THE DEVELOPMENT AND USE OP A SPEED VS. DISTANCE GRAPH TIME CALCULATOR THE INTERPRETATION OP LOCOMOTIVE PERFORMANCE

THE DEVELOPMENT AND USE OP A SPEED VS. DISTANCE GRAPH TIME CALCULATOR THE INTERPRETATION OP LOCOMOTIVE PERFORMANCE A Thesis Submitted in Partial Fulillment o the Requirements or the Degree o MECHANICAL ENGINEER By Carlton Shepard Hulbert B. S. in 1. E. 1954 Georgia School o Technology June 1, 1941

Sub-GQUBtitt o Gomaitte on Miraaeed Degrees

I DEVELOPME&T A. FEED OF PRIME INTEREST TO RAILROAD MEM IS THE MATTER OF TRAIN SCHEDULES AND SPEEDS, WHICH IS OFTEN REFLECTED DIRECTLY BY PUBLIC OPINION AND THEREFORE EARNING ABILITY. WITH THE ADVENT OF SUCCESSFUL COMPETITION TRAIN SCHEDULES WERE SHORTENED AND CONSEQUENTLY TRAIN SPEEDS WERE INCREASED. AS A RESULT, MORE ATTENTION IS BEING GIVEN TO SCHEDULES AND TO KEEPING TRAINS OM.SCHEDULE UNDER ALL OPERATING CONDITIONS.. AS A MEANS OF STUDYING ACTUAL TRAIM OPERATION WITHOUT HAVING TO RIDE EACH TRAIM, LOCOMOTIVE SPEED 3 RECORDER TAPES WERE MADE AVAILABLE. THESE TAPES ARE ESSENTIALLY SPEED VS. DISTANCE GRAPHS PLOTTING SPEED IN MILES PER HOUR AGAINST MILES TRAVELED. IT IS THEREFORE POSSIBLE TO DETERMINE THE ACTUAL SPEED OF ANY TRAIN, SO EQUIPPED AT ANY LOCATION, AND THE TAPE.REPRESENTS AS AUTOGRAPH.OF A TRAIM 1 A PERFORMANCE. SINCE THESE TAPES RECORD THE SPEED DIRECTLY -IN MILES PER HOUR, AND AS THIS SPEED IS FLUCTUATING A GREATER PART OF THE TIME, ANY APPROXIMATION OF THE TIME INVOLVED IS BOUND TO BE CRUDE* BECAUSE TIME IS ACTUALLY THE VALUE DESIRED, AND THE SPEED ONLY THAT REQUIRED TO MAKE m SPECIFIC SCHEDULE, -AH PROBLEM OF.CONVERTING THESE TAPES INTO TIME PRESENTED ITSELF.

It is true that complete studies are possible which will orecast a schedule or a particular rum with equipment o known characteristics} but here was presented almost the reverse perormance charted complete except or the time value. B. Description o the locomotive Speed Reeorder.- Although steam locomotives are over 10 years old* generally speaking automobiles have carried speedometers longer than have locomotives, he locomotive ran upon its own right o way and because enginemen carried certiied accurate time pieces and because railroad operation and saety depended upon these timepieces, the speed at which the locomotive was operated was determined "by the watch and the *mlle posts* 1 along the right o way* 'Time per mile 1 1 it is called, and it is still used to check speed by many railroadmen, including enginemen. However, speedometers appeared on locomotives and where they have been used or a suicient time, the enginemen have come to rely on them or their speed indication, rather than! t time per mile 1 5. One o the modern types o speed recorders is mechanically operated by a Hip diameter tt rictiom wheel 1 1 held in contact with the tread o the tire o the right back locomotive driving wheel. This riction wheel drives a centriugal type governor, spring loaded, through a lexible drive

shat made o one inch links, enclosed in a lubricated conduit* At a locomotive speed o 60 miles per hour. this, lexible shat turns 400 R.P.M. and indicates 60 SEPH on a suitable dial acing the engineman. This same mechanism moves a 2^N wide paper tape at the rate o one inch per two miles, while a pencil which is interlocked with the speed hand on the dial plats the speed on this moving tape* Tape is supplied in rolls up to 2400 miles In length and the used portion Is usually removed at each locomotive terminal and orwarded to a central point or examination, study and iling* A riction wheel drive or the speedometer is used instead o am axle drive or two reasons. 1-1* Sine or wear o the locomotive driving wheel tire does, mot aect the accuracy o the speed indication* 2* Attachment o the device to a driving axle is complicated by the act that crank pirns and rods are present and although the device may be located on any wheel which is in contact with the rail, a driving wheel is chosen so that any slipping o the locomotive drivers may be noted by the engimemem and recorded on the tape* he device is so geared that it will indicate and record back up movements as well as orward movements. This type o speedometer Is made in our speed ranges:- 60 MPH Instrument 0-60 MPH 90 MPH Instrument 10-90 MPH 100 MPH Instrument 10-100 MPH 120 MPH Instrument 10-120 MPH

