Richard Nakka's Experimental Rocketry Web Site

Launch Report -- Frostfire One  Rocket

  • Introduction
  • Rocket Description
  • Launch Report
  • Post-flight Analysis
  • Conclusion
  • Introduction

    This web page presents details of PRMS-2, the official designation of the test flight of the Frostfire One rocket. The Frostfire One rocket is, in essence, the Boreas 1 rocket that was utilized for Flight #5, with certain modifications and enhancements. The motor used for this flight was the recently developed Paradigm solid rocket motor, which was successfully static tested (PRMS-1) on January 12, 2003. As with the Epoch motor used for the Boreas series of flight tests, the Paradigm is powered by the new RNX epoxy-based composite propellant.

    Goals of the Frostfire One mission include:

    • Perform a high altitude test of the two-stage recovery technique
    • First flight test of the new Paradigm rocket motor with first ever rod & tube grain configuration
    • Test the RDAS flight computer for data acquisition and recovery activation
    • Determine the usefulness of an on-board radio transmitter
    • Test a smoke charge for visual tracking at apogee
    • Achieve a peak altitude greater than one mile (1.6 km.)
    View SOAR altitude simulation program output file for Frostfire One:  soar333.txt

    Rocket Description

    Frostfire rocketFrostfire One is comprised of the rocket that was utilized for the fifth flight of the Boreas series, with certain modifications and enhancements incorporated to meet the design goals. Alterations made to the PVC airframe tended to be minor, such as the addition of access ports and other penetrations required for the expanded payload. The existing fins, fitted with small tabs (with a 5o cant), were retained, in order to induce a slight roll to minimize dispersion from a vertical trajectory. This was felt to be particularly important for this flight which had a significantly greater altitude goal than Boreas. A two-stage recovery system is employed, nearly identical to that used for the fifth Boreas flight, whereby a drogue chute is ejected at apogee, followed by a fairly rapid descent to a lower altitude, at which point the main parachute is deployed. For reliability, a double-redundant system is used for drogue activation, consisting of an Air-Speed (A-S) Switch as the primary means, with an electronic timer as one backup system, and the RDAS constituting the second backup. The A-S and timer systems are integrated into a single Drogue Ejection Triggering (DET) module.The A-S switch was set to trigger as the rocket slows to a velocity of 90 km/hr. near the peak. The DET Timer was set for a delay of 19 seconds following liftoff, based on results of the SOAR simulation of the flight profile. The RDAS was configured to "Smart Recovery" mode, whereby drogue activation occurs when the on-board accelerometer discerns zero integration (i.e. rate of change of rocket velocity becomes zero, which occurs at apogee).

    Main parachute activation incorporates single-redundancy for reliability, and consists of a Main EjectionTimer (MET) system, nearly identical to that used for the drogue, and RDAS, which utilizes a barometric sensor to trigger main chute deployment at an altitude of 700 feet (200 metres). The MET timer was set to a delay of 90 seconds, which would trigger main chute deployment at a predicted altitude of 1500 feet (450 metres). In this scenario, RDAS serves a backup role.

    The RDAS unit was also configured to continuously monitor rocket acceleration and barometric altitude (following liftoff) at a rate of 200 samples per second, with the data being stored in on-board EEPROM for post-flight downloading. The RDAS unit is contained within a protective glass-epoxy composite canister. To ensure reliable operation in the cold weather expected at launch time, the canister is encapsuled within a glass fibre insulation sleeve. Active warming of the RDAS canister is accomplished with a chemical hand-warmer packet, inserted two hours prior to launch. Prior testing had demonstrated that the packet is capable of maintaining a temperate environment within the canister for over 8 hours.

