§0arir b ^ec0mnieiil) a Staatarlj (iaage FOR BOLTS, NUTS, AND SCREW-THREADS, • i , ‘ ^ FOR THE , UNITED STATES NAVY, INI A Y , 18 6 8. WASHINGTON: GOVERNMENT PRINTING OFFICE. 1868 . yWlflLD STiTIS STANDARD NUT CO. Manufacturers of UNFINISHED, SEMI-FINISHED AND FINISHED CASE-HARDENED With U. S. Standard Threads, ISTo. 4r7 Kingston Street, BOSTON, MASS. G-KO. H. ITOX, J^^ent & Treas. UNFINISHED NUTS. For Bolts, 1| in. & larger, 20 cts. pr. lb. “ “ If “ & smaller than 1|, 18 ‘ ‘ “ ‘ “ a •1 ( ( a “ If, 17 ‘ k Hi “ “ i Xr 9 ^ 16’ 18 ‘ ‘ “ “ “ X- U- ^ g, 20 1 ‘ ‘ ' “ & 1%, 25 •' , a i i “ “ i “ 30 “ i ki a SEMI-FINISHED NUTS. These Nuts are tapped and laced true on the bottom. For Bolt, 1 inch & lai-ger, 25 cts. per lb. “ “ 1 in. & larger than i, 28 “ “ “ “ “ h & tV “ “ “ “ “ I & in. 40 “ “ “ “ “ i in. 50 “ “ “ The dimensions of the unfinished and semi-finished Nuts are the same as the finished Nuts. Parties wishing Nuts to finish loill so state, arid they will he furnished of the jmoper dimensif^is. FINISHED NUTS. These Nuts are finished in a superior manner by improved gj at ent machinery, and case-hardened. The thread and oidside of every Nut are made to an accurate gauge and to the standard adopted by the U. S. Government. Tor ! Bolt. TMck- ness. Diam- eter. No. of Tk’ds. Price Each. j 3 in. 3 in. 5.00 21- 2f 4 i 4 ' 4 . 00 “ H 2J 4 n 2 ^ ~2.¥5 \ 2 2 H ' H " 'd. 50 ~ lKZ * 4 2i 5 T.ooi’ i If .80 1 u 2 f T .G 5 If If 0 _ 9 _ 1 6 G .55 li 1 ? ‘ 2 7 .45 H If Hi 7 .35 i 1 1 If 8 “30 i T~ .22 a 4 3 4 H Td^ .18 ! . J f 1 ] ‘T 6 ^ 11 “ 15 “ 9 1 T 6 A a 1 ~vr .12 i ^ i i 13 ' .To" I tV tV 2 A 14 “ “Too" ; 51 8 I ) 1 T 6 ~u~ .08 5 T 6 tV 1 9 ~\H~~ ""T 07 ‘ li., _ i 1 To“ “T(Tg" Nuts \ thicker, l.'i per cent additional. Nuts \ thinner, 15 per cent less. Check Nuts (Hat both sides) same di- mensions and price as thin Nuts. II, §, € 0 ‘ FORM OF THREAD. Flat top and bottom, J of pitch. A^ll IVvit.s of o\ix* iiiaiixiftiotiire lire forg:ecl, (not pxiiielietl,) "* from tlio Ixcst c < rv. APPROVAL OF DEPARTMENT AND BUREAU. Navy Department, Bureau of Steam Engineering, May 15, 1868. Sir : I have the honor to herewith submit to the department for its action, the report of the Board of Naval Engineers on a “standard gauge for bolts, nuts, and screw-threads for the United States navy,^’ and to recommend that its determinations be accepted as the navy standard, and that directions be issued to the various navy yards to govern their practice accordingly. I have carefully examined the report and fully agree with its con- clusions. Nor can I take leave of it without expressing my great admiration of the thoroughly scientific and practical manner in which the subject is treated. I respectfully recommend that the report be printed for distribu- tion to the navy yards and naval steamers. Very respectfully, B. F. ISHERWOOD, Chief of Bureau, Hon. Gideon Welles, Secretary of the Bavy. Navy Department, May 16, 1868. Sir : The standard for the dimensions of bolts and nuts, as deter - “^mined by the board, is, upon your recommendation, authorized for the naval service. GIDEON WELLES, Secretary of the Navy. Chief Engineer B. F. Isherwood, U. S. N., Chief of the Bureau of Steam Engineering, I' REPORT OF THE BOARD. Philadelphia, Pa., May 9, 1868. Sir : The board created by the Secretary's order of the 28th of March, and instructed to visit the establishments of the principal tool makers and machinery builders in Boston and Springfield, Massachu- setts ; Providence, Rhode Island ; New York city ; Newark, New Jersey; and Philadelphia and Pittsburg, Pennsylvania; to obtain infor- mation in regard to the present practice in the manufacture of bolts and' nuts, and to the relative merits of difiereDt systems of the same, with a view to recommending a standard gauge foP the navy, has performed the duty ask'igned it. The Board believing it desirable and important to extend the inquiry over as wide a range as practi- cable, also addressed a circular letter explaining the object of the investigation and asking for information, to the proprietors of all establishments known to its members, in localities not named in the order. To this letter replies were received, containing information and suggestions of material importance, which are embodied in the fol- lowing report. In any system of bolts and nuts, the prominent features, in the order of their relative importance, are as follows: I. Pitch of the screw-thread, or number of threads per inch. II. Form and dimensions of the screw-thread. III. Dimensions of the nuts. IV. Dimensions of the bolt-heads. I. — Pitch of the screw-thread. The first requirement of a screw-thread is that its inclination shall be such that the component of the pressure upon the thread surface, acting parallel to the inclined surface of the thread, shall be less than the friction between the thread surfaces, and between the bottom of the nut and the surface upon which it rests, so that the nut' may not run off under the influence of the strain upon the bolt. If this con- dition, simply, were satisfied, the depth of the thread, which in any 6 system must be a direct function of the pitch, would become so excessive as to unnecessarily weaken the bolt, by reducing its effect- ive resisting section. Moreover, the ratio of the force applied to the wrench, to the resulting tensional strain upon the bolt, would be so far increased that the bolt would twist off long before a proper tensile strain could be brought upon it. Practically, the condition to be satisfied is that the pitch