“SOME FUNDAMENTAL RELATEONSREPS OF
YRAFRC FLOW £354 A FREEWAY"

Thais {or fire Dogma of M. S.
MICHIGAN STATE UNNERSWY
36mm 3. Ryan
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This is to certify that the

thesis entitled

"Some Fundamental Relationships of
Traffic Flow on a Freeway"

presented by
Donald P. Ryan

has been accepted towards fulfillment
of the requirements for

M S degree in Civil Engineering

 

K/ZW ‘ 'l/f) LII/”MA L

Major professor ,

Date EL 3 f /#6/

0-169

LIBRARy

Michigan Sm.
University

 

 

 

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This study was made to detemine the relationshijga of ageed.
versus wolune, speed- vezm dxmaitywnd volwae versus density for a
new. The Metal rem nee-nay 111 Detroit ms selected so that
int-ems]. and. Mama). factors affecting traffic flow would be at a.
12111111111121. Tue primary factor ai‘fecting traffic flow weld be internal
friction. Speed, mm, m density are the characteflatica or
Mile flow for: which data. were seminal-ea we. analyzed.

813116.113 have been male 121 the past on this tapic by Greenshielfie,
Oleott, Barnett, and. others, each ha$1113 a difi‘emnt set of results
and relationships . There 13 sane mmt that the speed-mime
relationship 18 parabolic , Mt with a tendemcy four the unpal- porticm
of the curve to be linear. It is believed that the speed-density
relation 18 may curvilinear. The mime-density relation is
believed to be parabolic vith the vertex upward.

A set of linear regressim equations have been (10119109061 for
the area of nan-critical flow for the tin-ea m’amwelatmhips .

The settled. of analysis consisted primarily of a elm-analogical plot
of 031‘... and the F—linearity test. Other stfiistics used to sub-
statutethofindincamuwdetemlnatimofconelstim

111

coefficients, the 11th error of." estimate, and mi‘idenca limits
for shapes and standard Matinee.

The speed-volm relation has an acceptable set of regression
cqcatioas Vlth m linearity but 1:11.11 1m! correlation (3‘5 - 113:.) .
The arm-age reg-993m equation is 3 a 50.2 - 0.21’5 V. The regression
coefficients are simi’icantly non-zero. Tim cmbgdcel plot of
lane 1 under congestion inmtratca the need for swarming non-
criticel wd critical flow am the likelineca of the cutoff line.

The speed-density remake has an acct-29111119 net of regression
equations with good linearity and fairly good comlation (3s — 79;).
The average regrcacion ew'tion la 8 =- 58.0 - 0.3631). All regression
coefficient-:4 are aigflficcntly nun-zero. The demobgical plot of
lanes 1 anti 3 illwstrete the need for ceparathag ma-cfltical and
critical flow and the need for a cutoff line.

The volume-densiw I'eletioxmhip has an acceptable act of
regrecaim mqmticms with very good linearity and 32011 correlati
(“IS -- 951,15). The wrerma regression equation is V a 5.7 - 0.11731}.
111a raw-35131011 coefficients are significantly ranger-o. Ema aim». -
logical plot of lanes 1, 3 , and average illustrate the need. for
swung non-c tical and end-meal flow and the need for a cutoff
line.

mm results of 1.113 speed-volume axnflysia cliff‘er with Green-
ahiclrla results in tint the rate of space decrease with correcpwzflng

“3.111118 increase 13 mash higfizzer in his Mia and would not be a

iv

good eetlmote of Freeway Flow. The sgeed-«ianuity reeulte differ with
Greenshields in that his relation is can ilineer with much Lower woes .
Olco’et’s eq‘mfiizms, 8 a 53.7 - O.LT§D (foot lozxe) mid S a 23.5 - 0.3313
(slow 112118), also differ in values and rates of decreases of weed.

The linear voluee-deoai-ty relation de'temdned for tide analgesia in for
non-critical flow whereas! others have used all data and a parabolic
relation. In general, the linear ralabionehip, as der area in this
soak, agalLIhe the relatiom in man-critical flow and the area between
it (dummy cut at“ at 53 «can and Booed cut off at 1+1) 11191:) and critical

flow.

AC7G§BVLE )UEJT'XRT

The author is very appreciative for the permission to nee fiat:
collected for e oampreheneiva study of iraffio flow cooperatively
Isde by the Michigan State University Highway Traffic Safety Center,

the fiichigan State Highway Department. and the Bureau of Public Roads.

Appreciation 1e also expressed to the author's adviser.
Dr. Breuning. and to the numbers or the Civil Engineering Staff
for their eseistanoe. guidance, and encouragement. Special thanks

ere given to Dr, 5. D. flay) uh» helped me to initiate thie thesis.

T4,“)

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TABLE CF TAELES . . . .
Chapter

1. IE”. D"CIICfi.

II. R’T‘JIE! CF LI.

III.

IV.

V.

VI.
VII.

VIII.

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Descriytion of Test Area .
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Figure

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vii

Sysad-Veluwe fisgreaaicn flat-Gregnghgg1d. . , , ,

Vblume-fiensity Regreeeion Flat - Farabolie end

Lingfir e e e e e e e e e e e e e e 0 e e e e

ayeedénenaity Regreeeion Plot - Clcott and

Graenshiolde e e e e e e e e e e e e e e e e

Speed-anume Regroaeion Flat - Clcvtt'e Parabolic

Hap of Detroit ehowing study aite . . . . . .

Crone-section shaving equipment installation.

Pigturee of Ewap entrance to Expressway . . .

Pictures of field dateatnre ind Recieviug Unite

¥eluse~§enaity and Speed racnrtare. . . . . . .

RQ-Pen regardar and Eodified 3.0. Recorder. . .

Seniitivity Controls and Lpsed~defsator fiaunting.

{‘4peed-':’01me Chomhgiml Plot lane 1. . . .

speed-Volume €hron010;ioul Plot Lane 2 Thrudey

Speed-Yalume Chronological Plot Lane 2 Friday

arsed-volume Chron010gioal Tlot Lane 5. .
Pioturee of Light and Eeavy ¥clufiee . . .
Picture! of Eigh dansitye e e e e e e e e

Pictur.. of High dan.ifiye e e e e e e e e

Ticturee of Hinimun spacing at high epoade.

Speed Sensity Chronological filnt Lane 1 .
fipaed-fiensity Chronological Flat Lane 2 .
Speed-Density Chronological Plo‘ Lane 5 .
Valuma-flenaity Ghrtnological Plot LID. l.

Volume-fleneity Chronolcgieal Plot Lane 2.

0

Tage

10
1h
15
16

as:

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viii

Volume-Bensity Chronclagioal Plot Lane 5.
Speed-"whine C‘rxronalcgioal Plat. Average .
Sgeeé-Dansity Chrnnnlcgioal flat Average.
Volume-flmrsity ChronQICgioal Flat Average
¥¢lume~33neity iample Eeoarder Elot . . .
Sample figeeé leosrdar Plot. . . . . . . .
$ample 30~Han Weeardar Plat . . . . . . .
Samyle 0! Correlation Table 3/9. . . . .
Sample 0! Correlation Table 5 J. . . . .

fiamplfl of Correlation Tabl. V/D- e . . .

table

“WPUNH

ix

ZABIE O? TABIES

Speed-Venue Statistice eee e
Speed—Deneity Statistioe . . e
VOID-Denna: Statistic. . e
Three-Lane average satiation.

O

Remeaion Equation for all Relations . e

Weighted Values for Correlation Potential.

(1.7233332 I

nmsmmzsx

‘lfie inflame-1389.3. charm: mristics of trm‘f‘ic my; are alm’gra
resent. in a traffic stream are sprawl, volume, flansity, and haulzmy.
These (13155.“56‘6-‘31‘i-‘3t128 hate: canfizrin inWrrelatlanfidps much are

believed to vary with the aanetric (19:13:: or mail 71.3%.: , with a damage

in 03-3 or name of the chat-madame?» or with a Labi'i‘ja is... era of the

1‘“er frictiom .. 7

film ganuctric claw: 3.311 023 a 1"“acili-ty will have mmiierable
Mimi-lea on the emwnt to which the: mm: i‘r‘iu 945.1203 will be present.
Three of me :‘ricti' W3, interval, medial, and muggiml, can be miniaimd

internal friction

.a 1

throw: the cmmtric {3683.383 of Mum" '. Him.» - ,
is a..e<.oe.1 by chmages a weed, “3123.18, 93:1 6.9122 my.

