1842.1 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



1.35 



therefore give i the less effect than B's experiment ; or a velocity of 1-3 foot 

 per second for a force equal to the weight, B's being a velocity of 4 inches, 

 ■when the force equals the weight. The unit of force adopted by you lies 

 between these. However, the truth is, little dcpendance can be placed in 

 any comparison of this kind from want of analogy. Cut it appears to me the 

 Telocity § foot per second given by B, produces an effect equal to the weight, 

 and not its double, in his experiments. 



Much good would result from persons registering and publishing the 

 following d.ita, when engaged in pile drivingi Tfie piles — tunber, or other 

 material, of which they are composed) weight and length ; top and bottom 

 sections ; surface, whether rough or otherwise ; weiglit and shape of shoeing ; 

 head, whether furzy or strapped. Ground — the different strata passed through, 

 and their depths ; the depth driven at each stroke, with the weight of the 

 ram, and tlie height it fell from. These data would be of great benefit to 

 the practical man, and would furnish materials to the theorist, who, in ex- 

 aminations of this nature, fails most often from not taking in all the circum- 

 stances, or from defective data. 



Sundalk, Feb. 7, 1842. Jonx Neville. 



Sir — It appears that a difference of opinion exists as to the amount of 

 force with which a moving body strikes one at rest, as applied in the case of 

 pile-driving. This difference of opinion probably arises from considering the 

 force of imjiact as momentary ; but a force of this description is quite 

 imaginary, and cannot be assigned, unless we can comprehend infinity. Now 

 if one man can raise one ton one foot high in one second, he can raise it two 

 feet in two, cic. And whatever amount of force is expended in raising it 

 will be measured by the free descent of the same weight through the same 

 space, for if it were greater or less, the perpetual motion would be possible ; 

 therefore, on mechanical principles it must he equal. Hence a body raised to 

 any given height may be considered as an accumulation of force equal to 

 that which has been expended in raising it to that height ; and the amount 

 of this accumulation evidently includes two considerations — the amoimt of 

 force employed, and the time of its employment. Now this accumulation 

 being a certain definite amount of force, its expenditure will be regulated by 

 the same laws as that which produced it. If, then, a certain amount of force 

 be expended to raise a body one foot high, and this body fall through the 

 same space, its momentum will be equal to the force which has been expended 

 in raising it. Let it, after falling through this space, strike a body at rest, 

 and by the force of impact carry it through an equal space, the whole amount 

 of accumulated force being destroyed to effect this, the increments of the 

 generating and destroying powers may be conceived as nearly equal, but not 

 absolutely, for the descending body is supposed to descend through a greater 

 space than it had been raised through, on account of its forcing the resisting 

 body through some space, but as this is small and passed through slowly, it 

 is of no practical moment. If, then, a body fall through 10, 20, or 30 feet, 

 and earn- a resisting body through -j-^ of a foot, the force being destroyed to 

 effect this, the force of impact will be proportional ; that is, as often as -y— 

 of a foot is contained in 10, 20, or 30 feet, so will the weight of the descend- 

 ing body be to the force of impact. 



That such is the law of impact is plain, for if a falling body could strike 

 one having a velocity equal to its own in the same direction, the force of 

 impact would be nothing j it would be simple contact. If the velocity of the 

 body struck were less than its own, the force of impact would vary in pro- 

 portion, and its limit is absolute fixedness without elasticity : in the first case 

 it is nothing, and in the last it is infinite. Tlie elasticity of all bodies is 

 similar to that susceptibility of matter to be moved from place to place : it 

 is a property of matter opposing resistance to force ; and, as it relates to this 

 question, it is nothing more. 



Applying, then, these almost axiomatic truths to the case of pile-driving. 

 Let a be the space the ram descends through, b the weight of the ram, s the 

 space the pile is driven by a blow, and y the force of impact ; then we have 

 cb 



Now what practical deductions can be made from the preceding remarks ." 