This study is based on the 90 MPH Instrument but it is equally applicable to the 100 and 120 MPH Instruments. Diiculties are to be met when the speed is below 10 MPH due to Inaccuracy o the speedometer itsel in this speed range, short length o time and distance operated at less than 10 MPH and the detail and dimensions o the calculator developed. The 90, 100 and 120 MPH Instruments are similar and may be considered the same or the purpose o this paper. The only change necessary is in the cam, which will be taken up later. <3# Statement o Principles. Since such a graph as is produced on this tape is known as a speed vs. distance graph, there are certain known mathematical values, thuss- The area under the curve, FIOTBI 1, Page 5, is measured as a product o speed (MPH) and distance (Miles) which equals miles squared per hour, a meaningless unit. (See lote. 1.) I, however, this graph Is replotted using the reeiproeal o the speed vs. distance to the same scale in miles.'** The area under the curve, FIGURE 2, Page 5, is measured as a product o reciprocal speed (hours per mile) and distance (miles) which equals hours, a simple unit o time. (See lote 2.) lote 1. Technical Mechanics,Maurer & Roark, Page 140. lote 2. Technical Me chani c s,maurer & Roark, Page 141.

1710 S00 or ID a. w 0 3 O X 1/20.050 a UJ UJ CL CO o o 1/30,033 h~ g; 1/40.025 g tsc 1/50 /.020 / is m 1/80.0125 1/90.011 K.0000 1 h- 2 4 6 DISTANCE - MILES FIG 2 8 10 4 6 DISTANCE - MILES FIG. I TYPICAL SPEED VS. DISTANCE GRAPH AND CORRESPONDING RECIPROCAL-SPEED VS. DISTANCE GRAPH LOCOMOTIVE SPEED RECORDER

I t i s t h e r e o r e o b v i o u s t h a t u s i n g a p r o p e r p l a n i m e t e r a m d r e e i p r o e a l r u l e d c h a r t p a p e r u p o n w h i c h t h e t a p e c h a r t c o u l d b e r e p l o t t e d, t h e e l a p s e d t i m e c o u l d b e d e t e r m i n e d b e t w e e n a n y t w o p o i n t s o n t h e t a p e. A m y r e p l o t t i m g o c u r v e s, h o w e v e r, I n v o l v e s c o n s i d e r a b l e l a b o r, a n d i s. s u b j e c t t o e r r o r, a n d i t h e t a p e - i n o r m a t i o n i s t o b e r e a d i l y a v a i l a b l e i t s h o u l d b e o b t a i n e d r o m a w i d e b a s i s o a c t u a l t a p e s, t h e r e o r e, a s h o r t a n d - r e l a t i v e l y s i m p l e p r o c e d u r e i s n e c e s s a r y i m a x i m u m u s e i s t o b e m a d e o t h e s p e e d r e c o r d e r t a p e s. D. S o l u t i o n. I t w a s t h e r e o r e d e c i d e d t o c o n s t r u c t a m a c h i n e w h i c h w o u l d p l o t a r e e i p r o e a l s p e e d v s. d i s t a n c e g r a p h r o m a s p e e d v s. d i s t a n c e g r a p h ; - s o t h a t t h e r e c i p r o c a l s p e e d c u r v e w o u l d b e a c o n t i n u o u s l i n e i n s t e a d o a s e r i e s o p o i n t s. A s t u d y o t h e a c t u a l s p e e d v s. d i s t a n c e g r a p h s, a n d t h e r e c i p r o c a l r u l e d c h a r t p a p e r b r o u g h t u p s e v e r a l c o n d i t i o n s w h i c h I t w a s n e c e s s a r y t o s a t i s y b e o r e t h e m a c h i n e c o u l d b e b u i l t. 1. T h e v e r t i c a l d i m e n s i o n s o t h e 1 0-9 0 M P H t a p e w e r e n o t e q u a l l y s p a c e d. 2. T h e v e r t i c a l d i m e n s i o n s o n t h e r e c i p r o c a l r u l e d c h a r t p a p e r v a r i e d g r e a t l y. 3. A c a m c u t t o s u i t t h e s e r e q u i r e m e n t s h a d t o p e r m i t a 3 3 5 1 r a t i o o m o v e m e n t b e t w e e n 1 0-2 0 M P H s p e e d, o r

instance, and a 1 : 1 ratio o movement-between 7 -s9 MPH speed* 4* The 90 MPH tape measured two incites between 10 and 90 MPH, while the reciprocal ruled chart paper measured 15*86 between 10 ami 90 IPH. Many cams were tried but the great dierence' in ratio o movement made them sel-locking at certain speeds* Finally one method was ound where the cam ollower was attached ta*a orosahead sliding in straight line guides and the cam rotated about one end which was pivoted. Through suitable linkage the motion was transmitted so that when the machine was operated by the handwheels Im such a way that the ollower"was kept on the speed vs. distance graph chart line, the pencil plotted on a sheet o paper the exact corresponding reciprocal-speed vs. distance graph* The area under this graph could then he determined with a plamimeter and by using a suitable constant, the elapsed time could be obtained im minutes* The irst cam was cut to handle the 90 MPH speed recorder tapes, and later a second cam was cut or the 120 MPH tapes* It would bte possible to cut a cam to handle any speed recorder tape under 2^n im width with the present machine, and with a slight change in construction, is much wider as is practical to use in this type o recording instrument

