WEIGHING AT SEA WITH A GIMBAL PLATFORM by Charles Manfred St. Laurent United States Naval Postgraduate Sc m E JL WEIGHING AT SEA WITH A GIMBAL PLATFORM by Charles Manfred St. Laurent. September 1970 Thl6 document hat been apphX)\jQ.d ^on. puttie kz- l&cu>e. and 4a£e; aXi> cLUVvibuX^on iA untaruXzd. T ^79 I Weighing at Sea with a Gimbal Platform by Charles Manfred St. Laurent Lieutenant Commander, United States Navy B.S., United States Naval Academy, 1961 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN OCEANOGRAPHY from the NAVAL POSTGRADUATE SCHOOL September 1970 :,IBItAH?V.„_ "^ tfAVAL POSTGRADUATE SCHOOD /IOKTEREY, CALIF. 93940. ABSTRACT The use of a gimbal platform with two degrees of freedom under dampened pendulum motion allows a standard laboratory balance to be used to weigh scientific samples at sea. The maximum sample weight tested was approximately 120 grams, while the average accuracy obtained in samples ranging from 1 to 120 grams was 0.10% (± .05%). The sea conditions under which at sea weighings can be conducted vary with the size of the research vessel. The gimbal platform does not provide the stabilization necessary under adverse sea conditions. TABLE OF CONTENTS I. INTRODUCTION — - 11 II. BACKGROUND - — 13 III. GIMBAL PLATFORM DESCRIPTION — 15 IV. BALANCES EVALUATED — -- 25 V. PROCEDURES -- — 31 VI. RESEARCH VESSELS EMPLOYED - 34 VII. PENDULUM MOTION 50 A. UNDAMPENED FREE VIBRATION 50 B. DAMPENED FREE VIBRATION - — 61 VIII. RESULTS 67 IX. CONCLUSIONS -- - 88 APPENDIX A WEIGHT STANDARDS 89 APPENDIX B PENDULUM DAMPENING DATA 90 APPENDIX C FREE VIBRATION CURVES WITH VISCOUS DAMPENING PENDULUM 94 BIBLIOGRAPHY 108 INITIAL DISTRIBUTION LIST 109 FORM DD 1473 111 fLi v>\ AA LIST OF TABLES Table Page I Gimbal Platform Characteristics 15 II Dampening Fluid Specifications 20 III Relative Viscosity of Dampening Fluids 21 IV Balance Data 26 V General Ship Information 34 VI Sea Conditions on 15 May 1970 38 VII Sea Conditions on 13 July 1970 39 VIII Sea Conditions on 10 June 1970 44 IX Sea Conditions on 22-24 April 1970 49 X Pendulum Variables 54 XI Inertia Moments for Rotation about the B Axis 57 XII Restoring Moments for Rotation about the B Axis 58 XIII Natural Frequencies of Oscillation about the B Axis 58 XIV Natural Frequencies of Oscillation about the A Axis 60 XV Natural Frequencies of Oscillation about the A and B Axes 60 XVI Pendulum Weight and Viscous Fluid Combinations 63 Used in Dampening the Motion XVII Logarithmic Decrement and Viscous Dampening 65 Coefficient Values XVIII Dampened Natural Frequencies of Oscillation 66 About the A and B Axes XIX General Summary of At-Sea Weighings 67 XX Relative Positions of Weight Measurements Made on 68 15 May 1970 in Relation to Actual Sample Weight XXI Three Exceptions to the Relative Positions of 69 Weight Measurements made on 15 May 1970 Table Page XXII Weighing Data from Balance A on 15 May 1970 70 XXIII Weighing Data from Balance A on 10 June 1970 78 XXIV Weighing Data from Balance A on 13 July 1970 81 XXV Weighing Data from Balance B on 13 July 1970 82 XXVI Weighing Data from Balances A and E on 22 April 1970 83 XXVII Weighing Data from Balances D and F on 22 April 1970 84 XXVIII Weighing Data from Balance A on 23-24 April 1970 85 XXIX Weighing Data from Balance B on 24 April 1970 86 XXX Percent Error in Sample Weighings 87 LIST OF FIGURES Figure Page 1 Gimbal Assembly Showing Inner and Outer 16 Gimbals, Pendulum, Dampening Oil and Tank 2 Upper Assembly Component with Inner Gimbal, 18 Pendulum, and Pendulum Weights 3 Upper Assembly Component with Outer Gimbal and 19 Supporting Springs, and Outer Gimbal Dashpots 4 Gimbal Platform Operating at Sea 22 5 Gimbal Assembly Secured by Sand Bags and Planks 24 Showing the Two Visual Angle Indicators for each Axis Rotation 6 Gram Electrobalance Diagram 30 7 Weight Determination Procedure 33 8 NPS Research Vessel Showing Pilot House and 35 Wet Laboratory Locations 9 NPS Research Vessel Showing Wet Laboratory Location 36 10 Hopkins Marine Station Research Vessel Proteus 40 11 Hopkins Marine Station Reserach Vessel Proteus 41 Showing Location of Main Laboratory 12 Hopkins Marine Station Research Vessel Proteus 42 Showing Balance Location in Main Laboratory 13 USNS Bartlett Research Vessel 45 14 USNS Bartlett Main Deck Showing Two Balance Locations 46 15 USNS Bartlett 1st Platform Showing Balance Location 47 16 Gimbal Platform With Two Degrees of Freedom 51 17 Rotation of the Gimbal Platform About the B Axis 52 18 Characteristic Dimensions of Gimbal Platform 53 19 Inner Gimbal With Pendulum and Weights 56 Showing the B Axis of Rotation 20 Rotation of the Gimbal Platform About the A Axis 59 Figure 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 General Free Vibration Curve with Viscous Dampening Variation in Weighings Obtained on 15 May in The Sample Variation i The Sample Variation i The Sample Variation i The Sample Variation i The Sample Weight Range of 0.074-0.469 Grams n Weighings Obtained on 15 May in Weight Range of 1.679-5.342 Grams n Weighings Obtained on 15 May in Weight Range of 9.420-84.87 Grams n Weighings Obtained on 10 June in Weight Range of 0.073-0.469 Grams n Weighings Obtained on 10 June in Weight Range of 1.678-84.88 Grams Variation in Weighings Obtained on 13 July as A Function of Pendulum Weight Free Vibration Curve for Air Dampening With 18 Pound Pendulum Weight About the A Axis Free Vibration Curve for Air Dampening With 18 Pound Pendulum Weight About the B Axis Free Vibration Curve for 50W Oil Dampening With 18 Pound Pendulum Weight About the A Axis Free Vibration Curve for 50W Oil Dampening With 18 Pound Pendulum Weight About the B Axis Free Vibration Curve for 50W Oil Dampening With 36 Pound Pendulum Weight About the A Axis Free Vibration Curve for 50W Oil Dampening With 36 Pound Pendulum Weight About the B Axis Free Vibration Curve for 50W Oil Dampening With 54 Pound Pendulum Weight About the A Axis Free Vibration Curve for 50W Oil Dampening With 54 Pound Pendulum Weight About the B Axis Free Vibration Curve for 90W Oil Dampening With 18 Pound Pendulum Weight About the A Axis Free Vibration Curve for 90W Oil Dampening With 18 Pound Pendulum Weight About the B Axis Page 62 72 73 74 75 76 80 94 95 96 97 98 99 100 101 102 103 8 Figure 38 39 40 41 Free Vibration Curve for 90W Oil Dampeni 36 Pound Pendulum Weight About the A Ax Free Vibration Curve for 90W Oil Dampen 36 Pound Pendulum Weight About the B Ax Free Vibration Curve for 90W Oil Dampen 54 Pound Pendulum Weight About the A Ax Free Vibration Curve for 90W Oil Dampeni ng With s ng With s ng With s ng With Page 104 105 106 107 54 Pound Pendulum