    External view of Frostfire One                           Cutaway view of Frostfire One

    A Radio Transmitter, similar to that flown aboard the Cirrus One rocket, is included as part of the payload package. The alterations to this off-the-shelf unit were minor ones, such as elimination of the plastic case, replacement of the "rubber duck" antenna with a tubular one of equivalent length, and the installation of a toggle switch in parallel with the push-button transmit button. A 6.2 V lithium battery is used to power the transmitter. The intended purpose of the radio on this flight is to transmit the "beeping" sounds of the RDAS unit, which provides the ground observers with real-time status of the flight during the time the rocket would be beyond visual range due to altitude. The RDAS unit emits acoustic signals (beeps) which vary depending upon the status of the unit (e.g. standby mode, data acquisition, altitude reporting, etc.). If all works as intended, the radio transmitter therefore allows the ground observers to know the peak altitude achieved even before the rocket has landed, a rather neat feature!

    As an intended visual sighting and tracking aid once the rocket begins descent, a smoke charge system was devised and is incorporated into the rocket. The smoke charge consists of two small cylinders of 1/2" EMT each filled with 20 grams of cast potassium nitrate/dextrose of 56/44 ratio. This ratio was chosen for three reasons: lower casting viscocity, slower burnrate, and lower combustion temperature. The measured burnrate at ambient pressure was 1.5 mm/sec. The lower combustion temperature was of particular importance, as the cylinders are mounted within the aft fuselage airframe, just forward of the motor bulkhead. Two opposing 1" diameter ports were cut in the fuselage to allow expulsion of the combustion products. The burn time of the charges, which are simultaneously ignited by an electrical system, was designed to be 30 seconds. As an ignition aid, a BP/alcohol slurry was used to coat the end surface of each smoke charge. Ignition of the two charges is initiated by tension load in the drogue tether, which causes a small paper cylinder to collapse, tripping a microswitch (see figure below). Testing indicated a critical tension load of 18 lb (average) would cause the cylinder to collapse. The advantage to this technique is that the cylinder is completely rigid and does not deflect or otherwise distort until the critical collapse load is achieved, largely eliminating any likelihood of unintended activation of the ignition system. A safety shunt screw, removed just prior to arming the system, is also incorporated to elminate any possibility of inadvertent ignition of the charges during transport to the launch site.

    Power for the igniters is supplied by two 4 Farad ultracapacitors wired in series, and charged prior to flight by four tiny 1.5V alkaline "button" cells (click for electrical schematic). A full-out ground test of the smoke charge system installed in the rocket was conducted on March 2, 2003, with activation achieved by pulling upon the drogue tether using a lever bar. The test was successful, with simultaneous ignition of the charges, subsequent burning with a copious quantity of smoke being expelled for a recorded duration of 30 seconds. Some minor heat damage occurred around the ports, which was subsequently dressed with sandpaper.


    Technique for triggering ignition of smoke charges

    The motor being used for this flight is the 64 mm Paradigm solid rocket motor, a "J" class motor which delivers a total impulse of 1100 N-sec. with a thrust time of 3.0 seconds.
    The specific propellant formulation is RNX-57, consisting of 70% Potassium Nitrate oxidizer, 8% Ferric Oxide (burn rate modifier & supplemental oxidizer), and 22% Epoxy (fuel & binder). The "rod & tube" grain contains a total of 930 grams (2.05 lbs.) of propellant This is the first flight for this motor, which had been previously static tested once. The motor performed flawlessly in the static test, and consequently no modifications were made to the motor for this flight.
    Complete details on both this motor and the RNX propellant may be found on the respective webpages.

    Pre-launch weight of the rocket is 10.61 lbs (4.81 kg.); total height is 6.67 ft. (2.03 metres). The main parachute is once again the one metre diameter semi-ellipsoidal parachute, and the drogue chute is the same cross-type used previously. The static stability margin (distance between CP & CG) was 2.6 calibres for this flight, based on the Barrowman CP and the liftoff mass distribution.

    Launch Report

    Sunday, March 23, 2003
    The plan called for two rockets to be launched on this day, Frostfire One, and Rob's Smokin' Joe hybrid rocket, which has a similar altitude goal, and was the first test of his rocket with a thermally-stabilized NOX tank. We wanted to fly both rockets right after sunrise, when winds are calmest. As such, I arose that morning at the ungodly hour of 4 AM, and proceeded to pack up the rocket and other needed supplies for the long journey to the Ice Station Zebra launch site. At this time, I also activated and installed the hand-warmer packet into the RDAS canister. The weather at this time seemed quite suitable, as there was no wind, and the temperature was a few degrees above the freezing mark.

