psia50 psia100 psia

Table 4. Calculated First Light Slope Values

Pressure (psia) R2 m 15 0.9957 2.42 30 0.9945 2.50 50 0.9803 2.41

100 0.9924 1.85 It can be seen that the first light data correspond well to the expected relationship between induction period and

applied flux although the values of the exponent which are greater than 2 at 15, 30 and 50 psia are somewhat unexpected since, in theory, values greater than 2 should not occur. It is possible that some aspects of laser flux absorption by this propellant are non-ideal or perhaps that the simplified relationship between induction time and heat flux is not entirely applicable in this instance. It is of interest to note that data reported previously by China Lake for first light of AP-based composite propellants also shows m values greater than 2.v As noted previously in the literature for other propellants, this graph shows that changes in pressure have little effect on the time to first light values.

Figure 2 illustrates the difference between first light data and go/no go data for the 100 psia data for the Mk1

propellant cut surface. The typical deviation of the go/no go data from the first light data can be seen.

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Figure 2. Comparison of First Light and Go/No Go Data for Mk 1 Cut Surface, 100 psia

1

10

100

10 100 1000

Flux (cal/cm2-sec)

Tim

e D

elay

(mse

c)

Go/No GoFirst Light

All go/no go data derived from analysis of the Mk1 propellant, cut surface, is shown in Figure 3. A power line is

fitted to each series of data except for that obtained at ambient pressure.

Figure 3. Ignition Delay as a function of Applied Heat Flux and Pressure, Mk 1 Cut Surface

10

100

1000

10 100 1000

Flux (cal/cm2-sec)

Go/

No

Go

Del

ay (m

sec)

15 psia30 psia50 psia100 psia

The R squared values and calculated exponent for each data set are given in Table 5. It can be seen that the data

at 100 psia most closely corresponds to the theoretical relationship between go/no go times and applied flux. The data appear to deviate further from the theoretical relationship with the 50 and 30 psia data, and the ambient pressure data, as discussed earlier in this document, show an extreme deviation with a substantial increase in ignition delay at

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high flux. The exponent values derived here for the 50 and 100 psia data are close to the value of 1.3 determined for m by DeLuca et al during laser characterization of a metallized composite propellant at 315 psi.vi

Table 5. Calculated Go/No Go Slope Values for As-Determined Flux Data

Pressure (psia) R2 m

15 n/a n/a 30 0.9266 -1.08 50 0.8967 -1.39

100 0.9913 -1.46 In order to better incorporate the significant statistical variations in the data, the data were re-evaluated using

instead the go/no go durations with three times the standard deviation for each duration added to that duration. The predictive equations derived from these modified data are as in Table 6. These equations could be used for the purposes of interpolation to predict the go/no go durations for fluxes within those applied during testing

Table 6. Predictive Equations for Flux Data (With Standard Deviations Added)

Pressure (psia) Equation 30 Go/no go time = 17775q-1.14 50 Go/no go time = 76772q-1.52

100 Go/no go time = 44545q-1.54 For the purposes of extrapolating to predict go/no go times at higher fluxes, the potential deviation of the go/no

go versus flux lines from the above equations must be considered. Although the above equations could be used for extrapolations, there is some risk involved since it is not known with certainty that the relationship between go/no go time and applied flux will continue to hold to this relationship at higher flux values. This can be seen in the relatively low R squared values obtained for the low pressure (30 and 50 psi) data when plotting log time versus log flux and given in Table 5.

In light of the uncertainty involved with the prediction of go/no go times at higher heat fluxes, a very

conservative approach was applied to the extrapolation of go/no go times at high flux values up to 300 cal/cm2-sec. The approach used was as follows;

A. for 15 psi, an arbitrary value of 1000 msec for go/no go time at 200 and 300 cal/cm2-sec has been

assigned. The extremely long duration of this time value signifies that for all intents and purposes, the propellant cannot be ignited under these conditions but still allows the data points to be plotted,

B. for 30 and 50 psi, it is conservatively estimated that the go/no go values will plateau at 150 cal/cm2-sec, i.e. there will be no further reductions in time values on increasing flux and therefore the time values at 200 and 300 cal/cm2-sec will be unchanged from those at 150 cal/cm2-sec, and

C. for 100 psi, since the R squared value for these data suggests a very good fit and since the literature show that at higher pressures the tendency for the go/no go line to deviate from the predicted relationship is significantly lowered, the predictive equation shown in Table 6 was used to extrapolate to determine the required flux durations at higher flux values.

Table 7 shows the values thus derived.

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Table 7. Extrapolated Go/No Go Durations at 200 and 300 cal/cm2-sec Flux

Pressure (psia) Go/No Go (msec)

200 cal/cm2-sec

Go/No Go (msec)

300 cal/cm2-sec

15 1000 1000

30 62.5 62.5

50 40.8 40.8

100 12.7 6.8

Figure 4 shows a contour plot obtained from the data in Table 3 and also incorporating the extrapolated go/no go

values derived in the manner described above. It can be seen that there is a “plane” in the region of approximately 50 psi and above and 150 cal/cm2-sec and above. All combinations of pressure and flux in this region correspond to required application durations of less than or equal to approximately 40 msec. In general, therefore, application of a flux value of 150 cal/cm2-sec and over, at a pressure of 50 psi or greater, for at least 40 msec is predicted to ensure sustainable combustion with a very high degree of certainty.