In mm-cri tical 3.01:, internal :E‘ric‘sion 13 mistrial)! low, but
in critical film: this. friction builds up until congestim is carplete

and all traffic cows to a. halt. Tide occuz'leme takes place dizz'im

peak; flow. at a. time wi'mn the facility siwald be Motianiug flawlmdy.
Because of these breakdowns in operation, rugs 681m 1.: needed to
cistezuine mm. is Waning 11;; to the paint of critical flow

'13:: pwz'pnse of £1112; paper is to flea-tanning the relat Lanzhips of
Spam varmu 11131112163, 3903.6. versm (lensity, and volume versm-a aermity
in the area of nan-critical flow and to dctamine time line or area

between nonacritical flaw anti critical flaw.
729313 n11..Lu*-”*r indicabea the author reference in the bibiio.‘ '- ;;z~ap£3y unless
a fat.) mom is given.

N

The temelatimmlflya of the inimntal charge terist'lca of
traffic flow are detexrmtned and tested by statistical nwmoris and
tlmwgh “tine we of one {minute incremental chronologicszd. plots of

da“ .

CIIAPZCE II

FLL-T..T132’ OI“ . 3:35;“...

0:12- 53.2331 .1 0'3.“ 2'22 3:213 for $5.52" of "72-3., $011252, (1213.15.33,

and 51.3mm 53;) 5.2. the: statistic 5L}. ajgpmmlrz of m. 6-32225’1512132 .6
141.13 11:15 8.391123%; km to t1mreta.1.= " mmszrm ecu); it)" (r2522),

q
H . 3") ts- ’
£2; h.— ‘— ‘ ‘IIYQ‘B

relafiiansmp of 5.22:1 2.1.11 vol-.2215, 223.3. the 292212.; of
obtahmi $2832 a 193??? yawn-3.325... study. In 2.5.5.2 3130 ngz‘fiAc

01322232281012; it w . assumed that. 522154352 - 235. "mu 0:. v. 25121:... tram .125”

in 3:201:96 was at a. 251.113.232.51 3.11.5. 1-. r; a;;:»pzo;;122.t21y 2:35:51 to (3b a l 1 8/ 2.1.;

522222 151 2235212 5:32.:- 1.1mm 1.21? 1' 22:13; 8 equals 215221 in 511-125 per hour; 211:1

1.1 15 8. facts for 15.3.2 my: aim the of .75 52:29:23.5. This 1221125...

23.25.1031 p‘txureza an $2-3- flow of '3033 van. 531113 2222 can cmly be
maimed mmaih 122122.22, the "01. L122 for-2m." is not given because:
of its 3.132222122511122 11.322222, it (Lu-25 paint. to two sigiii‘icsmt

g

0:1».

.3283.

”_ ; ‘1."7' . 1,5 - .1 1~ n 0.4.: 's. U -.~.9 ~
A. 5.22 123-..”); 122523321. 212.... t .. ‘21. ”c. c: . .53 2.12-5.31 0., 93.52.2225

.52me point at about 153 mph the ”'2 “.22 comb till
Manes 111552" .12 cam.
13. The 25151115521 spar.- 1.11.3; 2.273251523230231 u * ":3. L3! 1m

percez't- * «31113112213 ' tine

1

H2 med. 1:312:12 2.532451595521233 23.33;; vi 212 2 52.2.5 51-: 3.1 mpgcatians

1‘03: 1512...].13 CLLW'eta int .. 013811111353 0;? a 292251-“011222 NH}... .331 73.3.13

221221321 was $01213. to ‘02 1.111225: , S 5. 143 - O.” 2 .‘v' 2.15.22 8 2:35.512 59.3.2;

L322 Pt: I: 8.1+ 0.7. the Aygcam for a. our ....;1.2 15.: t of" all symémls

and abbreviations. .

3:

in 31113313232 10.11“ 3.113. V equals 2311213 in vehicles per minute. 522
Figure l. B}; Begin: tint V :2 - 8, (I) being; 21.: .21.“ v), the ccyzation

becomrz‘s‘ S 2 1:3 . . 17112 eqy‘ai in 3.1213... 8 1‘11 .2: vi‘rh a. slrinht
camce . find. here Dr. Grew—3.7.3:: cal-is 22.;ng tint, for all 133222312251
191232225, tue 1132 any be w.--1-1 to be 3373.13... 3“; vi‘ ch 0333* 515,...
error. That stataient has been dis. Cam-3&1 pro and con x."+h no
d2..‘inite niacin . 80123323, 72:13:52 cum-‘23 were es tablzzzz‘aed on a.
11.5.7325. nmber oz‘.‘ obs 221.1131... 15 and fart .233 only mi ti: two and foam-
12.12 {1133112233 in rural 53:22.3.

1:2. '1'. w. Forbes-.5 used s 223255 of 32.3. 2:151 122.025.3232“ to
ob‘min dam: or his am. '3‘313 of speed, 2512..., 622311;},and headway.
The. film-3 obtained. in the: field were: (127010331 and an 22.22.1313 13 mule by
studying; the £132.13. The 33.13133 were then used an the basis for Inn-2321‘-
rang‘ed estimates. Fm the alt-{5139313, Fox-hes €013.31 a. reduction in speed
1.7.3.331 the whale per lane untreated from 003 vph to 3 90 win He also
continued that them was no .u- “:hxuzn 110111.153 1301.113 ., anl for. a. six-3.04m
(1121:1251 111531423, the 3212:3533 speed of each lane (of the three in one
dbectian) varied 11:13.27: 3.221133 can... ‘r.*ti:m.5 T3113 3.33; :cwnent is cont; ‘mry
to what earner: others have i‘o-mi. ‘1'512 curves of the s peed-30111.32 relaticm
Show a. definite trend may from the straight line relation Greenshi-elds
says 2:513 . Th: .32 212212.35 on the relations or 1232.. {Sic flow are
not emfprising as the $321" -fi 125 testec'i were mt similar in basic der- ign
characteristics .

A pram entitled "On 33.2mm Waves" by J. Lighthillm and
G. B. $.21:th offers a 2.2223; of traffic flow except that this is

related t0 "long era‘s-212:1 roads", whereas pwflms 3311:1123 were cwcemod

 

 

 

 

      

 

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with a. stationary mini; 82,3313“. 0:332 91‘ t2: tux-2‘22 229.....- or: the 2233:0321. i2:
tam: ';-3 ‘2241111 (333328 n32; 33:21:33 Ui h the relation '3': 3:23 229-331 is 11213-3211
related to ami‘ 533' Tue 15.23.36.323 * re 13222320321 23:23:: 6:33 23012731123243. 2":22031 32 3.1.33. sad
nun‘eer 0:? points can 33:33:33 2.21 a Large ini:e:.2:u:S-:I.n’x: 23-3-53 2:37-3:53 no 2:02-32:33
in high and low areas. Liam-fill acne-tend: that; 2:23 1:3 is a 12:: 3:33.32 d::.:.~.. biz:
intennlatian and that. “233238 1213;223:232" lint-e range 'pmf::3s:‘bly (1)622 not lie in
a. straflflt line.

ugh-UL]. ales can urea 23:33 3‘ .memW-ceJMQfiUn curve 303.32.232.—
doneity) 32:? his stung-f 23.2.2333 that 0:? G2zel‘n33m3 . Gr 32.33. 230133., ce32c5’32333231
the 333.133.33.333 of mix-2m 3.31:1 flew: ‘53 ti) be a. 33233232113123.10023-2‘ 8 t1": 3:213 want
them... 3.1 the 03:15:33, Vi .313 2:. 2:: 3332:2222 33:3: 23393.23“, 2132;321:211: 3:22.: :32: vale-3 0:."
are 132213321357 £22sz vpn. Emma-22', 1335;235:3111”: cm we 13:21 no one Imam-3.1m"
curve 63:32:96 . 3133.2 321333212331 3 3222.33.23.23: o. i’ angr-nnflnai'ely 1.33533 2:312, but
the cum was such the-.23 23233.3 could 042022? 4.3331 32. greet-3:23" merge in
cancentration. Ligtr-nhill canal-mes that traffic czmpaeitian, 5262313923212:
clan 1532, (22112212223 8.10325; flue highway, and mum charm varieties may alter
the relation at a: 3; 9:1 {531 ‘2" 2233. T1313 3.22:; 9.1333 33331-33331 by T. W. Forbes
who further iimlieflt 31112333931 (2&3me '13:: .1323 could (213213332 within a.
comzry L1 332:. 11.3.1 also canal-32:23:31 "13222; the (3:27.25- azme in the 12.11311"
of vehicles woiLd have acme affect on ”concmtz‘etrlrm” relations.