    When we arrived at the test site, a vast frozen lake, the sun was just rising, and a bit of a wind had picked up. This was a good thing, however, as a thin fog had blanketed the area, which then began to disperse. We proceeded to unload the rockets, launch support & video equipment, and load up the two sledges for the 3 kilometre walk out toward the central area of the lake. The partly-assembled Frostfire One rocket was carefully placed inside a ski bag, and slung over my shoulder for the journey. We soon discovered, as we began our trek, that areas of the ice were pocketed with slush a few inches deep. This was not a particular concern, as we'd been prepared for this possibility, and had made sure our equipment was suitably protected and that our boots were waterproof. The ice base was very firm, however, being nearly a metre thick.

    taking a break
    Author, with the Frostfire One slung over my shoulder.
    Taking a short rest on our trek to the launch site.

    After arriving at the site, the first order of business was to set up the EMT rail launchpad and other ground support equipment. I assembled my rocket while Rob got his ready for launching first. The two videocameras were prepared for filming the flights. One was placed on a tripod some 30 feet (10 metres) from the pad, and the other (digital) videocamera was to be used for capturing the flights (my job, as usual). By this time, Rob's rocket was set to go, so we positioned ourselves at an appropriate safe location, and commenced the countdown. The igniter fired on cue, however, owing to the design of the hybrid motor, it took several seconds before the NOX valve opened. When this occurred, the rocket lifted off the pad, rather lazily, and arced over slightly while gaining altitude. It was clear that the thrust was far below that expected, and the rocket achieved only a fraction of the expected altitude. The timer based recovery system did not have a chance to fire the parachute system before the rocket impacted on the ice some 1000 feet (300 metres) downrange. It was apparent that the thermal heating system for the NOX tank did not function properly or was not powered up for a sufficient length of time (an earlier static test had proven the effectiveness of the electric tank heater).

    Hoping this was not an omen of things to come, we then proceeded to load Frostfire One onto the launcher. Once this was accomplished, the angle of the rail was adjusted to about 5 degrees from vertical. Next, it was time to prepare the payload for flight. This was done with the aid of a comprehensive checklist. This involved first removing the parachute module hatch covers and the PVC ring that protected the delicate frangible coverings of the smoke charge ports. The Smoke Charge system was powered up and armed, the RDAS was powered up, and the DET and MET modules were verified to be functioning properly. These systems were then armed. Finally, the radio transmitter was powered up, and the transmit switch toggled on. Confirmation was made that reception was clear through the receiver unit. The entire procedure of prepping the rocket went smoothly, taking about 20 minutes time. It was now time to connect the motor igniter, and to arm the launch box. The videocamera mounted on the tripod was turned on, and we then walked to the launch position, which was situated 500 feet (150 metres) away, being at the end of the launch cable that had been reeled out.

    Frostfire on pad
    Author standing next to the Frostfire One rocket prior to flight.

    At this point in time, the light fog that was present when we had arrived had completely dissipated. The sky was broken overcast, with some low patches of cloud. The wind was very light at approximately 5 km/hr. from the NE. The flight conditions were acceptable, therefore, we prepared to start the countdown. The "all ready & all clear" signal was announced , and the countdown followed...5-4-3-2-1-zero!

    One second later, the sound of the motor could be heard and simultaneously, a smoke cloud began to form at the base of the rocket. Nearly immediately, the rocket rapidly lifted off, and the loud roar of the motor under full thrust could be heard. The rocket accelerated very quickly and in a completely straight and stable manner, leaving a dark grey smoke trail in it's wake.