Weight About the B Axis ACKNOWLEDGEMENTS A sincere debt of gratitude is owed to the following people, without whose help this thesis would not have been possible. To Mr. H. J. Higinbotham, Mr. A. P. Nelson, and Mr. E. J. Duley, of the U. S. Bureau of Mines Branch in Tiburon, California goes a special thank you for their assistance in providing information on their at sea weighing experiences and for the loan of the gimbal assembly and two balances. To Mr. E. Colli son of the CAHN Division of Ventron Instruments and to Mr. E. Betts of the Torsion Balance Company for each providing a balance for the research. A special note of thanks to Mr. Betts who made two special trips to the Naval Postgraduate School to assist in the inspection and preparation of three Torsion Balances and for taking the time to participate in one of the sea trials. A note of appreciation is extended to Mr. C. Barthel of Watson Brothers Scientific Instruments who also participated in one of the sea trials. Also, a debt of gratitude is extended to Professors J. J. Von Schwind and R. J. Smith of the Oceano- graphy Department who provided direction and advice during the preparation and throughout the research work. Lastly, a sincere thanks to my loving wife, Arilla, whose long hours of typing and understanding have brought this work to fruition. 10 I. INTRODUCTION With the advent of an increased interest in the OCEANS, by both civilian and government agencies, there has been a paralleling advance in the development of new and varied instruments to be used for gathering and analyzing data. An instrument that has been developed for many years but has not been able to provide accurate results on a rolling and pitching vessel is the standard laboratory balance. If this instrument could be used on a vessel, such that the weighing results were completely or even partially indepen- dent of the vessel motion, then in many instances analysis of oceanographic data could begin the minute samples were received, rather than having to wait until an inport period. Reduction of somewhat unproductive at sea periods, where oceanographic samples are available, but not processable, can be achieved through the use of a simple gimbal platform which allows the oceanographer to use a laboratory balance at sea under certain sea conditions. There are three specific instances where the satisfactory use of a balance would give the "scientist at sea" a quicker analysis of his data and make it more reliable. The first is in the taking of ocean bottom samples by means of a coring device. Approximately seven out of the thirteen major engineering parameters used to describe the ocean bottom are directly or indirectly dependent upon soil sample weighing. At present the cores are taken from the ocean bottom, sealed at the ends and immersed in salt water to prevent desiccation. The cores are then analyzed at the shore laboratory at a later date. The advantage of knowing what the bottom conditions are while on station, rather than weeks or months later backe in the laboratory, are apparent. 11 A second specific example is in the field of biological oceanography. During a six month euphasid gathering expedition in the North Atlantic, freezing of the specimens to permit analysis upon completion of the cruise resulted in unreliable dry weights because the specimens tended to dry even in the deep freeze. [Raymont, et al . 1969]. The third example is not related to oceanography, but concerns the determination of the presence of contaminants in military aviation fuel aboard naval aircraft carriers. The method used at present is a spectro- photometry analysis technique that occasionally gives erroneous results due to the abnormal light reflection characteristics of certain contaminant particles [Mr. B. Faulhaber, Personal Communication]. This results in fuel being considered satisfactory or contaminated when it may be just the opposite. A direct weighing of the filters would eliminate this possible error. Thus, if the laboratory balance can be made to satisfactorily perform at sea, the oceanographer will be able to enhance the gathering of data by providing a means to quickly and accurately analyze the data "now, not later". 12 II. BACKGROUND During the summer of 1966, the U. S. Bureau of Mines Branch in Tiburon, California invited various balance manufacturers to demonstrate the capabilities of their respective balances during an at sea evalu- ation aboard a small vessel. The results were unsatisfactory [Higinbotham, Personal Communication]. It was decided to explore the possibility of using a gimbal plat-form to place the balances on while conducting the at sea weighings. A surplus Navy MARK XIV MOD 1 Sperry Gyroscope was obtained and modi- fied to provide two degrees of freedom. By employing a pendulus motion system to keep the balance platform horizontal and to make the laboratory balance independent of ship motion, it was believed that satisfactory weighing at sea could be accomplished. This apparatus was placed aboard the research vessel Virginia City and used to weigh ocean bottom samples during an offshore drilling expe- dition covering the months of July-August 1967. The results obtained were within the Bureau of Mines accepted accuracy [Higinbotham, et al . , 1969], however, the weighings obtained were not correlated to the existing sea conditions and corresponding ship response for an empirical evaluation of the gimbal. Also, there was a lack of data regarding the pendulum motion. Subsequently, the gimbal platform was made available to the Naval Postgraduate School's Department of Oceanography for further analysis and evaluation aboard various research vessels. The principal of a gimbal supported arrangement to assist in instru- ment measurements at sea was first used in conjunction with gravity measurements [Dehlinger, 1964]. The at sea gravity measurement results 13 obtained with a La Coste and Romberg gimbal supported gravity meter show a high degree of accuracy when the horizontal and vertical motions of the vessel are nearly uniform and approximately sinusoidal. Also, the best measurements were obtained when the sea was parallel to the ship's motion [Dehlinger, 1964]. An improvement to the gimbal supported gravity meter was made by redesigning it operation for use on a stabilized platform which more nearly restricted the instrument motion to a single degree of freedom [La Coste, et al . , 1967]. Evaluation of this new system has shown that the gravity measurements have been as accurate as before, even under adverse sea conditions. Only under particularly adverse sea conditions, when the cross-coupling effects of the horizontal and vertical accelera- tions were excessive, did the gravity meter not perform well [Lafehr, et al., 1967]. Thus it appears that the use of a free gimbal platform is the first step in the development of a stabilized platform for satisfactory at sea weighings. 