Boosted Darts In Model Rocketry



A Research and Development report
submitted at NARAM-31, August 1989,
by the Spaceman Spiff Team, T-471



Copyright © 1997 by Chuck Weiss (cbweiss at frontiernet dot net) and Jeff Vincent (jeffvincent at verizon dot net).
This report may be copied for non-commercial use, provided this notice remains intact.
Potential commercial users should contact the authors for further information.

Abstract - Boosted Darts In Model Rocketry

Spaceman Spiff Team - NARAM-31

An experimental program was conducted to investigate the potential of achieving an altitude performance advantage from a boosted dart over an optimized conventional single-stage model in the same total impulse class. Theoretical considerations were addressed that considered design parameters that result in a predicted altitude advantage for the boosted dart configuration. A highly successful, safe, and reliable delay timing and ejection mechanism was developed for the dart which allowed empirical flight testing.

Flight tests results demonstrated an average twenty percent altitude performance advantage for the boosted dart over the optimized conventional single-stage model. Graphs and tables are provided that address boosted dart design parameters applicable to different engine classes for modelers who wish to conduct future boosted dart research. A perspective on the limitations of the dart delay timing and ejection mechanism within the restrictions of the U.S. Model Rocket Sporting Code is presented, as is a request to model rocket manufacturers to develop prepackaged mechanisms so that all modelers can take part in the boosted dart experience.

Chuck Weiss
Email: cbweiss at frontiernet dot net

Jeff Vincent
Box 523
Slingerlands, NY 12159
(518) 439-2055
Email: jeffvincent at verizon dot net


Table Of Contents


List of Tables, Figures, and Graphs


Introduction

A boosted dart is a rocket vehicle consisting of a rocket booster and an unpowered upper "stage" (the dart) which separates from the booster and coasts to apogee (maximum altitude). A boosted dart is of interest because theoretical considerations indicate that it can be propelled to a higher altitude than an equally-powered conventional single-stage rocket. The advantage results from design characteristics of the dart configuration which reduce drag during the coast portion of flight. These are discussed in detail in the Background and Theory section of this report.

An example of a boosted dart is the Super Loki Dart, manufactured by Space Data Corporation and used by NASA. The Super Loki is a four inch diameter booster with a 1.56" diameter dart which drag-separates and coasts to apogee. The dart portion carries an electronic payload. Both the dart and the booster are allowed to free-fall into the Atlantic Ocean.

Our knowledge of dart research related to model rocketry consists of published work by Jack Kane ("Some Thoughts On Boosted Darts", 1980 MIT Journal) and work conducted by Matt Steele and the U.S. Team in preparation for the C Payload event at the 1980 World Spacemodeling Championships. Unlike the Super Loki Dart, model rockets must contain a lightweight, compact, safe, and reliable mechanism for deploying a recovery device. Such a technological innovation would not only make model rocket darts possible, but make the performance of low-power darts competitive with conventional models. Kane's work theoretically discussed the altitude advantage of a boosted dart carrying an electronic payload to time and deploy a recovery system. No empirical evaluation was conducted. Steele's work (unpublished) was primarily empirical and achieved moderate success through the use of "underwater" fuse for a timing device and a black powder ejection charge to deploy the recovery system. The fuse protruded from the side of the dart (possibly causing significant drag) and was ignited by the modeler via a flashbulb just prior to launch. (Attempts to ignite the fuse from the booster resulted in inconsistent delay times.) The dart drag-separated from the booster. No altitude advantage was ever demonstrated. It becomes apparent that several problems remain unsolved in the application of dart technology to model rocketry.

The objectives of the study described in this report are as follows:

  1. To theoretically evaluate altitude performance characteristics of a model rocket boosted dart and determine if certain design parameters may result in a potential altitude advantage over an optimized conventional single-stage model.

  2. To develop a lightweight, compact, safe, and reliable delay timing and ejection mechanism capable of deploying a recovery device. This device will allow empirical flight testing of boosted darts.

  3. To empirically evaluate and demonstrate any altitude advantage predicted from boosted dart theory by comparing the altitude achieved by boosted darts to altitudes achieved by optimized conventional single-stage models within the same total impulse class.

