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i 70 852 07 PER SEC "TRAE. MaRINE REVIEW OER : VOW WNW VY VV FIG; oO: 200 1g0 1g0 The frequency of propeller blade imipuise "is about seven times the frequency we are looking for, and if it were exactly seven times we might conclude that we had located the cause, because any impu!se whose fre- quency is an odd harmonic of the natural frequency of the bar will ex- cite the fundamental vibrations in tee bar' Hor, it "we the fundamental and, say, tne third har- monic, their relationship is shown in Pie, 3: and. it. will. be noticed. that, during each half period of the funda- mental, there is an old impulse in the third harmonic, and these odd impulses, being alternately positive and negative, are just so timed as to excite the fundamental vibration. Of course, if the bar could vibrate in unison with this third harmonic im- pulse, it would do so; but, since it cannot, it vibraves in its fundamental mode. Any even harmonic impulse has the same number of positive and negative impulses in each half period of the fundamental, and it cannot, therefore, excite the fundamental vi- bration, We see that the agreement between the fundamental propeller impulse and the seventh harmonic of the vibration frequency is not sufficiently close to account for the large amplitude of vibration, therefore we must look elsewhere for the cause. Let us ex- amine the "beats" between the im- pulses of the four screws. The bottom line of the table con- tains the frequency of the odd har- monics of the vibration . frequency, consider and any impulse having the same fre- quency as one of these harmonics will help to excite the fundamental vibration in ques'ion. Let us compare these numbers with those in the ta- ble above them. We find no absolute agreement, but we find several which are sufficiently close to account for a vibration lasting, say, a quarter of a minute. Thus we have: 64 and 60 beating 4 times per minute. 192 and 188 beating 4 times per minute. 192 and 189 beating 3 times per minute. 170 160 192 and 193 beating 1 time per minute. It is probably the last two which are the predominant factors in excit- ing the vibrations, namely the seventh harmonics in the propeller impulses ol screws. 2, 3and 4. FREQUENCY OF BEATS BETWEEN THE VARIOUS HARMONICS OF THE PROPELLER IMPULSES. Harmonics. Pro: (Funda- 2 3 4° = 5 6 7. pellers. mental.) Tani 2a vats 47.1 94.2 141 188 235 283 330 and: 3.cnat Toe V0 D0. 30.5 37/640 52 Land 4s. 20:1 4032; 60) 80° 100-420. Lad DAN he eae 54:6, 109.2 "165 218.273 327 332 Bandas 2208 27 54 81 108 135 162 189 Sand doa... 27-62-55 83. 110. 138.165: 193 Frequency of the odd har- monics of the vibration 64.1 -- 192 -- 320 -- 449 Almost every part of the pallograph record shows intermittent vertical vi- 'brations of a much higher frequency Selecting a they and of small amplitude. portion of the record where 'lasted for five seconds, we find 41.5 periods in five' seconds, 1. (©. a ire quency of 83 per second, or 498 per minute. The corresponding frequen- cies af revolution of the screws, were: +a -- Frequency Revolutions of propelier per minute. blade impulses. Propeller |i. 167 e501 Propellerc2. 3... 164 492 Propeller suits a: 158 574 Propeller 4.03.0 oa 166 498 It is evident that this vibration is directly due to the propeller im- pulses. since the frequencies agree, and the intermittent character of the vibration must be due to the inter- ference of the impulses from the four screws. If all four screws ro- tated in the same phase and at the same speed, this vibration would ge greatly magnified. At certain times they will. rotate in the same phase, and then the vibration will be a maximum, but this cannot last for more than a few seccnds unless the speeds of revolutions are all equal. That these are forced vibrations is evident from the fact that they occur with the same frequency in the record of horizontal vibrations. This~record 167 shows these vibrations very angular in character, such as we would ex- pect in forced vibrations, and the ap- proximate sine form of the corres- ponding vertical vibrations may be accounted for by the frequency agree- ing more closely with one of the nat- ural frequencies of vertical vibration than with one of the horizontal fre- quencies. By varying the speed of the screws these natural frequencies could all be obtained. In one of the Mauretania's pallo- graph records which the writer has examined, there is a very pronounced intermittent vibration in both the vertical and horizontal planes, of fre- quency 9.7 per second, or 582 per min- ute. The seréws were running at 193, 194, 193.2 and 194.5 revolutions per minute, and the frequencies of blade impulses were 579, 582, 579.6 and 583.5,.80. that: these wibratione are undoubtedly forced vibrations due to the propeller impulses. The same record shows intermit- tently a low frequency horizontal vi- bration of 6 periods in 4.25 seconds, or 84 per minute, lasting for 10 or 15 seconds at a time. From its sine form we conclude that it is a natural period of horizontal vibration of the ship. If, as in the Lusitania, we try the beats, we see that the highest frequency of beats in the fundamental is only 4.5 per minute, hence we should have to go to the 18th har- monic to get a frequency of 84. We must therefore look elsewhere for the exciting cause. It will be noticed that the seventh harmonic of the vi- bration would have a frequency of 588 per minute, which is very near the frequency of the propeller blade impulse, and so we have here a case of a periodic impulse exciting vibra- tions of one-seventh tne frequency. We have thus accounted satisfactori- ly for all the vibrations of any mag- nitude which are measurable on the pallograph records of these two ships. The intermittent absence of vibration in this or any other screw steamer must not be attributed to the absence of periodic impulses, but simply to the interference of the periodic dis- turbances due to the several screws. Col. Graham D. Fitch believes that the plans for the improvement of Marquette harbor would be modified advantageously by extending the breakwater in a southeasterly direction from the end of the present break- water instead of extending it directly south- ward, This would facilitate the entrance of vessels in heavy weather and lessen the dan- ger of their being thrown on the beach. The estimated cost of the improvement is $303,000. Lieut. The steamer Rube Richards, which sunk three years ago in Sarnia Bay, has been giv- en by the Canadian government to the Bay City Wrecking Co., Bay City, Mich., for re- moving. She has been raised.