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The Admiralty Formula T THE December meeting of A the Society of Naval Archi- tects and Marine Engineers, E. A. Stevens Jr. presented: a paper on "A Substitute for the Admiralty Formula", abstracted thus: This formula was derived from the Admiralty formula as follows: D3 5 6 Noe pi es ow a =} oat As the length of vessels of similar models varies as DY, L (or length LWL) was substituted for this factor, which gives 5. Dé VE Now substituting this value of D'/, and taking C out of the radical we get 965) ee oe V yao HP® a Ds In order to simplify the formula D°/, was replaced by D. Tables Nos. 2, 3, 4 and 5 show the values of C as worked out for several types of vessels. Tables Nos. 9 and 10 and Plates Nos. 3 and 4, give, the writer believes, a very fair comparison of the relative accuracy of the new formula and the Admiralty formula. By simple solutions of the formula for values of its various terms it ap- pears that for ships of (1) Same length and displacement, power varies as J'*. (2) Same length and speed, power varies as D. (3) Same speed Di= and displacement, I Se eet aE we L In presenting the formula, the writer does not claim that it is an accurate means for estimating the speed of ships, but merely one that can be used for preliminary calculations in place of the Admiralty formula with more accur- acy. It is also easy to handle and re- quires less judgment and experience in its application. In reading the paper, Mr. Stevens Said: You will notice at the bottom that the Utah is mentioned twice, one with power varies as Mr. E. A. Stevens Jr. Evolves a Substitute for the Admiralty Formula reciprocating engines and one with turbine engines. The one with tur- bines is the actual results from the trial trip while the one with recipro- cating .engines is a supposed ship fitted with propellers of equal effi- ciency to the Delaware. This would give about the power required to drive her had she been fitted with reciprocating engines and propellers of the same efficiency as the Dela- ware. It is the same way with the curves on plate No. 3. The curves there for the Utah were from the trial results on Table No. 9;-and we notice that the indicated horsepower of the Utah was taken from her ef- fective horsepower and divided by the propulsive coefficient of the Dela- ware, so as to do away with any error due to propulsive coefficiency. I might also state that the degree of accuracy of the calculations is only that which can be attained on a 10-in. slide rule, as it would be impossible to work the thing out other than with a slide rule. Tribute to Mr. Stevens David -W. . Taylor:--This. is ~ the twenty-first general meeting of our society, so I presume the society may be regarded as having attained its majority, and I should like to note in connection with this paper what. seems to. be an appropriate circum- stance. I believe this is the first in- stance in which we have had a paper presented to us by the son of a member from whom in the past we have had numerous invaluable papers, and I hope we will also have many more in the future. Mr. Stevens, I think, has made a distinctive improvement on the ad- miralty formula. I also think it needs improvement. The trouble was with the original admiralty formula that it deals with a question in which there are a number of variables involved, speed, power, displacement, the Pro- portions, dimensions, etc., and it is impossible to satisfactorily cover a question involving so many variables when, as in the admiralty formula, you select only three--speed, displace- ment and power. Mr. Stevens has introduced the length, which is:9 very essential factor in the power required for a given speed, and in that way I am sure he has made a distinct 1m- provement. I think also it is an im- provement to put the coefficient as the first power of the speed instead of- as the indicated horsepower--that reduces the coefficient and makes less discrepancy between coefficiencies. ' The result, of course, is really the same. The Chairman:--When the idea is to interfere with a good old friend like the admiralty formula there should be some champions for it. Has it any friends at all? We have a family pride in having this son of one of our members bring out his first paper, and we want to have good discussion upon it, if it is possible. EK. H. Rigg:--The chairman asked if the admiralty formula had not a champion. Mr. Taylor gave me the hint. He complimented the society upon the fact that we had the son of one of our distinguished members reading a paper. I think we must re- member that the admiralty formula was gotten out by our fathers when they had not the facilities we have, and had not the experimental model basins which we enjoy. The admir- alty formula has been very useful, and served a useful purpose in its day. We do _ recognize its limitations, and it is gratifying to have an im- provement in that formula which we can take on with it. I would also like to draw your at- tention to the. fact that Mr. Stevens makes use in his paper of the ratio which Constructor Taylor uses in his manual, which you probably all know, and which does not need any flowers from me. Mr. Stevens uses the dis- placement-length ratio. To my mind that introduces a very important ele- ment in the accuracy of his formula. Moreover, it is good to see everybody working along a uniform line for technical expressions. If you under- take to study works on _ problems, you will find you have to look out for a lot of things; people use nearly the same terms, but not quite. I think -it is gratifying that Mr. Stevens fol- lows up with one of Mr. Taylor's expressions. D. 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