Background and Theory

Typical rocket flight consists of two phases, a powered boost phase and an unpowered coast phase. During the boost, three forces act on the rocket: the thrust of the rocket engine (a positive, upward force), the weight of the rocket (a negative force), and the aerodynamic drag generated (also a negative force). The net force accelerates the mass of the rocket vehicle upward. During the boost, the maximum net force, and thus the maximum boost altitude and maximum burnout velocity, are achieved with minimum weight (mass) and minimum drag. Minimum mass is self-explanatory. Drag is proportional to the drag coefficient, a measure of aerodynamic "cleanliness", and the reference area of the rocket, which is based upon its maximum diameter. Minimum drag can be achieved by reducing the drag coefficient (streamlining the rocket) or reducing the reference area (making the rocket smaller).

During the coast phase, two negative forces act on the rocket: the weight of the rocket and the drag generated. These forces decelerate the model from its burnout velocity to a velocity of zero, the point at which apogee is attained. The altitude achieved during the coast phase is represented by the following equation:

Coast Altitude = ß / (2 k g) * ln [ k v² / ß + 1 ]

where: ß = m g / CdA (known as the "ballistic coefficient"),

and where:

A graph of this equation (see Graph 1) demonstrates that maximum coast altitude is achieved with maximum burnout velocity and maximum ballistic coefficient. Maximum burnout velocity was discussed above. Maximum ballistic coefficient is achieved with minimum drag and maximum mass (g, for our purposes, shall remain constant). Minimum drag was discussed above. Maximum mass creates a paradox with the minimum mass requirement for maximum boost altitude and burnout velocity. Altitude calculations for various lift-off masses will indicate an optimum mass for a particular power and drag configuration.

This graph also demonstrates that rockets with equal ballistic coefficients and equal burnout velocities will achieve equal altitude. This forms a baseline for the evaluation of dart performance. If we can assume that a dart vehicle and a conventional model have similar boost performance (burnout altitude and velocity), then the dart must have an equal (or greater) ballistic coefficient to achieve equal (or greater) altitude. For model rocket darts, the loss of the mass of the expended booster engine results in a dart significantly lighter than a conventional model. This requires a similar reduction in drag to maintain the same ballistic coefficient. This is most easily accomplished by a reduction in reference area.

Using the above equation, Graph 2 illustrates this for B- and C-powered darts. The graphs depict the ballistic coefficient of various dart masses and diameters. The bold horizontal lines represent the ballistic coefficient of a B- or C-powered optimized conventional single-stage model. For each dart diameter, the curve represents the ballistic coefficient at that particular dart mass. A conventional B-powered model would have an optimum mass of approximately 27 grams (this value was obtained from Centuri TIR-100: Model Rocket Altitude Performance). Considering the mass of the booster, a B-powered dart could weigh no more than eight grams and still conform to the assumption of boost performance equal to a conventional model. At this mass, the 0.5" dart has a lower ballistic coefficient than the conventional model--it would not fly as high. Smaller dart diameters have higher ballistic coefficients, and thus would provide superior performance. By similar analysis, a C-powered boosted dart with a maximum dart mass of 16 grams would exceed the conventional model performance using any dart diameter calculated. With this knowledge, a dart diameter of 0.438" was selected for further research. This diameter has the advantage of superior performance for both engine classes, but a practical size for prepping and tracking.

The above method presents a good visualization of dart performance and a good approximation of required dart size. For a simple calculation, it gives a good idea of what will work and what won't. However, some of the assumptions may be too broad to accurately estimate altitude performance. For this reason, an in-depth study was made of the altitude potential of a conventional model and the selected dart size. A drag coefficient of 0.5 was selected for the conventional and dart models, as it was felt that this was representative of models of this type. A computer program was written to achieve this task. The program utilized an iterative method of altitude calculation, using a 0.01 second time interval. The resulting maximum altitudes and coast times for various conventional and dart configurations (variable booster mass and dart mass) were then plotted. A listing of the model parameters and the computer program may be found in Appendix II.

The results of these calculations can be found in Graphs 3-10. These results are summarized in Table 1. These graphs show us several things:

  1. The conventional altitude graphs show the optimum mass for the conventional model, for the optimization of the control models. For these models, it was felt that the optimum mass was unattainable, and data for a "practical" mass is listed in Table 1. This "practical" mass was the minimum possible mass that could be achieved, considering the mass of the engine, a typical airframe, and tracking powder. In the case of the B-powered model, it results in an altitude reduction of 23 meters (6.8%) below optimum. (For the B model, the engine alone is 22 grams of the alloted 25 gram mass!) In the case of the C-powered model, the difference proved insignificant (approximately two meters).

