Mass asymmetry and tricyclic wobble motion assessment using automatedlaunch video analysis

Ryan DECKER *, Joseph DONINI, William GARDNER, Jobin JOHN, Walter KOENIGArmaments Research, Design, and Engineering Center, Picatinny Arsenal, 94 Ramsey Avenue, NJ 07806, USA

Received 14 September 2015; accepted 10 November 2015

Available online 17 December 2015

Abstract

This paper describes an approach to identify epicyclic and tricyclic motion during projectile flight caused by mass asymmetries in spin-stabilized projectiles. Flight video was captured following projectile launch of several M110A2E1 155 mm artillery projectiles. These videos werethen analyzed using the automated flight video analysis method to attain their initial position and orientation histories.

Examination of the pitch and yaw histories clearly indicates that in addition to epicyclic motion’s nutation and precession oscillations, an evenfaster wobble amplitude is present during each spin revolution, even though some of the amplitudes of the oscillation are smaller than 0.02 degree.The results are compared to a sequence of shots where little appreciable mass asymmetries were present, and only nutation and precessionfrequencies are predominantly apparent in the motion history results. Magnitudes of the wobble motion are estimated and compared to product ofinertia measurements of the asymmetric projectiles.Production and hosting by Elsevier B.V. on behalf of China Ordnance Society.

Keywords: Aeroballistics; Artillery; Pitch; Yaw; Epicyclic motion; Tricyclic motion; Video analysis

1. Introduction

All artillery projectiles contain slight mass asymmetries thatare caused by a variety of factors including manufacturingtolerances, storage procedures, and the design itself. TheM110A2E1 155 mm projectile system contains a payload ofwhite-phosphorous (WP) used to identify impact locations andhinder visibility on the battlefield. Because WP fill has theability to deform and change shape at high temperatures, allM110A2E1 projectiles are required to be stored upright. If lefton their side for prolonged periods of time or at high tempera-tures, the WP material has the potential to collect on one side ofthe projectile, resulting in significant mass asymmetries.

The mass asymmetries can be one of two types. The first caseis when the center of gravity is located a small distance laterally offthe geometric axis of symmetry of the projectile (static imbalance)[1]. This will cause lateral throwoff at muzzle exit. The secondcase is when the principal axis of inertia is not aligned with thegeometric axis of symmetry of the projectile (dynamicimbalance). A dynamic imbalance will result in a small bodyfixed trim angle and potentially large initial angular motion. The

M110A2E1 projectiles in this study have WP collected on oneside, resulting in both static and dynamic imbalances.

A symmetric spin stabilized projectile without a dynamicimbalance exhibits what is known as epicyclic motion. In epi-cyclic motion, the nose of the projectile “cones” around theprojectile’s velocity vector at two distinct frequencies as

ζ ϕ ϕ ϕ ϕbalanced F

sS

se eF F S S= ++( ) +( )K Ki i0 0� � (1)

where ζ is the magnitude of the pitching motion, K representsthe oscillation amplitude, φ0 represents the phase shift, �ϕrepresents the oscillation frequency, and the subscripts “F” and“S” represent the fast and slow oscillations. The fast oscillationis known as nutation, and the slow frequency is known asprecession. Most artillery projectiles have only slight dynamicimbalances, making it possible to accurately model their sixdegree-of-freedom trajectories using only these two effects (aswell as the yaw of repose which affects the trajectory mostlynear the maximum ordinate of the trajectory curve).

A projectile with a significant dynamic imbalance will exhibita third frequency of coning motion following cannon launch.This motion is referred to by McCoy [2] as the “tricyclic” armbut will be referred to as “wobble” in this paper, since wobble isdefined as a fluctuating state of motion caused by a massimbalance.The wobble motion occurs at a frequency that is equalto spin-rate of the projectile. This motion is described in Eq. (2),

Peer review under responsibility of China Ordnance Society.* Corresponding author. Tel.: +1 973 724 7789.

E-mail address: ryan.j.decker6.civ@mail.mil (R. DECKER).

http://dx.doi.org/10.1016/j.dt.2015.11.0052214-9147/Production and hosting by Elsevier B.V. on behalf of China Ordnance Society.