of the thread shall be such that the tendencies of the bolt to yield to tensional and torsional strains are about equal. It is clear, how- ever, that if this condition were satisfied in the case of new bolts, having smooth and well lubricated thread surfaces, there would still be an undue tendency of the bolt to yield to torsional strain in con- sequence of increased friction resulting from rust, dirt, abrasion of surfaces and increased viscidity of the lubricant. A considerable margin should therefore be allowed, if practicable, to cover this contingency. Fortunately, however, the necessity for a determination of the proportions which satisfy the requisite condition, based upon a priori considerations, does not exist; for experience, which is generally the best guide in such matters, has already fixed the limits between which the system to be recommended must be found. We find but two systems in general use — one known as Whit- worth’s, deduced many years ago from the general practice of Eng- lish mechanics, and the other known as that of Mr. William Sellers, deduced more recently from the practice of American mechanics. Beside these, a system has been proposed by Kobert Briggs, Esq., Superintendent of the Pascal Iron Works of this city, where the system has been adopted. Mr. Briggs’s system does not dijBfer essentially in respect to pitch, so far as it is proposed to extend it, from the systems of Whitworth or Sellers. Its peculiar feature will be noticed further on. The following table (I) exhibits the practice of our mechanics, so far as we have been able to visit or communicate with them, and it may be presumed that the average practice of the entire country is fairly represented by it. It will be observed that of the establishments whose practice is embraced in the table, more than half have adopted either Whit- worth’s or Sellers’s pitches, while the others use pitches which, though generally not differing materially from either, do not conform to or seem to be based upon any system whatever. In order to exhibit more clearly the peculiarities of the different i % 'Uto r/.) 130 i‘l5 ■mo OIJ 030 ():>.} ()0(t -S -S > 1 7 systems, and of the more marked deviations from them, the diagrams of Plate I have been prepared. The abscissas of the curves represent the circumferences of the different sized bolts, whose diameters are figured at their termini, while the ordinates represent the corresponding pitches. The cir- cumferences are draw^i full size, while the ordinates are magnified twenty times. Table I . — Representing the number of screw-threads per mch on holts of differerit sizes in the systems of Whitworth^ Sellers, and Briggs; together with the numbers used in the practice of various screw-bolt manufacturers and machinery builders in the United States. 8 (•raa;g^s s.sSSug 'a) ‘sasija iJaqoa OQocoiOT}a)t^t^cocoio •SSBJ\[ ‘ja^seojo M '•00 ouiSag; ra'Be^g Avaj^ oo500QOt^t'-«oInio •Biqd^apBnqd; ‘sttog ^ qoiuaH Cqifflr}QOt^t^O«OOin •pjBi /Cab^i BiqdiapBnqa OODCO^CO^r-iOOiOOI^t-COtOlOlO •pjBi if ABij uo;soa 20 18 16 14 13 12 11 10 9 8 7 1 ® 6 5i 5 •no^sog ‘^uBAa:>jn;g -g •ifnBdcaoo 'J? qtJOMTB A\ 20 18 16 14 13 12 11 10 9 8 7 7 7 6 6 5 •uoisoa ‘iCtredmoo P'BojpBg uja^sBa •8SBJ\[ ‘oSaAiBO ‘8qJ0j\i uoap saray 20 18 16 i 14 13 12 11 10 9 8 7 7 6 6 5i 5 •ssBpi ‘ja:jsapjoA\. ‘pnog 'h ‘T 20 18 16 14 13 12 11 10 9 8 7 7 e 5i 5 •A -N ‘ifnBq^V ‘nosqoBp ^ puasnAvo j, I a ‘aonapiAOjg ‘djuqg uMOjg •unoo ‘naABH ^9N; ‘meg 'V ^ ’’3. OOOCO-^COC^-^OCiCXDt-t^COCoIom C-irHr-frHi-Hr-JrHi— 1 T K ‘q-iBAvaNj ‘’oo auiqoBi\[ Pino£) OOOCOTt*COC^r-*OOOOt^t^CO?OlOV^^ "BTqdiapB ■Iiqa ‘sqJOAV joiiog nosujBH OGOCO'^CO(^rHOOiaDl>i>COOOr>*l^COCDlOO Ci r-l rH r-< t-H . r-( .-1 q)jBA if ABjq Uifjqoojg •q:jjOAi;iqAi qdasof ooo?OTf a> oj 05 05 , : : rHr;oio»c^ Cl -j:; M jQOOOt'-l'CO<0«OCO«5«5kdlO MONGREL SYSTEMS. •pjojpBH ‘-^nsd •raoo suuB-aai j; s.^noQ 22&20 20&18 18&16 16& 14 14&13 12 12&11 12& 10 10 10 10 9 8 8 •SSBJV ‘najjBM ‘.^aiqis ^ saiMoua; 18 18 16 16‘ 16 14 14 12 10 10 9 8 8 8 8 8 7 7 •BtqdppBpq,! ‘gqjoM 8Ai|oraoooT; uiAvpiBg 00 22 18 14 10 10 10 10 10&8 8 8 8 8 8 8 •ajotni; •{Ba ‘XuBdxnoo ^ isanqaizBH 20 20 14i 14i 14i 14.5 12.2 10.5 10.5 8. 66 8. 66 8 7. 57 7.57 7.57 6.66 6.66 5 •ssBi\[ ‘ja^j -saojOjVi ‘naoH njnqqgBM 20 16 14 14 12 12 12 10 10 9 9 7 7 7 6 6 •no^soa ‘sir JO M ^nioa AlO 15 13 11 10 9 8 8 8 8 7 7 5 5 5 •uo:rsoa ‘iCnBdnioo soiJV poB s:}n2q; nBOiiaray 14 13 13 12 11 10 9 8 8 7 •nuoo ‘pjoj? JBH ‘qoBag ^ j^tupoo^i 20 18 16 14 12 12 11 10 10 8 8 7 '7 6 6 5 5 5 •BJaq^oaa qonqjB:rg 11 11 10 9 8 7 7 6 6 6 5 5 5 •no!} -soa ^rsBg ‘snpiv ^ .^Cb^obh 00 16 14 12 12 11 8 8 7 7 6 6 6 6 •sqjoA\. ROJi Ui^iqooja ^!^nog 16 12 11 10 9 8 8 8 8 8 8 6 & 8 8 6&8 •iCuBdraoo oniqoBH raa^Bg 24 20 16 14 14 12 12 10 10 8 8 7 7 7 6 6 6 5 •qjOA Avail ‘sqjOAi ROJi uoana o 16 13 12 11 10 9 8 8 7 6 6 6 5 5 5 •qjoA Avajq ‘sqjoAV Roji JaA;a q^JOKE 00 16 13 10 10 9 8 6 6 5 •pa ‘ao| -SntnipA\.