    Frostfire liftoff
    Moment of liftoff as seen from camera fixed on tripod near launchpad

    After approximately two seconds of flight, the rocket disappeared into a patch of cloud, and visual contact was lost by me (operating the videocamera) and by Rob. The sound of the motor could be heard for an additional two seconds, at which point we simply waited and gazed upward for any trace of the rocket. We were so transfixed on making visual contact that it didn't occur to either of us to listen over the radio receiver for signs of "life" ! However, after about 10 seconds, the deployed drogue chute was spotted. It was clear to us that this was too early for normal drogue deployment, so it was clear that something had gone wrong. Rob then noticed that the rocket was descending as separated entities. Just then, we heard, then saw, some fragments of PVC fuselage fluttering down. One fragment, to our surprise, landed no more than 15 feet (3 metres) from where we were standing...! It was apparent to us that one section of the fuselage was attached to the fully inflated drogue chute. Another section was spotted descending free-fall, in a horizontal attitude. After an additional 10 seconds, a loud "rushing air" sound was heard, characteristic of high speed ballistic descent, followed by a thud of impact. This occurred nearly simultaneously with the touchdown of the section that had been falling sideways. After an additional 15 seconds, the third section of the rocket that was tethered to the drogue chute landed gently. All three sections of the rocket came down within about 100 feet (30 metres) of the launcher.

    Sequences of the flight of Frostfire One
    from pre-ignition, to liftoff, to soaring skyward...

    Click on frames for larger images...

    Drogue descent
    Mid fuselage descending by drogue parachute

    Recovered rocket components:
    Left: Aft fuselage & impact crater; Centre: Mid fuselage & drogue chute; Right: Forward fuselage

    Click on frames for larger images...

    View video of Frostfire One launch (frostf1.wmv, 384 kb.)     

    Preliminary inspection of the recovered components at the test site suggested that most of the damage was confined to the rocket airframe. The DET module, contained within the mid fuselage which descended by parachute, appeared undamaged. The Radio Transmitter, RDAS unit and MET module appeared to have sustained only minor damage. Clearly, the stable horizontal descent and touchdown on a patch of slush both contributed to the survival of these payload components. The aft fuselage, which impacted at high velocity, destroyed the Smoke Charge triggering system, although the actual smoke charges were not damaged (and had not fired). The motor appeared to be unscathed and showed no sign of leakage or other abnormal performance. The main parachute, which apparently deployed (prematurely), was not recovered.

    Remarkably, damage was largely limited to the rocket airframe

    Post-flight Analysis

    Inspection of the video footage provided the following time intervals:

    • "Zero" to liftoff --        1.7 sec.
    • Liftoff to apparent burnout --        3.75 sec.
    • Liftoff to "thud" sound of aft fuselage impact --       24.3 sec.
    • Liftoff to forward fuselage touchdown--        24.6 sec.
    • Liftoff to mid fuselage/drogue touchdown --       39.5 sec..

    Post-flight teardown of the rocket revealed :

    • The motor was in perfect condition and appears to have operated flawlessly. It suffered zero leakage, and there was very little slag (10 grams representing a mere 1% of original grain mass). The cardboard inhibitor tube (0.036" thickness) was in such pristine condition that it could almost be cleaned off and reused.
    • The PVC airframe (lower, mid & upper fuselages) suffered substantial damage and was beyond repair.
    • Smoke Charge ignition circuitry was destroyed, but the actual smoke charge canisters were not damaged. Neither had fired.
    • DET (Drogue Timer & A-S systems) module, which was housed in the mid fuselage that descended by drogue chute was undamaged.
    • The Radio Transmitter and RDAS units both escaped damage. Both functioned normally in post-flight testing. Excellent flight data was recorded by the RDAS unit from liftoff to ground contact of the forward fuselage (when recording stopped due to the CPU being partly dislodged from its socket).
    • MET module (Main Parachute Timer) suffered only minor damage to the support structure and to the inertial switch.
    • The nosecone was chipped in one spot, but otherwise was not harmed. The antenna was not damaged.
    • The main parachute was lost. It was only realized that the parachute was missing when the rocket was being unpacked during post-flight inspection some hours after the flight. The tether lines (#4 & #3) connecting the main parachute to the mid and forward fuselages were both snapped due to overload.
    • The drogue ejection system had indeed fired. It was not possible to ascertain which system had fired the BP charge.
    • Examination of the main parachute system igniter filaments showed that both were still intact and that the BP charge did not fire.