 — the limit to pile-driving is the elasticity of the material driven. AiVhen 

 the matter to be driven through is of such a nature as to resist the penetra- 

 tion of the pile with a greater force than is measured by the elasticity of the 



material of the pile, further driving would be impossible. For instance, if 

 the elasticity of the pile be ji^. of a foot, the force of impact being GOO tons, 

 further driving would be impossible. 



It is stated in your Journal for December last, that the force of impact 

 GOO tons is the greatest blow that can be given by the pile engine imported 

 from America. The weight of the ram is 16 cwt., the descent 30 feet. 



Modifying the preceding formula, we have — =s, and calculating from the 



y 



30x16 

 above data, „,.„ =^ of a foot. 



Now if the limit of a pile engine's power be to strike a blow of 600 tons, 

 it is because the effect is lost in the material struck. In the succeding 

 number of the Journal it is stated that the abiUty of this pile engine to strike 

 with a force of GOO tons is an exaggeration ; but if the above principles be 

 correct, that assertion is a mistake. 



It is a question of some practical importance to assign the weight of super- 

 structure a pile will bear. The determination of y in the above equation is 

 the answer. For instance ; if the weight of the ram be one ton, the descent 

 20 feet, the distance the pile is driven by the blow half a foot, then 

 20 X 1 



. . =40 tons, the weight that would be required to sink it; a less 



0*0 



amount would not. If the distance which the pile sinks at each blow be 

 small, the elasticity must be taken into account ; its effect is to diminish the 

 result of eacli blow, that is, to make the divisor less than truth ; the quotients 

 would, therefore, be too large. 



Objections miplit be made to what is here stated. In relation to elasticity, 

 it might be said that the whole amount of force being communicated to the 

 pile, it could not be lost ; but its effect is to distribute the blow over a longer 

 space of time. It might be also said of two rams of different weights, say 

 one half that of the other, falling from the same height, that if the heavier 

 was required to sink the pile, the other would not. If effects be proportional 

 to their causes, the less would sink the pile half the distance of the other, 

 and the quotient would then be the same. 



I am. Sir, 



Truly yours, 



London, Feb. 10, 1842. ' ' V>'. G. 



Sir — I read with considerable interest, in your Januaiy No., a description 

 of the -American Steam Pile-driving Machine, and, having seen it myself, can 

 bear testimony to its accuracy ; but the table with which that description 

 concludes is so manifestly erroneous, that attention shoidd be called to it. 

 The table assumes that a body of one ton weight, falling through one foot, 

 would strike a pile or other object with a force equal to 8 tons, and the same 

 weight falling through 16 feet would strike with a force equal to 32-1 tons ; 

 so that, although the weight had been raised through 16 times more space 

 in the latter than in the former instance, and, of course IG times the power 

 expended to raise it, yet (according to the table,) the effect produced by 

 striking a pile is only quadrupled : what then has become of the remaining 

 12 parts of the power exerted in raising the weight, seeing only 4 out of the 

 16 have been spent in striking the blow ? Had the column headed " Force in 

 tons for a ram weighing one ton" been "Acquired velocity in feet per 

 second," it would have been about correct. Now the force exerted by a body 

 in motion, when striking an object, as a pile, is as its weight and the square 

 of its velocity, which has been long since demonstrated by Smeaton and other 

 writers, .\ssuming, then, with the author of the table before-mentioned, 

 that a ram of a ton weight, falling through a foot, would strike a pile with a 

 force of 8 tons, and as it would have acquired a velocity of 8 feet per second, 

 the same ram, falling through 16 feet, would have acquired a velocity of 32-1 

 feet per second, or 4 times the velocity in the former case; now 4= = 16, and 

 16 X 8 tons = 128 tons, instead of 32-1 tons, as in the table. 



There is, however, no authority for proving that a ram, falling through one 

 foot, would strike a pile or other body with a force exactly equal to 8 times 

 its own weight. I am inclined to consider its ppwer much greater than this, 

 though the precise amount it would exert as compared to a quiescent weight, 

 I am not prepared to answer ; indeed, it is a question undemoustrated by 

 any writer I am acquainted with. 



The laws relatiiij to the comparative forces exerted l)y bodies in motiou 