‘'O0 ^ sanop ‘jfasna 20 20 16 16 12 12 11 10 9 8 7 7 6 6 5 5 5 4 •XuBdnioo eaTqoBj\[ paAvoa 20 16 16 12 12 10 10 10 10 10 9 7 7 7 7 7 6 6 •ajouii^IBa ‘^RRH ^ lOon 20 18 16 14 12 12 11 10 9 8 7 7 7 7 6 6 6 6 •pa ‘oo;3nini •TTAi'q^-iOAvsanTqoH ^ RJapBH 20 18 16 14 12 12 11 10 9 8 8 8 6 6 6 6 6 6 •qjOA Avail ‘S^IJO^ UOJI if^rpAOil oao«dcoci(yir-4005c»«o;ococo>rtidxdid •OQ ani3na raBa^g aouapiAoja 20 20 16 16 14 14 12 10 10 10 8 8 8 8 6 6 6 6 .So 'O A i4»nM’»+orH .d .d .4 .d .d ^d a d ^d ,g 2 iucheB 11 12 The full red line represents Whitworth’s S 3 ^stem of pitches, so modified as to avoid as far as practicable the use of fractional threads. The law of the system would be represented by a fair curve, cutting this broken line in such a manner that the areas included between the two, above and below the former, should be as nearly equal as possible. The straight blue line represents the law of Mr. iBriggs’s system of pitches, the peculiarity of which consists in the fact that the pitches vary nearly with the diameters of the bolts. This gives excessively deep threads for the larger bolts, and thus seriously diminishes their effective resisting sectional areas. It is proper to remark however, in this connection, that Mr. Briggs does not propose to extend his system beyond bolts of two inches diameter, up to which point the pitches and corresponding depths of thread do not materially differ from other systems or the general practice of the countr}". The curve in black represents the law of Mr. Sellers’s system, the object of which seems to have been to effect a sort of compromise between the various practices of American mechanics, with the view of uniting them upon a uniform system, which would answer all the requirements of practice and at the same time relieve them from the serious inconvenience inseparable from the emploj^ment of different systems by different manufacturers of machinery. Mr. Sellers has constructed the following empirical formula, ^which determines his curves, and serves, independently of tables or other aids, to determine the pitch of the thread of any required bolt: in which d z=z the number of sixteenths in the diameter of the bolt, ~|- 10 ; a 2.909 ] c = 16.64, and p = pitch of the thread. A simpler and more convenient form of this equation, and one wliich is readily deduced from it is: 27 =: 0. 24 V D + 0. 625 — 0. 175 ; in which D represents the diameter of the bolt in inches. To illustrate the use of this formula, we take for example, a two-inch bolt, and let it be required to determine the pitch of the thread, and the number of threads per inch. Making^ the proper substitution, the formula becomes — 29= 0.24V 2 + 0.625 — 0.175 = 0. 24 VX^— 0.175 ' = 0.24x1.62 — 0.175 = 0.2138 of an inch, , . ■ ■ ■ • ■ 13 The reciprocal of this, or 0: 21 3 s = 4.68, gives the proper number of threads per inch. For the purpose of avoiding the use of troublesome fractions, the nearest convenient aliquot or 4| is taken. This will be found to correspond with the number of threads given in the table. In this slight deviation from the exact number given by the for- mula we have the explanation of the broken and irregular character' of the black dotted line, which represents the system of Mr. Sellers, as modified to mee^ the practical requirement of avoiding the neces- sity for complicated screw-cutting gear, by preventing, as far as prac- 'ticable, the use of fractional threads. The blue dotted line representing the practice of the Baldwin Locomotive Works of this city, although showing that a much finer pitch is used for nearly all bolts than is given by either Whitworth’s or Sellers’s systems, shows nevertheless, that the practice of this establishment is entirely without system. It is claimed that for locomotive and other special purposes, finer pitches are required in order to prevent the nuts from jarring loose and working off. When it is remembered, however, that the influence of pitch upon the’ tendency of the nut to turn upon the bolt is very slight, in com- parison with the effect of friction between the thread surfaces and upon the base of the nut, it would seem that the necessity for exces- sively fine pitches is more imaginary than real. Indeed an examina- tion of the practice of these works shows that the |-inch bolt, which from its size is we presume used as extensively upon locomotives as any other, has the same pitch as is recommended for the same sized bolt by both Whitworth and Sellers. We feel authorized, therefore, in assuming that either Whitworth’s or Sellers’s systems of pitches would answer the purpose of the loco- motive builders quite as well as the slightly finer pitches now used ; especially is this the case when the advantages to be derived from uniformity of practice are considered. The deviation of the practice of Messrs. Pusey, Jones & Co., from the average practice and in the direction of coarse pitches is equally marked, and shows equally a want of system. The entire practice of the engineers of our country would probably be found between these two extreme limits, and the average, if we could obtain it, we feel assured would not materially differ from the systems of Whit- worth or Sellers. In fixing upon a standard system regard should be had to the practice of the greater number of engineers, unless there be some- 14 thing radically wrong in that practice. As the only serious defect we are able to discover is want of system, and as the average practice may be represented by either Whitworth^ s or Sellers’s systems, we have only to select one of these as a standard. Considering these two systems we find no material difference exist- ing between them. In their general characteristics they differ in that, up to bolts of two inches diameter, the pitches of the Whitworth system are coarser and the bolts weaker than in the Sellers system. Above two inches the reverse occurs ; the pitches of the Whitworth system becoming slightly finer and the bolts slightly stronger than in that proposed by Mr. Sellers. The most marked difference, however, exists in the case of the J-inch bolt, which, in the Whitworth system, has 12, and