14 III. GIMBAL PLATFORM DESCRIPTION The gimbal platform used for conducting the at-sea weighings was a modified surplus Navy gyroscope, MARK XIV Mod I that was manufactured by the DODGE DIVISION of Chrysler Corporation, Detroit, Michigan, under license from Sperry Gyroscope Company, Inc. (now called Sperry Rand Corporation) in 1942 [SPERRY INSTRUCTION BOOK 17-1400CC, 1942]. The general characteristics are given in Table I. The internal assemblies of the unit were removed, while the inner and outer gimbals, spider element, outer gimbal supporting springs and dash pot assembly were re- tained in place as illustrated in Figure 1. TABLE I GIMBAL PLATFORM CHARACTERISTICS Height 35 inches Maximum Width 30 inches Total Weight 285 pounds Pendulum Weight 64 pounds (maximum) Pendulum Length 25 inches Table Top 20 by 21 inches Maximum Roll 15 degrees Note: Assembly can be separated into two units for mobility. A 20 inch by 21 inch balance platform was constructed out of fiber board and attached to the spider element. To provide for proper posi- tioning of the balance, a grid pattern of two inch squares was drawn on 15 U) fO -Q E •r— P J- c c 1— ( fO en ,_ c •r- «r— o §J CD .c c I/O •^ c >, a ^~ Q. J3 E E q CO #t re 0 Q- r™™ (O sz X3 a> •r— 4-> 3 3 O ■P E -O O OJ O c •r- >> t- O. •O •p* <£ 4-> L. S_ O 0) Q. Q_ Q. 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Q qj jQ 1 — UD qj co ui o UD LO LOUD r-» CO O CO LO CO CO CO "* CO CO i— o o o o O CD CD CD VDNOr- i— CO UD UD LOLOUDUD LOLOUDC0 LO O CD UD ud ud lo en UD LO CO o o o o CD CD O CD LDrvOr- r— CO CO CD LO CO LO LO LO CO CD CO O 00 co i — en o o o o o o o o IDNOr- i— CO o en UJ •i— 4-> to O ns •1— Q- a >> 4-> •i — •1 — +? c 4-> <+- •1 — QJ c •i — to u QJ <_> o O Q> o c CL to •r- c to •r" •1 — c > >> o CO , — ^ +J >> •1 — — , — 00 •r— +y +-> s- fO LO CO •i— ra QJ 1/1 en o to p— S- s- o O o Z3 QJ s. • CO u Q- +-> > •r— to S- U •r~ E > •1— QJ f0 C O > 4-> M- 13 to O C 3 1 — •r— o •i — c +J QJ +-> • 1 — CO ^Z ns M- 5- E 'o E •i — n3 JD E CD (J QJ E >, o £= QJ C o A3 O (1) CT) ^■HH MIMTIMJTITW 22 easily become immobilized by the placement of sandbags around the base plate and by use of two inch by six inch planks properly positioned as retainers. Only in rough seas did the gimbal platform tend to move when not secured. Figure 5 shows the two pointers and the two plexiglass plates used to record the movement of the table in the two degrees of freedom. Also, Figure 5 illustrates one method of holding the platform secure by means of sandbags and planks. 23 en c: c •i— o s •r— o +-> .c fO CO +-> o CO QC ^ c co rO •i — r— X Q- =C "O JZ c a ro 03 rO >> (J -Q •i— ■Q -a C cy I — I i. 3 ai u r— > r— ^— JD ro E ^ ai CO oo •r— CO > - < 2T O LO LO 1 — i~. r— 1— 1 O _i CO 1 CO O ■r™ •a: UJ UJ «=c 0 O —I 0 CQ CO ^ < «C 1— _J UJ LO 0 CQ C_> 0 CO CO O 0 LO 2: CO *d- 0 O 0 -o CO cC O 1 — CO O •1 *l _l 1 • 1 — Z3 «=c 0 O •r— 1 — CQ 00 U_ UJ C O LO O Z O O O O 0 -a LO LO r— +J 2: t— • • OJ < - 0 >- h- zz C_> O 1 — 1 1— 1 1 gram), higher electromagnetic forces require excessively large torque motors and currents. Figure 6 shows a simplified diagram of a Cahn Electrogram- balance. SAMPU Figure 6. Gram Electrobalance Diagram [Cahn, 1962] 30 V. PROCEDURE The general procedure in the collection of at sea weighing data was to repeatedly weigh specific samples on one balance at a time while varying the pendulum weights and the viscous dampening medium. For example, a shipboard location was first selected for the gimbal platform. Then the dampening oil was chosen. Next a range of samples v/as weighed with one specific pendulum weight. The pendulum weight would then be increased and the samples weighed again. When the last pendulum weight was used the dampening oil was changed and the procedure of varying the pendulum weights repeated. The complete operation was repeated with a new balance or at a new shipboard location. Hopefully, during this period, the vessel maintained the same heading in relation to the sea conditions. However, as discussed in Section VI, positive control of the vessel was not always possible due to other requirements. The majority of samples used were made out of commercial aluminum foil folded to various thicknesses and stored in aluminum tins. The heavy samples were either samll lead weights stored in aluminum tins or plastic snap top vials filled with paper clips. Prior to the at sea weighings, the samples were weighed in the laboratory on the balances which were to be taken to sea. After the sea trial, the samples were again weighed in the laboratory. This last weighing was primarily a check to detect for possible damage to the balance which might have been incurred during transit or while on board the vessel. In practice all post-sea trial weighings compared exactly with the pre-sea trial weighings. Occasionally a standard class S weight was used at sea. However, because of the whole gram multiple of the 31 sample, the reading was very often above or below the exact gram weight when estimating the balance equilibrium position. This occurred only when using a balance that required a dial manipulation to load the balance first in steps of even gram values and then in fractions of a gram. The standards that were used as samples are tabulated in Appendix A. Figure 7 shows the method by which unbiased readings were obtained with Balance A, even after repeated weighings of the same samples. The operator assumed a position such that the readings were obtained by looking directly down at the pointer, while the weight settings on both the coarse and fine dials are hidden from view, but still available for manipulation. The operator looked at the weight dials and read the sample weight only after determining the condition of equilibrium. Naturally, when using a balance with an optical read out, this procedure was not necessary. In conjunction with the at sea weighings, the environmental conditions were noted at least once an hour or after each individual weighing. The tabulated tables of sea conditions are found in Section VI. The exact position of each balance was determined in the laboratory such that the pendulum remained as nearly in the vertical as possible. In this way the balance weight was evenly distributed about the center of rotation and did not create adverse moments to influence the pendulum motion. Also, the balance was then in a level condition. These positions were marked on the platform grid lines and then used to place the balance correctly when at sea. The grid lines can be seen in Figure 7. 