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Figure 4. Predicted Conditions Required for Propellant Ignition

B. Igniter Design

Hardware Design The original Black Brant Mk1 igniter consisted of a 5.2 inch long rounded nylon basket holding both a booster

charge and a main ignition charge. Both charges consisted of boron/potassium nitrate pellets of various morphologies with an overall pellet charge of approximately 260 grams. This charge size had been calculated to produce sufficient heat discharge to initiate propellant combustion along the propellant bore while maintaining a suitable safety factor with regard to pressure produced in the motor by the igniter exhaust expulsion.

The improved igniter was intended to produce more reliable propellant ignition and, as such, was redesigned to

use a 14 inch long wire mesh basket to hold the pellets, thus producing a greater area of impingement of the igniter heat output on the propellant grain. The charge size required was determined using the methods described below.

Charge Size Determinations As an initial step in the igniter redesign, simultaneous with the ignitability testing described above, a variety of

analytical methods were employed to determine the initial ignition charge size required of the new Mk1 igniter to ensure reliable ignition. These methods are summarized below.

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Bryan Lawrence Method The Bryan Lawrence Equation is an empirical relationship between certain rocket motor parameters and the

energy required to obtain satisfactory ignition. It was developed by the US Naval Ordnance Laboratory based on 53 different rocket motors with varying propellant formulations, igniter compositions and grain configurations.vii The equation works by first calculating Q, the total energy required for propellant ignition, then determining the required ignition pellet charge from Q and the heat of explosion of the pellets. Q is determined using the following inputs; the bore area exposed to ignition products, length of grain, port area, and propellant ignitability (in cal/cm2).

Based on this calculation, the required igniter charge was 367 grams BPN. However, there is a disclaimer

appended to this method that a large tolerance on the calculated Q from the Bryan Lawrence equation (i.e. from Q/2 to 2Q) may result in acceptable igniter design. Using this entire tolerance range, the acceptable igniter charge weight could range from 184 g to 734 g.

Peak Mass Flow Method Peak mass flow to initial surface area is a method that has been employed by the Chemical Propulsion

Information Agency (CPIA) during consultation with NASA and Bristol. Industry guidelines recommend that the igniter mass flow over surface area should exceed 3.0 x 10-3 lbm/in2-sec.

In order to meet this requirement of mass flow in the Black Brant motor, and based on the Mk1 motor bore

surface area and the predicted igniter burn time, it was calculated that the mass of the igniter charge should be a minimum of 800 g.

Energy Delivery Method The Energy Delivery Method was an alternate method employed by CPIA during consultation with NASA and

Bristol. The following steps form calculations for the Energy Delivery Method; calculate energy available, calculate

energy per unit area, calculate energy delivery rate. These calculations involve mass of igniter charge, heat of explosion of pellets, initial surface area of propellant grain, and igniter burn time.

Using this method, an igniter charge of approximately 450 grams BPN would be considered to be only in the

“marginal” zone regarding ignition probability. It should be noted also that this correlation was apparently developed for an aft end igniter.

Instrumented Test Firings Since the above theoretical methods gave a very wide range of acceptable igniter charges, it was determined that

an empirical means of determining the required charge was needed. To this end, developmental testing was conducted on test models of Black Brant igniters to measure the actual heat and pressure output of the igniters in a simulated Black Brant Mk1 motor bore.

Igniters were tested in a free volume vessel that simulated the bore volume of a Black Brant Mk1 motor. The

throat diameter of the vessel was sized based on the nominal throat size of a Black Brant Mk1 motor and the forward section of the test chamber was filled with a cast inert propellant grain to replicate the geometry of the first 48 inches of the motor bore. The inert propellant used the same polymer as the propellant and had similar physical, mechanical and heat transfer properties. Four heat flux sensors were mounted in different locations along the simulated bore to measure the heat output of the igniter as the flame traveled down the bore. Initially, one Kistler pressure transducer was mounted on the igniter plug similar to the existing Mk1 igniter pressure port. For the last four developmental tests an Omegadyne pressure transducer was added to the head end of the fixture. The fixture was evacuated to approximately 1.4 psia prior to each test firing. Figure 5 shows the test fixture with the placement of the igniter and the four heat flux sensors. Dimensions shown are in inches.

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Figure 5. Instrumented Fixture for Test Firing of Igniters

A variety of igniter designs were fired in this vessel using various BPN pellet charges, and the heat flux and

pressure rise data obtained were used to determine the optimal amount of BPN pellets in the igniter as well as the optimal ratio of various pellet sizes and shapes.