in the Sellers system 13 threads per inch. The strength of this bolt is therefore much greater, and its liability to twist off very much diminished in the Sellers system. Again, Mr. Sellers’s system is one which, by the use of the formula, or equation of the curve representing its law, admits of indefinite extension. Moreover, by far the greater number of establishments which we have visited or with which we have communicated have either already adopted, intend, or are willing to adopt it. The board therefore recommends the adoption of Mr. Sellers’s system of pitches as the standard for the navy. II. — Form op thread. For the general purposes of bolts and nuts, there are four difterent forms of thread now in use. These are the ordinary sharp Y, the Whitworth, the Briggs, and the Sellers forms. The sharp Y thread. Fig. 1, Plate II, has its surfaces inclined to each other at an angle of 60°. A section of this thread is therefore an equilateral triangle, each side of which is equal to the pitch of the screw, and the depth of the thread, measured perpendicularly to the axis of the bolt, will be expressed by the formula. d z=zpcos 30° = . 866 p, in which p z= represents the pitch, d the depth of the thread, and 30° half the angle included between the thread surfaces. The effective diameter of the bolt is expressed by the formula c? = D — 2 X .866^. = D — 1.732 p. in which D and d represent the nominal and effective diameters respectively. Fi;) I. 'f Thmu! ) Pill.- II I'uf. ? iSrIlcrs TUiriid ! 15 The Whitworth thread, Fig. 3, has its plane sides inclined to each other at an angle of 55°, with the angle formed by these surfaces, at both the periphery and root of the thread, so rounded that the depth of the finished thread is two-thirds the depth of a Y thread, having its surfaces inclined at an angle of 55°. This form is represented more in detail in Fig. 4, where the depth of a Y thread is divided by lines parallel to the axis of the bolt into six equal parts, and the curved form secured by inscribing arcs of circles within the straight sides of the thread and the extreme dividing lines. In this form of thread the depth is determined by the formula d ■“ % V P 2. tan 27° 30' = .65 p, and the diameter of the effective section of the bolt by cZ = D — 2 X .65 = D — 1.3 The form of thread proposed by Mr. Briggs resembles that of the Whitworth thread, but differs from it, in that the thread surfaces are inclined at an angle of 60°, and in that the angles of the thread are rounded just enough to reduce the depth of the thread to 0.8 “for best workshop bolts, or to 0.75 jp “for. good merchantable bolts With this form, therefore, the effective diameters of the two classes of bolts would be cZznD — 2 X .8^. =:D — 1.6^, and cZ = D — 2 X .75 p. z= D — 1.5 p, respectively. Mr. Sellers proposes the form of thread represented in Fig. 2. It is simply the ordinary Y thread with surfaces inclined at an angle of 60°, and with the angles cut off at the top and filled in at the bottom to the extent of one-eighth of the depth of the Y thread each, so that the depth of the thread is three-fourths that of the ordinary Y form, and is expressed by the formula ^ = I ^ cos 30°. == .65 p. The effective diameter will then be cZ = D — 2 X .65 jp. z= D — 1.30 jp. 16 Collecting our results for the effective diameters of bolts having threads of the different forms, we have form, c? = D — 1.732 p. Whitworth “ c? = D — 1.3^. Brig-ffs “ 1.6 jp. Briggs ]c^ = D — 1.5p. Sellers “ dzzzJ) — 1.3 p. With equal pitches it appears, therefore, that the maximum effect- ive diameter of bolt is insured when threads of the Whitworth or Sellers forms are used, while the usual Y form insures the minimum effective diameter. The ability of a bolt to resist tensile strain varies as the square, while its ability to resist torsional strains varies as the cube of its effective diameter. In order to show more clearly the relative merits of the different forms of thread under consideration, we have constructed the follow- ing table (II). Table II . — Showing the tensional and torsional strengths of holts having the Sellers thread f as compared with holts having the common sharp V thread. Nominal diameter of bolt. d\ d,\ d,^ d?' i inch .02666 . 03422 . 004355 . 006331 1. 283 1. 454 5-16 inch . 04879 . 05760 . 010120 .01382 1. 231 1. 366 f inch . 07113 . 08644 . 018970 . 02541 1.215 1. 339 7-16 inch . 09847 .11902 . 030899 . 041064 1.209 1. 329 i inch . 13452 . 16000 . 04935 . 06400 1. 189 1.297 9-16 inch .* . 17488 . 20612 . 073139 . 09358 1.178 1. 280 i inch . 21855 . 25703 . 10217 . 13032 1. 176 1. 275 J inch . 33260 . 38440 . 19191 . 23833 1. 155 1.242 1 inch . 46649 . 53435 . 31861 . 39063 1.146 1. 223 1 inch . 61387 . 70060 . 48098 . 57305 1.141 1. 219 li inch . 77087 . 88360 . 67682 . 83060 1. 146 1.227 li inch 1. 0060 1. 1342 1. 0090 1. 2080 1. 127 1. 197 If inch 1. 1794 1. 3455 1. 2807 1. 5«05 1. 141 1. 218 If inch 1. 4664 1. 6486 1. 7758 2. 1170 1. 124 1. 192 If inch 1. 7161 1. 9293 2. 2481 2. 6798 1. 124 . 1. 192 If inch 1. 9712 2. 2231 2. 7677 3. 3150 1. 128 1.198 If inch 2. 3379 2. 6114 3. 5747 4. 2201 1.117 1. 181 2 inches 2. 6082 2. 9305 4. 2122 5. 0177 1. 124 1. 191 2f inches 3. 4782 3. 8495 6. 4870 7. 5527 1. 107 1. 164 2i inches 4. 2725 4. 7350 8. 8312 10. 303 1. 108 1. 167 2f inches - 5. 3686 5. 8854 12. 438 14. 274 1.096 1.148 3 inches 6. 2750 6. 9103 15. 719 18. 171 1.101 1. 156 inches 7. 5900 8. 2885 20. 911 23. 863 1.092 1. 141 3f inches 8. 8032 9. 6100 26. 119 29, 791 1. 092 1. 143 3f inches 10. 