Sumo. of the 2:33:33: recent 3. lean have also need or taste-:1 Greenshlelde '
linear and {anabolic relaticns. One of these is by E. S. Oleott.l3

In this at "’3 , tuxmals were used an testing: sites in the (233331-331-

nation of the effect; of 8136326. and Spacing on tunnel caged-tar. Tue

O.)

tm’mels are 302223331132 ideal in than the i‘ricvlonal onzzects raga-fling the
one-way two -lane flow 0'5: traffic: exist only hatez'nnlly and, i‘ur'the'..' re ,
only 112311121 lanes became lane changing; is not permitted. Because there
are more lance feeding traffic to and fun the tunnel, toll booths have
little effect 119011 the :E‘lcm of traffic.

Oicott tested the 11339322233313 that weed. and. density are approx-
inately 11.319.02.33 related as did Greenehielas . The general eqvmtion,

Y =2 c I m, was used for the relation with Y being average 313333.,

1 average density, c we I intercept, and m the slope of the line.
115% this relation, calculations were made for the data. and. linear
emufiions flarived.

52133 c9. 33113-33033 of this speed-density relation yielded an equation
232mm 3 33 29.6 - 0.2033 D for the 81.323951; lane with the highest percentage
0:? c :mercial vehicles and an equation 8 a 513.7 - 0.1373 D in the lane
with 11.2.;th eye-ed and no emerald vehicles. 55113 in significant in
that this report of tin Ford hat: a smile: situntinn. See Figure 3.

Olcott further fauna that the critical 6.33m: ‘55; 1:333 65 vrm at an
09th speed of 21. 312311. This 1:3 significant. as the values obtained. in
this rcgmrt are 3.3323333: '93.

By using the some ”basic equation and £1.31th the Speed-mime»
relation, a. parabolic cm've may be plotted. See Figire 1:. The apex 0:.“
the p: rebels: in, the optima density. Points lying above the optimum are
those val-me which occur at higlmr than average speeds. Mr. Olcott m-

thur malice-ted tlmt, when critical density is enceeded, for the same

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voluna a. lower average eyeed. is e "ye-21.211. This 11332.37 be (113.. partly to
hem clmmtceisticsm ‘1 ...ch (1:: .emmze w: 131.11; 15-3-3319 or awake 13.933.13.333.
It may be conclude-ii 3:113:31 Oleott. '5 report uni:- the basic relgztions

’4‘: i":

of G‘=3.~emshiel3is are satisfii'ace‘mwy ”‘0': the imam]. 33:13:33. '1” 33 01111133.... 1.31 -

ence being in the neweical relations; that is, "Mme 33-33111; ....m-.. cm the
speed-density cm or peel; values on speed-valmze curse. Even with
these 81: “1133131 bias, Olcott. feels that finr‘ther some] is heme: 1117 for

o. canyla :e mrstandizug .

A second traffic 331.333 sflxiy in tamaels was unle- by Site and Foot-.3324
and. they were timing to rehxte “'37wa 9.31:1 com: (3.413.333.2033 by com 21.31erim;
the effect 0' bot blame}... 5:12.323 seam} x1 for e. 3333311321 130 gable than in

stuiy. 31c 11.33221 flaw (3130.. e was the beam rel... tines! 31.1333:- 0"” Grem-
shieifls . They thmx‘m‘t; the line; rent-ion of speed. and aemity, and. the
parabolic rela‘isa of eye ed and 133311.333: , 1331.313. be the best for 1.1.11 tie].
(13.3.31 collect-13:13:. .

3m, airing the anal-min , they fmmd that. the kinematic vave
theory was quite useful in 3131 3332131131: 13333:) ewe” 1‘. 1.2m cement ati-m (Saba
Image:- more cezm'bi ens , but it 31331 not predict was; my the yet-terns
observe-i upstream and. (33:33:11.; ulce- 31 from a beet-‘3. xvii-3;. A "4.....1‘1‘erence in
results and pet-51322.30 1.3336. 3.41.1333 occm'red and the :1y thm 3:313 this was ceased.
by 11-31315, -'.‘le-1.aae film: withmxt passing. Another amuse may be chives reactions
anal behavior.

They L‘ertner cemluiictd thw- Congest-.3; d 131wF 9:“ most sections of the

tame]. had. relatively Little to (13:) with twee]. en .- alxmzzent , and they

11?.

-.
.1.

Q, ~ Q‘.Q_ ,. a. . . .' .. q, : - ~
conclu-z-;d. mat (... ce.x~1:.i.23.<.‘.a' .3311:

313113.13: 31:12.35 that. 2'1. 3.2:; W. e. 133.215.13.13 in
in'ber'yretlng f 71.03413 ‘13 1.1.1:}. te' . 11.71331“: these 142.;ii’3:.:;;-3.r)3'1.13 in 331.123., they
1113.1:- ted a nee-:1 for further research on the overall 23:3"3‘315321 o: 1;1°11.:T’f 1::
flow and 11.3.3 egg-gained: 3.0315 in tzamcl flaw.

A paper by J. Baguette imlmabecl 332m: "1.3.1:: 2:113:21 buff-5.1:" (333231.35. 0:3)
is one of the titaniumta traffic :L'Lmz 13-1.3...an The pez'atiaml
paint of a Mammy is s“ 1.111313 to the critical..- 1‘1...” print 03‘ steel,
1:33:13:th the yield. 1.131111". failure oer: are. .

Barnett futther emanasizes that 1.3.: wage-130133.11 rams-113:1. 1:: act
pardaolic but is n (“2021133111 c." 13.31 0.1" 1131623? 33111 131 27.11331“) Lie. ‘1!“ 01113115213 ; qut‘ler
pee}: cmliiimzs 8;:‘13 not. 13333 but 23130 vyh at an 131111331211er 8‘3)c~;;c'i 02'? £33 13131:.

$53.) far, the premium resear1'1 in t? @1313.» flow 1.3131152534321213 that

Greensmalfis' providiad the east logical bais to the 3391.12.33.323311313, but

2

13.1. theories have been quite con 331331331313 131.1 . The. con imam/15y (stems

'-

33.322.133.211” fan the :act 1.1.3333: he was the Tim t to (‘33 an eaten; 113 ‘e shyly
into this area. bemrer, 33mm controversy dues cone em those portions

of the cue/ea whet-11:: his data was 111313113110.htm; .

C 51:33:? :11 3‘11

11,—5.3? ‘D 0; ’--JJ. WW.) 7I

DOSCZ‘iE’Ti-im‘i 91‘ Test Arcs:
The study site of tin: research DV‘OJQ was 10- .3333. on them ”e1
Fox-<1 Freeman? at. longs Sires-:1; in Deficit. The 33-2321 13 a. six-131e,

O

6.1212126. and mic-vsmra‘wa <1. mama-<1 fire-:19.- ‘ 10:53.01 my 3221.21.21 223.1
.9 U 42 3

tn: .2113: tutti-n 02" t1“... 3 CTD 3.27.9.1 is same 13 13.2

3.22:; 1012». Ii: 1:3 3 part

.9
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of 1213 -- 21.22.2122- Pant c: 91 — r32- .21? 0.30 to Detroit.

Its-ta mm collmiml on the 125m: ca 99.: . nu 2.22". lanes: 0L the Ford by
using cleawmdz: 12-2-2211? 9911;211:211; s..2rpm.322:1 02:03: the: 1~o.923..?a.3r . TL:
1921-3222:»: 0.: 9911;121:211 war: war 3:1 cm rape: 2218.1 brain .5- fate-11:11 to steel
" was of." a. bribe. 1322.» r9"?- ég: 34222170.“: 1313338 mused cm 13.1: far 31:13
or the 312111: “taut-e s 212213 that t3m9 were 1.1912 3112122 tr.) app-z-‘amcftzimg traffic .
(zwwmwm traffic.)