  2. The altitude graphs show the expected altitude increase of the dart models over the conventional models. For the B-powered models, the increase is 60 meters (19%) over the "practical" model. (The predicted advantage over the optimum B model is 37 meters [11%].) For the C-powered models, the increase is 108 meters (20%).

  3. The dart altitude graphs show the optimum dart mass for each engine type, allowing the optimization of the test darts. Note that these masses are greater than calculated above, resulting in greater launch masses for the dart models. Apparently the altitude performance of the dart is much more dependent upon the ballistic coefficient of the dart than the optimum launch mass. To simplify, the dart models coast so much better than the conventional models that they can withstand the penalty of a slightly higher boost mass.

  4. The dart altitude graphs show the effect of variations in booster mass on the altitude of the dart models. Low booster mass is imperative (as one might expect from the theoretical conclusions reached above).

  5. The dart coast graphs show the desired dart delay time to eject at apogee, for the construction of the delay train devices.

Graph 1 - Coast Altitude vs. Ballistic Coefficient

Coast Altitude vs. Ballistic Coefficient

Graph 2 - Dart Ballistic Coefficient vs. Dart Mass

Dart Ballistic Coefficient vs. Dart Mass

Table 1 - Theoretical Altitude Results


Estes B6 Engine

Configuration:             Optimum       "Practical"
                         Conventional    Conventional     0.438" Dart
Maximum altitude:           338 m           315 m           375 m
Coast time:                 6.1 sec         6.5 sec         7.2 sec
Launch mass:                 25 gm           35 gm           NA
Optimum dart mass:           NA              NA              15 gm
Booster mass penalty:        NA              NA           -15.4 m/gm

Estes C6 Engine

Configuration:             Optimum       "Practical"
                         Conventional    Conventional     0.438" Dart
Maximum altitude:           550 m           548 m           656 m
Coast time:                 7.1 sec         7.3 sec         9.0 sec
Launch mass:                 37 gm           40 gm           NA
Optimum dart mass:           NA              NA              21 gm
Booster mass penalty:        NA              NA           -11.5 m/gm
     Note: The booster mass penalty is the number of meters lost for
every extra gram of booster mass (calculated at the optimum dart
mass).

Graph 3 - B6-6 Conventional: Altitude vs. Launch Mass

B6-6 Conventional: Altitude vs. Launch Mass

Graph 4 - B6-6 Conventional: Coast Time vs. Launch Mass

B6-6 Conventional: Coast Time vs. Launch Mass

Graph 5 - B6 Dart: Altitude vs. Dart Mass

B6 Dart: Altitude vs. Dart Mass

Graph 6 - B6 Dart: Coast Time vs. Dart Mass

B6 Dart: Coast Time vs. Dart Mass

Graph 7 - C6-7 Conventional: Altitude vs. Launch Mass

C6-7 Conventional: Altitude vs. Launch Mass

Graph 8 - C6-7 Conventional: Coast Time vs. Launch Mass

C6-7 Conventional: Coast Time vs. Launch Mass

Graph 9 - C6 Dart: Altitude vs. Dart Mass

C6 Dart: Altitude vs. Dart Mass

Graph 10 - C6 Dart: Coast Time vs. Dart Mass

C6 Dart: Coast Time vs. Dart Mass

Experimental Method

I. Timing and Ejection Mechanism Construction

Figure 1 is a detailed depiction of the delay timing and ejection mechanism, henceforth referred to as the delay train/ejection assembly (DTEA, pronounced "dee-tee"). The DTEA is depicted prepared for flight. With the exception of the delay train material, all attempts were made to utilize materials commonly used by today's model rocket flyers. The delay train material, or "grain", was purchased from Vulcan Systems and was used according to the manufacturer's specifications. The DTEA was constructed separately, with the final step being the insertion of the grain into the assembly. The DTEA casing was made from fiberglass tubing, which was resistant to the heat of the burning grain and ejection charge. The ejection charge was provided by four 3/4" pieces of green (medium speed) thermalite. The thermalite is separated from the delay grain by a wooden bulkhead constructed from a 1/4" diameter hardwood dowel. A 1/16" hole is drilled through the center of the dowel. The thermalite ejection charge is ignited by an internal Centuri Sure-Shot ignitor extending from the top of the delay grain, through the bulkhead, and into the center of the surrounding thermalite.