32 s- -a O) u o s- Q. c o ■»-> ro +-> Q 01 (D i- en •r" 33 VI. RESEARCH VESSELS EMPLOYED Conducting repetitive experiments at sea presents many problems, not the least of which lies in the interpretation of the data. It is apparent that it is impossible to achieve identical "laboratory" conditions under which different tests of the same nature are being conducted. In order to obtain data on at-sea weighings that covered a wide spectrum of condi- tions, three. different oceanographic research vessels were employed. The general vessel characteristics are tabulated in Table V and represent in size the majority of oceanographic vessels that are presently employed by various government agencies, civilian firms, and universities. TABLE V GENERAL SHIP INFORMATION CHARACTERISTICS BUILT CONVERTED LENGTH BEAM DRAFT DISPLACEMENT CREW SCIENTIFIC COMPLEMENT NPS 63 HOPKINS MARINE USNS FOOT STATION VESSEL OCEANOGRAPHIC VESSEL PROTEUS VESSEL T-AGOR-14 WW II 1946 1969 1963 1969 - 63 ft 100 ft 208.3 ft 13.75 ft 24.16 ft 39.4 ft 3.25 ft 11.6 ft 14.25 ft - 186 tons 1339 tons 4 6 26 2 9 15 The Naval Postgraduate School oceanographic research vessel, shown in Figures 8 and 9, is a Naval air-sea rescue boat which was converted 34 m e ro o en c ■i — S t/> o C .c O oo • i — +-> i^ 03 ■ >1 ^ ^r o o +-> s- ro rd S- CD o c/} JD O) ro CC _l tn +-> D_ CD CO O) s- ZJ CD 35 WET LABORATORY Figure 9. NPS Research Vessel Showing Wet Laboratory Location 36 for basic oceanographic work in 1963. The boat is mainly used for famil- iarizing students with oceanographic instruments and for limited research in Monterey Bay. Figure 8 shows the wet laboratory where the gimbal platform was located. This location places the platform 1.2 feet above the water line, on the vessel center line and 45 feet from the bow. Assuming the center of pitch of the vessel is approximately 60-80 percent of the ship length from the bow [Rakoff, 1962], this places the platform in the most advantageous position for minimizing roll and pitch effects. On the sea trials of the 15th of May and the 13th of July the vessel was positioned with the bow directed into the swells with its propulsion being used to merely maintain the proper heading. Under these conditions the vessel can be considered to be experiencing motions in the plane of symmetry, i.e., surging, heaving, and pitching iKorvin-Kroukovsky , 1961]. The actual sea conditions under which the weighings were made on the NPS vessel are found in Tables VI and VII. The research vessel PROTEUS is owned and operated by Hopkins Marine Research Station, a marine biology extension of Stanford University. The vessel is a converted fishing boat and is shown in Figures 10 and 11. The gimbal platform was located in the main laboratory space directly above the shaft, 3 feet below the water line, and 61 feet from the bow. Using the 60-80 percent assumption in locating the center of pitch, the gimbal assembly was again found to be located in a favorable position. The gimbal's position is indicated in Figure 12. Two weighing trials were held while biological trawling was conducted and, as a consequence the ship's relative position with regard to the sea conditions could not be controlled. 37 CO D- zz. 0 cr> O *■•*,, i — 0 CO O CM O CO CM • • ^3- *3" ro 1 ■^f 1 ^f 0 1 1 _l CO r— CO C\J CO 1 — co O CT> CM r— UJ CO 00 UJ O > cr> O ~\ uo 0 CO 0 CM 0 CO CM ir> CO CO 1 *3- 1 *3- O 1 1 «d- •"" CO C\J co 1 co O en CM ' 0 cr. 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D- C_> -M zn h- +-> 2T 4-> zn 1 — c 1— « UJ 0 O Q 1 — 1 Q h- zn ~T~ . — » CC 00 1 — 1 UJ 00 UJ Q 00 UJ Q- 00 00 OO 00 0 1— i CD UJ az CD UJ <=C CD UJ UJ CD CD 2: O CD X 1— 1 CD D- UJ CD D_ Q 2: CD s: CD 1 — 1 S_ Q S_ OO ZC S- OO — '. S_ m S- rn __l cn _J cn CD cc s: CD 2: o-> CD UJ _J CD 1 Q CD Q D- CD D- UJ 1— c CD »— 1 CD 1 — 1 2: uj -0 UJ 2: -0 2: 1— 1 T3 i— 1 h- X "O X -a UJ 1— < 3—' 3 1— 1 *— <• 1 — 1 ZC rc cC cC * — ' 00 00 00 CO 38 TABLE VII SEA CONDITIONS ON 13 JULY 1970 VESSEL: NPS WEIGHING TIME SWELL DIRECTION (degrees true) SWELL HEIGHT (feet) WIND DIRECTION (degrees true) WIND SPEED (knots) SHIP HEADING (degrees true) SHIP SPEED (knots) WATER DEPTH (feet) MAXIMUM SHIP ROLL (degrees) MAXIMUM SHIP PITCH (degrees) CASE A CASE B CASE C CASE D CASE E CASE F AND AND AND AND 18/50 ' 36/501 54/501 64/501 0955 1000 1015 1050 1115 1230 330 320 300 300 300 300 3-4 3-4 3-4 3-4 4-5 4-5 340 310 320 320 300 300 1-2 1-2 3-4 3-4 4-5 6-8 340 310 295 300 300 300 0 0 .5000 120 120 96 120 136 180 3-4 3-4 4-5 4-5 4-5 4-5 2-3 2-3 2-3 2-3 3-4 3-4 1 Represents pendulum weight (lbs) and S.A.E. oil weight number. 39 to CD +-> O s- CD to CO CO > i- fO -t-> (/) CU S- Q_ o O) S- CD 40 to 3 01 -l-> o i. Q_ , 0) to to >> o -»-> .c <0 o S- s- o M- H3 O +J OO c o O) •r— c +-> • 1 — fO S- o ca o s: _1 to O) c E •r- •r- ^. 2 Q. o o .c 31 oo (1) S- 41 Balance Location Figure 12. Hopkins Marine Station Research Vessel Proteus Showing Balance Location in Main Laboratory 42 The initial trial was made with the vessel proceeding at approxi- mately ten knots with the seas broad on the starboard bow. The second trial was conducted with the ship proceeding at approximately three knots with the seas off the port quarter. The actual sea conditions for both trials are listed in Table VIII. Comparison of the results obtained indicate that the best measurements can be obtained when the vessel is parallel to the sea direction [Dehlinger, 1964]. Of the three vessels used in conducting the at-sea weighings, only the USNS BARTLETT (T-AGOR 14) was built as an oceanographic vessel from the keel up. This vessel is shown in Figure 13. Two of the three balance locations used are shown in Figure 14 and the other location is shown in Figure 15. The scientific office location was utilized in port to initially check the balances for proper operation. Most of the weighings were conducted while the Bartlett was engaged in deep sea coring. Thus, at most times the was drifting slowly. Since the ship remained downwind of the coring cable to avoid tangling the cable in the screws, the waves were normally broadside. The vessel then was generally experiencing only rolling, side-swaying, and heaving motions [Korvin-Kroukorsky, 1961]. The wet laboratory location was on the vessel center! ine, 6.6 feet above the mean water line, and at frame 56, which is 106.8 feet from the bow. The first platform location was again on the centerline, 2.0 feet above the mean water line, and at frame 40, which is 77.6 feet from the bow. Both positions are forward of the center of pitch using the 60-80 percent rule. While making weighings at the first platform position the vessel was headed at first directly into the seas and later directly downseas. 