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ζ ϕ ϕ ϕ ϕ ϕimbalanced F

sS

sw

se e eF F S S w= + ++( ) +( ) +( )K K Ki i i p0 0 0� � (2)

where the subscript w represents the wobble oscillation and prepresents the projectile spin-rate. All three “coning” motionsrotate the nose of the projectile in the same direction as thespin-rate, which for all U.S. artillery projectiles is clockwisewhen looking from the base toward the nose. Illustrations of theinitial coning motion are shown in Fig. 1 for a projectile withand without a significant dynamic imbalance.

2. Test description

To investigate the effects of improper storage, eightM110A2E1 WP projectiles were stored on their side at hotconditions to induce a mass asymmetry. After their inertialproperties were measured, four of the eight asymmetry-inducedprojectiles were reheated while upright to restore their massdistribution to normal balanced conditions.

In May of 2015, the four re-balanced and four imbalancedprojectiles were fired at Yuma Proving Ground, AZ. Launchvideo for each of these test shots was recorded using twoTrajectory Tracker rotating-view high speed optical systems onopposing sides of the azimuth of fire.

3. Data analysis

The launch videos were then analyzed using the automatedflight video analysis (AFVA) system [4]. This analysis processeseach frame of a launch video to segment the shape of the projectileand identify key points such as the nose, center of gravity (CG) andbase locations. The pitching motion history estimated from eachcamera is then corrected and combined to determine the resolvedthree dimensional (3D) pitch and yaw motion history for the first~150 m of flight. A screen shot of the AFVA extracting theprojectile shape of an M110A2E1 projectile is shown in Fig. 2.

The resolved pitch and yaw histories from AFVA for roundswith (left) and without (right) dynamic imbalances are shown inFig. 3.

The next step in the analysis was to isolate the wobble motionfrom the resolved pitch and yaw histories. To do this, reasonableestimates for the nutation and precession frequencies weredetermined. For the M483 projectile (which is a ballistic matchto the nominal M110A2E1), those values were roughly 72 Hz forthe fast arm, 17 Hz for the slow arm, and a spin-rate of 136 Hz

for an average muzzle velocity of 420 m/s. Using these values,only the magnitudes and phase shift angles for both the fast andslow oscillation modes needed to be matched to resultingpitching motion history. This was done by first aligning the fastoscillation and then incrementally adjusting the slow oscillationuntil the difference between the epicyclic fit and the raw pitchdata resembled a steady harmonic oscillation. The final step wasto fit a sinusoid oscillating at the spin-rate to the isolated wobblemotion. This process is illustrated for one of the imbalancedprojectiles (which clearly illustrated wobble) in Fig. 4.

The complete results for all eight rounds are shown in Fig. 5.It required several iterations of parameter adjustments to arriveat a best-fit for the epicyclic motion of the projectiles, and it wasespecially difficult for the projectiles that were restored tonormal levels of inertial asymmetry. In addition, all eight ofthese rounds exhibited a relatively low amount of total pitchingmotion, making it especially difficult to determine the correctepicyclic parameters. Still, it was possible to isolate the wobblemotion for each of the rounds fired. Once isolated, it was clearthat the projectiles with mass asymmetries exhibited signifi-cantly more wobble motion.

One unexpected benefit of this analysis was that it illustratedthe precision of the AFVA method to measure projectile orien-tation. Previously, it was determined that AFVA measurementswere within 0.1° of on-board electronic measurements [5], butclearly the data from this test smoothly show fluctuations inpitching motion much smaller than 0.01°.

Fig. 1. Epicyclic and tricyclic projectile motion (after Ref. 3).

Fig. 2. Automated flight video analysis (AFVA) orientation measurement.

114 R. DECKER et al. /Defence Technology 12 (2016) 113–116

4. Discussion of results

As described by McCoy [2], the magnitude of the wobblemotion (tricyclic arm) for a dynamically imbalanced but gyro-scopically stable projectile is

KI

I Iw

E

T P

≈−

(3)

where IP is the inertia along the projectile spin axis, IT is thetransverse moment of inertia, and IE is the product of inertiaresulting from.