068 11. 003 31. 946 36. 497 1.093 1. 142 4 inches , 11.716 12. 723 40. 108 45. 384 1.086 1. 131 4f inches 13. 307 14. 427 48. 546 54, 784 1. 084* 1.119 4f inches 14, 996 16. 602 57. 960 65. 353 1.083 1. 127 4f inches 16. 726 18. 113 68.417 77. 090 1.083 1. 127 5 inches 18. 550 20. 070 79. 894 89. 916 1.082 1. 125 inches 20. 766 22. 372 94. 632 105. 820 1. 077 1.118 si inches 22. 762 24. 532 108. 60 121. 510 1.078 1,119 5f inches 25. 21 0 27. 070 126. 57 140.840 1. 074 1.113 6 inches 27. 353 29. 403 143. 05 159, 470 1.075 1.115 The first column contains the nominal diameters of the bolts; d=. effective diameter of bolt having the common Y-thread; and the 17 effective diameter of bolt liaving threads of the Sellers or Whitworth forms; ^ expresses the ability to resist tensile strain of a bolt having threads of the Sellers or Whitworth forms, as compared with that of d ^ the same bolt having a thread of the ordinary V form. expresses the ability to resist torsional strain of a bolt having threads of the Whitworth or Sellers forms, as compared with that of the same bolt having a thread of the ordinary Y form. From the table it appears that in the |-inch bolt the Sellers or Whitworth form of thread insure 28 per cent, more tensile strength than the sharp Y thread; while in the extreme case of a G-inch bolt the tensile strength is still seven per cent, greater. The effect upon the ability of the bolt to resist torsional strain is still more marked ; the I -inch and 6 -inch bolts being respectively 45 and 11 per cent, stronger with the Sellers or Yfhitwortli than with the common Y thread. In the more frequent case of the inch bolt, the tensile and torsional strengths are, respectively, 14 and 22 per cent, greater with Whit- worth’s or Sellers’s threads than with the Y thread. The Briggs form possesses an advantage of the same kind, but much less in extent. An additional and very serious element of weakness in the Y form is the sharp angle at the root of the thread. The precise amount of the weakening effect due to this cause cannot, in the present state of our knowledge, be stated ; it is nevertheless known to be very con- siderable — probably not less than 20 or 25 per cent. This element of weakness is practically eliminated in all the other forms of threads. In order to show more clearly the importance of preserving the torsional strength of bolts, or of limiting the depth of the screw- thread to the smallest practicable amount, we have instituted the following comparison of tensional and torsional strains upon bolts: The torsional or twisting strain upon a bolt, due to screwing up the nut, has its application upon the thread of the screw, and results from the friction between the thread surfiices, together with that compo- nent of the load which has to be overcome in order to move it up the inclined plane formed by the screw surface. It follows, therefore, that in bolts of different sizes, this twisting force will have its point of application at distances from the axis varying directly as the radius or diameter of the bolt, and the measure of its effect will be the product of the force exerted, multiplied by the arm or the dis- tance between its point of application and the axis of the bolt. 2 18 If then we put T — the measure of the resistance of the bolt to torsion; d diameter of the bolt, we shall have r oc d\ But the force to be exerted in order to produce the effect r, or to twist the bolt asunder, varies directly as r, and inversely as its lever arm; and, as before stated, this lever arm varies directly as the diameter of the bolt. Hence, if we put F = the force applied upon the screw-thread, we -have F oc oc oc Whence follows that the force which may be safely applied to the surface of a screw-thread for the purpose of turning the bolt, or which may be transmitted to it through the medium of the nut, varies as the square of the diameter of the bolt, or in accordance with the same law that governs the tensile strains which may be placed upon bolts or other cylindrical rods. If the inclination of the screw-thread be constant for all bolts, and the coefficient of friction between the thread surfaces be uniform, the force F will always be the same function of the load or strain upon the bolt; in other words, there will always be the same relation between the tendencies to break the bolt longitudinally and to tAvist it off. In the case of the system of pitches recommended, however, the inclination of the screw-thread is not constant, it being greater upon small bolts, and gradually diminishing as the bolts become larger. The force F required to strain a large bolt up to any desired limit, neglecting friction, varies Avith the tangent of the angle of inclination of the thread; and since the effect of friction will be the same Avhat- ever be the pitch or angle of inclination, it will folloAv that the largest value of F (relatively) would be required, and the greatest tendency to tAvist off would therefore exist in the smallest bolt ; yet the abso- lute difference between the inclinations of the threads of the smallest and largest bolt is so slight, and as 'the effort required to overcome the effect of inclination of the thread is so very small, Avhen compared AAuth that required to overcome the friction, that Ave might, without appreciable or considerable error, regard it as constant. We Avill, hoAvever, take the most unfavorable case — that of the J-inch bolt, the smallest of the proposed system — Avhcre the inclination 19 of the thread is at