Fbbiwaby 19, 1880.] 



FOREST AND STREAM. 



57 



MEASUREMENT. 



TN ortl»r ;tki*t a queation.'Jsimplo anough la Itself , may bo ex- 

 -*■ plalnad to tha best advantage, it will be advisable to first ob- 

 tain a clear understandinir of tuo purposes to be kept in view. The 

 object, and the only object, of measurement and time auowati ce 

 among yachts is to eltuiinale differences of sixe, so that the real 

 comparative value of various models may be established by the 

 test of racing. 



Itis quite manifest that if one vessel outsails another smaller 

 than herself, the result is not a true indication of the relative 

 merits of the two, until a correction has been applied to the 

 larg-er one.and whereby the effect of her excess in size will be elim- 

 inated—wiped out, as it were. The result as it would then stand 

 represents a just comparison of the value of the models for 

 speed. We established from this the first axiom :— 



I. Measurement and time allowance are applied for the purpose 

 of eliminating differences in size, and for that purpose only, so that 

 variety in size may not he a hindrance to the practical comparison 

 »f variety in stuxpe. 



The object settled clearly in our minds, the next step will be 

 naturally directed to the means by which the ends of measure- 

 ment and time allowance are to be attained. 



That the reasoning adopted shall be logical and free from all 

 secondary disturbances whereby side issues would be created, we 

 will devote attention to the simplest and plainest case Imagin- 



able. A. and B. -li 

 elding whether A.'s Finlu. 

 tons, possesses the lines 

 ment of speed. The sec 

 sailorizing, foul bottom c 

 both yachts, so that tl 

 shadowed byirrelevani i 

 leads bylOm. at the finisl 

 the 10m. represents a ci >n 

 speed of VHnbacli over sfti 

 vantages of the momeuti 

 with this advantag 



tch their yachts for the purpose of de- 



c, of 100 tons, or B.'s Shellback, of 120 



• shape most, favorable to the develop- 



ndury considerations of wind, tide, 



i the like, we presume to be equal in 



question at issue will not be ovor- 



irs. The race H sailed, and Finback 



inc. It will notbe. pretended that 



range of the superiority in point of 



■li, for the latter has had the ad- 



ue to her excess of twenty tons. If, 



or, the rival Finhaeli has, neverthc- 



inh 



less, beaten her by 10m., the question becomes, by howmuoh 

 more would she have been boateu with the momentum ot twenty 

 tons ("power," among yachtsmen) obliterated? The answer to 

 this Is to be looked for in the tabulated allowances whioh experi- 

 ence has shown to bo the amount duo as a correction for the 

 excess of 120 tons over 100 tons. When this " allowance" has been 

 added to the actual period (10m.) by which the larger boat has 

 been outsailed, then we will have a correct expression in time of 



a tno value of the two vessels' models for speed. 

 t well be plainer than this, and since sound 

 allow for differences in size, our second 

 iter of course :— 



hasit upon which time is to be allowed, and 

 ly eorreet system of measurement must be 



the differor 

 Certainly n 

 logto oomi 



axiom folk 



II. Si:r U 



tha-cf"iT a 

 based upon size. 



If a little digression be permitted, we will here explain a phe- 

 nomenon, common enough in practice but explicable upon a ra- 

 tional basis to comparatively few, and also thereby meet an ob- 

 jection which we know will occur to almost everyone when try- 

 ing to accept, for once and all, the two axioms above mentioned. 

 We allude to the well-known fact that size per se is an advantage 

 altogether apart from model, and that size should be paid for to 

 the full extent, even though the excess may be used for filling up 

 a vessel's model, and deteriorating from her speed. To obtain an 

 accurate and correct estimate of her altered model in competi- 

 tion with another, it is'neoessary to make her account in full for 

 the increase of size, in spite of such increase havingered interf 



with speed, for an 

 crease of " power," no matte 

 tha other and time allowanc 

 for the very purpose of neul 

 and not in the resultioftspee' 

 may be indu .: ed1 

 axiom I. before their eyes tl 

 time allowance, and declaim 

 pay for heavier tonnago beca 

 her speed— in fact, may have 

 j ust to find out how much s 

 come that she must, nevcrtl 

 must be clearly understood 

 scheme of measurement nnt 

 proposition, and never get 



of E 



io of Itself carries with it an In- 

 hat its elfsat on model one way or 



granted, aooording to axiom 1., 

 MHS such a difference in power, 



A little reflection on this point 

 a. i ii i! is through failing to have 

 nd the purposes 01 



v.Cn 



lakli: 

 othai 



al test of close reasoning. 

 Why a larger vessel has a natural advantage 

 vill be gleaned from the following figures : - 



promoted 

 made a slower boat. But then it is 

 ower than another she may have be- 

 cless, pay for her increased size. This 

 and anyone wishing to advance a 

 allowance must first master this 

 tray, or his logic will not bear the 



a smaller o 



Tonnage. 



Speed, 



Momentum. 



Ratios of Resistance. 



100 

 200 



3 knots. 

 2 knots. 



300 

 100 



Say 2. 

 Say 3. 



100 

 200 



6 knots, 

 it knots. 



