On long and short connecting rods

Oa L o n g a n d Short Connecting Rod~.

~0~

great for trains to descend, without the use of the breal~ no power was lost; and the cost of worMng was no greater than on a dead level, for the whole of the additional power required to overcome gravity, while ascending the incline, was restored in descending, par. licularly when the planes were of great length, and at a convenient inclination, in which latter ease there would be a slight saving in working an undulating line. The safety from collision between the trains was much argued upon ; and it was stated to be impossib[efor the trains to approach nearer than three miles to each other, unless at the stations especially appoifited for the purpose; single lines of railway could, thereibre, be worked with safety. The coat of working was then examined, and taking for data the results of the expenaes on the l)alkey line, and supposing the system to be adapted to a line of 11"2 miles long, similar to the London and Birmingham Railway, on which tile cost of working, with loeonlotives, was stated to be Per train per mile, for haulage, 15 pence. ,, " for maintenance, 81} " The cost of working the atmospheric apparatus would be Per Irain per mile, K)r llaulage, 5 ~ pence. " " for maintenance, 5~" With the additional advantage of traveling at a mean speed of 50 miles per ho~r, instead of between 20 and 25 milas with the ]oeomotire system. ~ I a j e 1.--A diseussion ut~on the atmospheric railway was extended to such a length, as to preclude the reading of any papers; but as many points, both of the theory a~d praetiee of the system, remained to be examined, it was decided, that the discussion should be renewed at the next meeting, June 4th, a(ter which a report of the proceedings will be given.

~'OR T I ! F , J O U I { N / t ~

0~" TtII~; FI{A2'¢][~I,I~ I ~ $ T I T U T E .

On L o n g a~d ,Y/tort Connecting Rods.

B y T. W. BA~W~.LL

In the Journal of the Franklin Institute, for April last, page ~ 0 , notice was taken of an important error on this subject, contained in a paper copied from a foreign periodical, (the "Civil Eng. and Arch. .Iotlrll.,) where it was contended that the force transmitted t h r o u g h lhe connecting rod, in its own direction, decreased with its decrease of length, in the ratio of the cosines ; and that with a short rod greater pressure came on the axis. The gross error respecting the transmission of force, was alone noticed at that time; the increase of pressure by the shorter rod being considered of comparatively slight import~ notwithstanding it being said, that " i t is the chief thing to be guarded against;" but no statement of the absolute value of this increased pressure is made for a given rod, nor of comparative values for diftic.rent rods. Tile i]mt is admitted of an increase of pressure for fi'ielion by a short rod, and it is now proposed to exhibit~ in a plain, practical way, what it is worth, carefully keeping in view that

Civil Englnee~'ing.

108

undeviating law, that sine q~ct ~on in mechanics--"equahty of effect under all modes of aetion~for, however accutc and accurate we may suppose our calculations to be, if' they result not according to this law they must be wrong ; and we hold the converse of the proposition--equally reliable--if in accordance with it, they must be right. Let P 1~, fig. 1, be the lel~gth of stroke =-100, the crank P, C = 5 0 , then the path of the crank wiK be P B E ~ 157.08 ; now the pisto~t of a rosary engine would describe this path under the constant lever 1:I C ----- 50, and with a ibrce of.6366 X 157.08~ 100 tbr eflbet. b ' i g . 1.

......

/'" /

/

;17

/

""

. . . . . .

2-" . . . . . . . . . . . . . . . .

i',,

:

(':

"-..." '.,~,

--

I Y"

{~,

I~VIi

- -

\

:l:~

"

.~.

"'

$

The efibciive lenglh of lhe eranlc, or ,,leverages" is, ia all cases; equal to the perpendicular drawn from the direction of the rod lo the, axis, a s G C , where F C , iscrank, a n d F X , rod. The r e d l y X, or F X, is indefinitely long, so as lo preserve its parallelism~ in describing the distance of lhe stroke, in its own direction~ ~ 100, and to give an efl'eet equa[ to the rotary engine, will require a force of 1. multiplied into its distance, I00. The mean leverage to produce this equal effect under force I. is ,31.83, for the required force is inverseiy asthe leverage, or the distance described. Then we say inversely, if force .6366 be lee. 50, so will ibree 1. be lee..°,1.89, and lev. G 0~" 31.83 is to lee. 13 C, 50, as distance P E, is to distance P B E. The crank at F C, is in position for: mean effective leverage = G C, 31.83. The pressure on the axis is xvith the parallel rod equal 1., or what is required to meet the equal force 1. ou the piston~ the mean leverage being 81.83, and to increase this pressure on the axis, when using the same crank and length of stroke, we must show a less leverage under a greater force. The foregoing parallel rod X and X, is the longest possible, and the minimum is the ]ength of the c r a n k ~ a n d we proceed with nearly the shortest possible, or as rod 60, to crank 5 0 , ~ f o r errors, if they exist, are brought out most vividly by extremes. Nod H A, -----60, perpendicular to the crank, is at its maximum leverage, but at its mean of position and time, in reference to the force transmitted in its own direction, being as the cosines inversely. T h e mean leverage is proportional to the sines, when rod and crank are at right a n g l e s ~ t h e n as sine B C 50, give lee. 31.83, so wilt sine H M, give lee. 24.459, or we can draw the cir. arc, as shown by" the governing leverage G C~-31.83, and K L, is the mean leverage for rod

60.

Leverage 31.83 × force 1. gives 31.83 for effective lever, and to

On Long and Short Connecting Rods.