    RDAS flight data:

    RDAS data
    Fig.1 -- Complete dataset of the flight from liftoff to ground contact

    Comments on complete dataset:
    • The time duration from start to end of data stream was 24.7 seconds. This is in agreement with the video footage of the time duration from liftoff to ground contact of the forward fuselage.
    • The altitude data is based on barometric (air pressure) sensor readings. As such, the apparent altitude is valid only during normal flight mode.
    • A flight anomaly occurred at the 2.70 second mark, when both acceleration and barometric altitude data suddenly spiked.
    • The acceleration reading of zero g's is characteristic of free fall descent of the forward fuselage from the 4 second mark onward.
    • The linear slope of the altitude decay curve is characteristic of terminal (constant) velocity being achieved from the approximately 10 second mark onward. This slope translates to a constant descent velocity of 74.6 feet/sec. (22.7 m/s.).
    Initial flight phase

    RDAS data
    Fig.2 -- Acceleration data for first 4 seconds of flight

    RDAS data
    Fig.3 -- Apparent altitude data for first 4 seconds of flight

    Comments on initial flight phase data:
    • Acceleration data was quite constant for the first 2 seconds of flight, as would be expected for normal ascent (the motor has a constant thrust profile). The acceleration then gradually decays, with two small anomalous spikes at the 2.45 and 2.65 second marks. A small anomalous pressure spike also occurs at the 2.73 second mark.
    • A significant anomalous event occurs at the 2.700 second mark, when a deceleration spike of -5.8 g's occurs, followed by a positive acceleration of +19.8 g's at the 2.705 second mark.
    • Two more significant events occur: a deceleration spike of -20.3 g's at the 2.770 second mark, followed by another large deceleration spike of -62.5 g's at the 2.975 second mark.
    • The barometric altitude data between the 2.72 and 3.05 second marks is fictitious. Rather, the pressure being sensed is a result of the rocket's abnormal attitude experienced between this time duration.
    • The cyclical readings of both apparent altitude and acceleration following the 3 second mark are characteristic of tumbling.
    Processed data

    RDAS data
    Fig.4 -- Barometric and integrated accelerometer data

    Comments on processed data:
    • Accelerometer data is particularly valuable, as it is possible to obtain altitude (or distance travelled), as well as velocity over the duration of the flight, through numerical integration. This is illustrated in Figure 4, where the integrated accelerometer data is presented as velocity, and the integrated altitude data is superimposed. It is seen that the accelerometer data is in excellent agreement with the barometric altitude data. (a rather neat affirmation of the superbly engineered design of the RDAS system...!). The method employed considers that velocity is the time derivative of displacement, and acceleration is the time derivative of velocity. As such, integration of the acceleration data yields velocity, and integration of velocity data yields distance travelled (altitude in this case):

      where v(t) is velocity as a function of time, z(t) is altitude as a function of time, t is the time duration, Dt is the time increment, and N is the number of data points integrated (the sigma notation denotes a summation of the acceleration and velocity data points).
    • It can be seen that the significant anomalous event occurred at an altitude of 800 feet (244 m.) at which point the rocket was travelling at a velocity of 382 MPH (171 m/sec.). The actual peak altitude achieved by the forward fuselage section (housing the RDAS) would appear to be approximately 1300 feet (400 m.). These numbers make it all the more remarkable that the payload survived at all!
    Actual versus predicted:

    RDAS data
    Fig.5 -- Comparison of RDAS data to design (predicted) flight profile.

    What went wrong?

