IntroductionThis report presents details of the flight of the Frostfire 3 rocket. The Frostfire series of flights occur exclusively during the winter season (hence the name) taking advantage of an expansive frozen lake as a launch site, allowing for higher altitude flights. This allows for use of more powerful motors. The Frostfire 3 utilized the new "L-Class" Liberty rocket motor, which was designed in late 2004 and first test fired in January of 2005. The successful static test firing paved the way for the use of the Liberty motor in the Frostfire 3 rocket. The two earlier Frostfire rockets were powered by the "J-class" Paradigm solid rocket motor.
Goals of the Frostfire 3 mission include:
Frostfire 3 was equipped with a two-stage recovery system, similar to that used for the earlier Frostfire flights, featuring separate drogue and main parachute deployment (drogue deployment occurs at apogee and main deployment occurs when the rocket descends to a lower altitude). The main reason for a two-stage system is to greatly reduce downwind drift, particularly important for high-altitude flights. Two completely independent systems were used for both drogue and main parachute triggering. The primary system was an RDAS flight computer and the backup was an electronic Timer based system, consisting of the Parachute Ejection Triggering (PET) module used on previous flights. The R-DAS unit also served as a flight data recorder, measuring and storing accelerometer and barometric data continuously throughout the flight, at a rate of 100 samples per second.
The R-DAS uses accelerometer based drogue activation and a barometric main chute activation. The PET Module consists of two electronic timers -- one for drogue activation and the other for main activation. Both timer circuits are completely independent, and are designed to be activated at liftoff by separate g-switches. The delay durations were determined based on the SOAR simulation and on the expected descent rate of the rocket. The PET Module is the same one used for Frostfire Two as well as for the Zephyr series of flights. For this flight the Air-Speed drogue triggering system was disabled.
The R-DAS unit was housed within a protective glass/epoxy canister. Since the R-DAS has a low-end operating temperature limit of 0oC (32oF), to ensure reliable operation in the cold weather expected at launch time, the canister was fitted with an electric "heater". The heater consisted of 11.6 feet (3.5 m.) of 0.025 inch (0.64 mm) diameter nichrome wire wound in a spiral fashion around the canister. The nichrome wire was bonded to the canister with a layer of epoxy. The heater was designed to have two settings -- high and low, delivering an average output power of 6 and 2 watts, respectively. A power supply external to the rocket consisted of 4 AA NiMH cells, each was a capacity of 2300 mA-hrs. The only difference in achieving the different power settings was having the batteries in series (high power) or in parallel (low power). Testing indicated that at the high setting, the batteries would function for 2 hours, at the low setting, for about 5 hours. To help minimize heat loss, the R-DAS canister was wrapped in a sleeve of fibreglass insulation. Prior to power-up of the R-DAS, the heater would be disconnected and the element leads shunted to ensure that the coiled wire would induce no adverse effects. A digital thermometer was used to monitor the temperature within the canister. The PET Module does not require any thermal protection, as the timer circuits were designed for operation at a temperature as low as -20oC (-4oF).
As was the case for Frostfire Two, a total of three parachutes were used for recovery. For the drogue system, a pair of 70 x 22 cm. ("1/2 metre") cross-type parachutes were employed. Average descent velocity was predicted to be 58 ft/sec (17.7 m/s) during drogue descent. The main parachute was a single 150 x 50 cm. ("1 metre") cross-type parachute used on earlier flights. Following main chute deployment, the anticipated descent velocity would reduce to a gentle 26 ft/sec (7.9 m/s). Based on these decent rates, the PET Drogue Timer was set at 24 seconds following liftoff, based on an expected peak altitude of 11700 feet (3560 m.). The PET Main Timer delay was set at 193 seconds from liftoff, based on a main deployment at 1200 feet (350 m.). The R-DAS was configured for main deployment at 1000 feet (300 m.). The R-DAS backup timer feature was invoked as well, being set at 24 sec. for drogue triggering, and at 195 seconds for main.
Both the drogue ejection charge and main ejection charge consisted of 1.3 grams of Crimson Powder.
Payload module consisting of Timer Module, and R-DAS encased in heated canister.