Attention to detail is critical in constructing the delay train/ejection assembly. First, the internal Sure-Shot ignitor is placed through a loose bulkhead so that it extends 1mm beyond the face of the bulkhead on the delay grain side. The Sure-Shot should be closely examined for breaks or separations that would terminate its burn and cause the ejection charge to fail. A small amount of slow cyanoacrylate glue is used to secure the Sure-Shot to the bulkhead on the ejection charge side. The glue is allowed to dry and the connection is checked to insure that the Sure-Shot cannot slide in the bulkhead. Four pieces of 3/4" thermalite are then evenly spaced onthe first third of a 1" long x 3/4" wide piece of masking tape. The thermalite/tape strip is then wound around the long portion of the Sure-Shot so that the Sure-Shot is centered between the four thermalite strips. Another 1" x 3/4" piece of tape is wound around the circumference of the bulkhead and the thermalite bundle to secure the bundle to the bulkhead and relieve stress on the Sure-Shot. This combination produces a snug fit of the bulkhead inside the fiberglass sheath. The delay train end of the fiberglass sheath is examined to insure that no burrs that could gouge or produce channels in the surface of the grain are present. The bulkhead/thermalite bundle is then slid a measured distance into the sheath and secured in place with three drops of thin cyanoacrylate glue applied to the delay grain side of the bulkhead. Care is taken not to drop glue directly on the protruding Sure-Shot. The assembly is allowed to air dry. A one inch long 3/8" O.D. cardboard spacer/insulator is then placed over the fiberglass sheath so that 5mm of the sheath extends beyond the spacer at the delay grain end. The cardboard spacer/insulator is glued to the sheath with thin cyanoacrylate glue. Finally, the delay grain is slid into the assembly and pushed snuggly against the bulkhead and internal Sure-Shot with a wooden dowel. The exposed end of the grain is covered with a removable paper cap until ready for prepping. The assembly is now complete. The typical mass of the completed DTEA is 2.5 - 3.0 grams.


Figure 1 - Delay Train/Ejection Assembly (scanned at 100 dpi)

Download Figure 1 in .TIFF format for printing (scanned at 300 dpi, 112 Kbytes)

Delay Train/Ejection Assembly

II. Booster and Dart Construction

The theoretical consideration of the design parameters resulted in the booster and dart construction depicted in the scale drawing of the test models, Figure 2. The booster was constructed of Apogee BlackShaft PT-18 tubing (nominal 18mm). The transition section was constructed of six lb/ft³ balsa, turned on a Unimat modeler's lathe. The transition section was center-drilled so that 1 cm of the dart's body tube is seated within the transition section. This exposes the delay train ignition fuse to the break-through burn of the booster engine at burnout. A paper/cyanoacrylate laminated collar was used inside the transition section for a smooth fit with the dart tube. The booster fins were constructed of 0.020" Apogee Waferglass as indicated in the drawing.

The balsa dart nose cone was turned on a Unimat modeler's lathe. For the altitude test flights, the dart body was constructed of 7/16" O.D. (0.438" or nominal 11mm) Garolite tubing (paper/phenolic resin laminate). This material was chosen to help increase the mass of the dart to the optimum mass without compromising tracking powder and recovery device capacity. Some preliminary test dart bodies were made from rolled paper, bonded with cyanoacrylate or aliphatic resin glue. Darts of two different body lengths were constructed. A six inch body tube was used for B-powered darts, while a 6.5" tube was used for C-powered darts. The increased length of the C models was to increase mass and tracking powder capacity. The dart fins were constructed of 0.015" Apogee Waferglass, the planform may be seen in the figure. The dart recovery system consisted of a 3/4" x 24" red plastic or aluminized mylar streamer. The shock cord consisted of fourteen inches of 27 pound squid line attached to a four inch piece of fine music wire. The squid line was attached to the music wire by a thread wrapping, covered with cyanoacrylate glue, to minimize obstructions within the body tube. The music wire was hooked at the open end and attached to the forward end of the delay train assembly by two wraps of nylon-reinforced strapping tape. The hooked end stopped the wire from sliding beyond the strapping tape.

Through the use of the Barrowman center of pressure equations, the model was designed to have a minimum one caliber stablility margin in the boost configuration. The dart was designed to have a minimum two caliber stablility margin during the coast phase. The forward center of gravity of the dart permitted the use of smaller fins, but larger fins and a more conservative stabiliy margin were chosen to prevent any dynamic stability problems.


