202 



THK CIVIL KNGINEER AND AltCllITECT'S JOURNAL. 



f.It'NK, 



RAILWAY CURVES. 



Sir — Being myself one of those who are wilhiig to profit (through 

 your columns), by the experience of others, I take the liberty of for- 

 warding a system for setting out curves by ordinates, which, being per- 

 fect in theory, only requires great exactness in tiic execution, and 

 depends but little upon instruments ; it is, I believe, in frequent use, 

 but which I have recently adopted from my own deductions ; these re- 

 marks may be found usehil by some of your younger readers, and may 

 lead to something better from ciders in the profession. 



Let AB and CD be two straight lines, whicli are required to be 

 united by a curve ; say for convenience of a mile and a quarter ra- 

 dius, or 100 chains ; by producing the two lines the angle AFD must 

 be ascertained with great exactness ; (tlic angle of its supplement being 

 much less, may be taken with less liability to error). With EC for the 

 radius, the angle CEF may be ascertained, for supposing AFD is 148' 

 ■20', EFC is 74° 10', and therefore CEF is lo° JO'. By this means CF 

 & BF will be found '28 ;J6 links, B & C being the commencement of 

 the curve. These points having been measured oH' from F, com- 

 mencing with the odd links, viz. ;3(i, and leaving pegs at every chain, 

 the ordinates may be set off at i ight-anglcs according to a table to be 

 calculated in the following manner, and which will do for any curve 

 of a similar radhis. 



In the accompanying diagram, EG is the radius. 



GH is the sine. 

 EH is the co-sine, and 

 HB the versed sine, of the arc BG. 

 Now HB = GF and BF -= GH, therefore the ordinates will be 

 versed lines, where tlie length on the tangent is equal to the sine. 



Again, HB = EB — HE, and HE=v/EG^— GH-, therefore FG^ 



EB— v^^G' GH^ ; or, with o for ordinate, /• for radius, *■ for sine, 



and V for versed sine ; o= r—v'r-s-, the table is then calculated thus 

 at every chain. 



The ordinate at 100 links = 100-00-— »/ 100.00^ — L00= and witii 

 the assistance of " Barlow's Tables of Factors' Roots, &c," a table may be 

 made to any usehd length in a few hours, thus — 



again 100 00- — 

 —■2 00^ = 



100 00' — 10000 0000 

 _ 1 00" = 1 0000 



10000 0000 

 4 0000 



0!)9() 0000 



999'J 0000 



sq. root of which = 999n-490>S sq. root of wliich = 9997-9998 



deducted from 100-=: -oOO'iof a hnk. deductedfroml00-= '2-000-2 



To obtain the square root of the above immbers it is convenient to 

 drop the last four figures of o, and alter the decimal point in the root 

 two tigures. 



The result of these calculations will be — 



at 1 chain 



2 



3 

 1 



5 

 6 

 7 

 8 

 9 

 10 



Tliese ordinates may be made available on the curve of any radius, 

 by multiplying the lengtli on the tangent, and its respective ordinate by 

 the BUiltiplicr of tiie radius ; thus for 80 chains the multiplier is -8 — 

 so at 80 links the ordinate is -40 



at 160 1-00 &c. 



But it would he better to use a table calculated at every chain, and 

 it might be vforth while for some party with a little spare time to pub- 

 lish a set of ordinates at every useful radius, say from 10 chains to 500. 

 The greatest accuracy is required in taking the angle, as otherwise 

 the starting of the curve will be incorrect, and the curves in the centre 

 will shoot past each other. 



Where the angle of the two tangents approaches a right angle, it 

 may be advisable to work the ordinates as far as they can be correctly 

 done, and then, by reversing them, to lay oil' another tangent. 



I am your obedient servant, 

 — -— — Surveyor. 



A SUBSTITUTE FOR A RAILWAY TURN TABLE. 

 (From the American Railroad Journal.) 



Having been led, by the objections attending the running of loco- 

 motives backwards, or with their driving wheels in front, to consider 

 some method of turning them and their trains morecfficienlly than the 

 common turning-table, which only admits of one or two cars being 

 turned at a time, and having devised a plan which would, I think, 

 effect this desirable end, I take the liberty to solicit for it your kind 

 attention. 



That locomotives do not run as well backwards as forwards, will I 

 think be readily conceded. That the liability to run off the rails, and 

 that the wear of the driving wheels is much increased, have been proved 

 upon a road which has coiue under my observation, beyond the shadow 

 of a doubt. 



Tin; plan would, I think, be found simple and effective. The saving 

 of time and man ut I labour would, 1 doubt not, be found to be con- 

 siderably over the common turning-table, and at the same time it 

 would be found to answer very well the purpose of turn-outs at water 

 stations. The preceding diagram will explain the plan in question. 



Let us now suppo^e the track laid, and provided with switches at 

 the intersections, and a locomotive, with a train of cars behind it, at A. 

 It moves over the first half of the turning track, B (which is the 

 ([uarter of a circle), and stops at C, where the track is made straight 

 for 150 or 200 feet, or for the purpose of receiving or discharging 

 freight quite out of the way, the straight line may be extended to any 

 convenient length. The switch is then changed at D, and the loco- 

 motive, with lis train moves backwards, over the other half of the 

 turning-tr.ick, K, into the main trunk at F, thus having been turned 

 completely around. 



That additional room would be required is true. By adopting, 

 however, a radius of curvature for the turning track of 400 feet, which 

 would be quite sufficient, and making 150 feel at B, .straight, the 

 whole distance out of the main trunk would be but 550 feet. 



Washington Co. Geo. January 5, 1839. Y. B. HOLCOMB. 