To aid tracking of the rocket during descent, a smoke generator module was included as part of the rocket payload. The smoke generator consisted of a grain of 82 grams of 56/44 potassium nitrate/dextrose, cast into a tube of 1" EMT. To reduce mass, the walls of the tube were turned down to 0.020" (0.5 mm). The grain length of 82 mm was expected to provide for smoke generation of just under one minute. A 556 based timer similar to that used for the parachute system was constructed and used for activation of the smoke charge 155 seconds after burnout. This was expected to trigger the charge at an altitude of approximately 3500 feet (1060 m.) during drogue descent. To protect the rocket interior from the combustion heat, the smoke charge tube was wrapped in a ceramic paper insulator, then covered with aluminum foil tape.
Smoke generator module.
An experimental device, which I've deemed a "Pyrotechnic Release Device" (PRD), was being used for the first time aboard a rocket. The purpose of the PRD is to release the tethering line that ties the aft fuselage to the rest of the rocket. The intent was to have the aft fuselage (with attached drogue chute) separate from the rest of the rocket once the main parachute has deployed. As such, the rocket would complete the final descent phase as two separate entities, to avoid any possibility of tangling of the drogue and main parachutes. The operation of the PRD system is as follows. When electrically triggered, a small pyrotechnic charge contained within the PRD fires, forcing a retention pin to move, releasing the lug to which the tether is attached. The method of triggering the PRD is essentially identical to that used for triggering the smoke charge of the Frostfire One rocket. A tension load in the main tether, resulting from main chute deployment, causes a small paper cylinder to collapse, tripping a microswitch. Testing indicated a critical tension load of 10 lb (average) would cause the cylinder to collapse. The PRD was robustly designed to handle shock loads of 600 lbs. (2.7 kN) and could "release" a load of up to 100 lbs. (450 N.)
Pyro Release Device
(Click for larger image) (Click for exploded view)
The fins used on the Frostfire 3 rocket were originally designed to be fitted on the Zephyr rocket. The fins were contoured to a NACA0005 symmetric aerofoil shape. It was later decided to use them for Frostfire 3, owing to their inherent stiffness and resistance to flutter, which was felt to be important for supersonic flight. It was found that six of these fins were required to achieve an acceptable stability margin, owing to the rather short span of these fins. The resulting minimum static stability margin was 1.77, which was the condition at liftoff.
The rocket motor used for Frostfire 3 was the recently developed Liberty "L" class motor. This motor uses the RNX-71V potassium nitrate/epoxy/iron oxide propellant in a "Rod & Tube" grain configuration. In terms of design, this motor is very similar, but larger than the Paradigm used on the two previous Frostfire flights. Static tested on January 16, 2005 as test LRMS-1, the motor performed basically up to expectation, delivering a total impulse of 3337 N-seconds and an average thrust of 200 lbs (890 N.), with a burn time of approximately 4 seconds. However, problems with preparation of the propellant, complicated by the large mass required, meant that the delivered thrust was lower than expected and the burn time was longer than expected. The problems were overcome and the propellant for the flight motor (designated LRMS-2) was expected to deliver results much closer to design. The total propellant mass was 3207 grams (7.07 lbs.). The motor had a constant Kn = 958. Ignition of the motor was with a pair of "Spitfire" igniters.
Left: Liberty rocket motor and author
Pre-launch weight of the Frostfire 3 rocket was 17.87 lbs (8.105 kg.); total height was 6.91 ft. (2.11 m.).
To aid navigation on the featureless frozen lake, to and from the launch site, and for distance measurement including distance from launch pad to touchdown, a GPS (Global Positioning System) unit was being tried for the first time. The unit was a Garmin eTrex 12-channel model. For transportation, a snowmobile was also being used for the first time on this expedition. The rockets and support equipment were hauled on two wooden toboggans hitched to the snowmobile, tied one behind the other.
Launch ReportTuesday, Feb.22, 2005
In addition to Frostfire 3, two additional rocket launches were planned to take place on this particular outing. As was the case with the previous two annual Frostfire expeditions, my friend Rob Furtak had designed and built an impressive new rocket, which he'd christened "Straycat". This rocket was of comparable size to Frostfire 3 and similarly featured lightweight all-composite construction. This formidable rocket was powered by a "K-class" KNDX motor, which had been previously static fired a number of times. The first planned launch, however, was of the SkyDart, which was to serve as a "sounding" rocket to determine winds-aloft speed and drift direction. Last winter's flight of Frostfire Two had brought to light the importance of having this knowledge prior to flight. In order to achieve maximum altitude, and therefore more valuable data, SkyDart was configured to have minimum weight. As such, the peak altitude was expected to be nearly 2000 feet (600 m.). As had been the case with the previous SkyDart flights, the motor was the A-100M fitted with the Pyrogen-DED system for parachute deployment.