The final design contained a total charge of 447 grams BPN. The test process culminated in three firings of the

final design prototype model, conditioned at 70, 120 and -10 °F, under initial vacuum conditions. Figure 6 shows a typical output recorded for 3 of the 4 heat sensors (designated HF1,2 and 3) as well as the pressure sensor (designated Pk) during a test firing of such an igniter; in this case the final design prototype fired at -10° F. Table 8 summarizes output data from the three firings of the final design model, giving durations for which the igniters sustained a bore pressure of 50 psia or greater. Heat Flux A and B refer to the readings from the sensors which recorded the highest heat outputs. Note that heat flux units in this figure and table are in W/cm2 rather than cal/cm2-sec.

All these qualification igniters, regardless of initial conditioning temperature, provided a minimum internal

vessel pressure of 50 psia, while maintaining a minimum heat flux of 627 W/cm2 (150 cal/cm2-sec) for at least 40 msec, thereby meeting or exceeding the minimum ignitability requirements determined during the laser ignition characterization of the propellant described earlier. This design was therefore considered suitably robust for use in the Black Brant Mk1 motor. The designated charges size of 447 grams is in the same general range of the charges sizes calculated via the various theoretical models but do not correspond exactly to any of the calculated charges.

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Figure 6. Heat and Pressure Output from Instrumented Igniter Test Firing

0

1000

2000

3000

4000

5000

6000

0 0.1 0.2 0.3 0.4 0.5 0.6

Time (sec)

Hea

t Flu

x (W

/cm

^2)

0

20

40

60

80

100

120

Pres

sure

(psi

a)

HF 1HF 2HF 3Pk

Table 8. Summary of Final Igniter Design Test Firing Outputs

Heat Flux A (W/cm2) Heat Flux B (W/cm2) Test Fire Conditions

Duration A (sec)

Min Max Ave

Duration B (sec)

Min Max Ave

-10°F, 1.4 psia .068 2222 5257 3574 .063 633 905 788

120°F, 1.4 psia .070 1212 3263 2410 .039 632 781 715

70°F, 1.4 psia .067 1073 3978 2450 .037 633 839 732

III. Static and Flight Tests

Following redesign and build of the improved igniter, a Black Brant Mk1 rocket motor incorporating the new igniter was static fired at the Air Force Research Laboratory (Edwards Air Force Base) facilities in August 2006. The motor was affixed to a six degree of freedom test stand and conditioned to 90°F and fired at ambient atmospheric pressure. The motor fired without incident, demonstrating the efficacy of the redesigned igniter.

Subsequent to the static test, a Black Brant Mk1 motor with a new Black Brant Mk1 igniter was flown on a

Black Brant 11 vehicle on September 23, 2006 from Wallops Flight Facility. The new igniter successfully ignited the motor at an altitude of approximately 46,000 ft. This is the highest ever ignition altitude for a Black Brant motor. The vehicle flew within acceptable tolerance from the flight prediction and the mission was considered to be a success.

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IV. Conclusion

An empirical process of measuring propellant ignitability and subsequently designing the igniter to produce the required combination of heat flux, pressure and duration was used to produce a suitable igniter design for the Black Brant Mk1 motor. The final charge size found to be necessary was in the range dictated by standard methods of prediction, such as the Bryan Lawrence equation, but was significantly above the nominally required amount as predicted by that method.

The redesigned Black Brant Mk1 igniter has been demonstrated to produce efficient ignition of the rocket motor

under high altitude conditions.

Acknowledgments

The authors wish to thank the following individuals and organizations for their extremely helpful assistance and advice during the course of this research; NASA Sounding Rocket Program Office, NASA Sounding Rocket Operations Contract (NSROC), CPIA, Rob Stowe and other scientific staff at DRDC Valcartier, Bob Geisler.

References

i Ohlemiller, T.J., Caveny, L.H., DeLuca, L. and Summerfield, M., Proceedings, Fourteenth Symposium (International) on Combustion, Pennsylvania State University, PA, U.S.A., pp 1297-1307, 1972. ii Zanotti, C. and Giuliani, P., Propellants, Explosives, Pyrotechnics, 23, 254-259, 1998. iii Strakovskiy, L., Cohen, A., Fifer, R., Beyer, R. and Forch, B., Laser Ignition of Propellants and Explosives, ARL-TR-1699, 1998. iv Beyer, R.B. and Fishman, N., Progress in Astronomy and Rocketry, pp 673-692, 1960. v Atwood, A. I., Price, C. F. and Boggs, T.L., Proceedings, 22nd International Annual Conference of ICT, Karlsruhe, Germany, 44-1 – 44-15, 1991. vi DeLuca, L., Caveny, L. H., Ohlemiller, T. J. and Summerfield, M., AIAA Journal, 14, 7, 940-946, 1976. vii Eriksen, J.M. and Haugen, S., AIAA-90-2467, SAE, ASME, and ASEE, Joint Propulsion Conference, 26th, Orlando, Florida, July 16-18, 1990.