its maximum, and consequently where the tendency to twist the bolt asunder is also at its maximum. Let W = load or strain upon the bolt. d — inclination of an element of the thread surface lying midway between its root and periphery. p z=z angle of friction. F = force applied upon the element of the thread surface whose inclination is 0. Then F 1 = W tan (d + p>) The value of p is determined by the coefficient of friction, which is equal to tan p. Taking the coefficient of friction — tan p — 0.124, we have Again p =: 70 04'; circ. Nov/ for the |-inch bolt, having 20 threads per inch, the pitch will be .05 of an inch, and the diameter of the circle lying midway between the root and periphery of the thread will be X 3.1416 .2175X3.1416 0.6833 tan u — ,05 r=.0732 and Hence 0.6833 dz=z4:^ 11 '. d + p = 4:^ IV + 7° 04'. = 11° 15'. F — W tan (d + p.) =z W tan IP 15'. rz:0.2W. The ultimate tensile strength of a J-inch wrought-iron bolt, with 20 threads per inch of the Sellers form, and consequently having an effective diameter of 0.185 of an inch, will be about W — .7854x0.H85x60000 = 1612. 8 pounds : whence F =: 0.2x1612.8 = 322.56 pounds. It appears, therefore, that a force of 322.56 pounds must bo exerted upon the thread, in a direction tangent to the circumference of the bolt, and perpendicular to its axis, in order to break the bolt longi- tudinally. Let us next see how great a force F' must be applied at the same 20 point, and in the same direction, in order to twist the bolt off. For this purpose 500 pounds may be taken as the force which is required to twist off an iron rod one inch in diameter; the force being applied at a distance of 12 inches from the axis of the rod. Then, since the force to be applied varies directly as the cube of the diameters of the rod, and inversely as the lever arm with which it acts, we have 500x0.^85x24 F'; .2175 348 pounds, nearly. It appears, therefore, that under the conditions assumed, the bolt having the form of thread which insures greatest strength, and the surfaces of the threads being clean and well lubricated, the tenden- cies to yield to the tensile and torsional strains are about equal. Practically, however, the threads of screws are often in a more unfavorable condition than that assumed, owing to accumulation of dirt, abrasion of the surfaces and increased viscidity of the lubricant, all of which increase the friction, and consequently the tendency of the bolt to yield to torsional strain. In view of these considerations the necessity of selecting that form of thread which insures the maximum strength of bolt, seems to be imperative. As a matter of peculiar interest in this connection, let us next ascertain how much the friction between the thread surfaces may be increased by the causes just mentioned, before the bolt will yield to the torsional strain required to strain it up to one-third its ultimate tensile strength — a limit which should of course never be exceeded in practice. To satisfy this condition we have 348 = Jx 1612.8 tan((9 + ^); whence tan + = 0.647, and But {d + p)=i 32° 54'. <9 = 4 ° 11 ' /. P =: 32° 54'— 4° IP = 28° 43', and tan./>=.548 — increased coefficient of friction. Comparing this result with the coefficient of friction between clean and well-lubricated surfaces, we find that the friction may be in- creased = times, nearly, before the bolt will be twisted off, 1 ' 21 while straining it up to its safe limit of tensile strength, by screwing up the nut. The Whitworth and Sellers forms of thread satisfying the require- ment of strength equally well, it remains to examine them in reference to their relative abilities to satisfy other conditions, such as suitable bearing surface and ease of perfect execution. The bearing surface of the Whitworth thread is practically limited to the straight portion of the surface; while in the Sellers thread, the entire surface between the flat at the top and bottom may be regarded as effective bearing surface. In this particular, therefore, the preference must be awarded to the Sellers thread. In regard to the execution of the Whitworth form of thread, we remark that its angle is such as not to admit of ready verification, and its curved top and bottom require such a multiplicity of special tools, and such skill on the part of the workman, that the requisite degree of uniformity of practice, auiorg different manufacturers, is believed to be entirely impracticable, if not impossible. xkraong all the establishments visited or communicated with by us, onl}^ one has been found where this form of thread is used. We refer to the printing press manufactory of Messrs. R. Hoe & Co., of New York city, where the thread has been in use for about thirty years. The fact that this thread, in itself undoubtedly the best form ever proposed, has been so long before the public, and has met with so little favor from our engineers, is of itself the strongest and the most conclusive argument that can be urged against its practicability. The angle of the Sellers thread being 60 ^, admits of easy construc- tion and ready verification. The cutting tool used in the production of this thread is precisely like that employed in cutting the common y thread, except that its point is flattened by a certain definite amount, which is determined by accurate steel gauges, now being manufactured by Messrs. Brown & Sharpe, of Providence, R. I. It has been urged by some that the Sellers thread will degenerate into the Whitworth form. That the Sellers thread degenerates there can be no