This method, although it did away with replotting the curve by hand, still made it necessary to make two rums irst over the actual speed vs. distance graph, and second, plamlmeterlng the area under the newly drawn curve. The tracer arm o the planlmeter was then attached to the plotting arm, and instead 1 o replettimg the curve, the planlmeter ollowed the reciprocal speed curve accurately, and with proper manipulation, the area under the reciprocal curve was measured simply by ollowing the original speed vs. distance graph. The area uhder the reciprocal speed vs. distance graph is obtained in square inches, which represents time in minutes, using the proper constant. This constant depends upomt- 1 - Units chosen or the abscissa and ordinate o the reciprocal speed vs. distance graph. 2. Constant o the planlmeter. 5. Minutes per hour equals The unit chosen or the abscissa is the mile which measures inches and ooineldee with the distance scale o the speed vs. distance graph* The unit chosen or the ordinate depends upon the dimension o the reciprocal ruled chart paper, in this Instance, 14 inches, which makes one unit equal 140 inches. The constant o the planlmeter in this case is * 3 ; that is, the reading o the planlmeter Is multiplied by 0. 3 to get square inches.

l n l c i n T h e c o n s t a n t o t h e m a c h i n e i s t h e r e o r e s - e s 0 # Q 5 x 8 0 8 0 * 0 2 5 7 3 i r r ^ * r ~ h a t i s, t h e t i m e i n m i n u t e s b e t w e e n a n y t w o p o i n t s e q u a l s t h e p l a n i m e t e r r e a d i n g x 0. 0 2 5 7, w h e n 1 4 r u l e d c h a r t p a p e r i s u s e d * r e c i p I a 7 r e c i p r o c a l r u l e d c h a r t p a p e r i s u s e d, t h i s c o n s t a n t b e c o m e s s - I a 0 5 = * x 6 0 s 0 * 0 5 1 4 ' 7 0 x 0 * 5 " r e c i p r o c a l r u l e d c h a r t p a p e r i s u s e d, t h i s c o n s t a n t b e c o m e s s - 0 * 0 * 0 3 x 6 0 m 0 * 0 7 2 5 0 x 0 * 5 T h e p l a n i m e t e r u s e d i s a r u l e p l a n i m e t e r c a p a b l e o m e a s u r i n g a n a r e a w i t h i n a r e c t a n g l e, t h e m a x i m u m d i m e n s i o n s o w h i c h a r e ' 1 6 * x 6 * A p o l a r p l a n i m e t e r c o u l d b e u s e d t o m e a s u r e t h e a r e a u n d e r t h e r e c i p r o c a l s p e e d v s * d i s t a n c e g r a p h, b u t t h e d i s t a n c e m e a s u r e d o r e a c h s e t u p o t h e p l a n i m e t e r w o u l d n e c e s s a r i l y b e l i m i t e d b y t h e l e n g t h o t h e m e a s u r i n g a r m * S i n c e t h e r u l e p l a n i m e t e r a l l o w s m e a s u r e m e n t s t o b e m a d e u p t o 6 0 i n l e n g t h, ( e q u i v a l e n t t o 1 2 0 m i l e s o n t h e s p e e d v s * d i s t a n c e g r a p h ), i t w a s d e c i d e d t o m a k e u s e o t h i s i n s t r u m e n t * T h e m e a s u r i n g r o l l e r o t h i s p a r t i c u l a r p l a n i m e t e r r o l l s o n a s p e c i a l s u r a e o o n a s t e e l t r a c k s o t h a t t h e c o n s t a n c y o s u r a c e i s n o t i n t e r e r e d w i t h *

1# Description o Machine Pictures* FIGURE 9 & 10* gs.11,12. The machine chassis is made o steel* moving along a 72" track on ball bearing sheave wheels controlled through a "distance" hand wheel geared to a stationary rack. The "speed 1 1 wheel turns a screw which moves a crosshead in guides through a 14" stroke* corresponding to.the ordinate distance dimension o the reciprocal ruled chart paper. To this crosshead is attached (1) planlmeter carrier arm* (2) reciprocal speed vs. distance charting pencil* and (5) cam ollower* a small precision ground ball bearing which Is held In contact with the cam through a spring arrangement. This cam ollower, integral with the crosshead, moves in a straight line and the cam swings on a cam holder which is pivoted at one end. The cam holder is connected through two levers and a bell crank to a pointer which is used to ollow the speed vs. distance graph. The "speed" wheel makes 80 revolutions to give the crosshead the 14" stroke, and the"distamoe" wheel in making one revolution causes the machine to travel about 4 " or 9 miles to the scale o the tapes used. The planlmeter "rule" is placed on the table top about the center o the 14" stroke o the crosshead, and the planlmeter carrier arm (1) is carried just enough higher to clear this rule, ormally, pencils are not inserted in (2), the charting pencil holder, as this step is skipped by the

1 1 S P E E D V S. D I S T A N C E G R A P H T I M E C A L C U L A T O R S I D E V I E W C R O S S H E A D S P E E D W H E E L S P R I N G B E L L C R A N K C A L C U L A T O R T R A C K F I G. 9.