43 OO C3 UJ h- o CD lo *3- LO o CO CM LO CM CO O CO LO CO o CO CO I lo o cd O CO i CM o LO <3" LO I LO ^1- I CO oo CO o LD LO LO CM CD CO CO O CO CO LO CO LO CO CO I CM o en CD CO i CM O CO LO LO I LO I CO o LO LO CO LO o CO CO LO CO CO CM CD CO CO I CO LO CT) O CO I CM CD 00 LO LO I LO CO CJ JD. E zs c o LO CO o CD O CT. •— i o UJ CO o oo 2: o • — i I— i — i Q O o Ul oo LO CM CO CD CO CO 1 — LO O CD *• — r— CO CO ^f o CO CO LO r — *3- CM CO O CO CO CO o CO o LO ^- cr> i CD 1 1 o CM LO LO co o 1 — o CM 1 r-. 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Sea conditions for all runs can be found in Table IX. The BARTLETT has a designated gravimeter room located on the first platform at frame 47 off the centerline to port. This space was not available for use at the time of the sea trials. 48 O LO CO O *3- LO C\J 1 CT> 1 i i — CM i — co «vl- UJ cc LO LO _J «=C H— 1 QC o LO o LO CM LO • LO r^ ^" CM 1 CM 1 CO i 1 CO CTi CM o r — LO CO _J o CC LO i— _l O-i — OOCOLOCM cc «3- o r— I— CM LO r— _J o >-> O or lo lo Q. i — O CM O r^ o co *d- ^ K? CD CO CO LT H- CM CO i— I— _J LO O CC CTi r-s. _j o_ o co lo o CTi i— i— i o cc O- O- r— XI ~^ cC i o O LO l—i CM ^" CM CM CM \ CM LO CO r— CO CO CO UJ CM LO _i z: i— CO o I— LO _l LO 2T Mlfi O O CC CM I— I LO 0_ i — I— --^ <: i o o <3- •— « O ~ £^ 'S33Li93a 2-L JO 1101. dIHS WnWIXVW V HUM lN3S3yd 39HnS LO LO o o i — LO • o LO co CM 1 CM 1 co i 1 CO «tf CM o 1 — "* CM CM LO O O r~" o o 1 LO LO 1 co 1 CO o CM O ■ — ^ CM CO LO o O r— CO • o LO CM CM 1 CM 1 CO 1 1 CO CM CM o 1 — ^t- 1 — __l _J O-I cC eC 1— 1 S- CD J- 0_0)Q_ i_4_>c_j+j o)i — +-> ^+-> re »— io)»— 1 O UJ _JO>C_> O t-< O t— -^rc S- :n -~^ UJ (/> Oi GO I 4- UJ LO UJ O LO UJ O- L0 CO CTILO LO CD CC O) i-h 0) UJ CtC O) UJ -— - <=C O) UJ .— - UJ E O) O) ^ I— 1 O) Q O) 3 Md)D.WljJ(l)Q.WOOS"D2 O) t— t OS- S_cO|_ QS-wPXi-l/)+) x: o O S- rc ai_i D)\i en o cr> oaps Si w cd ujujujo) io)ujooo)0— cl "OUJTJ>i-i2:"OZ-^>-'"Di-iA:| — <4_ x — IX| — "O uj — E ro =5 +-> i— O ■o C 4- X •r- < CO ro CD O CD c S- -r- CU S c o c _c i— < oo CD S- Z5 CD 56 where oo was found to be 7.42 sec" . Thus, J, becomes a constant for rotation about the B axis and is given as: Vi W (14.0) (5.88) (7.42)2 = 1.495 in-lb-sec' J^, the mass moment of inertia of the lower pendulum rod and weights was determined from the formula: 1 r 2 dW J2 = f r2 T = 2, 2"1 1 , y A1A T" 1 2. x ,. 2 hfc al a2 ■ g ( r } 3- + (y^a h) (L ■ y, - -3- 12 (5) where the pendulum rod was considered to be a uniform thin rod, and the pendulum weights were considered to represent a hollow cylindrical shape placed around the pendulum rod. Using Equation (5) for the three cases we obtain the respective inertia moments listed in Table XI. TABLE XI INERTIA MOMENTS FOR ROTATION ABOUT THE B AXIS CASE I II III u2 2 ul (in-lb-sec ) 4.07 1.495 32.51 1.495 42.94 1.495 5.57 34.01 44.44 Setting K = (W2r2 - W,r,) in Equation (3), where W^ is a constant and equal to 82.32 in-lb for all cases, the values for K listed in Table XII were determined. 57 TABLE XII RESTORING MOMENTS FOR ROTATION ABOUT THE B AXIS CASE K (in-lb) I 327.30 II 631.05 III 898.80 With these values of J and K, the respective natural frequencies of oscillations were computed for each case by letting sin e s e in equation (3) and solving for w from to = / -j — . Table XIII lists the natural frequencies of oscillation about the B axis. TABLE XIII NATURAL FREQUENCIES OF OSCILLATION ABOUT THE B AXIS CASE w (sec" ) f (cps) I 7.669 1.2206 II 4.308 0.6856 III 4.497 0.7158 For rotation about the A axis (see Figure 20) the only change required in the quantities determined previously for rotation about the B axis was that of the polar moment of inertia of the inner gimbal . The outer gimbal, which is symmetrical about a line perpendicular to the A axis and through the center of the system, does not contribute to any moments and consequently has no moment of inertia about the center of rotation. By measuring the period of oscillation of the inner and outer gimbal about the A axis experimentally and utilizing equation (4), the moment 58 POINT 0 Figure 20. Rotation of the Gimbal Platform about the A Axis 59 of inertia was calculated to be: i Wlrl 04. 0) (5.88) Q 7,7 /. 1K 2, J, = — k- = — * — * — 5-^— = 5.767 (in-lb-sec ) 1 u> (3.778)^ where co was found to be 3.778 sec" . By computing a new J and letting sin 65 9 in equation (3), the natural frequency of oscillation for each case was computed in the same manner as before. The results are listed in Table XIV. TABLE XIV NATURAL FREQUENCIES OF OSCILLATION ABOUT THE A AXIS CASE co (sec" h f (cps I 5.768 0.9180 II 4.060 0.6462 III 4.296 0.6837 Table XV summarizes the results of the independent pendulum rotation about axes A and B. TABLE XV NATURAL FREQUENCIES OF OSCILLATION ABOUT THE A AND B AXES CASE A AXIS B AXIS f (cps) f (cps) I 0.9180 1.2206 II 0.6462 0.6856 III 0.6837 0.7158 60 B. DAMPENED FREE VIBRATION In analyzing the effects of viscous dampening on the pendulus motion about the A and B axes, it was first necessary to determine the viscous- dampening coefficient, c. It was assumed that c was linear and proportional to the first power of the velocity [Tse, Morse, et al . , 1964]. The units of the coefficient in a rotational system are in in-lb-sec. The single- degree-of-freedom system, with free vibrations and viscous-dampening, is given by mx + cx + Kx = 0 (1) where m is the mass of body, x is the linear displacement, c is the viscous dampening coefficient, and K is the spring constant. The three terms in the equation represent the inertia force, the dampening force, and the spring force. For rotational motion equation (1) can be written JQ 6 + c e + K e = 0 . (2) The solution of equation (2) involves a factor which diminishes with time, an oscillatory term for the vibration, and two constants of inte- gration. The system's motion can be described as being either over- dampened, critically-dampened or under-dampened. The critically-dampened coefficient is given by c = Ju [Den Hartog, 1956]. A solution of the form G = eQ e"bt cos pt (3) where the constant b and the damped natural frequency of oscillation p are defined as: 61 b = 2J. (4) P = (5) satisfies equation (2) for all values of time with the phase angle of motion equal to zero. This result is plotted in Figure 21 and holds for i/ p all values of