doubt, but the same objection applies with equal or greater force to the other forms. The board is, however, unable to discover that such degeneration would be attended by any more serious incon- venience than would result from the deterioration of the other forms. It is of the opinion that the amount and effect of wear upon the thread and upon the taps and dies with which it is cut, would be less serious in the case of the Sellers than in the case of either of the other forms proposed. An exception may possibly exist in the case of the Whitworth form, which cannot however be recommended, on account 22 of the difficulties with which its accurate production, in the first instance, is attended. All the advantages of the Whitworth over the ordinary V thread, as regards strength and liability of the edge of the thread to injury, with the additional and very important advantage of ease of produc- tion, being possessed by the Sellers thread, and in view of the marked favor accorded it by engineers generally, the board unhesitatingly recommends it as a standard for the navy. III. — Dimensions of the nut. Nuts may yield either by the stripping of the threads or by burst- ing. In order that the thread may not strip, the depth of the nut must be such as to offer a resistance to shearing strain, at the root of the thread, equal to the resistance of the effective section of the bolt to tensile strain. The resistance to shearing strains in iron being only 0.8 the resist- ance to tensile strain, it follows that the cylindrical surface, formed by the junction of the root of the thread with the body of the bolt, should be to the effective transverse section of the bolt in the ratio of 1 to 0.8. Again, owing to the flattening of the thread at top and bottom, only of the pitch is effective to resist shearing strain. Hence, putting H zz: the requisite depth of nut to meet the require- ment under consideration, we have the following relation: .25 TT 0.8X0. 875 ;r d H. whence .25 c?zz: 0.7000 H; and H=^cl = 0.357(1 Hence for new and perfect fitting threads, 0.357 of the effective diameter of the bolt would meet the requirement of strength to resist stripping of the thread. But when, in consequence of wear, the fitting of the thread surfaces ceases to be perfect, the strain upon the thread is no longer a shearing strain, and the thread acts in the capacity of a beam fixed at one end and loaded at a little distance out. In that case a greater depth of nut is required. Probably a depth of nut equal to half the nominal diameter of the bolt would, in all cases, be ample to meet the requirement of strength alone. Again, the depth of the nut should be such as to afford a good hold for the wrench, and, what is still more important, should be such as to afford an extent of bearing surface upon the thread which will effectually prevent undue abrasion of its surface. It is difficult to decide upon the pressure per square inch to which . 23 the surface of a screw thread may be safely subjected. However, as nuts having depths equal to the nominal diameters of their bolts are found to work well in practice, a determination of the pressure habitually borne by their thread surfaces may throw some light upon this point. The following table (III) shows the effective areas of bolts of the different sizes, the projected areas of their thread surfaces, within a distance equal to their nominal diameters, and the ratio of the two : Table III . — Showing the ratio of the pressure per square inch upon thread surface^ to the tensile strain per square inch upon the effective section of the holt, ( Sellers thread.) Nominal diameter of bolt. — D. W a II 1* w Projected bear- ing aurface of thread— s ~s‘ Nominal diameter of bolt.— D. i =«• sji (15 — Projected bear- ing surface of thread — S. s 's' -j- inf'll . - . . 02688 . 11105 .242 2 inches 2. 3019 7. 5573 .3046 5-16 inch . 04524 . 17696 .2556 2i inches 3. 02.32 9. 6471 . 3134 J inch . 06789 . 25536 .266 2^ inches 3. 7188 11. 8990 .3125 7-1 6 inch . 09347 . 34826 .2684 2% inches 4. 6224 14. 4881 .3190 •.1 inch . 12566 . 45949 .273 3 inches 5. 4283 17. 2221 .3150 9-16 inch .16189 .58461 .2769 3i inches 6. 5009 20. 4158 . 3188 ^ inch . 20174 . 72222 .2795 3^ inches 7. 5477 23. 5849 . 3200 j- inch . 30190 1. 0470 .288 3J inches 8. 6416 27. 0337 . 3196 i inch . 41969 1.4303 .293 4 inches 9. 9929 30. 8820 .3235 1 inch . 55024 1.8813 .3112 4^- inches 11. 328 34, 9236 .3244 l-g- inch . 69399 2. 2877 . 3033 4i inches 12. 743 40. 3586 .3157 ir inch . 89082 2. 94245 .3027 4J inches 14. 250 43. 2728 .3288 inch 1. 0568 3. 5310 .2993 5 inches 15. 763 48. 4000 . 3260 inch 1. 2948 4. 2507 .3051 5i inches 17. 572 53. 4950 .3290 li inch ]. 5152 4. 9925 . 3035 5i- inches 19. 267 58. 6676 .3280 inch 1. 7460 5. 7750 .3023 5^ inches 21. 262 62. 7850 .3286 1 j inch 2. 0510 6. 6572 .3081 6 inches 23. 098 69. 8540 .3310 The projected area of thread surface is found as follows: Let D nominal diameter of the bolt the depth of the nut. d — effective diameter of the bolt. n = number of threads per inch. Then the projected surface S = 5 TT (D^ — d") X D 71. It will be observed that as the bolts increase in size, the pressure per square inch upon their thread surface increases — varying between 0.'24 of the tensile strain for the |-inch, and 0.33 for the 6-inch bolt. These pressures seem excessive; but we find upon examination that the under surfaces of nuts are uniformly subjected to pressures quite equal to these. For example, let us take the case of a 2-inch bolt and its nut. Taking the largest proportions used, the short diameter of such a nut would be four inches; while its effective bearing surface — the area of the circle inscribed within its base, less the section of the bolt — would be 12.5GG — 3.142 = 9.424 square inches. 