H CO ««««

r t n n n n t t t u s e o t h e p l a n l m e t e r o n t h e r e c i p r o c a l c u r v e a s I t i s b e i n g g e n e r a t e d. T h e a c c u r a c y o t h e m a c h i n e h a s b e e n o u n d t o b e w i t h i n 1 %, w h i c h I s w i t h i n t h e a c c u r a c y o t h e l o c o m o t i v e s p e e d r e c o r d e r s. I I. U s e s. 1. F i n d i n g t i m e b e t w e e n a m y t w o p o i n t s o n a t a p e. F I G U R E 3. a g e 1 4. T h e t a p e i n q u e s t i o n h a s t h e t w o p o i n t s k a n d B w a c c u r a t e l y l o c a t e d a n d i s p l a c e d o n t h e m a c h i n e. T h e t a p e o l l o w e r I s p l a c e d o n t h e s t a r t i n g p o i n t A a n d a p l a n l m e t e r r e a d i n g i s - m a d e. T h e t w o h a n d c r a n k s ( t h e s p e e d w h e e l a n d t h e d i s t a n c e w h e e l ) a r e m a n i p u l a t e d s o t h a t t h e p o i n t e r o l l o w s " :. t h e a c t u a l s p e e d l i n e t o t h e e n d p o i n t l o c a t i o n, t h e d i s t a n c e ; w h e e l i s h e l d a s t a n d t h e s p e e d w h e e l i a t u r n e d u n t i l t h e c a r r i a g e a r r i v e s a t t h e z e r o m " B p o s i t i o n C,. T h e s p e e d w h e e l i s t h e n h e l d a s t w h i l e t h e d i s t a n c e w h e e l i s t u r n e d u n t i l t h e p o i n t e r r e a c h e s p o i n t, D v e r t i c a l l y I n l i n e w i t h s t a r t i n g p o i n t " A ", w h e r e t h e d i s t a n c e w h e e l i s s t o p p e d a n d t h e s p e e d w h e e l i s t u r n e d u n t i l t h e p o i n t e r I s a t t h e s t a r t i n g p o i n t " A ". T h e ' p l a n l m e t e r i s r e a d, a n d t h e d i e r e n c e b e t w e e n t h i s r e a d i n g a n d t h e o r i g i n a l r e a d i n g i s m u l t i p l i e d b y t h e c o n s t a n t, t h u s : - 3 3 5 x 0. 0 2 5 7 «8. 6 m i n u t e s r o m n A n t o n B n T h i s p r o c e d u r e i s t h e n r e p e a t e d t o o b t a i n a c h e c k o t h e p l a n l m e t e r r e a d i n g. I t w i l l b e s e e n t h a t w h i l e t h e a c t u a l o l l o w e r o n t h e t a p e t r a v e r s e s t h e a r e a A ~ B ~ 0 ~ D ~ A,

t i i L 1 4..100, U J OC U a. t n ; OC => o I..050 a i u u a. NOTE - LOCATION OF LINE "CD" DEPENDS MERELY UPON CAM DETAIL WHICH ENABLES PLANIMETER TO REACH THE ZERO LINE " C'D* " ON THE RECIPROCAL CURVE AREA = 3.59 SQ. IN. = 8.6 MINUTES _j.033 '< o o <r.025 a. o.020 ac.0167.0143.0125^.oilk,. 0 0 0 0 4 6 8 DISTANCE - MILES FIG. 4 oc 9 0 8 0 X 7 0 --1- t 4 6 DISTANCE - FIG. 3 MILES E X A M P L E O F F I N D I N G T I M E B E T W E E N A N Y T W O P O I N T S " A " A N D " B " O N A S P E E D V S. D I S T A N C E G R A P H