The weather had been unsuitable for the entire week leading up to the eventual launch day. Even though we were set to go earlier, the launch expedition had to be postponed. At long last, the weather forecast had predicted suitable conditions for Tuesday the 22nd. Even though it was cloudy and light snow was falling when I arose at 4:30AM, I was reasonably confident that the skies would clear up by expected launch time, as promised by the weather forecasters. As such, I proceeded to do the final packing of my two rockets and the paraphernalia needed to support the launches.
When we arrived at the lake around 6:00 AM, it was still snowing lightly. Dawn was breaking and the sun was nearly visible through the thin cloud layer. We proceeded to unload the snowmobile and pack our gear onto the two toboggans that were to be towed in tandem behind the snowmobile. All temperature-sensitive electronic gear, such as the cameras and FRS radios, were placed inside a styrofoam-lined "cooler" to keep these items from getting overly chilled. Using rope, we fastened the cargo to the toboggans in a secure manner, for the long over-lake journey to the launch site, which lied about 1/3 way across the lake's span. It was 6:30 by the time we were set to depart on our nearly 7 km. trek. Just prior to closing up the transport box that housed the Frostfire 3 rocket, which had been partly disassembled, I switched on the power to the R-DAS heater. To conserve battery power, it was put onto the "low" setting . I'd planned to monitor the compartment temperature during our journey. The air temperature at this time was -5oC, quite mild, so I was confident that the .low power setting would suffice, at least for now.
Rob and our "snow-train". Taking a break during the trek to the launch site
The journey went surprisingly smoothly. The snowmobile performed admirably, pulling its load of two persons and two fully loaded toboggans without complaint, despite the deep, powdery snow covering the lake. The toboggans also behaved well, obediently following the machine without any threat to spill their precious cargo. A check of the R-DAS compartment temperature half-way to the site showed that the heater was maintaining a comparatively balmy 25oC internal temperature. The snow had stopped falling shortly after our trek had commenced, and the sky had appeared to be clearing. However, as we came to a halt after arriving at our destination some hours later, snow was falling once again.. And quite heavily. I felt, or should I say "hoped", that we were merely experiencing a "snow squall" -- a short-lived, localized precipitation event. A scan of the sky overhead revealed that the clouds appeared be rather thin, and blue patches were visible - a good sign. Rob used his mobile phone to make a call to "home base" to get the latest word on the expected weather. The report concurred with my expectation so we decided to wait it out.
Rob decided to demonstrate his brand new rocket motor ignition system with a built-in, handy-dandy "Electric Automated Ignition Retrieval System". The system featured 1000 foot (300 m.) long electrical leads for the remote launch box, and a power winding mechanism to make easy work of reeling in the extensive line. The demonstration was impressive. We also began to unpack some of our gear, such as the launch pad, and began setting up in anticipation of improved weather. Our patience paid off, and by noon, the sky had largely cleared, and we were set to launch the SkyDart rocket. Surface winds had, fortunately, remained remarkably light. The igniter was installed in the SkyDart's A-100M rocket motor, the ignition leads were connected and the system armed. We headed to where the remote launch box was located, about 250 feet distant. Rob announced the countdown, and on "zero" pressed the launch button. The motor showed no sign of life and after a few minutes, we investigated and found that the igniter bridgewire had burned, but had failed to initiate the igniter's pyro compound. We concluded that my "power-hungry" igniter had failed due to insufficient power being supplied by Rob's new ignition box. We swapped out Rob's ignition box for my system which was capable of delivering the needed power, having been used with this sort of igniter in the past with excellent reliability.
By now, it was noon. On the second attempt, the motor fired successfully, boosting SkyDart Flight SD-4.to its highest yet apogee. Just then, the parachute was seen to deploy, followed by an audible "pop" sound heard nearly two seconds later, delayed by the distance. The rocket drifted downrange, indicating a slight wind, and touched down in the soft snow about a minute later, at a distance estimated at approximately 500 feet. At the recovery site, we used the GPS to obtain the exact touchdown distance from the launch pad, which was recorded at 585 ft. (178 m.). We were now aware of the winds-aloft direction and extent, being just over 7 mph (12 km/hr) based on the flight of this convenient "sounding" rocket.