Figure 2 - Test Models (scanned at 100 dpi)

Download Figure 2 in .TIFF format for printing (scanned at 300 dpi, 100 Kbytes)

Test Models

III. Working Principle

The working principle of the boosted dart is very simple. In the prepped configuration, an external Sure-Shot ignitor is held against the outside surface of the delay grain by a small bundle of wadding and masking tape (again, see Figure 1). This Sure-Shot ignitor extends through the transition section of the booster and is exposed to the uncapped end of the booster propellant grain. When the booster engine burn breaks through the top of the grain, the pressure and heat from the engine simultaneously blows the dart free of the booster and ignites the Sure-Shot ignitor leading to the DTEA. It is assumed that this occurs at (or very near) the maximum velocity achieved during the boost phase. The delay grain is ignited and burns the appropriate amount of time during the coast phase of the dart before igniting the internal Sure-Shot ignitor and the surrounding thermalite. The gas produced by the thermalite serves as an ejection charge, pressurizing the tube and ejecting the tracking powder and recovery device. The dart coast phase is, therefore, analogous to the coast phase of a typical model rocket.


IV. Delay Train/Ejection Assembly Static Testing

An extensive static test program was conducted to insure the reliability and safety of the DTEA.

The first part of the test program involved several burns of the grain material inside the fiberglass casing to test the heat resistance of the casing material. The loaded casings were placed on a brick or metal surface and ignited electrically using thermalite ignitors.

Three tests of the completed DTEA were run to insure that the mechanism could expel the tracking powder and recovery device. The DTEA was friction-fitted into body tubes containing tracking powder and recovery devices similar to those intended for use in flight tests. The body tubes were suspended vertically on a string during the tests.

Two additional tests were conducted using booster motors and simulated boosters to test ignition of the external Sure-Shot ignitor. All static test results were positive. No particular attention was given to delay times in the preceeding tests.

Delay times were static tested by taping the DTEA to a metal rod inserted into the ground above a blast deflector. The DTEA was ignited with a thermalite ignitor and the time between the the observed ignition of the delay grain and the ejection charge was measured. The time was measured to the nearest hundredth of a second with a stopwatch. A total of nine DTEA timing tests were conducted. Two grain materials with different burn rates, both supplied by Vulcan Systems, were tested. Three tests each of seven second, nine second, and nine second (fast burn) desired delays were run. Results of these tests are listed in Table 2.


V. Flight Tests

1. Preliminary Flight Tests

Four preliminary flight tests were conducted to test the reliability of the boosted dart configuration. Due to the experimental nature of the project, a limited number of range personnel were employed to assist with the observation and recovery. Three darts with 7.2 second delays and Estes B6-0 boosters and one with an 8.6 second delay and an Estes C6-0 booster were tested. All models were launched from a tower launcher. The weather conditions were: a temperature of 75° to 80°F, five to fifteen mph winds, and limited visibility due to haze and the cloud ceiling.

2. Final Flight Tests

All final flight tests used for evaluation were conducted on one day, with weather conditions of: a temperature of approximately 80°F, winds of five to ten mph, and limited periods of good visibility. The flight plan included four Estes C6-0-powered boosted darts with two each of 8.6 and 10.2 second delays, three C6-7-powered control models, three B6-0-powered boosted darts with 7.2 second delays, and three B6-6-powered control models. The control models, considered optimized conventional single-stage design, are illustrated in Figure 2. The controls were constructed of CMR RB-74 tubing, NC-74P nose cones, and 1/32" plywood fins. These models were sanded and finished with dope and thin cyanoacrylate glue.

A two-station tracking system was set up on a 512 meter baseline. The baseline was sufficiently far from the launch area to prevent any closure problems at low azimuth angles. The trackers were zeroed on the opposite tracker and the launch area, and were re-zeroed periodically through the day. The geodesic equations were used for the reduction of the tracking data. As in the previous test, only range personnel essential for the recovery and tracking of the models were employed. Models were prepped for flight and massed. The mass of all B control models was adjusted to 35 grams and the mass of all C control models was adjusted to 40 grams. The mass of the darts were adjusted to near optimum mass with tracking powder or lead ribbon ballast. The dart mass and launch mass (mass of dart and booster) were recorded. All models were launched from a tower launcher. Results of the flight tests, including masses, tracking data, altitudes, and closure percentages are presented in Table 3.


