1845.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



101 



COMPARATIVE LOSS BY FRICTIOX IN BEAM AND 

 DIRECT ACTION STEAM ENGINES. 



A paper purporting to be a inatliematical investig;>tion of this sub- 

 ject was read in February 1S13, before tlie Institution of Civil Engi- 

 neers, by Mr. William Pole. It is hero proposed to examine the 

 correctness of Mr. Pole's investig.itions ; for though the period of 

 publication be by no means recent, the subject is not one of merely 

 passing interest which renders a postponed review useless, and as 

 the paper has been rewarded by a "Silver Telford Medal," it comes 

 before the public with the authority of the Institution of Civil Engineers, 

 and therefore if inaccurate, may deceive many who take for granted 

 the conclusions of a mathematical paper which tliey are unwilling or 

 ■will not take the responsibility of investigating. 



It may as well be stated, without circumlocution, that the object of 

 the present review will be to show that errors are committed in Mr. 

 Pole's paper, not merelv of a casu il nature or numerical, but arising 

 from assumptions so essentially false that they can scarcely be sup- 

 posed to have been promulgated by a person adequately acquainted 

 with theoretical mechanics. It will also be here attempted to be 

 proved that these erroneous conceptions totally vitiate the practical 

 tabulated results deduced from them. 



We will first, before entering on the discussion, premise that Mr. 

 Pole's piper is founded on the following prelirain.iry considerations, to 

 which we do not at present olTer any objection : — the friction alone in- 

 vestigated is that, which arises at joints ami axles by the strain caused 

 bv the action of the engine itself: the friction arising from tightening 

 "stuffing" or "packing" the parts is excluded ; the laws of friction 

 .assumed are those usually laid down in mathematical books, though 

 Mr. Pole is doubtless aware that experimentalists are by no me. ins 

 agreed upon their absolute accuracy ; the total friction at a joint is 

 made to depend on the degree of pressure at that joint, and the space 

 passed through by th'' rubbing surface, conjointly; the whole pressure 

 of steam is reckoned uniform, and =P; the inertia and weight of the 

 machinery is disregarded. We now proceed to quote the first case ex- 

 amined by Mr. Pole, and his explanation of the figures. 



ju- ^aB™ 



«'10. Figs. Sand 4, show the direct action engine; fig. 2 the vi- 

 hrating engine ; and fig. 1 the supposititious arrangement referred 

 to in the next Article. It is almost needless to add, that only as much 

 of each is shown as is necessary for explanation, other parts being 

 omitted to avoid complexity. ° 



"In the following calculations, a, b, c, d, Sec, represent the radii of 

 the bearings marked A, B, C, D, &c., respectively in the figures: 

 r = AB, the radius or length of the crank; / = BC, the length of the 

 connecting rod ; and P is put for the supposed uniform pressure act- 

 ing on the piston, or transmitted through the engine. 



"The friction will be calculated in each case for a single stroke of 

 the piston, I. e, for a semi-revolution of the crank, from B' to B'". | 



That for the back stroke, completing the circle, will be equal to this 

 in amount. 



"It will be advantageous in some few instances to simplify the ex- 

 pressions by taking approximations; but in all these, the deviation 

 from the truth is so slight as to be unimportant, and not affecting the 

 general correctness of tlie result. 



" 11. We may first examine the simple arrangement shown in fig. 

 1, where the uniform force of the piston is supposed to act upon the 

 crank pin B in a direction always parallel to itself and to the Ime 

 15 , B'". This would assume the connecting rod indetinitely long, 

 which cannot exist, except in hypothesis: the arrangement may there- 

 fore be called for distinction, the 



Hi/jjol/ietical Engine. — The friction to be determined will be that 

 npon the two bearings A and B, the crank shaft and the crank pin. 



" 12. For the bearing B. The pressure upon this bearing vfill be 

 constant, by the supposition, and =: P : therefore the Ksis/awce from 

 friction will also be constant, and =: m P. 



" Now if 6= radius of gudgeon, the apace passed through by the 

 rubbir>g surface will = 6 multiplied into the angular distance the 

 guilgeon moves in its bearings. This angle, in a semi-revolution of 

 the crank, will = 1S0°= it; and the surface will pass through a 

 space = IT 6 ; whence the loss by the friction of this bearing in a semi- 

 revolntion, will, (Art. 7), = m P ir b. 



" 13. Fur the bearing of the crank shaft A. The pressure upon this 

 is not constant, as it is on B, but varies with the position of the crank. 

 When this latter has moved from B' through any angular distance 

 B' A B, which call e, the force P acting upon B will be resolved into 

 two; one in the direction of the tangent B T, tending to turn the 

 crank round, and the other in the direc!i(m B A (or A B if 9 7 90") : 

 the latter vvill be the pressure upon the bearing A, and will be found 

 by tlie rules of statics to be= -j-P cos 9, the upper sign being taken 

 when e I 90", and the lower from 90° to ISO': hence the resistance 

 from friction =: -f- m P cos 0," &c. 



We do not transcribe the whole of the investigation, as the above 

 furnishes all that is requisite for our purpose. It will be seen that in 

 (12) the pressure at B is assumed as uniform, and = P. Nothing can 

 be more remote from the truth, and we really cannot help observing 

 that, to use the mildest terms, it seems almost incredible that a person 

 who understood the fundamental laws of motion could make the as- 

 sumption. The pressure at B depends not only on the steam pressure, 

 but also on the amount of work to be done — the resistance ottered by 

 the crank, and its consequent velocity. If we suppose this resistance 

 zero, the pressure at B will be zero also ; — so far from its being almays 

 zizP, it will he never equal to it while the engine is in motion; for if the 

 two ends of the piston rod were acted upon by two equal and opposite 

 forces F, we should have a system statically disposed, and the piston 

 would be at rest, or move forward with uniform velocity which it does 

 not, since it changes its direction many times in a single minute. 



This one simple consideration ought to be quite sufficient to set the 

 matter at rest ; but as the whole of Mr. Pole's conclusions depend on 

 this fitally erroneous principle, we may be forgiven for adducing a 

 few illustrations to show that the pressure in such a case as the pre- 

 sent depends on the resisiance which the prime-mover meets with. 



If a body lying on a smooth table be drawn along it by a string pass- 

 ing over the edge of the table, and fastened to a second descending 

 body, does Mr. Pole suppose the tension of the string = the im- 

 pressed moving force, namely, the weight of the descending body? 

 If the problem be worked correctly, it will, we think, be found that 

 the tension depends on the mass of both bodies. 



If two particles descend vertically by their weight alone and one 

 of them lie upon the other, is the mutual pressure equal to the im- 

 pressed moving force of the highest — its weight? If Galileo be 

 any autliority there will be no mutual pressure at all. 



By D'Alerabert's principle, the effective moving forces of a material 

 system are equated with the impressed ; by Mr. Pole's, the impressed 

 moving forces may be equated alone. 



The following consideration also might, we should have thought, have 

 prevented the above assumption being made — the piston rod moves with 

 variable velocity ; when the crank is at its highest or lowest, very 

 slowly; when the crank is horizontal, rapidly. How then can a body 

 acted on by constant forces alone (as the piston rod is, if the steam 

 pressure at B, reaction at B be constant) move rapidly and slowly by 

 turns? 



The following is offered as an attempt to calculate correctly the re- 

 action in one of the simpler cases of the problem. 



A constant vertical force P acts at the end of the piston rod E, and 

 the forci> retarding rotation has a constant moment N about A. To 

 determine the motion, neglecting weight and friction. 



m, the mass of B E, M k' the moment of inertia about A of A Q and 



14 