    The hypothesis that arose immediately after the incident was that the drogue parachute was triggered prematurely. This seemed to be a plausible explanation and appeared to be consistent with observations and with RDAS flight data. From the acceleration data of Figure 2, a large positive acceleration of +19.8 g's at the 2.705 mark could be a result of the drogue charge firing, accelerating the forward fuselage upward. The deceleration spike of -20.3 g's at the 2.770 second mark could have be caused by the drag force of the inflated drogue chute, bearing in mind that the time interval between the two events is a mere 65 milliseconds. The second and much larger deceleration spike of -62.5 g's at the 2.975 second mark would seem to have been a result of main parachute deployment, as the broken tethers were proof that a large force (and thus acceleration) would have been imparted to the forward fuselage. Although the main ejection charge had not fired, the parachute could have been released as a result of a structural failure of the airframe at the joint between the mid and forward fuselages, owing to the high speed of the rocket at the time of the event.

    However, inspection and testing of the three systems that were designed to trigger drogue ejection turned up no faults. All operated normally in post-flight testing. The A-S system is, by it's nature, a simple design. The anomalous event occurred while the motor was still thrusting and the rocket accelerating, and not after burnout when the mercury switch would be triggered. As such, the only way the A-S system could conceivably have triggered the ejection charge would be by means of a dual failure of both the air-speed switch (e.g. flap detachment) and of the mercury switch (e.g. shorted terminals), neither of which were evident. The drogue timer system also functioned normally in post-flight testing, and was a well-proven system, having been employed on all five Boreas rocket flights. The RDAS incorporates a dead-time feature during the first 3 seconds of flight during which none of the igniter outputs can be activated. The anomalous event occurred at the 2.70 second mark, and as such, the likelihood of the RDAS having triggered the ejection charge would seem to be very remote.

    An alternative hypothesis surfaced after it became apparent that premature triggering of the drogue ejection charge was not a likely source of the catastrophic anomalous event. Curiously, a while back there was a discussion on the aRocket discussion forum about the potential stability risks associated with induced roll of a rocket (rotation about the longitudinal axis). I suddenly wished I had paid more attention to that discussion, considering my rocket was fitted with fin tabs to do exactly that! Research was obviously in order, and I set out to find out as much as I could, in a limited time frame, about the subject of roll-inducement and associated stability issues.

    Inertial Roll coupling

    Also known as Pitch-Roll coupling or Yaw-Roll coupling, Inertial Roll coupling is a "resonant divergence in pitch (or yaw) when roll rate equals the lower of the pitch or yaw natural frequencies", according to Reference 1. In other words, this term describes a phenomenon whereby dynamic instability of a rocket (or other flight vehicle) develops under certain flight conditions with potentially catastrophic consequences, if that vehicle has the mass and geometric configuration that makes it susceptible.

    The concept of roll and pitch is shown in Figure 6. If a rocket rolls, it will rotate about its own principal axis, the line of least resistance, rather than the flight path (geometric axis), as illustrated in Figure 7. The position of the principal axis is determined by the particular placement of items of mass that make up the rocket. If the angular difference between the principal axis and the geometric axis is sufficiently large, and if the rocket rolls sufficiently quickly, the destabilizing moment from the inertial forces will overcome the stabilizing aerodynamic moment provided by the fins. The centrifugal force due to the roll will cause the nose and tail to try to swing out perpendicular to the rotation axis.The rocket will become directionally unstable, with the pitch angle continually diverging, developing a wobble or coning motion, to the point where the vehicle's structural limit is exceeded, leading to break-up. In order for the rocket's principal axis to be different than the geometric axis (dynamically unbalanced), the distribution of the various components that make up the mass of the rocket would have be uneven, with respect to the centreline of the rocket (geometric axis). Components of the rocket such as the fuselage, fins, nosecone, and motor are generally symmetrical about the rocket's centreline axis, and would not contribute to dynamic imbalance. However, certain items of mass, typically payload items, may have a centre of gravity (CG) that is not in line with the centreline of the rocket. It is these items that offset the principal axis and lead to dynamic imbalance and the potential for inertial roll coupling.