109

make lev. 24.453 equal, requires a force of 1.302 X lev. 24i453== 31.$3. Cosine M A, is 49.095, then inversely, tad. H A 60, i s t o force I; as cosine M A 49.095, is to force required == 1.302. While it is shown that tile increase of force, to the shm-t, makes it equal for effect t o t h e long, l e v e r a g e - - t h e terms imply that a less distance is due, but under a greater fbrce, although the stroke = 100 remains common to both. We believe the presentation of this point is novel, and the explanation brings with it coinciding proof of what is here advanced. The statement for explanation partakes of the suppositions, but, in effect, is actual and inevitable. When lines are used to represent ibrces, it is only in the directions of their lengths that they indicate values ; H A, m a y change place parallel with itself, as by the dotted line h a, without expressing eft~et, but instead of being at h a, if it be found at b e, it wilt show the exertion of a force in its own direction .~-a e, while passing the horizontal distance A e. In this manner the distance :N E = 76.8~5 is attained, during the stroke, equivalent in mean to the direction of the rod I t A, under the force due to it of 1.302 for a e A, and N E P, are similar triangles, and a e : A e : : N E : P E ; anddis. N E 7 6 . 8 ~ ° 5 x f o r c e l . 3 0 2 - - - - 1 0 0 I b r e f f e c t . Dis. N E 76.825 is to dis. P B E 157.08 as lev. K L 24.453 is to lev. B C 50, andPE:NE::GC:KL. Fig. 2. c~

M'"

/ ....

__

7xL

......

.

(

/

/

i%;

......

c

i i .......... ,---L a

-b Cb

e

Fig. 2, delineates the relative properties of four connecting r o d s - - i n length A 60, B 100, C 200, and X infinite, stroke 100, crank 50, and force on piston 1.--arranged in tabular form, showing the leverage, multiplied by the force, equal the standard leverage 31.83 ; a n d that the force, multiplied into the distance~ gives, in all cases, equal effect ---- i 0 0 :

Rod.

I,everage.

Force.

Equal Lev.

Force.

Dis. of.Action,

~t~¢v-.¢i,

A~ al=.~4.4:).J X 1.30~ = 31.83 1.:J02 × ae=76.825 ---- 100 ]~. D/-----28.47 X 1.118 = Sl.S3 1.118 X 5e--89.445 = 100 C, c Z = 8 0 . 8 8 x 1.031 = 31.83 1.031 X ce-----97, == 100 X, .'c Z= 31.83 X 1. = 31.83 1. X xe=100. - - 100 Accurately, the whole pressure for a given rod is as the leverage inversely, and the extra pressure over the parallel rod, as the difference of the given leverage, and the standard 31.83 ; bu.t as these are supposed to be unknown quantities, we cannot use them. Therefore VoL. V I I I , 3 3 ~ S ~ a I ~ s - - N o .

2 , - - A t r G V S T , 1844.

10

1 I0

Civil Engineering.

if we take rods B, of once, and C, of twice, the length of stroke, to establish a ratio of extra pressure for friction, we find B is .118 per cent., and C, .031 per cent., which is sufftciently near the convenient ratio of the squares of the rods inversely, to maim that the rule ibr practice. Then say the additional pressure for friction over the parallel, or infinite, rod, is, tbr once the length of stroke 12 per cent., for twice 3 per cent., and tbr thrice l~ per cent. The wflue of the pressure tbr friction is matter of opinion, but if tile amount of friction with the parallel rod, exclusive of the piston, and its rod, which arc. lint affected by the changes, be set down of its power at t5. per cent. Once, tile stroke will be 12 pp. et. additional ----- 16.80 ,, Twice, " " 5 " " ~ 15.45 " rihrI,(?, ~; ¢; lax '~ " ~-- 15.20 '; From tbes~ data tile c~gineer may- sac the extent of power saeririced fi)r the convenience of a short connecting rod, which, we apprehend, is tound much less than had been generally supposed. CiJ~ci~aali, 201h J ~ e , 1844.

On the Mktgnesian Limeslones.

B~j Mr. C. It. S m T m

This paper was a continuation of those formerly read, treating on tim sand:~Ioncs and oolites; on the present occasion Mr. Smith proceeded with the subject by describing the great beds of magne.~ian limestone, which lie, with little intervals, from Nottingham and Tynemonth, and more especially those between Mansfield to Knaresborough, an extent of about seventy miles. In this district stone is found combining the carbonate of 5me and magnesia fi'om the lowest amount of the latter, to proportions comprising pure dolomite--of course, they vary greatly, both in appearance and quality, and that even in cases when the substances are, chemically speaking, the same : ~ a m o n g the best of these stones, as building materials, are the Bolsover, Roche Abbey, Barnham Moor, and IInddlestone. The first named has been tested in the Norman Church at Southwell, which remains in a state of high preservation; b a t much, aa Mr. SmRh particularly insisted upon, depends upon the situation of the beds from which the stone is raised ; tlle remains of Roche Abbey, tbr example, and the church at Tukhill, both built with the stone which Sir C. Wren distinguished as second only to Portland, are in a perihct state, with all the sharpness of the mouldings preserved, whereas buildings in tile neighborhood erected with the same material during the present century, but without due regard to the choice of the beds, are already in a state of decay ; so also with regard to the Burnham Moor stone, m a n y Roman remains at York are in a far better condition than the works of the middle ages in that city, not excepting the cathedral, and others at Hull, Beverly, and Tadcaster, built with the same stone. The 0adeby stone is found to decompose rapidly; a specimen used in London, perished in about fourteen years, and yet this stone is found within a short distance of Conisbo-