Author with the SkyDart rocket just prior to this rocket's "sounding" flight.
The StrayCat rocket was loaded onto the launch pad for the ensuing flight. Pre-launch checkout of the recovery system went well. Both the G-Wiz unit and the Timer module were functioning normally (the StrayCat rocket had been likewise equipped with an electric heater system for its flight computer, a brand-new G-Wiz unit). While Rob made the final connections of the motor igniter to his ignition system, I set up the tripod mounted videocamera, which was positioned about 50 feet (15 m.) from the pad in order to capture a close up of liftoff.
The weather at this time was near-perfect. The sky had scattered clouds, but the sun was shining and there was no surface wind. We collected the FRS radios for communication, as well as my digital videocamera, then rode the snowmobile to the location where the launch box had been placed, having been reeled out to the full 1000 feet (300 m.) extent for this flight. We were located roughly downwind, with the sun at our backs to aid visibility of the rocket in flight. At the site, I made myself comfortable in the portable lounge chair that we'd brought along. I was to operate the videocamera, and as such, experience had taught me that sitting comfortably, rather than standing, made for a much more stable platform to shoot the rocket during ascent, particularly important under high zoom condition.
Rob gave the all-clear signal over the FRS radio and commenced the countdown. Five-4-3-2-1-zero! Immediately, a immense cloud of white smoke appeared at the base of the launcher, and in less than a blink, StrayCat was streaking skyward, leaving a dense white trail of smoke in its wake. After the brief one-second burn time, the rocket had soon climbed out of sight. The unnerving silence that followed was eventually broken by a comforting "pop" sound some 20 seconds later, as the drogue charge fired. We knew that the rocket would not likely be visible until the smoke charge would commence burning at an altitude of 3500 feet (1000 m.) having been set to be triggered by the G-Wiz. We scanned the sky, nevertheless, hoping to perhaps catch a glint of the sun reflecting off the rocket. The searching proved fruitless. However, after about two minutes, a second, faint "pop" sound was heard off in the distance, directly downwind. We knew then that the main parachute charge had fired and that the rocket should be visible. No smoke trail or other sign of the rocket was seen, however. After a half minute of frenzied hunting, Rob excitedly shouted that he'd made visual contact with the rocket. It was descending under the safety of the main chute, approximately ¾ mile downrange. Shortly after, StrayCat ended its epic flight with a soft touchdown on the frozen lakebed. At the recovery site, the rocket was found to be in nearly perfect condition. The smoke charge had not fired, explaining the absence of a smoke trail during descent (it was later determined to be a problem with the igniter). The new G-Wiz unit had worked flawlessly, and recorded the peak altitude as 7600 feet (2300 m.). The GPS reading indicated that the rocket landed 3710 feet (1131 m.) from where it lifted off. The range was something of a surprise, as this indicated that the winds-aloft were now more brisk than had been indicated by the SkyDart "sounding" flight. Indeed, based on the recorded flight time of 153 seconds, the average wind speed carrying the rocket downrange was a formidable 17 mph (27 km/hr).
Rob cradling the StrayCat rocket. Momentous liftoff of StrayCat.
By this time, it was 12:30 pm, exactly 6 hours after we'd departed on our trek to the launch site. After unpacking the Frostfire rocket from its transport box , I began to reassemble the rocket. Admirably, the R-DAS heater had managed to maintain a compartment temperature of 26oC (79oF). Reassembly of the rocket was straightforward, and consisted of making a field joint of the aft and mid-fuselage sections using aluminum tape, which served as a frangible connection. Frostfire 3 was then installed onto the launcher, and checkout of the on-board electronics begun. As usual, a pre-launch checklist had been prepared, to ensure safety and reliability. This procedure was completed without any hitches. Both the R-DAS and Timer modules were functioning nominally. The smoke charge was then armed and the electrical connections to the heater system severed and stowed. The final step of the pre-launch procedures was to connect the motor igniter to the ignition box, confirm continuity and arm the system. I then powered up the tripod mounted videocamera for the close up footage. Rob and I then jumped on the snowmobile and headed out to where the launch box was located.
Frostfire 3 rocket & author.