Tamera we tut) worm): in the deiniLy of the 51222-33 area: one
is on the vest 515.: of the brim}: approximately a. quarter of a mile
11:23:22. T319. o“- er rap is on me- east side: 0; L...‘ - 1.12121: 33 agazmr‘ grimly
600 feet distant. In. gaqeral, 1:111: sec-1:12:11 of freer-m“ is typical in
design of mod-cm £19221... 2:. ‘32 eFigwe 7 for 2 21;) crash of Ionyo.

Figure 5 is a 215;) of the 13-33mm wean slimming time stub; site
in relation to the Ford and 1239 C333. lem 6 is a exam-section of
the Ford. 3.": the 102130 mmmma giving roadway width: and the positioning

of thee $113,112”: eat.

13

Figure 5:

IL
Map of Detroit area showing study site location

 

 

 

 

 

 

 

 

 

 

 

 

 

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16

Figure 78 Ramp details -~- entrance to Ford.

 

 

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Ramp Entrance, Edsel Ford Expressway, Detroit. View
shows Michigan Avenue in relation to entrance.

 

 

L .

Hump, Edsel Ford EXpressway, Detroit. View shows the
Ramp is void of any frictional features and is long
enough to provide for attaining speed of expressway and
proper merging when headway is ample.

1.3

1:12; trementa 1:132;

 

At the conclusion or." a preliminnn' narcotics-£1011 to determine
tine type of instrwmntation that 1.01le beat yield the dxraired infor—
mation, a decision was mach: to use the Bearing—Rogue 23 Per. Record-3r
as tkze core unit. Aéjitional units were need-22d to comb .2: the
iz'm‘izrzzxiautation necessary for the collection 0:" volume, dens 1.123., and
hewimay data. These unite coxmis'tei 0:? a unified modal of the RC
Streeter-Amet "A1313 tron" digited recorder, modified mdele oi‘ the M’J—ll
Electzc ~451111.51: Electronic Cycle Computer em‘n comzected ”1:11 at;
Esterline-mmus Graphical Recorder; 1206111126. 2:06.913 01' the 3—2.1
Elec arc-1mm Baler Speed {deter and ammonia"; Est-erline- 1*- rods
Graphical Speed. Recorders 3 and three imael FD~M mectl'o-é-fatic Overhead
2135.10: Vehicle notes tors .

Bach vehicle that passe the ”point” or field. 31211.43, 1.135 demoted
by the yeti-marl miisr Mammy. This im'omation was then sent over
telepiwne wires to the receiving; station. Here the tafomation went
to a repeater relay where the im‘omation was sent to two recording
dexicea—me EEO-pm recorder and a Volmo-Eemity Computer. See Figures
8 and 9..

The LID-pen recorder contains a one ~1mndred foot roll of graph
paper that can be awed. to Operate at 13:10:15 constant speeds. There
are twenty pens built into the instmnent and each is actuated by a
six-volt relay. Tue pens make lozuzitmiinal lines on the moving paper
rolls except when a pen is actuated and than the pen mares mom-ally

apprordmately one eighth of an inch. Each relay is wired to 1:913 terminal

19

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21

posts on the panel in the rear of the whine. Sag Figm 9.

In this sfiwiy, one pm for eaca Lana ms used. Emir gamma
relays were coxmectea to telephome wires . The telephone wires were
connected. to Radar Vehicle Datectors. The room. detecting devices,
in mm, sent an electrical impulse to the 20~Paa Eczcorder each time
o. velficla passed. bomb}: I. atectorr. Tue EEO—Pen Becoréer then plot ed
this impulse on the marina; paper. The impInse weaved as a lateral
line , thus distinguishing it from the aroma]. lon3itudinal 11mm villain
was a plot of thne. By comting the lateral lines for a. given time
period, volume was obtained.

The apeed and volune density recording devices operated in a
manner 51231113.“: to the m-Pan Racorder. That is , information was sent
over telephone lines to be plotted. by the recorfiing instrmut by
making 8 Lateral line acroos the paper. For these recorc‘aers, the length
of the lateral line variefl, dogmxfiing upon the 3p eed or volwxe of vehicles.

A line that is plot ted on a graph regflims the interpretation
of its value by a person therein: a digital recorder prints the exact
value . The ini'oxmtion printed by me one digital recoracr was volume
0:“: traffic for one lane for one nrmute of time. This was the character
of the Streetcar knot 11.6. Digital Recorder as ccmpmred with the
Esterline-«Mxmm mhical recorder. However, each recorder served its
purpose satisfactorily.

The detecting tie-does Operated on the radar prim 139 e ; that is ,
the sending; and receiving; of electrical impulses. The speed detecwr

measures the time difference between signals (Lwflsee) received and

convert: this: 1311' 12111.11: ion "to electrical mares"; , This :1 "rent 1:3
received by the recorder and plotted on a scale fairs: 1112:3918 ZIPII 1:23 11:31
of an E11381? sac-ale. The overhcai vehicle detector 11335-113 in that
received 132113.369 causes the electrical circuit to be broken far as
1mm; as a vehicle is 32171:: the rage of 139111131215. This bans-:91: in the
current 113 recor' 1:11 on the file-Pm gamma]. recoraer as a lateral line.
fiance, the: (1121;111:113 heave-:11: lateral 1111113 will be time spacing or
headway". This 83:38 impulse was. also sent in 123212: 1101122162 density
caupaw: 3211.31.31.13, each 13m: was net plat-taxi finiizfiiwlky as in the
EO-P-m or spamd rmonmw } but {.113 i-rgxilgze was 30:13 to 9. 13031113115021” 1112.33.11“:
3111111191131 1:911:31: 06:2:11 “1:13 aid-1:11, and 1411.11.15 at Spacing-1:1 known-211:3
01' time . L102, 1.1.3 maizmtion 1331:5116. flax: 131:: volume ' twity c:<1.:;:uf;::r
was dafa 1.21:; grated 011111“ six-“:1" t 1393111013 0:1‘ 4:51:19- . 11:12 plot 0:1.“ 1311' ch
would 32:31.: amazingly the 31:11:12 of traiizic in :relatigm to time.

1:250:12 an; 611129. c' 11113. be collectrfi for 13:31:, all of the 1:1 2:11:11: :11:
had to be timnrgjfly 1:231:31: T323 116162333115 1:313. ‘12:: L12 installed at the
study 101: aizion and the are-cowm‘e or nearing mics 11151111181 at t? 1::
rmaivmg station: T19 111315633113 tzwwgtwi 111:: Wanna-Mon over telephone
line-s to the recordem . The use of telcgbme lines for the tram 21:31 531-311
of data was also a. factor 1mm}: n21: msitafzad 1,231: pmligzxixmtsy tasting;
and 111130 Emily tawny; firms the 13:11:11 were actually obtaining €211.11 for
the I‘éflé‘a‘zmh pmject. See F1332 10 for “’11: field 3:111 receivim; instal-
lation: .

The field. 1:1.11‘12111La‘sion 0:115:13 11:13. of? 31131213; the cavern-3&3. mama"

31.1.»:123115 and spa-118.1. 11:31:13.3; brwzets above the mafimy. The brackets

W‘Q elmacd r' 33.1" 3 to the batter: flag-3 of an exterior hem of the

23

Figure 10: Office and field equipment installations.

~. ..._ 1,...

 

_—___:._.. __

 

 

 

Recording Equipment: Recording devices are of three types;
Two volume-density, one twenty—pen, and two speed recorders.
Oable behind equipment is a Bell Telephone line used for
transmitting data from field (one mile distant) to office.

If‘ s I
4 - .
. .
u- 45. .u‘!
_ . ’ ‘ ' ‘fiu‘ I.. a I‘

a ...... 3". rg‘“ _-. ~ 7
' '1“, ,_-
' ‘ \l; 3' ‘—._

‘-—,

‘ ‘
W.-

er‘

.‘-c.