24 The effective section of the bolt (with V thread) would be 2.053 square inches. Hence the ratio 2.053 9.424 — .207 shows that with the largest proper tions of nut, Avitli the deepest thread, and with the weakest bolt, the pressure, per square inch, on the base of the nut is 0.207 of the ten- sile strain per square inch upon the bolt. Again, taking the same bolt, and the smaller but more usual pro- portion of nut, where the long diameter is made twice the nominal diameter of the bolt, the ratio of the two areas is 0.276. It appearing, therefore, that the rubbing surfaces of nuts are habitually subjected to pressures nearly equal to and in some instances greater than those which would result from the proposed form of thread, with depth of nut equal to nominal diameter of bolt, we are •of the opinion that for permanent bolts, where the nut is rarely dis- turbed, the depth of the nut should be at least equal to the nominal diameter of the bolt. For special cases, where the nut is constantly being turned, its depth should invariably be made greater, in order to prevent a too rapid destruction of the thread surface. The next, and only remaining point to be considered, in' connection with the nut, is its tendency to burst. In Fig. 5, let T = load on bolt. p = normal pressure upon one half the thread, resolved in a direc- tion perpendicular to any single element of its lielicoidal surface. B = component of P acting in a direction perpendicularAo the axis of the bolt.

=|D + tV /i = D. ■ The following table (IV) gives the results obtained by the use of tliese formulae for all the sizes of bolts. The only instance where the values in the table differ from those given by the formulae is in the numbers of threads per inch, which are so far modified as to use the nearest convenient aliquot part of a unit, so as to avoid, as far as practicable, troublesome combinations in the gear of screw-cutting machines. D = n — H = Then 27 Table IV. — Proposed standard dimensions of holts and nuts for the United States navy. BOLT. NUT. HEAD. Diameter. j Threads per inch. Short diameter. Depth— H. Short diam- eter — dn. Depth— Xominal— D i Effective— 1 ^By formu- la — ?i. Standard number. Hexagon — dn. Square — dn. J. .185 20. 24 20 i i i i 5-16 .240 17. 45 18 19-32 19-32 .ii6 19-32 19-64 8. 8 .294 15. 38 16 11-16 11-16 &. 11-16 11-32 7-16 ..345 13. 80 14 25-32 25-32 7-16 25-32 25-64 J. .400 12. 60 13 i- 1 i 7-16 y-16 . 454 11.55 12 31-32 31-32 9-16 31-32 31-64 .507 10. 72 11 1 1-16 1 1-16 f 1 1-16 17-32 i .620 9. 39 10 If 11 f 11 i 1 ,731 8. 40 9 1 7 16 1 7-16 1 1 7-16 23-32 1 .837 7. 63 8 11 If 1 11 13-16 U .940 7. 02 7 1 13-16 1 13-16 n T 13-16 39-32 H 1.065 6. 50 7 o o 11 o 1 1! 1.160 6. 08 6 2 3-16 2 .3-16 If 2 3-16 1 3-32 LV 1.284 5. 72 6 2-1 21 H 2f 1 3-16 l| 1. .389 5 41 5^ 2 9-16 2 9-16 11- 2 9-16 1 9-32 If 1.491 5. 13 5 2f 2f H 21 M U 1. 616 4. 90 5 2 15-16 2 15-16 H 2 15-16 1 15-32 o 1.712 4, 67 44- 3i 31 2 31 1 9-16 h 1. 962 4.31 31 31 21 31 H 2. 176 4. 01 4 3| 3| 21 31 1 15-16 2. 426 3. 77 4 41 41 2f 41 21 3 2. 629 3.56 3i 41 4f 3 4f 2 5-16 3f 2. 879 3.36 31 5 5 31 5 21 31 3. 100 3. 20 3} 5| 51 31 of 2 11-16 3| 3.317 3. 06 3 5f 5f 3f 5f 21 4 3. 567 2.93 3 6i 6i 4 61 3 1-16 4i 3. 798 2. 82 21 61 61 41 61 31 4i 4.028 2. 72 2f 6i 6| 41 6| 3 7-16 4f 4. 2.56 2. 62 2-1 7-1 71 4f 71 3f 5 4. 480 2. 54 21 7i 7i 5 7f 3 13-16 5f 4.730 2. 46 21 8 8 51 8 4 51 4. 953 2. 39 21 81 51 8f 4 3-16 5| 5. 203 2. 33 2f 8i 5| 8f 4f 6 5. 423 2. 26 2.1: 91 91 6 91 4 9-16 COXCLUSIOX. Ill conchidiiig this report the board desires to say, that in recom- mending the system of Mr. Sellers as a standard for the navy, it has been governed by considerations other than those suggested by tlie merits inherent in the system itself. Fully realizing the importance of entire uniformity of practice in private establishments, as well as in the navy, we were naturally desirous to select a system which, while meeting all the essential re" quirements of a system, would be most likely to be generally acquiesced in and adopted. So far as we have been able to confer with engineers and manufac- turers, either personally or by letter, we have heard but one opinion expressed in regard to the importance of uniformity of practice. Many liave already adopted the Sellers pitcli; others are graduall}- adopting it, while others still express their willingness to adopt it 28 A majority, we confidently believe, are now willing to adopt Sellers’s form of thread also, provided it be made the standard. As a proper auxiliary we suggest the importance of having all necessary guages manufactured by a single establishment, as by that means only can entire uniformity bt secured. Finally, the board would respectfully but earnestly urge upon the Bureau the importance of a carefully conducted series of experinaents upon bolts and nuts, with a view of determining the precise effect of friction between their rubbing surfaces under varying loads and under the varying conditions of actual practice. We have the honor to be, very respectfully, your obedient servants, THEO. ZELLER, Chief Engineer U. S. Navy. ALEXANDER HENDERSON, Chief Engineer U. S. Navy. D. M. GREENE, First AssH Engineer V, S. Navy. Chief Engineer B. F. Isherwood, U. S. N., Chief of Bureau of Steam Engineering. O 9