600 

 1,200 



18 



36 



The comparison is made between schooners of 100 tons and 200 

 tons. Assume that a certain wind will drive both alike fast (S 

 knots) owing to the larger one having a somewhat clumsier form, 

 and that their resistances can be represented by 2 and 3 respec- 

 tively. When the speed of tho two has increased, let us say, to 

 6 knots, in consequence of a freshening of th j wind, the momenta 

 will have grown from 200 to 000 and from 400 to 1,200, exhibiting a 

 much wider limit at the higher speed than at tho lower. 



Speeds. 



Hatios of Re- 

 sistance. 



Difference . 



Ratios of Dif- 

 ference to Re- 

 sistance of 

 smaller vessel. 



Difference of 

 Resistance due 

 to difference of 

 form. 



2 



2-3 



1 



0.5 



( 300 

 1 (100-200) 



8 



18-36 



18 



1.0 



( 400 



1 (200x2) 



If the whole of this inereaso in momentum be necessary to 

 overcome the increased resistance offered by tho clumsier model, 

 then the two vessels will still remain sailing side by tide. If, how- 

 ever, only a portion thereof is required to balance tho increased re- 

 sistance, then the remaining " power," or momentum stored up > 

 will serve to dr.vo the 200-tonner at some speed greater than six 

 knots, and she will forge ahoad of the smaller schooner in spite 

 of the latter's finer model. To continue upon our assumptions : 

 The resistance in ordinary models increases as the square of the 

 speed at low velocities, hence that of tho 100-tonner will at Bix 

 knots be represented by eighteen. That of the 200-tonner. how- 

 ever, we accept as increasing in a slightly faster ratio owing to 

 oluffer form, and if taken as tho 2} powor of the speed will 

 amount to 36, as noted in the second table above. The same table 

 shows in the third column the differences between tho resistances 

 and in the fourth those differences have been referred to tho re- 

 sistances of the smaller schooner. Now It is evident that if at 

 two knots an excess in momentum of 200 was required to over- 

 come the larger vessel's clumsiness, the amount required at six 

 knots will have increased above 200 in the same proportion as the 

 ratios 0.5 and 1.0. In other words, 400 out of the difference be- 

 tween 1,200 and 600 will be used up in overcoming the excess of 

 resistance due to inferior form, leaving a momentum of 200 as 

 yet unused. This will exert itself in di-iving the larger vessel at 



a greater speed than six knots, from which it follows that when 

 tka 100-touner aequlres that rate the 800-tonner will go by her. 



From tha abovu it will appear plain enough that to or.talm a 

 oorrect expression of the superiority of the smaller vewel's ferai 

 for speed the larger one must be made to account for her total 

 exoess of size (100 tons), for the whole 100 tons has come into play 

 — first, in making up for want of good form ; and second, in actu- 

 ally driving her ahead. In estimating the difference between 

 two forms it is manifest that difference In size must pay, no 

 matter where found. Axiom I., therefore, holds in all eases. 



The next requisites will be granted by all without argument 



III. A perfect system of measurement for time allowance must not 

 place a premium upon any one form in particular, but must leave the, 

 designer absolutely untrammeled in all directions alike. 



Any rule which takes into account only one or two dimensions 

 necessarily compels the designer to extend in the directions or 

 direction not taxed. Only one special form or type can be tho 

 outcome of suoh a rule, independently altogether of the desira- 

 bility of suoh type for other purposes than evading just compen- 

 sation to rivals in a race. Ample proof of this is to be found abroad 

 and at home. In England, where length and beam are taxed, 

 yachts grow narrower and deeper from year to year. In America 

 where length generally supplies the standard, yachts grow 

 shorter, stumpier, wider and deeper with each succeeding sum- 

 mer. On the other hand, the Royal Nova Scotia V. S. finds its sys- 

 tem, in which all three dimensions are considered, not only thor- 

 oughly satisfactory from a theoretical point of view, but capable 

 of matching the greatest varieties in type from one extreme to the 

 other. 



IV. No system of measurement should be permitted which has a 

 tendency in practice to produce pndesirablc or dangerous psctv- 

 llarities. 



No words need be wasted upon this. If it Is found in practice, 

 as has been asserted, that measurement by size has a direct influ- 

 ence upon freeboard, and will compel owners to cut it down to 

 the minimum permissible for summer racing, thereby losing in 

 orulsing oomforts and endangering their vessels in squalls and 

 short seas, it is not very difficult to circumvent this objection. 

 Adopt a standard " depth for measurement " for different classes 

 or sizes of vessels, make such depth depend upon length or other 

 suitable factor, and the yacht designer will at once build up to 

 the limit and not short of it. Danger of low freeboard will then 

 be removed. 



V. The system must admit of ready application and veHficalion in 

 practice. 



Though the exact size of a vessel is to be attained only from 

 drafts or plans, a sufficiently approximate rule can be devised for 

 every-day praotice which will place the adoption of a theoreti- 

 cally correct system within the capacity of the smallest club. 

 Substitute for the gauging or calculating of cubical contents 

 the simple multiplication of the three principal dimensions, 

 length, beam and "standard depth," and the whole problem has 

 been solved. A tape line, a plumb bob and a man who can read 

 numbers is the whole stock in trsde . Such a rulo is founded upon 

 logic and common sense, is unassailable mathematioally, and Is 

 the only one which will in addition conform to tho demands of 

 the five axioms mentioned in this article. 



Any rule which does not conform to them is faulty in concep- 

 tion, and certain in the end to prove vicious in effect. 



— A cricket match was played at Acapulco, Mex- 

 ico, in 1876 with a temperature of 135 degrees in the 

 sun. 



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