Fql‘:« _‘

 

 

 

Lonyo Bridge Location: View shows overhead vehicle
detectors on downstream side of bridge. Speed detectors
are in the shadows. The detecting devices were not

readily discernible when approaching the bridge and did
not affect the traffic flow in any way.

‘72.
*0

steel hem bridge. file Speed deflectors were placed in a similar manner
at first until extensive testing finally yielded data that‘vas satie-
i‘ectory when the detectors were near the ground. This mate it secret-33am
to enclose the speed detectors so that they would not be discernible from
the traveled.roadwayu The enclosure was s.box with an Opening in one
side Just large enough for the detector to emit and receive its impulses.
The box.was then Located.approximstely 30 inches above the ground and
eight feet fran the side 0:? the mad. With all equilment installed
and tested.for satisfactory'eperstion, it was then assumed that the
data oollected.uould be the best.possible'becanse it would be void.of
most human errors. See Figure 11 for speed detector mounting.

The date that was collected‘oy the detectors would not be
caxplete with just one set up. This was due to equipment limitation.
The radar Speed detector could'be adJusted to discern individual cars
‘in.one lane of trafric. However, only two speed.detectors were avail~
able for the three-lane highway; This.mesnt that the information desired
for each car (speed snd.spacing) sould.hsve to be obtained in steps.
The first stop was to secure the Speed and.spscina data (includes volume)
for lanes 1 and 3 and.spscing (includes volume) only'on lane 2. ‘When
this had! been canpleted, the speed cqaimmt was moved so that speeds
vere detected in lane 3 by one detector and in lanes 2 and 3 by the
other detector. By snfiatrscting the speeds recorded in lane 3 frcm the

speeds of 2 and 3, the speeds of lane 2 were then discernible.

25

.othmoaocm Non wca wcfipCSCE honoopmv vmwmo

 

 

.wcfiac308 Aopooumv voomm vcm uaoupnoo h va>aaaocom

.thpoopom vwonuo>o w:«
van a
you gopoa puma raw maoup:oo hpu>apamWWm

 

 

J: 2&2 1 i 1 J

as

fin—

Date. Cellec tel:

 

It would be Emcee ble to say that the data collected was emu
plate-213* void of emcee, but it was 088de that the instmnt errors
we min-or . The ahead detec tore were ace-mete to -_+_ 2 12:93.1 for all
Speeds, which 1.»: better time Olcott's method of speed detectioa which
1153 magma ace-hwy, éegemm 1am the epoefl of the veificlee (the
greater the speed the larger the career) . The overheafl detectors were
cagpehle of fleet gushing care tint Mai as litile as; sis: feet hearlmy.
file ream were cmflfl 11-32031 and be int-emitted ue accurat ely as the
detec Tera could detect .

In obtaining; data for this etufiy, it m desirable to take
333131ch 6mi4t3 perioés of peak traffic flaw or, in other writs , have
sufficient when to came a @creue in speed and an increase in
density, than proclmizxg a teasing m of 1:11.. 21:: . Since the (letecting
unite were :mmrteai an the inbound. traffic law: , the peak flaw of traffic
would be in the naming; A tine was selected to 11le time peak flow
of traffic end with flow cmditiom Just prior and mediately following
the peak. Fm mhme comt recordis obtained from the City of Detmit,
Dagmrhneht an? Streets and Tire-31¢, the time of 62% mm». was eelectai
an the starting point and 8sz am. ae- the mix: point. The 13303512) of
traffic generally occurred between these times.

All 6312; gathered for tide study were chaise-flied by one minute
inter-mu. The belief has alxm'e been to use smwlee of flats. taken at

five «minute or longer tear-ale. It in the belie-1’ of this manor that

with valuable infer ' tie): has been lost 61m '03 (Lemming effect camel
by averaging data We:- a '1 he #3131136 pence. This is because (hiring any
given five-udnute smiple 01 data, the ext: €12.03 could. 0: 241‘ “01.1., M
were”, they mild be hast.

The (nth-e inetellapien or. equ. giant we: Law-met more desirable
new Ulcott'e or Keenan’s ..1 Gloott collected his data in a. tunnel with
his oheem‘ere aa‘ifiecent to the 1m of traffic . The weavers were mn-
131110311 ed and this rarely ocwm; hence, it aw have heel sane enact
upon the ("1112623. 0.13:. hex: 1:121 11111111 3 1113021.; r—lixs-e 83:15.1 rile-e 111p aezze ably
1:1an 9.»:“05‘ e the permeet. This ”as. 311‘ tclJ heal ease ei’ feet upon
émivers as arivers freer “spec-sit traps” and tend to else than as new: as
they see it. Hammer-,1 the (genie-event used in 131113 813111;; was very hard
ta Glace-m. SLY-1e overheei 2w detectocs were reamed above the weave}:-
or: the far side of the bridge and. were not vie i‘hle to the 61.23.131- until
8.1" tar he had passed mule? than. The 313312.11 mtec‘l'ere, as maritime:
earlier, were manta-<1 in a. box and pagitionecl 021'" 1 the 211113;; 7.1;; 11-: 11323.-

tely eight feet. The box did not here the mewmce 01‘ being related
to a £39661 train; hence, there was no effect upon the Life13 {hie

2121133111111; equipment was a 1122:.th meimlation, aggrozizmtely th'; ~i‘3uz'ths-

1

of a 1:11.”.13 5mg"- This means that. tum 13.3 non ecle “ obecrxetrs ”’ the

E

field. With this tyge 01’ mainlletion, 1b was t‘imwght to be the best
”101163.013 ior collec ting-w with accurately 3:1-u. vi. 1121 the least effect upon,
the 11:13.11" 16.
The mjority 031:9)?" class at tidied let-we driven by pcqple writing; it
2 12:41 Detmit. It. 1m,me"e1ove, use med Mat nmt arrive: ‘3 vaulti

be i‘millar with the bid?

23

The posted speed. 11111.12: for the Ford Rmressuw are 5'5 mm: Mum
ond ho mph minimum "men conditions permit”. Tractor-trailer units and
buses were restricted. to Operating only on the outside Lone. However,
this as not My canned with as an occasional tnmk or bus would
be in the center lane mains 8W trucks in the outer lane. The
umber of trucks or buses observed on the inner lane was negligible
due to the high speed of the lane, the fact of a. 1‘15 mph maxim speed
limit for trucks, find “.190 the lav restricting their use to the outer

Ime .
gear; of 1113,1315:

In the past, many analyses have been made on speed, volume, and
density data with results being; partly linear and per-rtly curvilinear
relationships . Sane or? the questions that have been asked. regarding the
sigzii‘icahce of relationships have not been wavered. One question is:
that is the significance or We entirely different relationships for
one set 0:? data? Therefore, which relation is more aimificantu
critical flow where congestion prevuls or now-critical flaw where
flow is relatively free? Mthexmore, one might ask, vhat is critical
flow or m1: is non-critical flow? I: the-re o. GTE?! area between criti-
cal flow and mn—criticxl flow and can it. be dei‘ined?

This analysis will be made on the basis of determining I. linear
relationship for data in the non-critical flow area and then with the
aid. of this relation detemine the dividing line or area. between
critical flow aid non-critical flow.

The main steps in the analysis of the (lam canals Led of calculam
ting several statistics, making a chronolcgjical plot of data, ma. than
mating. to correlate the two into t set of loficu defletions. This will
be time for each lane ai‘ fists. and than for a ambled lane analysis.

The first stag, (:3.chth the satisfies, imolved the develoy-
ment of a correlation tables which Show. n'unex'lcally as well as awh-
ically the the-way dis tri‘euthm of apeea-wolune, speed-(lensity, and
volume-density. The table produced the £01le statistics needed in
the analysis: 11 (amber of data. Web?! (the am cf the ‘1 values),
are (the am of all Y2 valueshix (the sun of the x mluas),§X2 (the sum
or all :2 mum), mix: (the procmct mm of all 1 times I values).
The times of but lea used and diamante-d New atlas are found in
Figures 32, 33, and 31; in the Appendix.

Once the move-listed statistics were calculated, other statistics
and test thereof were made. The first. tan values dctemined we the
means for X and I data. These are given in Tables 1 through it as i and
Y. The means were calculatecl by the equations

i a XD + {fix/~26)!
am! f; 3 7;, + {'1 Y/Nji'y-
fixer-e X0 and Y0 are estimates of fend f and mere 1; and 1x - the
clam interval.
The next statistic ta be calculated was the £3le35: of the regression.