(grey-tinged snow surrounding launch site is residue from the StrayCat exhaust)
Once again I positioned myself in the "director's chair" and prepared to film the flight, while Rob readied to "go for countdown". For this launch, we'd invited the local conservation officer to be a guest spectator. We all took up our respective viewing positions, and after making the "all clear" announcement, Rob commenced counting down to ignition of the Liberty motor: 5-4-3-2-1-zero!
Nearly immediately, a cloud of black smoke appeared at the base of the rocket, signaling successful firing of the igniter. Within a second, the smoke cloud mushroomed in size and the Frostfire 3 rocket began to rise from the launch pad. Acceleration was very swift as the rocket ascended skyward accompanied by the exceptionally loud noise of the large and powerful Liberty motor under full thrust combined with the jet-like sound of the rocket tearing through the air at ever increasing speed . The rocket rose in a very straight and stable manner, leaving in its wake an ink-black exhaust trail, which thinned as the rocket's velocity grew.
Left: Liftoff of Frostfire 3 rocket
However, after approximately two seconds of continued stable ascent, the rocket was observed to take on a pronounced "wobble". The wobble quickly became more pronounced, made all the more apparent by the wavelike pattern of the smoke trail. After about 4 seconds of flight, at an altitude estimated at approximately 1500 feet (450 m.), the Frostfire 3 rocket succumbed to the aerodynamic loading imposed by the pitching oscillations, and was seen to break apart. This event preceded burnout of the motor, which occurred shortly after.
As breakup occurred, the main parachute was seen to deploy and instantly blossom. It was clear from the limpness of the canopy that the parachute had torn away. Two sections of the rocket could then be seen tumbling downward. The shrieking sound of high speed flight continued for several seconds after breakup, suggesting that at least one section of the rocket was continuing to ascend. Approximately10 seconds later, a "pop" sound was heard, indicative of the drogue parachute charge firing. At this point in time, only the slowly descending main canopy and the two tumbling sections that had broken away were visible, but shortly after, the nosecone was seen to land close to where we were positioned, followed by touchdown of the two tumbling sections. There was no sign of the remainder of the rocket nor any sign of the drogue chute, which had presumably deployed. A short while later, the jet-like sound of a rocket descending ballistically was faintly heard, which increased in intensity. This section was then seen to impact the frozen lake at high speed, approximately 500 feet (150 m.) from where we were situated. The last part to touch down, the main chute canopy, landed a few minutes later approximately ½ mile downrange.
We then proceeded to recover the various components of the Frostfire 3 rocket. The nosecone was found nearby, half buried in the snow, but undamaged. The aluminum tape "coupler" had been fractured at the location where it interfaced with the forward fuselage.
The aft fuselage was recovered next. It was this section that had come in ballistically. Examination showed that it had separated from the mid-fuselage at some point during the flight. Damage to the aft fuselage was largely limited to the coupler section, with some slight damage to the actual fuselage. The six fins were all still attached and were undamaged. Both drogue chutes were still housed within, and had the appearance of being undamaged. The motor was present and had no obvious signs of damage or malfunction. Being still housed with the fuselage meant that closer examination would have to wait until later.
The forward fuselage was recovered nearby. There was no damage whatsoever to this portion which had tumbled down from the sky and landed in the soft snow. However, the smoke charge canister was missing, clearly having been jarred loose and tossed out at some point during the flight, most likely when the rocket broke apart. The Timer module was still housed within and appeared to be undamaged. The tether for the main chute was still attached to the bulkhead, but was broken at the opposite end that was originally attached to the mid-fuselage bulkhead. The eight shroud lines for the main parachute were also attached to the quick-link that joined the two tethers, The stitching that fastened each of the shroud lines to the canopy were torn away.
The final major portion of the rocket to be recovered, and perhaps the most important, was the mid-fuselage, which had likewise tumbled to a relatively soft landing in the snow. The damage that was immediately apparent was to the forward portion of the fuselage. The fuselage wall was fractured approximately half way around the circumference, with the depth of the fracture coinciding with the depth of the coupler that joined the mid-fuselage to the forward fuselage. It was also noted that the PRD had fired and released the tether that connected the mid-fuselage to the aft fuselage. This immediately explained why the drogue chutes had not deployed, even though the ejection charge had been heard to fire. Other than the damaged forward portion, no other damage was observed at this time to the mid-fuselage, giving hope that the electronics were likewise not damaged.
I had managed to follow the ascent of Frostfire 3 with the videocamera. We were hoping that this footage, combined with R-DAS flight data and the physical evidence (since all components were recovered and were in good shape) would provide us with the answer as to what went awry with the flight.