    What makes a particular flight vehicle susceptible to inertial roll coupling? The most obvious condition is the presence of roll. For a rocket, roll may be produced by fin tabs, asymmetrically airfoiled fins, or even misaligned fins. Another condition, as mentioned, is the configuration of the vehicle that leads to dynamic imbalance, such as offset items of mass that result in non-coincident principal and geometric axes. A second condition is the existence of a large difference between the roll moment of inertia and pitch moment of inertia for the vehicle. This is typically the case for rockets , which have all the mass contained within the fuselage (low roll inertia) and have long fuselages with heavy motors, payload, etc. (high pitch inertia). From reference [1], this susceptibility can be expressed in terms of a coupling inertia ratio given by (Ix-Iy)/Iz for any flight vehicle, where Ix is the roll moment of inertia about the geometric axis, Iy is the pitch moment of inertia about the geometric axis, and Iz is the yaw moment of inertia about the geometric axis. Coupling tendencies increase as this ratio approaches a value of -1. For most rockets, the pitch and yaw moment of inertia are equal, owing to symmetry, and the roll moment of inertia is usually written as IR. The coupling ratio then reduces to IR/IL-1, where IL= Iz = Iy (longitudinal moment of inertia). Techniques for computing (or experimentally measuring) the moments of inertia of a rocket are detailed in Reference 2.

    The moments of inertia may be readily estimated if a rocket is idealized as either a solid cylinder or a cylindrical shell (hollow cylinder):

    IR = 1/2 mR2         IL= 1/12 m(3R2 + L2)         Solid cylinder
    IR = mR2               IL = 1/2 m(R2 + 1/6 L2)       Cylindrical shell

    where m, R & L are the mass, radius and length of the cylinders, respectively.
    Substituting the expressions for IR and IL into the expression for the coupling ratio leads to the following simplified relations:

            Solid cylinder

            Cylindrical shell

    As can be seen, the mass terms cancel out, and we are left with the coupling ratio being solely a function of the idealized rocket's L/R ratio. This is plotted in Figure 8, with diameter, D, used instead of radius, for convenience.

    moment of inertia chart
    Fig.8 -- Inertial coupling ratio with respect to a rocket's L/D ratio

    This figure shows that rockets, in general, have an inertial coupling ratio approaching minus one. A typical rocket with an L/D = 10, for example, would have a ratio of between -0.970 and -0.985. For Frostfire One, L/D = 24, resulting in an inertial coupling ratio of about -0.995. From their inherent geometry, rockets in general, and the Frostfire One in particular, have a high susceptibility to inertial roll coupling.

    Two additional factors which can contribute to the potential for inertial roll coupling characteristics are low longitudinal stability and longitudinal flexibility of the rocket (including aeroelastic effects) as explained in Reference 3. Again, Frostfire One scores "poorly" on both of these counts. The small fins, which are adequate for static stability, provide a low response time with respect to pitching (overdamped), and the low modulus PVC fuselage, which includes two joints, has an appreciable potential for flexing in flight. The joints, which are secured with nylon "shear" screws, had been something of a concern from the start, as there was some tendency to flex under bending load.

    Evidence of Inertial Roll Coupling

    Although the Frostfire One rocket certainly was susceptible to this mode of instability, based on the above, is there evidence that this abnormal flight behaviour led to a catastrophic failure? There are, in fact, some clues that support this hypothesis. A close look at Figure 2 reveals that the acceleration of the rocket begins to drop fairly significantly as the anomalous event draws near, including two small deceleration spikes. This would suggest that the drag on the rocket was increasing, consistent with what would be expected if the rocket was becoming dynamically unstable and was beginning to wobble. Of course, this could alternatively be explained as being a consequence of normal thrust decay, however, the motor has a completely neutral Kn profile with a burn time of about 3 seconds. Another clue is that the anomalous event inititates with a sizeable deceleration spike at the 2.70 second mark. This would appear to contradict the hypothesis that premature ejection charge firing occurred (which would generate a positive acceleration initially). A deceleration spike may be consistent with structural breakup of the rocket at the forward joint, followed by tumbling as evidenced by the cyclical acceleration pattern immediately following the event. At this time, the main parachute would have been released and instantly blossomed, generating the very large deceleration spike seen at the 2.98 second mark.