-. F I G U R E 5, t h e p l a n l m e t e r a c t u a l l y t r a v e l e d t h e p a t h, A - B C - D - A, a n d t h e t i m e i a p r o p o r t i o n a l t o t h e a r e a A B C D 2. L o s s o t i m e d u e t o a s l o w d o w n, F I G U R E 5, P a g e 1 6 P o i n t " A 1 1 r e p r e s e n t s a n y l o c a t i o n a t w h i c h a r e d u c t i o n I n s p e e d i s. n e c e s s a r y a n d p o i n t W G N r e p r e s e n t s t h e l o c a t i o n w h e r e t h e o r i g i n a l s p e e d i s r e g a i n e d. B e t w e e n t h e t w o p o i n t s " A * a n d N G N t h e r e o r e, t h e r e a r e t w o l i m e s, o n e t h e a c t u a l s p e e d l i n e, A B O, a n d t h e o t h e r t h e s p e e d l i n e a s w o u l d a p p e a r i n o s l o w d o w n h a d b e e n m a d e, A G. h e p o i n t e r i s p l a c e d o n p o i n t " A 1 1, a p l a n l m e t e r r e a d i n g t a k e n, a n d t h e. p o i n t e r i s c a u s e d t o o l l o w t h e a c t u a l s p e e d l i n e A - B - O, t h e n r e t u r n e d o v e r t h e d i r e c t r o u t e G t o A. h e p l a n l m e t e r r e a d i n g i s t a k e n, c h e c k e d w i t h a n o t h e r m e a s u r e m e n t, a n d t h e m m u l t i p l i e d b y t h e c o n s t a n t,. 2 5 7 : * * 6 7 x # 0 2 5 7 ~ 1. 7 m i n u t e s l o s t d u e t o s l o w d o w n. I t w i l l b e s e e n t h a t w h i l e t h e a c t u a l o l l o w e r o n t h e t a p e t r a v e r s e s t h e a r e a A B C, F I G U R E 5, t h e p l a n l m e t e r a c t u a l l y t r a v e l e d t h e p a t h A B G, F I G U R E 6. 5. L o s s o t i m e d u e t o a s t o p. F I G U R E 7, P a g e 1 7. D i e r e n c e i n t i m e b e t w e e n r u n n i n g A t o a t c o n s t a n t s p e e d a n d m a k i n g a s t o p a t B. T o o b t a i n t i m e l o s t, p l a c e p o i n t e r a t p o i n t " A *, F I G U R E 7, r e a d p l a n l m e t e r, a n d m o v e p o i n t e r t o B ~ C *» A # -

t. 1 0 0 ui OC Ui CL V> OC O X o UJ. 0 5 0 a. o. 0 3 3 < a t a. c. 0 2 5 5. 0 2 0 ac 0 1 6 7. 0 1 4 3 O I 2 5 ^ c. 0 1 1 1. 0 0 0 0 4 6 8 1 0 1 2 D I S T A N C E - M I L E S F I G. 6 I 4 6 8 1 0 1 2 D I S T A N C E - M I L E S F I G. 5 E X A M P L E O F F I N D I N G T I M E L O S T D U E T O A S L O W D O W N B E T W E E N P O I N T S " A " A N D " C " O N A S P E E D V S. D I S T A N C E G R A P H

t j 1 7 # 1 0 0 a: yj C L C O Q 3 O X.050 a u U L J C O < a o ec C L,033.025 o.020.0167.0143.0125-.011 K,0000 4 6 DISTANCE - FIG. 8 MILES Z E R O ) 4 6 DISTANCE - MILES FIG 7 E X A M P L E O F F I N D I N G T I M E L O S T D U E T O A S T O P A T P O I N T " B " O N A S P E E D V S. D I S T A N C E G R A P H

l l l e a d p l a n i m e t e r a n d o b t a i n a r e a u n d e r t h e r e c i p r o c a l c u r v e, w h i c h m u l t i p l i e d b y t h e c o n s t a n t e q u a l s t i m e l o s t d u e t o t h e s t o p : * * 1 2 x 0 * 0 2 5 7 5 # 1 m i n u t e s, r o m t a p e * I t w i l l b e n o t e d t h a t t h e t a p e s d o n o t r e c o r d s p e e d b e l o w 1 0 I P H, a l t h o u g h t h e t a p e m o v e s t h r o u g h t h e i n s t r u m e n t w h e n e v e r t h e l o c o m o t i v e m o v e s * I t i s t h e r e o r e n e c e s s a r y t o m a k e a n a l l o w a n c e o r t h e t i m e s p e n t b e l o w 1 M P H w h i c h i s n o t s h o w n o n t h e t a p e * T h e t i m e a n d d i s t a n c e s p e n t i n r e d u c i n g s p e e d r o m 1 M P H t o a s t o p i s v e r y s m a l l a n d i s c o n s i d e r e d n e g l i g i b l e * A c c e l e r a t i n g h o w e v e r, t a k e s m o r e t i m e, a n d t a k e n r o m a c t u a l d y n a m o m e t e r t e s t s w i t h p a s s e n g e r t r a i n s, a m a l l o w a n c e o 3 0 s e c o n d s o r 0 * 5 m i n u t e s i s u s e d o n a l l s t a r t s, w h i c h a l l o w a n c e i s a d d e d t o t h e t i m e o u n d a b o v e w i t h t h e c a l c u l a t o r, t h u s : - 3 * 1 * 0 * 5 s 3 * 6 m i n u t e s i s t h e a c t u a l t i m e l o s t d u e t o s t o p p i n g a t p o i n t,, w i t h s t a n d i n g t i m e z e r o * F I G U H E 8 i n d i c a t e s t h e r e c i p r o c a l c u r v e o r F I G H I 7. r e c o r d s * 4 * L a y o u t o s c h e d u l e s h a s e d o n a c t u a l l o c o m o t i v e s S u c h l a y o u t s a r e m o s t c o n v e n i e n t l y a r r a n g e d o n a d i v i s i o n b a s i s ; d i v i s i o n s u s u a l l y r a n g i n g r o m 1 0 0 t o 2 5 m i l e s i m l e n g t h, a n d e a c h d i r e c t i o n c o n s i d e r e d s e p a r a t e l y * T h e l o c a t i o m o a l l i x e d p o i n t s i s l a i d o u t t o t h e s a m e s c a l e a s t h e s p e e d r e c o r d e r t a p e s, l n e q u a l s t w o m i l e s