This is the value shat-m in the Tables 1 among!) k as nS/x' This value

we ob gained from the equation
m A .. it... NQXY) " (@062 Y/
y/x "' " - a L
‘X ”(l X ) - (fix)
The cmfl‘idence 1mm“ f0? the Slopes of the regressions were determined
by the agent uion

94,12 ; '7'“).
W '5‘“? Sb :2: SV/x / 3x 1W
given sy/x a the atmziard error 0'? estimate (see Page 52)
St -= the standard dmdation in X direction
and where tx/gm-F: e I value obtained fmn Table 3 of Crav3
The purpose of the slime ccmfiimce limits is to determine whether the
siege 33/3 is a valid actuate for the regression.
Regressions are determined so that an analytical relationship my
be obtained. The relat 101133: 11) is hgqcomesized to be linear b’t 18
teeter). for lincuity by the F-linesrity test.
The Folinearlty teat indicates the relative linearity of data.

The F test was made with the equation

Fm”. A” (M’kl

IV (1": ’1’)
wéar‘e/W '3 C " W’

I z NéXV)1
C = F?“ “ $77 ]’

cm? “I: (.jEiY w€(é)iz/§n)

i

9‘
)g

L0
H

Calculation: of the F valtm stwuld be 1.. nos thant he 9972 level to be
accepted. Values of 1" larger than the 9579 level would be rejected, but
this bit of information is Just as word. w it helpn explain the
relation as much as weep tabla? values. If the F—linearuty test is
rejected, a. new lower when? line will be used arm a raucalculation made.
this will be rcgjeated until an acceptable F toot is none.

Heart is the calculation of the correlation coefficient. This
calculation is uoed to L3.E:’f.I-€ll“.'413.‘ 1e whether the regress ion coe “’ficient is
aiglii‘icantky non—zero. The null Emmi-moon is tested; that 13, it is
believed tit at t; to ecmession coefficient is zero. The «nation mad

for determining the correlation coog‘ficlnnt is

,4 _._; A/z'xy -- (zx){2Y) __
“Tl/LNZ’XZ -:(2x)2! ysz— (2 V) 3

w
‘p-

15: resulting r values are larger than the 93% level values, the hypo-
thesis is resected. and. t can ts. on be said. that the coefficient is
significantly non-2.62m. The closer the value 01‘“ r to l, in general,
the g: ter the significance of nonwzem and correlation of Y on X.
hm the r Wession coal: iciont sqwedura-«it may be soon that the
remasion of I on X accounts for (1'2 x100) per cent. or the variance
of Y. The larger (me pe centage the better the explmabion of Y on X.
The last statistic used in the mmlysis 13 the stanémfl error of

estimate which dctezmnos the scatter, in the ordinate (Y) deviation,

of the 93:22.;- .red pants about the r3131 32:31:13 11.33. T213... 2:13;, be 21313121335.

by either the equation

.' ' E
S .. 'éxzzyz -- (2x201
5/ ..-. ....
A ?/ (AW-Z) 21x2

or 12316: equation

 

n (3113112. “‘2: 01‘ Y 2312233
and £7 : st " G 21:13....11 of Y values

A large val .ue of ream; 63:23 13 more 2112wa scattered, whereas a

322/2:

mall Sy/x 1122112232223 the 213222 to be relw Avek’y cloae to the reg). esaion

line; 32221, as far as 2:122:22. 17.1.02: 13 concernei, small values of Sy/x

32": 11.03236 2122511 .2113 gee-228.2152: thia 5.1.0 .121 1111109. oe re ”1321.231; smooth—11Wim;

traffic. It is inter; 22101:. 2.0 1.102: 232232: cues the 222231.202: of Gaga and

large error 9'3 2:524 :2. The qmtity 311:2 ea’iuates that part of t.-e
2.1mm 011‘ I left Lmezrplaima‘d by the rear 325:: on 01" Y on X.

Tm statistics calcm’oefi winch pm'allel the ataudm'd error of
3521.131221- ure the 32322515. 622213121321. for 2.112 X 3221‘! area-21035. I‘m-.23
are 51 ren by the 3211321033

Sy- X’szz M...(_éy)z:
-/ ”(~~U

 

 

5 ,2 W/W/Ui ><"Z -; (2 UL-

33

The squared values, $32 and 832, we the variances and may be used. in
the second eqxntian given for the atanflazd error of esti'aaise. The
standard. deviations indicate the relative scatter of data may be
correlated to the type of flow.

the second step in the analysis is the making 02‘ the chronological
plot of data. This is a successive plot of data. from the beginning of
the study period to the eml. The plot is made by taking two pairs of
data m5. locating than on a graph and then Grazing an arrow between
than indicatm which :2ch first accordjmg no time. To help dis-
121123211911 data in critical flow fi'om non-critical flow, the points and
arms are show: in rcfi. The cutoff line is 32mm. in blue. The
chronological plot gives an illustration of some of the statistics
calculated in step one. The clnmologgical plot will also help to point
out the difference hem-an data in critical and arm-critical flow.

The correlation 01' flats and logical deductions 1111.1 @133 tbs
chapters on ”Analysis oi." Data", "Same 15132133311231 Relatiomshipa of

Traffic Flow on a. Fromm", and the "Conclwim".

mm Iv
MIALYSIS OF FIELD mm

Analysis of .Qpceda‘y'olzme Relationehigi

Speeds used in the regression analysis were limited to those above
1:1) minutiae 34.0 mph line being the dividing; line between non-critical flow
and critical flow. Critical flow is that Mia-meat of vehicles which
occurs then too many vehicles are operating such that lane changing and
passing are restricted and apeerla are, therefore, necessarily reduced.
Ron-critical flow is that claimant of mflclce which allows lane changfing
and. passing; as (lee irerl. Therc is one speed—mime line in Plan-e 12
which cmseen the critical speed line with the renaming speed-volmnc
lines in this critical area. and they emerge. to be very erratic in
occunence.

The chronological plot of data also gives an imlication to a
greater range in speeds in the critical flow was as co'maced to the
non-critical flow. The latter region of flow has a range of six mph
while the critical region of flow has a range of some 31 mph.

Pmalklimg; this line of thowfixt is a coaszpafiwn of average speed.
charges . Average speed increases per (me-minute intem‘al in nonncritical
film: we 1.94 mph wneicas in critical flow, amrace increases are 3-5r3
mph. Average speed decremes are, respectively, 1.7? mph as caipma
with 15.113 mph. Toe stamii'icancc of this camarieon is that changes in
cocoa. $151 volmze are more pzmmmccd in the critical flow and, thus ,
reflect increases in internal friction to such a degree tint it became

difficult for the traffic stream to overcome this internal friction.

3x.

 

 

 

1131mm: , when the 1"le tua‘izion in speed is less pzmmced, as is
illustrated.1n Figure 13; the gape: at affect of further congestion is
not present and small increases in internal friction are soon dissipated
and the. lane speed soon mar-eases back into the region of non-critical
flow; Aaarage speed increases and.dacreasea are 2.15 and 1.7fimph for
this lane which compares to volumes found for lane 1 in the region of
rum-critical flaw.

Figura 1'5, Which is o. weed-voltage 1319?. 01' lane 3, 1111»: tra‘braa
data.vhere average apaed.increasea ana decreases, 3.23 analh.lk,
respectively, are similar to thaac of lane 1, but ccqplete cangeaaiou
does not occur w it did in lane 1. This may be due to the fiffarence
in densitiaa‘betmaan lane 1 and 3. Lane 1 has an ave?age density of
61.k vgm,vhich.1a more than twice lane 3's dansity'of 26.7 vgm.
Density in related to heaauay in that headway is the reciprocal of
densitym This means .h t the headway for lane 3 is twice that of
lane 1 and amid, therefore, be more likely to accamodate the large:
flanges in speed with less Effect to traffic flmr in that stream. It
would? therefore, seem Eran this analyaia that danglty, or its
reciprocal-aheaduayu-ia a.mora critical characteristic of the three
being studied.

Far each of the three miles , regression analyses were also made
1n.ordar to determine an analytical relationship between the two

chwacteriatica .