View photo montage of flight.
The aft fuselage and nosecone of Frostfire 3 lying amidst the blanket of snow.
More photos of the Frostfire 3 mission:
The footage from the two video cameras was very good. The hand-held digital videocamera captured the complete ascent and breakup of the Frostfire 3 rocket. The last few seconds and subsequent ground impact of the aft fuselage was also captured. Both cameras recorded the "pop" sound of the drogue charge firing. From inspection of the two video footages, the following times were excerpted:
Post-flight teardown of the rocket revealed :
Graph 1 -- Altitude & acceleration data from R-DAS
Bear in mind that the R-DAS was housed in the mid-fuselage, so this data is for that portion of the rocket only. The acceleration spike at the 19 second mark resulted from the firing of the drogue charge. The rocket "inertial" altitude and velocity during the ascent phase were next calculated by numerical integration of the accelerometer data, yielding the plot shown as Graph 2:
Graph 2 --Altitude & velocity obtained from integrated accelerometer data,
When I initially reviewed these results, I was quite puzzled. Not only because of the large discrepancy between the barometric and inertial altitudes, but even more so because the apparent "apogee" times are in disagreement. The maximum barometric altitude is approximately 5950 ft. (1814 m.) which occurred at t = 15.0 sec., while the apparent maximum inertial altitude is 7523 ft. (2293 m.), at t = 18.3 seconds into the flight. I suspected this discrepancy was somehow a result of the breakup of the rocket and its affect upon the R-DAS sensors (pressure transducer for barometric altitude, and accelerometer for inertial altitude). One obvious effect is clear by looking at the graph, which shows a massive decline in the barometric altitude following breakup which occurred at t = 2.53 seconds. This was undoubtedly due to ram air effect. After the forward fuselage broke off, the R-DAS compartment (previously sealed except for the static ports) would have been pressurized by ram air entering the compartment through a hole that now existed in the compartment forward bulkhead where the main parachute tether had been anchored. The tether had snapped when the main parachute deployed, leaving the hole.
To begin to unravel the puzzle it became important to try to determine which result was valid (if either). Fortunately, the sound of the "pop" from the drogue ejection charge was clearly picked up by both videocameras. As such it is straightforward to estimate the altitude based on the sonic delay -- the time it took the "pop" sound to reach the ground. Both video recordings gave the time from liftoff to the "pop" sound as 24.3 seconds. Since there was no measurable difference between the two recordings, the rocket could be assumed to be directly overhead, meaning that the ascent was essentially vertical, and as such, the distance determined from the sonic delay should correspond well with actual altitude. From the R-DAS data (Graph 1), the acceleration spike corresponding to drogue ejection occurred at t = 19.1 seconds.
Therefore, sonic delay = 24.3 - 19.1 = 5.2 seconds.
s = 1068 (5.2) = 5550 feet.
The following data was derived from analysis of the R-DAS data, based on the assumption that the inertial data is, nevertheless, valid until the point of breakup of the rocket:
The sonic delay analysis provided confidence that the barometric data is valid, at least that portion of the data collected as the rocket (i.e. mid-fuselage) was travelling slow enough, around the point of apogee, that the ram air effect was no longer significant. How then, could the apparently skewed data from the accelerometer be explained? Looking at Graph 1, it is seen that the barometric altitude curve "band" is unusually wide, especially in comparison to the corresponding curve for Frostfire Two, recorded under a normal flight condition. This indicates an oscillating pressure reading. It makes sense that, following breakup of the rocket, that the pitching moment that was great enough to fracture the rocket's airframe, would induce a post-breakup pitching of the rocket (aft & mid-fuselage portions, that is, which remained connected). In other words, the rocket would then be sent tumbling wildly on its upward trajectory.