T h e m a x i m u m a l l o w a b l e s p e e d s a r e t h e m p l o t t e d o m t h i s t a p e o r t h e w h o l e d i v i s i o n, a n d a c t u a l s p e e d v s. d i s t a n c e g r a p h s p e e d s m u s t n o t e x c e e d t h e s e l i m i t s a t a n y p o i n t. A c t u a l s p e e d r e c o r d e r t a p e s a r e t h e n s e l e c t e d o r t r a i n s o a s p e c i i c n u m b e r o c a r s a n d t o t a l t r a i n w e i g h t o r t h e d i v i s i o n i n v o l v e d. A s u i c i e n t n u m b e r o t a p e s i s u s e d t o i n s u r e r e p r e s e n t a t i v e p e r o r m a n c e. A c o m p o s i t e s p e e d v s. d i s t a n c e g r a p h i s t h e n s k e t c h e d I n, o l l o w i n g t h e p r o i l e o t h e l i n e * c a r e u l l y, a n d t h e i n i s h e d g r a p h i s t a k e n a s r e p r e s e n t i n g a c t u a l g o o d o p e r a t i o n o v e r t h e d i v i s i o n o r a c e r t a i n w e i g h t t r a i n. T i m i n g p o i n t s a r e s e l e c t e d r o m a c t u a l t i m e t a b l e p r a c t i c e. A l t h o u g h a t r a i n m a y n o t m a k e a n y s t o p s b e t w e e n d i v i s i o n p o i n t s, t i m e i s s h o w n a t v a r i o u s i n t e r m e d i a t e p o i n t s, b o t h o r t h e u s e o t h e e n g i n e m a n i n c h e c k i n g h i s p r o g r e s s o v e r t h e d i v i s i o n, a n d t h e t r a i n d i s p a t c h e r i n m a k i n g d e c i s i o n s a s t o o p e r a t i n g m a t t e r s. T h e s e i n t e r m e d i a t e t i m i n g p o i n t s a r e a l s o n e c e s s a r y s o t h a t a l l o t h e r t r a i n s o n t h e d i v i s i o n a r e i n o r m e d a s t o p a s s i n g a n d m e e t i n g t i m e s, e t c. T h e c o m p o s i t e t a p e i s t h e n p u t o n t h e t i m e c a l c u l a t o r a n d t h e t i m e b e t w e e n e a c h t w o t i m i n g p o i n t s d e t e r m i n e d. A s a m a t t e r o i n t e r e s t a n d i n o r m a t i o n, t h e t i m e l o s s e s d u e t o e a c h s t o p a n d s l o w d o w n a r e a l s o d e t e r m i n e d a n d r e c o r d e d o n t h e c o m p o s i t e t a p e. T h e m a j o r i t y o r a i l r o a d t i m e t a b l e s g i v e t i m e t o t h e

nearest minute, although in congested territory the hal minute is sometimes used* For the composite tapes, time is computed to the nearest tenth o a minute in order to obtain more detail, and to aid In adjusting the inal time accurately to the nearest minute* his method thereore actually represents a train plotting Its own timetable, and by careul use o existing locomotive records enables the ormulating o a railroad timetable which gives proper proportioning o overall division time between various timing points* Timing points either require the services o an operator, towerman or an automatic device which t t 0S s n trains as they pass a particular point without the services o an operator* The term n S is an abbreviation in standard usage meaning a Hrain report 1 1, and comes rom the term, 11 Out o Station* 1 * D# Recommendations or timetables based on results o a schedule layout using proper proportioning o time between timing points* Time in minutes and tenths as obtained by the time calculator represents the perormance o a train with a given number o cars making stops as noted on the graph* It stands or the best perormance possible tinder good operating conditions with a similar type locomotive* Any o the conditions listed below will require more time than is shown:- 1* Bad weather 2* lead or side wind, or both 3* lad rail condition (slippery rail)