 

 

 

 

_
A
.
b
.
_
4 ‘
r

-Y‘ , !_
l

 

 

 

Values for the slopes of the regression line for lane 1 were
(40.17 md (-00.13; "for lane 2, (40.2.7 and (3)101; and for lane 3,
(-30.27 and (-40.23. A cucnlatlon of the 93,3 com'iamce units for

Jane 1 ix‘fiicate @111; all the $109.29 lie v1 1.12.111 the 11:11.19 weal->1: for

the 1mm 2 Friany data. winch bad 23 positive slaps. fizeme limits are:
4.32 < m < -o:2 for 18112 1 and 43.129 < m < «3.35 for lane 3. The
significance of the cozu’iannca limits is that may 93101.! that the slopes
of all but one 01" the regnsaion lino-s lie 1211111511 {are 95235 confidence
limits.

It is the author '6 bell-:21" that the Immune slope for the apeed~
VOllIJLG relatioros‘fdp of lane 2 occut'reo. by chance and. not by a nomal
dishi‘oution of data. The 1:12. 61 of: the line mdor normal circms'ma
3:113 Wen that @143 slope of the reyession is negative. This can be
m'mwr substantiated because 0;? the may fan-tom which 111111161199 13211:
relationship such as the increase in internal friction as mime
increases; or as volme increases, density increases; or as density
increase-35 , speed dmreascs 3 and as speed increases, the deg: ired headway
increases. See Figure 111 for plot of data.

Theseiore, excludim; the Luna 2 regression fmm this analysis,
it can be said that :11 regression slopes are satisfactory and for
lane l we slope is qrproxima‘belcy 0.172, «0.231 for lama 2, and 0.232
for late 3.

Each of the mggressions were tested for linearity of relationships .

The results of this test inCdcated at the 95"}; level them was no basis

14].

for rejecting we hjmotheais tint the remtimshi'a of speed-mlmle um.
linear. Tue rem {:3 of the: F»linemrity test and the values of F at; the
95;: level are 52mm in Table l. The maul-“s anther inc‘zicate that;

there 13 some has is for saying that speed and mime are linearly" relay-25.
in the area. of non-critical 381m: all-£3. not in the ems. 0:? critical flow.

The he in:- Wic‘n points out the previc-zw aquarium is file cinnam-
logical plot of speedwolmme (Ema for lane 1 . This plot indicates guts
forcefully the need to handle the critical flaw by itself and wt to
group» 11; with all the 6333. with 3.1138211: 01‘ 1:1qu to fit mat we
regreasicm ‘00 it. Th wafer-e, treating file data. separately, we can say
flat the area of non-er: tics; flow is linear and a 'bem‘iency for critical
flow to be non-linear.

The square of the comrclation coefficient as determined do mt offer
too much help in emwning the valence of Y on X. 0:113,' 03% of the
regression of Y on X is ewlaflled by tile- analy‘sis . I’mmver, the null
mmtheaia that the population of weeds and 'mlmes has. 2. 2:0 cor»
relation was rejecteé in afll cases except lane 2 much had. the positiwe
slope. It; is siwii‘icanfc that there 13 some comelation awn-m thougfil
the r2 percentage for each mammals is relatively law.

The next items to be tes ted. were the sthfi émriatiom for awed
and. volume and stanflmfl error 0.: estirmte. Stamé’aré deviations of
volmze for Lane 1 mtg-e fmn 2.11 to 2. "1'3 with a. com‘ic‘lenca intern}. o:
1.63 < Bx < 2. 8h . Steward dun-muons of trolwme for lane 2 range Em

2.02 to 2.08 with a confidence intem'al of 1.96 < sx < 2.79. Ami, the:

_ H _.z ..I. 51 c _ ... _ is”... flush. \six‘fianm

WgJ

em ~VC'ZAEE 11114121021 SIA‘Z‘E'IIJB

arm“ 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

mums W} 1 ME 2 .. w 3 1
__ 11m 1111 * 15.13 11 my: 111m: 1791
H 30 1+7 (.3 G) 2.9 56
i’ 25.7 28.1; 30.8 32.0 113.1 23.9
{1 113.0 1.8.0 1.1.3 1.5.1:. 1.3.1. 1.11.1
1113/: 41.179 41.1.66 «9.231 0.013 4?. 41.2.31
c LL76 52.7 511.6 116.1 1:3... 1.9.2
I 0.355 0.035 1.07 1.05 1.03. 0.2.2.1
{)5 2.11.2 2.11 2.02 2.03 2.23 2.22
_ 1'. 43.621 .0523 43.632 0.9213 41.630 41.9-1.
f ) 0231.9 0.232 0.215 0.230 0.2425 A 0.235
51/215322 1.98 1.37 1.31 1.11 1.3)
115m? 0.623 3.91 1.83 1.72 1.21. 1.3.2.
A a, 0.507 0.866 0.13.5 1.02 om 0.37:;
8; 2.11 2.73 2.30 2.55 1.91 19.
71mm A ...... ...... -..: -... ...... ......

 

I."

l.

l .l a .v 6
I’ I .‘ 'D.’
o
'I.‘ 1,- I I. -1
O l I fit. I

0*- O I.
n n A o \.

ll"|.

h3

onward deviations or vcmne 1‘01:- lane 3 were fun 1.91 to 1.931 with
a confidence Later-ml of 1. 590 < 51‘ < 2.39. The smficwce of this
detezmination is that the confidence intem'al of lanes 1 91m 2 indicafisec
13115:: the standard deviations of volxme for merge lanes are within the
confidence limits of how lanes; and that. each standmffl cleviafiian could
be a valid estimate of the other. The confidence limits of lane 3
indicate that the estimate or stamitac‘d deviation of either lane 1. or 2
Wald not. necessarily imlica‘T-x the standard ficviation of lane 3 . This,
however , should follow as the wastage and range of volume values for
lanes 1 mad 2 are much different 1mm those oi.“ lane 3.

The B'bandmfl error of eating-hes rmge 1m 0.8-2 to 1.97 with all
values being larger than their respective a tanflaxd deviation for the
Y directim. This would intimate was the actual deviation in the Y
direction is less than the estimate of error about the rcgcccsion 1n
the Y direction. This umld be a. result of a greater variance in the
X value or volume values . I

One filing that should be 1101266. in the cm‘onologflcnl plot of weed-
volme (13123 is the fact. that critical flow (congestion) does not alvagm
occur mediacely following peak flow. There is sane Clem after peak
non-critical flow before 001 #9331011 occurs. This can be seen in
Flame 8. mrthenwzc, 13cc}: minute volmcs do not necessarily ocwr
in non-critical flow but. are mare likely to occur dwing critic-a1 flow
when speeds are between 35 and k-O mph for Lanes 1 and 2 and 30 to 35 mph
for lane 3. Flame 1 and Flame ’1 also Meats: that critical flow

occarrcd. on lanes 1 mi 2 1.11m the speeds were less than 145 mph mm 1.1m

'\

1.02.0003 1.21.00 1:01: 3.) '3: .3 1' 1 4110". 00 001' :11 0.- * .10. L000 3 has: 01:..ju-zly
(13.530.110.211. 0110:1100 11'. 1.11.201; the 1.011.110 10.14:: 110.0 1'10: 15 0:) 2i} '30‘151-100
1:10;“.le “:1“- e.

F 1. 3.1008 13 11.1. mg.) l) 13-.” 1.11131: 00' .0 03:0 1.20:2..1‘10210 11:30.03 01‘ 1.2.0.210.

High 30.3. 101: 2.1010105 , 111.311 0.03:. low 6.12:2..;lt._:r, 011:. high 3.11 low 11133354313 .

1.- ' ., .1' m! e. - .w‘ . :_...-
5.32.1... ’31:; 0.. 300:2. - 012...... .‘* P010...-10:.'-;--.2.**23
”.-..J‘u. “ ~ ._ A

——.——'

 

Q)

50000.3 “3% 0:20 imatefl as- 0011-0113100]. 83.0.5.5. 1.43 mph 01 :1 as 01*]. Ric-0':
b01013 L) :00 for 1:12. amalamluue cud 0*- 0:~.1-...:0. 1 :3; 0:31.013 . This 0211;»-
oi‘f 11.110 3213—; be 000.0 13.1 Fig-.1220 233 Which 1:3 8 .03}: 20.10.0115. .3; p13. 0310.10 1..