    There is also photographic evidence that inertial roll coupling (or similar behaviour) was occurring as the rocket was accelerating toward it's maximum velocity. In the sequence of launch photos presented earlier, a close examination of the 7th and 8th frames suggests that the smoke trail has taken on a slight, however distinctive corkscrew pattern. This is highly consistent of the expected behaviour of a rocket beginning to become unstable and taking on a wobbling motion.

    Ancillary Observation

    An interesting observation was made while conducting the post-flight inquiry into this flight. It had been noticed that the motor "roar" sound, as recorded by the video, was appreciably longer in duration than the expected burn time of the motor (3.75 seconds versus 3 seconds). Not much was made of this at first, but it later dawned upon me that this discrepancy should be expected. In other words, that the "roar" of a rocket motor as heard by an observer on the ground must be of greater duration than the actual "roar" of the motor (i.e. as heard by an observer "on-board" the rocket). This curious fact is due to the finite (and relatively slow) speed of sound, which results in a time delay for the sound waves to reach the ground. As an example, consider a rocket motor with a burn time of 2 seconds. If burnout occurred at an altitude of 1000 metres, the "apparent" burn time, as evidenced by the "roar" sound as heard by those on the ground, would be close to 5 seconds! Since the speed of sound is approximately 340 metres/second, the last vestiges of sound produced by the motor at burnout would take nearly 3 seconds to reach the ground from a distance of 1000 metres. Adding this delay time to the burn time of 2 seconds gives the total apparent burn time of close to 5 seconds. Also interestingly, the Döppler effect comes into play, as the sound waves produced by the motor are effectively stretched due to the velocity of the rocket. As such, the sound heard by those on the ground would continually get deeper in pitch as the rocket climbs ever faster toward burnout.


    Despite the occurence of a catastrophic event that terminated the flight of Frostfire One prematurely, some of the goals of the test flight were nevertheless achieved. The Paradigm rocket motor proved itself in flight with a flawless performance, and in particular, proved the viability of a rod & tube grain configuration. This is quite significant, as this configuration provides for a constant Kn profile, which has certain advantages such as better nozzle efficiency. This design also allows for high volumetric propellant loading, and lessened structural demands on the casing which is not exposed to combustion heat, eliminating the requirement of dedicated thermal insulation.

    The RDAS functioned very well in it's role as a flight data recorder, providing invaluable data over the duration of the entire flight. Without this data, little more than guesswork could have been done with regard to assessing the cause of the flight anomaly. This aspect is particularly important, as an understanding as to what went wrong is key to avoiding future problems due to the same cause.

    The usefulness of the radio transmitter was not fully assessed on this flight test, however, it did apparently operate over the course of the flight as evidenced by the audio signals recorded on the videotape (a receiver was placed close to the videocamera microphone). The radio transmitter will definitely be flown again for a more complete assessment.

    Evidence suggests that there was not any fault with the parachute triggering system. Although the two-stage recovery system was not drawn upon for this flight as planned, it is now believed that the drogue system operated "normally", with drogue chute ejection likely being triggered by the A-S system as the rocket tumbled after the catastrophic event. The drogue chute proved its structural worthiness as the deployment occurred at a relatively high velocity.

    It presently appears that inertial roll coupling may well have led to dynamic instability and consequential structural overload (bending moment) and breakup of the rocket, occurring at the forward/mid fuselage joint. Further investigation will need to be conducted before any firm conclusions can be reached. This analysis will involve an accurate determination of the principal axis of inertia of the Frostfire One rocket, calculation of the expected roll rate at the time of the anomalous event, and the determination of the natural pitch frequency of the rocket, and the evaluation of these parameters to determine the likelihood of coupling. This launch report will be updated in the future with the results of this additional investigation.

    Reference 1    Coupling Dynamics in Aircraft: A Historical Perspective, NASA SP-532 (1997) , R.E.Day
    Reference 2    Topics in Advanced Model Rocketry, G.K.Mandell, G.J.Caporaso, W.P.Bengen
    Reference 3    Coupled Aeroelastic Analysis of a Free-flight Rocket, D.S. Livshits, S.Yaniv, M.Karpel

    Last updated

    Last updated April 17, 2003

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