4 * L o c o m o t i v e u n a b l e t o d u p l i c a t e p e r o r m a n c e d u e t o b e i n g l e s s p o w e r u l t h a n t h o s e u s e d i n m a k i n g t h e c o m p o s i t e t a p e, o r d u e t o m e c h a n i c a l t r o u b l e s, l o w s t e a m p r e s s u r e, p o o r i r i n g c o n d i t i o n s, e t c. 1. I n t e r e r e n c e w i t h o t h e r t r a i n s. 6. U n s c h e d u l e d s t o p s o r s l o w d o w n s. T. B e l a y s d u e t o a n y r e a s o n ; t r a c k w o r k, b r i d g e w o r k, e t c. 8. M o r e c a r s o r t r a i n o g r e a t e r w e i g h t t h a n t h a t u s e d i n m a k i n g t h e c o m p o s i t e t a p e. I t i s t h e r e o r e e v i d e n t t h a t a t r a i n s c h e d u l e s h o u l d b e p r e p a r e d w i t h a m a r g i n o s a e t y t o c o m p e n s a t e o r a n y o t h e a b o v e l i s t e d c o n d i t i o n s i i t i s t o r e p r e s e n t a t i m e t a b l e w h i c h c a n b e o l l o w e d b y t r a i n s u n d e r a l l c o n d i t i o n s, e x c e p t i n g a c c i d e n t s s u c h a s w a s h o u t s a n d l a n d s l i d e s w h i c h c a n n o t b e o r e s e e n. L i k e w i s e, a t i m e t a b l e g e n e r a l l y d o e s n o t s p e c i y a m a x i m u m n u m b e r o c a r s o r t r a i n w e i g h t i n p a s s e n g e r s e r v i c e, b u t i s m a d e t o h a n d l e a s w i d e a v a r i a t i o n i n o p e r a t i n g c o n d i t i o n s a s i s p r a c t i c a l. I n s o m e o r e i g n c o u n t r i e s, c e r t a i n p a s s e n g e r t r a i n s a r e r i g i d l y l i m i t e d i n t r a i n w e i g h t i n o r d e r t h a t a s t s c h e d u l e s m a y b e a d h e r e d t o. H o w e v e r, s i n c e e a c h a d d e d c a r r e q u i r e s m o r e e n e r g y t & p u l l i t, i t i s o b v i o u s t h a t e a c h c a r a d d e d o v e r t h a t u s e d o n t h e c o m p o s i t e t a p e w i l l r e q u i r e m o r e t i m e o r t h e t r a i n t o c o v e r t h e d i v i s i o n. A l t h o u g h l o c o m o t i v e s a r e d e s i g n e d t o h a v e r e s e r v e

capacity to cope with conditions as they arise which require more power, the wisdom o shortening schedules and Increasing train weights beyond practical limits may well he questioned i the n On Time 1 1 percentage is to he kept to a satisactorily high igure* o the passengers, an 11 m Time 1 1 arrival is usually much preerred, even though the overall time is longer, to a shorter time, and have the train put them into their destination or transer point late* Saety demands that maximum allowable speeds not be exceeded and thereore timetables should represent perormance that it is possible to maintain in the ace o all expected diiculties* 1* Solution o Special Problems*. 1* Possible means o Shortening Schedules* a* lerouting trains* This methodlis sometimes resorted to when an alternate route is available which will lessen traic congestion* The alternate route is charted, irst locating ixed points, then assigning the maximum allowable speed which would be permitted over the new route* Grades are taken into account and the speed vs* distance graph sketched in, using as a basis any locomotive speed recorder tapes available over this route* The time calculator then gives the time over the new route, and I enough time can be saved by using the new route over the original route, the trains may be rerouted to advantage* I no time can he saved by the alternate

route, Its use will depend upon some actor other than time saving. Under this seme heading in a territory where congestion o trains causes progressive delays to ollowing trains, it is oten possible to install additional automatic signaling to operate trains "against the current o traic 1 1 during certain periods o the day when opposing traic is light. This is done under strict control to avoid any possibility o two trains entering the same track in opposing directions* It involves certain expense in additional equipment and in order to obtain a igure on total time saving the speed recorder tapes may again be reerred to. Since some time is lost due to slowing down or a crossover move rom one track to another, the new alternate route must alleviate congestion and more than oset the delay due to slowing down or the crossover move. A base tape is prepared and the location o the crossover is plotted thereon and the probable train perormance on the crossover is sketched in. The time calculator will then give the time lost due to slowing down or the crossover and this igure may be used in estimating the economies o the proposed remedy which, in eect, provides the use o an additional track during peak periods o traic. b. Raising maximum permissable running speeds:-*