t-> Cc/2J ) , i.e. the under-damped case where c = c . u O *» 0 The combined results of a decreasing exponential factor and a sine wave is a "damped sine wave", lying in the space between the exponential curve and its mirror image. Figure 21. General Free Vibration Curve with Viscous Dampening 62 In order to determine the dampening constant, c, the oscillations of the pendulum were recorded on a constant speed movie camera for each axis of rotation under the different load conditions. From a knowledge of the camera speed (24 frames a second) the maximum left and right angular displacements were recorded as a function of time. The pendulum weight and dampening fluid used for each run are given in Table XVI and the respective curves are shown in Appendix C, with the data recorded in Appendix B. TABLE XVI PENDULUM WEIGHT AND VISCOUS FLUID COMBINATIONS USED IN DAMPENING THE MOTION RUN 1 5 6 7 8 9 10 WEIGHT (lbs) 18 18 36 54 18 36 54 MEDIUM (Air or S. A. E. oil) Air 50W 50W 50W 90W 90W 90W Measurement of successive maximum ordinate values at times t-, and to = (t, + T), where T is the period of oscillation, gives 6, = 9 e 1 and 0O = e e *■ 1 ' and their ratio 2 o e'1 1 - I2-I . ebT . (6) eo 8-^*1 + T) The second ordinate is thus seen to be equal to the first multiplied by the factor e"bT. This factor, which is smaller than unity, is the same for any two consecutive maxima and is independent of the amplitude of oscillation or of the time. 63 Taking the natural logarithm of each side of equation (6) gives el bT = In -i- . (7) e2 The term bT is called the logarithmic decrement [Den Hartog, 1956]. Now for each of the vibration curves, 9,, 02, and T were measured, b was calculated from (7), and c was calculated from (4). In order to eliminate possible errors due to small errors in establishing the zero displacement for each vibration curve, the total amplitude (left dis- placement + right displacement), between the exponential envelope was measured at successive maxima and used in equation (7). Table XVII is a tabulation of the period of oscillation (T) , the logarithmic decrement (bT), and the viscous-dampening coefficient (c). Table XVIII is a comparison of the calculated natural frequencies with the observed or measured natural frequencies. From Table XVII, it is seen that the viscous-dampening coefficient, c, is greater for the Z axis than for the B axis for respective weight/ fluid combinations. This is accounted for by the presence of the two dash pots on the A axis as discussed in Section III and as shown in Figure 3. Once the outer gimbal rotations were less than approximately four and one half degrees, the gimbals failed to strike the piston dash- pots and therefore failed to provide additional dampening. From Table XVIII it is seen that the measured natural damped fre- quencies increase with increasing pendulum weight and decreasing fluid viscosity except between runs 7B and 10B. Since the viscosity of 90W oil is less than 50W oil, it can be concluded that the measured frequency 64 TABLE XVII LOGARITHMIC DECREMENT AND VISCOUS DAMPENING COEFFICIENT VALUES A AXIS B AXIS RUN 1 T (sec) 1.58 bT 0.0488 c (in-lb-sec) 0.344 T (sec) 1.42 bT 0.0278 c (in-lb-sec) 0.218 5 1.77 0.4539 5.046 1.71 0.4806 3.113 8 1.75 0.4055 4.588 1.67 0.4290 2.862 6 1.68 0.4120 18.143 1.63 0.4187 17.155 9 1.66 0.3935 18.143 1.62 0.3735 15.583 7 1.63 0.4539 27.130 1.59 0.4125 23.064 10 1.62 0.4626 27.821 1.61 0.4055 22.389 of 10B should be greater than 7B. This inconsistency is the result of an incorrect data point in determining the logarithmic decrement. The large differences between the measured and calculated natural frequencies of oscillation can be considered to be a result of the trunion bearing friction of each axis and the fact that the pendulum weights were not completely cylindrical. The slots were alternately parallel to the flow of motion as shown in Figure 2. This would increase the dampening factor and subsequently decrease the natural frequency of oscillation. Another reason for lower frequencies is that adjacent weights allowed oil to pass between them, creating a small dash pot effect. As mentioned in Section IV, with this type of gimbal platform, where the center of rotation is below the balance platform, the moment created by the balance weight will subtract from the restoring moment thus increasing the time required to reach equilibrium after an initial pendulum displacement. 65 TABLE XVIII DAMPENED NATURAL FREQUENCIES OF OSCILLATION ABOUT THE A AND B AXES RUN MEASURED CALCULATED MEASURED CALCULATED (cps) (cps) (cps) (cps) 1 0.6329 0.9180 0.7042 1.220 5 0.5650 0.9171 0.5814 1.219 8 0.5714 0.9164 0.5988 1.220 6 0.5952 0.6450 0.6024 . 0.6844 9 0.6024 0.6451 0.6135 0.6855 7 0.6135 0.6822 0.6289 0.7146 10 0.6173 0.6822 0.6211 0.7147 66 VIII. RESULTS Table XIX shows the total number of at-sea weighings made aboard the three research vessels. Of this total, 210 weighings were made on balance A, 24 on balance B, and the remaining number were made on the other balances listed in Table IV. TABLE XIX GENERAL SUMMARY OF AT-SEA WEIGHINGS DATE VESSEL NUMBER OF WEIGHINGS 22-24 APRIL 1970 BARTLETT 50 15 MAY 1970 NPS 90 10 JUNE 1970 PROTEUS 63 13 JUNE 1970 NPS TOTAL 44 247 Because of the various operating requirements of the vessels, the weighings on 15 May 1970 represent the only sea trial where three fluids and three different weights per fluid were used with the vessel experi- encing wery nearly identical sea conditions throughout. Also, the ship was able to maintain the same heading with respect to the direction of seas during this period. Figures 22, 23, and 24 show the weighing results of 15 May 1970 where pendulum weight is plotted versus sample weight for the 10W, 50W, and 90W fluids. It is apparent that the weights recorded for each pendulum weight are consistently influenced by the dampening medium to the same degree (with one exception) for each pendulum weight. Without 67 recording the specific weights obtained, Table XX illustrates the ordered arrangement of weights obtained by placing the dampening fluid number in its relative position about the actual sample weight line to indicate weight readings greater than or less than the actual weight. TABLE XX RELATIVE POSITIONS OF WEIGHT MEASUREMENTS MADE ON 15 MAY 1970 IN RELATION TO ACTUAL SAMPLE WEIGHT GREATER THAN ACTUAL WEIGHT 90W <;AMPI F- 10W 50W -WEIGHT- 90W 50W 90W LESS THAN ACTUAL WEIGHT 50W 10W 10W 27 45 54 Pendulum Weight (lbs) For each of the three pendulum weights one exception to the arrange- ment shown in Table XX was noted. Each exception was for a different sample weight as is shown