This could explain the oscillating nature of the barometric pressure signal. More profoundly, this could also explain the skewed accelerometer data. A tumbling rocket would generate centripetal acceleration, the direction of which is inwards along the radius vector of the circular motion. The R-DAS accelerometer would interpret this acceleration as a "negative" (aft-acting) acceleration. Instead of two components of acceleration, as would be the case for a normal flight, there would have been three components -- acceleration due to gravity, drag, and rotation, all effectively acting downward. Numerical integration of the resulting skewed accelerometer data that was done to obtain velocity and inertial altitude could conceivably give the result shown in Graph 2, and thereby explain the greater than actual inertial altitude, and explain the apparent delayed "apogee time". Mathematically, this made sense, but was it realistic that a tumbling rocket could produce the required magnitude of centripetal acceleration? To answer this final piece of the puzzle, I performed calculations to estimate the rate of rotation needed to produce the required centripetal acceleration. Centripetal acceleration is given by:
where is the angular velocity (rads/sec.) and r is the radius of rotation. In this case, r is the distance between the rocket's centre of gravity (cg) and the accelerometer. Angular velocity is related to rate of rotation (symbolized here by capital omega) as , with units of rotations per second.
The first step in this analysis was to fit a quadratic curve through both the inertial altitude plot and the barometric altitude plot. A quadratic curve (2nd order polynomial) was chosen to simplify the analysis (as will be shown later), although it can be seen from the results shown in Graph 3 that the quadratic curve fits are quite good, at least in the region of particular interest for this analysis (i.e. around apogee).
Graph 3 -- Results of curve fitting the plots of inertial and barometric altitudes
The equations for the two curve fits are as follows:
z(t) = -18.154 t2 + 676.3 t + 1227 (inertial based altitude)
where z(t) is altitude as a function of time, t. Taking the first derivative of these two functions provides for the rate of change of altitude of each, or velocity as a function of time. The second derivative provides for the rate of change of velocity, or acceleration as a function of time.
dz/dt = -51.9 t + 780 (inertial based velocity function)
d2z/dt2 = -51.9 (inertial based acceleration)
The result gives both accelerations as a constant. Since we are interested in the difference of these two acceleration values (which is assumed to be attributed to the centripetal component only), this result is quite convenient, which is why a quadratic function was chosen to fit the two curves. Of course, in reality the downward acceleration of the rocket would not likely be truly constant. However, the intent of this simplified analysis is to estimate the centripetal acceleration and subsequently the rotational rate of the rocket, to see if it seems reasonable. As such, the conjectured centripetal acceleration is:
ac = | -51.9 - (-36.3) | = 15.6 ft/sec2
Taking the reciprocal of this value may make more intuitive sense. The reciprocal, which represents the time period of rotation, is 2.2 seconds . This would certainly seem to represent a reasonable and realistic value for an expected rate of rotation, or "rate of tumble" of the rocket (aft and mid-fuselages) on its upward trajectory following breakup. As such, the hypothesis that the tumbling of the rocket could account for the discrepancy between the R-DAS inertial and barometric data seems justified. This represents, therefore, one possible explanation. Other explanations, such as transducer error or cold temperature effects, cannot be ruled out.
As a final note on the R-DAS data, the lag in barometric altitude (compared to the inertial altitude) shown in Graph 2 during the initial part of the ascent is most likely accounted for by the intentionally undersized static ports, which would have restricted the rate at which the R-DAS compartment pressure tended to equalize with the ambient pressure outside of the rocket.
The other aspect of the Frostfire 3 flight that was puzzling was the more profound question as to why the rocket become apparently unstable and began to wobble, then worsen to the extent that the rocket broke apart? Especially considering that the initial climb was remarkably stable. Examination of the video footage provided clear evidence as to why the rocket broke apart. The oscillating motion leading up to the instant of breakup meant that the angle of attack had become quite severe at the extremes of the "swing". In combination with the high velocity of the rocket (mach 1.23), this would have induced a large aerodynamic bending moment on the rocket airframe, which eventually well exceeded the design limit of 225 in-lb (25 N-m) which had been based on the strength of the aluminum tape coupler. The actual bending moment was obviously significantly greater than this. Not only did the tape fracture, the fuselage suffered structural failure as illustrated in the photo shown below.