The present operation is obtained rom actual locomotive-records and the proposed speed limits plotted on the same chart* By using the proile o the line, the new speed vs. distance graph may he sketched in, and the dierence in time may be obtained by the time calculator* c* Elimination o Stops or Slowdowns s-> The present operation at any point o speed restriction is obtained rom actual locomotive records* he proposed elimination would allow speeds as sketched In, taking into account the proile o the line* he time lost is then calculated and would represent the saving i the stop or slowdown were eliminated* 2* Cost o Stops and Slowdowns* This igure has been calculated many tines and by many methods, most o which take into account many items which cannot be classed entirely n out o pocket 1 1 expense. In order to obtain readily an estimate which may be quickly arrived at, the actual speed vs* distance graphs rom the locomotives are used. In 1I0U11 1 1, Page 2S, the time lost due to slowing down ro A to B is ound on the time calculator, the time consumed rom A to C had no slowdown been made, and the time rom B to 0* From the igure it will be noted that line AC denotes a train running without change o speed and the

uel rate (pounds o coal per hour) may be readily estimated. Likewise, the curve BC represents the acceleration ater slowing down rom A to B. Practically no coal is used rom A to B, only enough being ed to keep the ire in readiness or acceleration. For the accelerating period, the coal rate may also be readily estimated. Thereore the loss o eoal due to this slowdown Is equal to time BC x lbs. coal per hour BC minus tine AC x lbs. coal per hour AC. Since the amount o water evaporated by a locomotive boiler is roughly proportional to the uel burned, this same method may be used to estimate the amount o water lost due to a stop or slowdown. The amount o coal or water ound by the above means may be converted into dollars by applying the proper cost igures which are in eect in the locality in question. Putting into igures the example shown in FIGURE 11, Page 26, it is ound that the time AG equals 8.1 minutes, and the time BC equals 10.7 minutes. Probable coal rates are as ollows:* Running, lbs. coal per hour z 7000j per minute s 117. Accelerating, lbs. coal per hour z 11000j per minute» 183. Thereore: 10.7 x 183-8.1 x 117 s 1010 lbs. coal lost due to the slowdown.

26, 4 6 DISTANCE - MILES FIG.II 10 12 DISTANCE - MILES FIG. 12 T Y P I C A L S P E E D V S. D I S T A N C E G R A P H S L O C O M O T I V E S P E E D R E C O R D E R

Since the amount o water evaporated by a passenger locomotive boiler, may be approximated at 7 lbs* water per lb* coal while running, and 6 lbs. water per lb* coal while accelerating, it ollows that5- Sal* water evap* per min* 3 7000 x 7 3 98 gal* per tox mlnmte while running, and:- #al* water evap* per min* 3 11000 x - 132 gal* per minute, while accelerating* thereore in the case in FI00BB 11* Page 26j 10*7 x 132 8*1 x 98 3 618 gallons o water lost due to the slowdown* I the cost o coal is $4*00 per ton, the cost o the slowdown in uel alone is:*» 1010 x 400 s #2*02 m m " 3* Determination o the Amount o Slipping which occurs when a locomotive loses traction* this igure is usually expressed in two ways} irst as the maximum driving wheel speed as compared with the actual locomotive speed, and second, how many extra revolutions o the driving wheels were made during the period o slipping* A typical slip has been reproduced rom a speed vs* distance graph indicating a maximum driver speed o 90 MPH

WITH A LOCOMOTIVE SPEED OF 50 IPH IM FI3DBB 12, PAGE 26* SINCE THE TRAVEL OF THE SPEED RECORDER TAPE IS DIRECTLY PROPORTIONAL TO THE DISTANCE TRAVELED FEY THE LOCO MOTIVE DRIVING WHEELS, IT DOES MOT THEREFORE INDICATE LOCO MOTIVE DISTANCE TRAVELED DURING PERIODS WHEN SLIPPING OCCURS* POINTS A AND B, FIGURE 12, INDICATE ACTUAL LOCOMOTIVE SPEEDS JUST BEFORE AND AFTER A SLIP OF THE DRIVING WHEELS* IT IS ASSUMED THAT THE SPEEDOMETER FRICTION DRIVE WHEEL DOES NOT LOSE CONTACT WITH THE DRIVING TIRE DURING THE SLIP* FHE TIME CALCULATOR IS RUN OVER THE ACTUAL LINE ON THE TAPE FROM A TO B (0*62 OLIOS-)' AND THE TIME COMPUTED AS 0*5 MINUTES, FHE ACTUAL LOCOMOTIVE SPEED DURING THIS SLIP FOLLOWS THE REGULAR SPEED LINE FROM A TO B TO THE POINT C, AND IS APPROXIMATELY 50 MPH* FHE ACTUAL DISTANCE TRAVELED BY THE LOCOMOTIVE AC EQUALS SPEED (50 MPH) X TIME (0*5 * 60 HOURS) EQUALS 0*416 MILES, AND WILL ALWAYS BE LESS THAN THE DISTANCE AB* DISTANCE CB THEN EQUALS THE DISTANCE TRAVELED BY THE LOCOMOTIVE DRIVERS IN EXCESS OF THAT TRAVELED BY THE LOCOMOTIVE DURING SLIPPING* IF THE LOCOMOTIVE INVOLVED HAD DRIVING WHEELS 79 w IN DIAMETER, THOSE WHEELS WOULD HAVE TURNED 158 REVOLUTIONS, WHILE WITHOUT SLIPPING, THEY WOULD HAVE TURNED ONLY 106 REVOLUTIONS *