in Table XXI. Each sample was weighed ten times under different pendulum weight/ fluid combinations. In every instance the least per cent error of total sample weight recorded was that obtained with the 90W oil. The corre- sponding pendulum weights used were 27 pounds once, 45 pounds twice, and 64 pounds six times. The per cent error in total sample weight was always less than 0.10%. The weighing data is tabulated in Table XXII. 68 TABLE XXI THREE EXCEPTIONS TO THE RELATIVE POSITIONS OF WEIGHT MEASUREMENTS MADE ON 15 MAY 1970 GREATER 50W SAMPLE 50W 50W 10W WEIGHT---0.074 2.947- 5.342 90W 10W 90W LESS 10W 90W 27 45 54 Pendulum Weight (lbs) Since the relative order of increasing viscosity magnitudes is 10W, 90W, 50W5 Figures 22, 23, and 24, and Tables XX and XXI indicate that in general 10W oil under-dampens the pendulum motion, the 50W oil over- dampens the pendulum motion, and the 90W oil most nearly represents the desired critically dampened condition. There appears to be no consistent correlation between the logarithmic decrements listed in Table XVII with the relative position of the weighings in different fluids as listed in Tables XX and XXI. It is seen that use of the 45 lb weight pendulum results in the greatest difference between the respective logarithmic decrements about the A and B axes and agrees in general with the greatest distance between the 50W and 90W curves (which appears at approximately the middle of the pendulum weight range) of Figures 22, 23, and 24. Figures 25 and 26 show the weighing results of 10 June with 10W and 50W fluids and with the vessel on different headings for each trial. As a result of adverse weather the trials were suspended early in the 69 >- cc o r— o CO cc j— o LO o LO ^3" LD LO 2^ OO O _ O UJ O o cr> 2: r- - i— i 2: ►-< < X _J X cC CO eC O cm 6 Q CD •— • O O cr> O LO 2: «d" O- O 2: lo O LO LO SI «* Q CD s: cr> CM o LO CM r-«. 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Variation in peighings Obtained on 13 July as A Function of Pendulum V.'eicht 80 TABLE XXIV WEIGHING DATA^ FROM BALANCE A ON 13 JULY 1970 VESSEL: NPS BALANCE LOCATION SAMPLE Al _ DIFFERENCE5 ERROR {%) SAMPLE A2 DIFFERENCE ERROR (%) SAMPLE A3 DIFFERENCE ERROR {%) SAMPLE A4 DIFFERENCE ERROR {%) SAMPLE A5 DIFFERENCE ERROR (%) STANDARD J 54.579 10.880 101.409 99.985 56.598 WET LAB 3 PENDULUM WEIGHT/DAMPENING OIL* 18/50 36/50 54/50 64/50 54.578 -0.001 0.002 10.898 +0.018 0.165 101.375 -0.036 0.035 99.985 0.000 0.021 56.610 +0.012 0.021 54.577 -0.002 0.004 10.890 +0.010 0.091 101.375 -0.034 0.034 99.980 -0.005 0.002 56.599 +0.001 0.002 54.561 -0.018 0.033 10.870 -0.010 0.091 101.389 -0.20 0.020 99.975 -0.10 0.002 56.599 +0.001 0.002 54.580 +0.001 0.002 10.891 +0.011 0.101 101.400 -0.009 0.009 99.986 +0.001 0.000 56.598 0.000 0.000 General Notes: Weighings made with vessel maintaining station, ship head 310°-340° true, ship speed 0-.5 knots. Wind direction from 310°-340° true, speed 2-8 knots. See Table VII. 1 See Figures 8 and 9. "Weights in grams. Pendulum weight in pounds, oil designated by S.A.E. number, i See Appendix A. 'Difference = STANDARD minus WEIGHING. 81 *3r h- > r— U- 0 c CD 0 «x CO rn CO CO CNJ CO O CO i — 0 o» 2> LU r^ O 0 ■ — CD O CO 0 O •— 1 — 1 r— O CO 0 0 r>. CNJ O C «3- 0 CO 3Z LU JO 1 — 1 «=c C3 s A3 DC 0 0 c O C O 0 0 c 1 — 1 J— cC 1 1 LU 2: > 3 21 Z3 _J 25 CU cu CO • • ZD Q 27 LU LO 0 c 0 CO _J 2: O «3" LO r— CNJ CO CO Z3 LU • 1 — 1 LU NO^D 1— CD •=3- r~~ 0 CD CO o_ to I— CO CD 0 r-. 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See Appendix A Centerline, main deck wet laboratory. See Figure 14. 5 Centerline, first platform. See Figure 15. c Pendulum weights in pounds, oil designated by S.A.E. Number. Personnel Code 4. difference = STANDARD minus WEIGHING. g Class S standard weight. 85 TABLE XXIX WEIGHING DATA2 FROM BALANCE B ON 24 APRIL 1970 VESSEL: BARTLETT BALANCE LOCATION: CENTER LINE FIRST PLATFORM STANDARD K " TRIAL 5 TRIAL 6 TRIAL 7 SAMPLE lmq^ DIFFERENCE5 .. ERROR {%) 1.02 1.12 +0.10 9.80 1.06 +0.04 3.92 1.04 +0.02 1.96 SAMPLE lOmg DIFFERENCE ERROR {%) 10.06 10.06 0.00 0.00 9.98 -0.08 0.80 9.96 -0.10 0.99 SAMPLE lOmg DIFFERENCE ERROR {%) 10.06 10.12 +0.06 0.59 SAMPLE 20mg DIFFERENCE ERROR {%) 20.06 20.00 -0.06 0.30 20.08 +0.02 0.10 20.10 +0.04 0.20 SAMPLE 14 DIFFERENCE ERROR {%) 73.76 71.44 -2.32 3.15 73.38 -0.38 0.52 SAMPLE 14 DIFFERENCE ERROR (%) 73.76 74.34 +0.58 0.79 General: All weighings made with 64 pounds pendulum weight and S.A.E. 90W oil. See Table IX for sea conditions Notes: 1 See Figure 15. > "Weights in milligrams. See Appendix A. Class M calibration weight. 'Difference = STANDARD minus WEIGHING. 86 aft. Therefore, the balance beam should be orientated appropriately depending on which degree of freedom (roll or pitch) is experiencing the greatest rotation. In Table XXIX, Trial 5 was with the seas on the beam, Trial 6 was directly into the seas, and Trial 7 was directly down seas. From the few data points, it can be seen that the weighings during Trial 7 more closely approach the true sample weight and have less of a range of percent error than do Trials 5 and 6. Table XXX tabulates the maximum and minimum percentages of error in total sample weight for all weigh-ins. It is seen that the differ- ences between actual sample weight and the observed values is approximately a constant, and therefore, the percent error decreases with an increased sample size. TABLE XXX PERCENT ERROR IN SAMPLE WEIGHINGS BALANCE A BALANCE B SAMPLE MAXIMUM MINIMUM SAMPLE MAXIMUM MINIMUM WEIGHT ERROR ERROR WEIGHT ERROR ERROR (gram) (%) (%) (gram) w m 0.073 46.58 0.00 0.0740 22.43 0.52 0.212 22.17 0.47 0.2130 6.67 0.00 0.469 10.87 0.00 0.4714 1.40 0.30 1.679 3.58 0.12 0.001 9.80 1.96 2.947 1.73 0.03 0.010 0.99 0.00 5.000 0.52 0.00 0.020 0.3Q 0.10 5.340 0.60 0.00 6.469 0.37 0.02 9.420 0.52 0.00 10.882 0.18 0.07 54.579 0.03 0.00 56.604 0.02 0.00 84 . 