Data


Table 2 - Delay Train Static Test Data


Vulcan Systems Slow Grain

Test   Desired delay   Grain length   Measured delay    Percent error
  1       7.0 sec          0.28"         7.12 sec          -0.56%
  2       7.0 sec          0.28"         7.02 sec          -1.96%
  3       7.0 sec          0.28"         7.35 sec           2.65%
                         Mean delay:     7.16 sec
            Standard deviation (SD):     0.169 sec
                           +/- 3 SD:  +/-0.51 sec (+/-7.1%)
       Coefficient of variance (CV):     2.36%


Test   Desired delay   Grain length   Measured delay    Percent error
  4       9.0 sec          0.33"         8.85 sec           2.47%
  5       9.0 sec          0.33"         8.80 sec           1.89%
  6       9.0 sec          0.33"         8.26 sec          -4.29%
                         Mean delay:     8.63 sec
            Standard deviation (SD):     0.327 sec
                           +/- 3 SD:  +/-0.98 sec (+/-11%)
       Coefficient of variance (CV):     3.79%

Vulcan Systems Fast Grain

Test   Desired delay   Grain length   Measured delay    Percent error
  7       9.0 sec          0.56"        10.20 sec           0.29%
  8       9.0 sec          0.56"        10.18 sec           0.10%
  9       9.0 sec          0.56"        10.13 sec          -0.39%
                         Mean delay:    10.17 sec
            Standard deviation (SD):     0.036 sec
                           +/- 3 SD:  +/-0.11 sec (+/-0.39%)
       Coefficient of variance (CV):     0.35%

Table 3 - Flight Test Data

             Launch   Dart          Tracking Data
   Model      mass    mass     Az1    El1    Az2    El2    Altitude   Closure         Comments
B Control 1    35      NA     21.25  56.5   20.0   52.5     382.7m     2.19%      ---
B Control 2    35      NA     26.25  53.5   30.25  55.25    405.2m     2.10%      ---
B Control 3    35      NA       -      -      -      -        -          -      No track - poor visibility
B Control 4    35      NA       -      -      -      -        -          -      No track - poor visibility
B Dart 1      33.3    14.5      -      -      -      -        -          -      No track - Tracker 1's view obscured
B Dart 2      35.4    15.1      -      -      -      -        -          -      No ejection observed
B Dart 3      36.2    15.2    23.55  61.25  21.0   57.25    463.9m     1.15%    6.5" dart, 7.2 second delay
B Dart 4      34.5    14.0    27.5   54.5   35.5   60.0     464.2m     0.56%    6.0" dart, 7.2 second delay
B Dart 5      35.9    15.6    37.0   52.25  43.25  54.5     449.6m     2.05%    6.5" dart, 7.2 second delay
B Control 5    35      NA     14.75  44.25  35.0   62.5     359.6m     3.59%      ---
B Control 6    35      NA       -      -      -      -        -          -      No track - poor visibility
C Control 1    40      NA       -      -      -      -        -          -      No track - poor visibility
C Control 2    40      NA       -      -      -      -        -          -      No track - poor visibility
C Control 3    40      NA       -      -      -      -        -          -      No track - poor visibility
B Dart 6      37.0    16.4    24.5   49.75  39.5   60.25    422.3m     1.18%    6.5" dart, 8.6 second delay
C Dart 1      44.5    18.4      -      -      -      -        -          -      Not launched - poor visibility

Note: All masses are recorded in grams, all tracking angles are recorded in degrees.
      The tracking baseline was 512 meters.

Results and Discussion

I. Static Tests

Results of all static tests were positive, demonstrating a high degree of reliability of the DTEA. The fiberglass casing sufficiently resisted the heat generated by the grain material. The short residual burn of binding resin noted did not prove to be a problem when the fiberglass sheath was enclosed inside the cardboard spacer/insulator and the dart airframe. The tracking powder and recovery device were vigorously expelled from the body tube in all tests. It is important to note that in all of the static tests where the DTEA was not restrained, no motion was generated during the burn of the delay. In several cases, insufficient pressure was generated to blow the charred wadding and ignitor wire from the base of the DTEA. These observations demonstrate that no significant thrust was generated by the DTEA.

The results of the DTEA delay time tests are listed in Table 2 of the preceeding Data section. The desired delay time, measured delay time, and percent error from the mean time is presented for each test burn. The mean delay time, the standard deviation (SD), the mean plus or minus 3 SD, and the coefficient of variation (CV) is presented for each test group. These give a statistical illustration of the precision of each DTEA group.

The accuracy of the nominal seven second delay was very good, with the mean (7.16 seconds) being within 2.3% of the desired delay time. The precision was +/-7.1% (0.5 sec) at the 3 SD level. The mean measured delay (8.63 sec) of the nominal nine second delay (slow grain) was within 4.2% of the desired delay with comparable precision of +/-0.98 sec or 11% at the 3 SD level. Although the accuracy of the mean delay time (10.17 sec) of the nominal nine second delay (fast grain) was somewhat lower (13%), the precision was remarkable (+/-0.11 sec or +/-0.35% at the 3 SD level). This is perhaps attributable to the grain itself and experience gained in preparing the DTEAs.