It would follow that a linear relationship would existbetween the wobble amplitude and the measured product ofinertia for each of the projectiles in this test. Unfortunately, thefour projectiles that had their mass asymmetries corrected werenot re-measured before firing. Since their true products ofinertia are unknown, typical values for the M110A2E1 projec-tile are used for the projectiles that were restored to normallevels of mass asymmetry [6]. The comparison between theproduct of inertia and the measured amplitude of wobblemotion is shown in Fig. 6.

From the data in Figs. 5 and 6, it is obvious that two distinctgroupings of wobble amplitudes were measured. One groupcorresponds to the four projectiles with significant massasymmetries and the other is the group of four projectiles that werereturned to normal conditions. Since the products of inertia werenot measured for the four rounds that were restored to normal

conditions, it is difficult to truly assess the validity of therelationship between the wobble magnitude and the measuredproduct of inertia.

When compared to the expected relationship which wasgenerated using Eq. (3) and typical inertial properties for theM110A2E1, it is clear that the wobble amplitudes measuredusing AFVA are roughly 32% lower than would be expected forprojectiles exhibiting such large mass imbalances. This isbelieved to be attributed to residual settling of the WP duringlaunch, effectively reducing the product of inertia to somedegree before the projectile leaves the weapon muzzle. Thispossibility is being investigated in a separate study.

Altogether, the results of this analysis suggest that it may bepossible to quantify and predict the expected wobble motionfrom measurement of mass imbalance, but a much large data setis required, with a greater distribution of projectiles withvarious inertial asymmetry levels.

5. Conclusions

This effort demonstrated that the AFVA method is able tomeasure subtle fluctuations in projectile orientation. Even withsmall amounts of total yawing motion, the parameters thatdefine the epicyclic motion can be estimated to match thepitching motion histories of artillery projectiles. Once this fit isestablished, fluctuations smaller than 0.02° can be extractedfrom the pitching motion history and analyzed.

Fig. 3. Orientation history of projectiles with (left) and without (right) induced mass asymmetries.

Fig. 4. Isolating and fitting the tricyclic motion.

115R. DECKER et al. /Defence Technology 12 (2016) 113–116

The wobble motion of projectiles with induced mass asym-metries was therefore clearly apparent and measureable. Withfew data points collected during conventional spark rangefirings, or with the relatively low precision of yaw cards or someon-board measurement techniques, it may be the case thatAFVA is the only method to quantify wobble motion of artilleryprojectiles available in a cost-effective manner.

It was shown that projectiles with large product of inertiavalues exhibited larger amplitudes of wobble motion than pro-jectiles without large mass asymmetries. However, a more-complete sample set is needed to fully quantify the relationshipbetween inertial asymmetry and wobble motion.

References

[1] Carlucci D, Jacobson S. Ballistics: theory and design of guns andammunition. Boca Raton, FL: CRC Press; 2008.

[2] McCoy R. Modern exterior ballistics: the launch and flight dynamics ofsymmetric projectiles. Atglen, PA: Schiffer Publishing; 1999.

[3] Koenig W. M110A2E1 aero predictions. Aeroballistic simulations. NJ:U.S. Army Armament Research, Development, and Engineering Center,Picatinny Arsenal; 2015.

[4] Decker R, Kolsch M, Yakimenko OA. A computer vision approach toautomatically measure the initial spin-rate of artillery projectiles paintedwith stripes. J Test Eval 2014;42(4):828–41.

[5] Decker R. A computer vision-based method for artillery characterization[Ph.D. dissertation]. Monterey, CA; Naval Postgraduate School; 2013.

[6] John J. M1122, M483, M110A2E1 mass properties and POIs.Measurement data. NJ: U.S. Army Armament Research, Development, andEngineering Center, Picatinny Arsenal; 2015.

Fig. 5. Extracted wobble motion fitting for all rounds.

Fig. 6. Wobble amplitude vs. product of inertia.

116 R. DECKER et al. /Defence Technology 12 (2016) 113–116