Fracture of mid-fuselage due to structural overload
Why did the rocket begin to oscillate, and why did the oscillation continually worsen? Structurally, the rocket was exceptionally stiff, owing to the composite sandwich construction and the use of taped joints (which are inherently rigid), and as such, it is unlikely that it was an aeroelastic problem. Unlike Frostfire One which had canted "fin tabs", there was no feature to induce longitudinal roll and as such, the issue of inertial-roll coupling that doomed Frostfire One would not seem to have played a role in the perplexing behaviour of Frostfire 3
As mentioned earlier, the minimum static stability margin of 1.77 was determined using AeroLab software. This minimum value represents the condition at liftoff. This margin would have improved as propellant burned off with a consequential forward shift of the centre of gravity (CG). Adding to this improvement in stability margin would have been the aftward shift of the centre of pressure (CP) predicted to occur as the rocket's velocity increased through the transonic phase of flight. Could it be that the software prediction of CP, used to determine the stability margin, was inaccurate? Note that Stability Margin is defined as the distance between the CP and CG, divided by the rocket body diameter. To attempt to answer this question, I did two things. First, I performed my own CP calculation using the classic Barrowman method, and compared this to the AeroLab prediction of Barrowman CP. The results were consistent, being within two percent. Note that the Barrowman method provides a good estimation of CP in the subsonic flight regime.
As such, it was next desired to determine how accurately AeroLab predicts CP in the transonic/supersonic regime of flight. Conveniently, I happened to be in possession of a comprehensive technical report that provided extensive data on the NASA Hawk sounding rocket, which is basically quite similar to the Frostfire 3 rocket in general shape. This supersonic rocket has a conical nose and trapezoidal fins, differing mainly in the comparatively short length-to-diameter ratio.The Hawk is shown in the figure below.
data for the NASA Hawk rocket
The report provided not only all the dimensional data of the rocket, but also the stability characteristics, including CP data. The CP characteristics of the Hawk rocket had been derived using sophisticated computer software (TAD II) together with wind tunnel data. From the dimensional data, it was straightforward to construct the Hawk in AeroLab and obtain the predicted CP over a range of velocity up to Mach 6 (the maximum velocity of this version of the Hawk, incidentally, was Mach 3.5). A comparison of the AeroLab results with respect to the published data is shown in Graph 4, which plots the distance from the nose tip to the location of the centre of pressure (Xcp) as a function of Mach number.
Graph 4 -- Results of comparison between published and AeroLab centre of pressure location
As can be seen, the two curves compare favourably. The maximum deviation between the two occurs at Mach 2, with a deviation of about 5%. This is considered to be, in engineering terms, a very good correlation. Therefore it would seem reasonable to expect that the AeroLab CP prediction for the Frostfire 3 rocket was accurate, and that basic stability issues were not central to the calamitous behaviour of the rocket.
One possible answer to the puzzle may involve the behaviour of the aerofoiled fins that were featured on the Frostfire 3 as the rocket velocity approached the speed of sound (Mach one). The technical article Transonic Shock Oscillations on NACA0012 Aerofoil ( Shock Waves, Vol.8, Iss. 4, 1998) describes how in transonic flow, following an initial disturbance such as change in angle of attack, a shock wave induced flow separation could occur on one side of the aerofoil. This would change the effective geometry of the aerofoil (decrease in camber) which would deflect the wake off to one direction. With an asymmetric wake and effective negative camber, the shock on the opposite surface would move rearward. As the velocity of airflow and the velocity of the moving shock wave are in the same direction, the strength of the shock is reduced and consequently the boundary layer remains attached to that surface. Meanwhile, the effective change in geometry of the aerofoil should move the other shock forward which should initially increase the shock strength, but as it moves forward into lower airstream velocities a weaker shock results, causing the boundary layer on the upper surface to reattach. This would result in a positive camber with a new shock on the opposite surface moving forward. The cycle then repeats itself, resulting in an oscillating pitching of the aerofoil (and of course the vehicle to which it is mounted).
This concept is illustrated in the figure below:
The aerofoil profile on the Frostfire 3 fins were made to NACA0005 profile. This shape is basically the same as NACA0012, except that the thickness-to-width ratio was 5%, rather than 12%. As such, a similar transonic phenomenon may well be possible, and could conceivably explain the oscillatory behaviour of Frostfire 3.
As a final note pertaining to the post-flight analysis, the R-DAS accelerometer data was analyzed to estimate the performance of the Liberty rocket motor. Knowing the mass of the rocket (as a function of time) and using the aerodynamic drag force prediction from SOAR, the motor thrust was calculated for the duration of the burn. The result is plotted below, together with the design curve.
Performance of Liberty motor in comparison to design
Note that the result after approximately the 1.8 second mark is of less validity, owing to the oscillatory nature of the rocket which clearly would have induced much greater drag than that predicted for stable flight.
ConclusionAlthough the flight of Frostfire 3 was not the successful one that had been hoped for, it is notable that some of the key goals were achieved.
NASA Hawk fin design