One factor influencing our ability to match the exact desired delay time was trying to allow for the lag time of the internal Sure-Shot ignitor burning through the bulkhead to the thermalite ejection charge. The burn rate of the grain provided by the manufacturer was also approximate and did not prove to match predictions. We decided that the measured delays were close enough for our flight tests. Since the DTEAs were prepared in batches, we believed that it was more important to know the delay time than risk introducing error by the preparation of new batches. The preparation and testing of new batches would have been impractical due to limited supplies, time, and finances.

No failures were observed for a total of twelve static tests involving completed DTEAs (three preliminary and nine timed tests). The accuracy of the DTEAs was considered acceptable and the precision excellent. The ability of the DTEA to perform its function was demonstrated. The static test results demonstrate that the DTEA is a safe and reliable delay timing/ejection mechanism.


II. Flight Tests

1. Preliminary Flight Tests

All three B6-0-powered darts functioned flawlessly, with the red tracking powder cloud clearly visible from the launch site. Unfortunately, the C6-0-powered dart penetrated the cloud ceiling and the ejection cloud could not be observed. However, the sound of the ejection was thought to be heard by some of the range personnel. Proper functioning of the C dart remained uncertain since it was not recovered. Only one of the B darts was recoverable due to poor model visibility. The success of the preliminary flight tests allowed for the scheduling of final flight tests with tracking.

2. Final Flight Tests

The final flight test data is listed in Table 3 in the preceeding Data section. All of the data listed in the table was collected on the same day. Deviation from the original flight plan was necessary due to poor tracking visibility. After three failed attempts to track C-powered single-stage control models, plans to track C-powered darts were abandoned. (In fact, attempts to track C-powered darts on two different outings were abandoned for the same reason. Because of the range personnel required to conduct tracking, we were limited to flying on weekends, and the weather was not very cooperative in that regard this year.) With this impediment, we concentrated on obtaining useful data from B-powered darts. Some of the darts originally intended for C-powered flight were used for B flights. The extra half inch of body length proved to be insignificant.

The data shows that in all test flights, the B6-0-powered boosted darts achieved a higher altitude than the B6-6-powered control models. Control model altitudes for three flight tests ranged from 360 to 405 meters, with a mean altitude of 383 meters (SD = 23m). Altitudes for the three darts with 7.2 second delays ranged from 450 to 464 meters, with a mean altitude of 459 meters (SD = 8.4m). B Dart #6 was not included in the group for statistical calculations because its delay and mass were not optimized. (In spite of this, it still achieved a greater altitude [422m] than the control models. The dart was originally prepped for C-powered flight, but was flown with a B booster due to visibility limitations.) The mass of each dart was within one gram of the optimum mass for that configuration (except as noted above). As previously discussed, the launch mass of the B control models was 35 grams. The mean altitude achieved by the B darts is 76 meters (20%) higher than the mean altitude achieved by the control models. Results of a two-tailed T-test show that the two groups are significantly different at a 99% confidence level. While the relative altitude increase is in line with the theoretical calculations, the altitudes are higher, indicating that the models demonstrated a lower drag coefficient than originally estimated.

Several other significant observations were noted. The flight trajectories of the dart vehicles were very good, with only minor weathercocking observed. When sky conditions permitted, a smoke trail was clearly visible for approximately the last twenty percent of the coast portion of the dart flight. Seven out of nine boosted dart flight attempts (including the preliminary flights) were known to perform correctly. The success of the one C dart mentioned previously remains uncertain. No ejection cloud was observed for one B dart during the final flight tests. It is suspected that this apparent failure was due to a crack in the external Sure-Shot ignitor leading to the DTEA, rather than the DTEA itself. Special attention was given to the condition of the Sure-Shot in all following attempts.