880 0.01 0.00 101.409 0.04 0.01 101.990 0.02 0.00 87 IX. CONCLUSIONS The use of a two degree of freedom gimbal platform, with damped motion, enables certain standard laboratory balances to operate satis- factorily at sea under varying sea conditions. The gimbal apparatus must be placed on board the vessel such that the vessel motions will have a minimal effect on the gimbal platform and in turn on the laboratory balance. The vessel center! ine and center of pitch provide the best position. The ship on which the gimbal platform is to be used must position itself such that its motions and associated accelerations are at a minimum. The ship's maximum speed while using the gimbal platform, will depend on the prevalent sea conditions. However, a course parallel to the direction of seas is the most advantageous in determining weight measurements at sea. The gimbal platform should have removable pendulum bob weights and should be constructed so that the balance platform is at a minimum distance from the center of rotation. Removable weights and a means to lengthen or shorten the pendulum rod will allow for a change in the natural damped frequency of the apparatus. Balances to be used at sea should not operate on a fulcrum point or knife edge principle. The balance should have internal viscous dampening and present a mechanical readout. The balance should be corrosion resistant, have a small degree of internal compensation for out of level conditions, be shielded from air currents, and should be as light as possible to exclude additional external forces from influencing the pendulum motion. 88 APPENDIX A WEIGHT STANDARDS1 STANDARD BALANCE USED DATE WEIGHTED PERSONNEL CODE A A 28 APRIL 1970 1 B A 9 JUNE 1970 1 C A 6 JULY 1970 1 D A 18 MAY 1970 1 E A 22 MAY 1970 4 F B 28 APRIL 1970 1 G B 14 JULY 1970 1 H B 13 JULY 1970 3 I C 12 JULY 1970 2 J A 4 AUGUST 1970 1 K B 28 APRIL 1970 1 L E 28 APRIL 1970 1 M D 28 APRIL 1970 1 N F 28 APRIL 1970 1 All Standards were weighed on a laboratory table except for STANDARD H which was weighed on NPS Vessel while in port, 89 RUN 1A APPENDIX B PENDULUM DAMPENING DATA DISPLACEMENT DISPLACEMENT (Degi ^ees) TIME (Deg rees) TIME L R (Seconds) RUN L R (Seconds) 12.9 0.00 IB 13.2 0.00 12.0 0.83 11.6 0.75 11.9 1.67 11.3 1.46 11.3 2.42 11.2 2.21 11.0 3.21 10.2 24.33 10.5 3.96 10.0 25.04 9.0 11.13 9.5 39.17 8.4 11.92 8.9 39.92 7.0 21.67 8.1 49.71 6.8 22.46 7.9 50.38 5.3 29.42 7.7 64.42 5.2 30.08 7.3 7.0 6.7 7.2 7.0 6.6 6.2 65.13 71.88 72.58 79.38 80.04 88.17 88.92 5A 13.8 0.00 5B 13.0 0.00 9.2 0.88 10.0 0.96 7.2 1.71 7.2 1.79 5.6 2.50 6.1 2.67 4.9 3.29 4.0 3.54 3.6 4.08 4.1 4.33 3.5 4.88 2.6 5.17 2.0 5.67 2.8 6.04 2.3 6.50 1.5 7.00 1.3 7.38 1.9 7.71 1.6 8.17 0.7 8.71 0.9 8.96 1.2 9.38 1.0 9.83 0.2 10.42 0.3 10.63 1.0 11.13 0.8 11.38 0.0 12.08 0.7 12.86 90 APPENDIX B (Continued) PENDULUM DAMPENING DATA DISPLACEMENT DISPLACEMENT (Degi ^ees) TIME (Degrees) TIME RUN L R (Seconds) RUN L R (Seconds) 6A 13.4 0.00 6B 12.5 0.00 9.7 0.96 9.9 0.83 7.8 1.83 7.5 1.71 6.0 2.67 6.0 2.50 5.1 3.46 5.0 3.38 3.9 4.29 4.5 4.13 3.3 5.08 3.2 5.00 2.7 5.96 3.0 5.79 2.1 6.75 2.0 6.67 1.5 7.58 2.0 7.46 1.1 8.46 1.4 8.25 0.6 9.33 1 .8 9.13 0.9 9.96 1.0 9.96 0.4 10.71 0.5 0.2 1.0 0.8 0.6 11.25 12.00 12.83 13.67 14.46 13.1 0.00 9.5 0.92 7.4 1.83 5.8 2.75 4.3 3.54 3.5 4.46 2.7 5.33 2.0 6.13 1.5 7.08 0.9 8.08 0.8 8.83 0.5 9.75 0.3 10.58 7B 12.5 0.00 9.5 0.83 7.1 1 .67 6.0 2.46 4.1 3.25 4.0 4.00 3.0 4.71 2.9 5.54 2.0 6.29 2.0 7.17 1.0 8.00 1.5 8.75 0.5 9.58 1.0 10.21 0.4 10.96 0.7 11.83 91 APPENDIX B (Continued) PENDULUM DAMPENING DATA DISPLACEMENT (Degi ~ees) TIME RUN L R (Seconds) 8A 14.3 0.00 10.7 0.92 8.5 1.75 °6.5 2.63 5.5 3.50 4.2 4.38 3.5 5.25 2.5 6.17 2.2 6.92 1.4 7.92 1.3 8.79 0.8 9.75 0.7 10.54 0.3 12.88 0.1 13.75 9A 15.0 0.00 10.5 0.96 8.7 1.79 6.7 2.63 5.8 3.46 4.3 4.25 3.9 5.08 2.9 5.88 2.8 6.67 1.9 7.50 1.7 8.38 1.0 9.21 1.0 10.08 0.5 10.88 DISPLACEMENT (Deg rees) TIME RUN L R (Seconds) 8B 14.6 0.00 10.1 0.88 7.9 1.71 6.0 2.54 5.3 3.29 4.9 4.08 3.4 5.00 2.9 5.71 2.7 6.54 1.9 7.38 1.9 8.17 1.0 8.96 1.2 9.67 0.8 • 10.38 9B 14.0 0.00 10.3 0.83 8.1 1.71 6.1 2.46 5.2 3.21 4.2 4.04 3.8 4.79 3.1 5.63 2.5 6.50 2.0 7.29 1.9 8.17 1.5 8.96 1.3 9.79 1.0 10.58 92 RUN 10A APPENDIX B (Continued PENDULUM DAMPENING DATA DISPLACEMENT (Degrees) TIME L R (Seconds) 15.0 0.00 10.1 0.92 8.2 1.67 6.2 2.50 5.5 3.38 4.0 4.17 3.8 4.92 2.8 5.75 2.5 6.58 1.9 7.33 2.0 8.17 1.0 9.00 1.3 9.83 0.7 10.58 RUN 10B DISPLACEMENT (Deg: rees) TIME L R (Seconds) 14.6 0.00 10.1 0.88 7.9 1.71 6.0 2.54 5.3 3.29 4.2 4.08 3.4 5.00 2.9 5.71 2.7 6.54 1.9 7.38 1.9 8.17 1.0 8.96 1.2 9.67 0.8 10.38 93 o in CM O CVJ _m c o o O ~ -in X <: o o k Q CC 1—4 o i— • >■ u; CL a: C3 ^f CVJ O CO CD ^ (saaj5a CM O C\J sf CD ® O W ^ !N3!A!30VldSia 94 o o CD o X CO LU n: o CO o CD o 10 o o o CM c o o 0) (ft [- =5 o o DC en o O £ a: ^CVJOGOCO^OJOCVJ^CDQDO (saaj6ap)iN3[AJ3 0VldSia 95 CVJ O CVJ ^ CD O C\J <3" (sa©j5ep)iN3W30VTdSia 96 cy 6 co (o st (saajDd CSJ O CM st CO €0 O CM lN3W30VldSia A. 97 CO QD O CM ^° (saaj6ap)iN3IAI3DVldSia 98 SfCVlQCO (D^CVJOcM^t (0 CO O W ^ (saaj6©p)iN3iAI30VldSia 99 CMO<0^CVlO(V|5t (D (D O CM ^ (saajBap)iN3iAl3 0VldSia 100 CVJ O CD CD ?? (sadj6a (M O CJ ^ (D ® O W 't ±N3^30VldS!Q 101 CVJ O CD CD (saai6a !N3IAI30VldSia 102 O4OOOC0 Security Classification DOCUMENT CONTROL DATA -R&D i Security cfas si fie ation of title, body of abstract and indexing annotation must be entered when tfie overall report is classified) \ Originating ACTIVITY {Corporate author) Naval Postgraduate School Monterey, California 93940 2fl. REPORT SECURITY CLASSIFICATION Unclassified 2b. GROUP 3 REPOR T TITLE Weighing At Sea With a Gimbal Platform 4 DESCRIPTIVE NOTES ( Type of report and, inc his ivr dates) Master's Thesis; September 1970 5 auThORiSI (First name , mtodle mt tia I, la st name) Charles Manfred St. Laurent 6 REPORT DATE September 1970 7a. TOTAL NO. OF PAGES 110 7b. NO. OF RE FS 11 »B. CONTRACT OR GRANT NO b. PROJEC T NO 9a. ORIGINATOR'S REPORT NUMBER(S) 9b. OTHER REPORT NOISI (Any other numbers that may be assigned this report) 10 DISTRIBUTION STATEMENT This document has been approved for public release and sale; its distribution is unlimited. II. SUPPLEMENTARY NOTES 12. SPONSO RING M1LI TAR Y ACTIVITY Naval Postgraduate School Monterey, California 93940 13. ABSTRACT The use of a gimbal platform with two degrees of freedom under dampened pendulum motion allows a standard laboratory balance to be used to weigh scientific samples at sea. The maximum sample weight tested was approximately 120 grams, while the average accuracy obtained in samples ranging from 1 to 120 grams was 0.10% (± .05%). The sea conditions under which at-sea weighings can be conducted vary with the size of the research vessel. The gimbal platform does not provide the stabilization necessary under adverse sea conditions. DD,T:..1473 lPAGE " S/N 01 01 -807-681 1 111 Security Classification A-81408 Security Classification key wo R OS ROLE W T Weighing Balance Pendulum Motion Gimbal Platform DD ,F.T..1473 S/N 0101-807-6821 112 Security Classification A- 3 I 409 {jay lord ^= SHEIF BINDER ^^ Syracuse, N. Y. \ —- Stockton, Calif. ; 124278 S1524 St. Laurent c.l Weighing at sea with a gimbal platform, Thesis 124278 S1524 St. Laurent c.l Weighing at sea with a gimbal platform. thesS1524 Weighing at sea with a gimbal platform. 3 2768 001 97690 5 DUDLEY KNOX LIBRARY