It is realized that the altitude advantage demonstrated by the B-powered darts flown in this study does not directly translate to a competitive advantage in this engine class, since the possibility of flying 13mm staged mini-A models must be considered. Although the empirical data verifies the altitude advantage theoretically predicted, not all elements of dart flight are completely understood yet. While the analysis predicts an altitude advantage for the configurations we studied theoretically, it remains for flight testing to prove the advantage of the configurations we did not empirically test, as well as other configurations (such as a two-stage mini-A-powered dart vehicle). Revised theoretical tables and graphs pertaining to mini-A-, B-, and C-powered boosted darts are presented in Appendix I. As a result of the flight tests, the boosted dart and control vehicle drag coefficients have been adjusted downward, from 0.5 to 0.3. This figure is more in line with the altitudes empirically observed. These graphs may be used for future reference for similar dart models. The smaller darts for mini or staged mini models (a dart diameter of 0.25" or 0.313" is suggested) present definite technological challenges.

A final comment should be made regarding the DTEA as it is presented in this report. The authors do not advocate the use of the DTEA for NAR competition flying since its use and construction may not meet the requirements of the United States Model Rocket Sporting Code. The DTEA was developed strictly as a research tool. The authors believe that the DTEA has been demonstrated safe and reliable within the requirements of the NAR Safety Code for research and development. The authors drew both upon professional experience and experience gained assisting in the manufacture of engines for the 1987 U.S. Internats Team in developing and conducting this project.


Conclusion

The objectives of this report were as follows:

  1. To theoretically evaluate altitude performance characteristics of a model rocket boosted dart and determine if certain design parameters may result in a potential altitude advantage over an optimized conventional single-stage model.

  2. To develop a lightweight, compact, safe, and reliable delay timing and ejection mechanism capable of deploying a recovery device. This device will allow empirical flight testing of boosted darts.

  3. To empirically evaluate and demonstrate any altitude advantage predicted from boosted dart theory by comparing the altitude achieved by boosted darts to altitudes achieved by optimized conventional single-stage models within the same total impulse class.

In conclusion, we believe that each of the objectives pursued was achieved:

  1. Theoretical parameters were evaluated to determine design characteristics that would result in an altitude advantage for a boosted dart over optimized conventional single-stage models in the same total impulse class. For the B-powered darts, a performance increase of 19% was predicted.

  2. A compact, lightweight, safe, and reliable delay timing and ejection device was developed. This device was used to conduct flight tests of boosted darts.

  3. A set of flight tests were conducted to compare the altitude performance of the boosted dart with an optimized conventional single-stage model. These tests demonstrated a 20% altitude performance increase for the dart models.

In addition, tables and graphs are provided addressing considerations such as optimum mass and desired delay times for researchers who would like to conduct future research with boosted darts. Areas for future research include verifying predicted altitude advantages for other power configurations and solving the technological problems associated with lower-powered boosted darts (in particular, the mini-A-powered model). Finally, the experimental nature of the DTEA and its incompatibility with the U.S. Model Rocket Sporting Code for most competition flying is emphasized. We hope that this work will inspire manufacturers to market a prepackaged DTEA. Such a development would open a new realm of model rocketry, allowing other modelers to take part in the boosted dart experience.


Cost Estimate

The total expenditure on this project was approximately $105, broken down as follows:

* delay grain from Vulcan Systems            $15.00
* thermalite and Sure-Shot ignitors          $10.00
* miscellaneous Estes engines                $30.00
* Garolite tubing for darts                  $10.00
* Apogee components for dart models          $10.00
* CMR components for control models          $ 8.00
* balsa block for balsa parts                $ 2.00
* printing and copying costs                 $20.00

Other items such as an Atari ST computer, software, and printer, lathe and assorted shop tools, triple-beam balance, launch controller and tower launcher, tracking scopes, and walkie-talkies were items available at hand.


Bibliography

Estes Industries. Technical Note TN-1: Model Rocket Engines. Penrose, CO: Estes Industries, 1972.

Estes Industries. Technical Report TR-10: Altitude Prediction Charts. Penrose, CO: Estes Industries, 1967 (revised 1971).

Kane, John. "Some Thoughts On Boosted Darts", The Journal Of The MIT Rocket Society - April 1980, 1980.

Malewicki, Douglas. Technical Information Report TIR-100: Model Rocket Altitude Performance. Phoenix, AZ: Centuri Engineering Company, 1970.

Mandell, Gordon; Caporaso, George; and Bengen, William. Topics In Advanced Model Rocketry. Cambridge, MA: The MIT Press, 1973.

Steele, Matt. A telephone conversation about his work on boosted darts for the C PL event at the 1980 World Championships.

Stine, G. Harry. Handbook of Model Rocketry, Fifth Edition. New York, NY: Arco Publishing Company, 1983.


Appendix I - Revised Altitude Charts


Appendix II - Model Parameters and Altitude Program


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