In 10.10 01112311011) 4.1001 313.32: 0... 1.21.; 129-12114“... i 3."; {11500, 1.3.1 1 0.30 0-.
the 310 .100 1.75.00 02. 0.10 01100.73. for: 6.0 0.1211104; 21-1-1; 1* 0.1. .101. 0:11 21:1-

t

critic a]. {100' r 3;; 33. :03. 3.23. a 8”":‘2‘31323 0:.“ 011001-60 0. 1‘3; 1.4.3.030 b12101: 51.3 2:03.71

Q *1 a our-.‘n'u' w . 7’." -Hu 8 4 --.- . _ " _'_ . ”‘4‘ . “. '
8&0» 3.1.0"; 8 a (wing-11.0; O... ’1‘) Vt;.'ll£.l£.3d p23}. 10:: 41.4.1.5 8:22.18.) 01 31:01:13.3 1701::

1212-52 tee-.251 0.0 b21125 {201:1 *100 1:: 0731 01.00.]. “‘- 10:: 0.3 12030 tin-30 003.003 1.0101!
1:2.) 3:931 in the 5;)... 2- 3~t1~2=01 .1'20 "2.1.013. This is the 003.2100 0.2:" I *0 11110:: 00.07::
on F132“: 23.

In thifl plot of "“38 f 3: lane 1, as in the 0100014011010 plot, the
rings-:0 spec” ...-:3 is an 110110001011 of the we of 131.00. The range in
mun-0:; “iti .01 £1.00: in 01.2: mph v.2 1:110 the range in 0.101031 flow is 33. 1:22:21.
The range of (lanai-ties 13 35 1.3221 for mn'l-cx'itical flow to 57 2.0011 for
critical 1100. N: at only is the me in 6.011121%w ..J 1114:1010 cri+ical
flow, but. than aremge minute 02 19:1.“0 in 020.010" is also greater. The
800120.30 0.11.3113 1410212100 in 1200-011tical flaw is 7.73 V1012 711110 112
011110011ch it is 10.115 m. The 0.02830 cit-11.010: chem-axe in non-
critical flaw is: 7.5!: 1:123 while in critic 311911.210 *"10 rig-00.30 is
13.3.13 qr. 11.1000013'0 31+ and 7:31,» 111000800 1.1 we dmmity 02101500 in

a.

01101001110011113 1.115203 at s. c..*ri-‘...I.:;0l :10 clay o; 5311, a

1+5
Figure 16: Illustrations of varying densities.

F-b --—-——--—.‘—-_—— _ - - -

 

 

Light Volume, Light Density. Edsel Ford Expressway,
Detroit. View is looking West, upstream.

 

 

 

 

High Volume, High Density. Edsel Ford Expressway,
Detroit. Traffic is approaching critical flow conditions.
View is looking West, upstream.

A6
Figure 17: Illustrations of varying densities.

 

 

 

High Density, Low Volume, Low Speed. Edsel Ford

Expressway, Detroit. Note the headway caused by the truck
in relation to other vehicles.

 

 

High Density, Low volume, Low Speed. Edsel Ford
ExPressway, Detroit. Note the bus in lane two and the
headways caused by it in relation to other vehicles.

 

b7

Figure 188 Illustrations of varying densities.

 

 

 

Density: Edsel Ford Expressway, Detroit. Note the
denSLty in lane two. Traffic is free flowing and
average speed is approximately AS MPH.

 

 

 

 

 

Density: Density in lanes two and three have reached an
operating maximum and traffic is forced to reduce its
speed to zero for short periods of time.

 

[4?
Figure 19: Illustrations of small headways at high speeds.

 

 

 

 

Headway: Edsel Ford Expressway, Detroit. Note the
minimum headway between these cars, actually less than
twenty feet, at speeds between 50 and 60 MPH. Time
spacing of these cars is approximately 0.5 seconds.

 

 

Headway: Edsel Ford EXpressway, Detroit. Note the
minimum headway between these cars, actually less than
25 feet at speeds between 50 and 60 MPH in both lanes.
Car in the center lens has little effect on spacing.

 

 

 

 

 

 

 

52

1.0.16 vim increase reduces the he ”may per vehicle from 96 feet to 80.7
feet. This is almst a car length rmtion in healing,- for the average
dens ity chaage. Roaster, the :wacimum density chaise was .1113 a density
or 63 vpm to a density of 1.03.5 rpm-4 1.0.5 1:pr density was»;

This is a. decrease in hammer from 88 feet to 52.7 feet. Such density
charges could not take place at higher speedsuthis occ 'rred at 13

mph, due to drivers‘ desired the headway between can-s. At 13 mph, the
this 12359333 is 1.99 seconds which is close to the tare-second headway
that is mmlly consi flexed as average . The maximum density attained

, was 11]. vgxa or e. heating; 01" 1.17.6 feet.

It shy-11d be nosed. that; the chronological plot of data indicates
that maxtmss density does not occur with mirmmm spec. .,

It was pointed out in the speed-volume analys is that with 32.2811
chances in speed there was little affect on tit-5131c ilow in tne criti-
cal flow area. This is also true in the speed Mai-by relationships.

It can be seen in Figure 21, for lane 2, that there are only a few

points in the below is“) mph and shove 55 vpn group. The speed chmge and.
density changes are similar to those of lane 1 for critical flow. Awewme
dens ty increases in critical flow are 7.1 ups with decreases being 3.3
m. In non-critical flow, the average dmity increase is 9.2 1:121

vi an average decreases being 7.8 m. This is not a significant
difference heme-en critical flow and nan-critical ilow.

A look at F1312? 22, lane 3's speed-dweity plot, gives a swimmer,

different picture of the missions-snip. The critical speed line of hi) mph

8851311315138 3 51321111313 of 1101.11.33 in the critical 1101; 31:23 1. 1.31.1132: 11112-1
cities lee-‘13 flaw £212 5'5 11:19.3 c: ifiical 6.3131113! of." lane 1,111 all instances
except one 113123.12 the 13.2132 113‘; is 53.1 1.1.1. $335.11 series of pain-1.1.1.1. meld.
inflicate that for tide 1.31:2 critical r 11111211133; should be less than 53 V‘pill.
The plotted data in-i'lcat .23 that be tween 30 to 35 1m is the critical
(Imity area. Farther-mm, it can be seen in 3111311319.... ”1‘ that ilmztuatimm
in density are greater in to. area rm 31) 1.111;: and up than in the non-
cri ticel flow 1112;113:111.

F1311- eech 0.1" the t2 112.12 13.12.15, 2.183111111111101 3.2.3.3623 1.12:2 3113.313
01-51311 to 6.21.. e an 3.211331131111231 31131311011133.1119 b2 31:22.13 the speed mi.

2.211113; chmazztc: 3:32:31.

Val-236113 for the 61.73-17.18 of 1112.11133312113503 lie-e for lane 1. are

H 0.1311 1.11111 M 0.13:; :01.» lane 2, () 0.21.11 1.1.1.1 M 0.31:); am: for

Lane 3, ( -) 0.3.. and ( ) 0.110% A calmnetion of the 95-} confidence

...:

5:114:13 1' 0 lane 1 indicate that all the 6103:1873 lie vi 13111.3 the 11311321313 .

‘1

The limits are (-) 0.?19<m <(-) 0.053. Cale 31.1.1.1“. 1.0113 for the 03.1.3:-
lenes give 1:. ts which 3.111.: alcazpws all of the calculated 510512.11; .
This 1.1313111 imply, 1.11313, that any silage could be a: eetirmte of the
31292 of the regreeszim line far the speed-61.212.131.213 relatirm. See
Table 2 for these 311:1 other statistics.

One thing mat is pointed out: in Le r23:2.s..0n calculations is
the flats; 10:: lanes 1 md 3 Vickie-:3. a reject: an 1.1 the 31—11111 2.111.121.1133; test
when all densities; were 13.131311. Densities went as 2110.1 as 105 11.51:: in

lane 1 and 72 11pm tor lane 3. A cutoff at 63 13:11 1112.3 used ior Lane 1's

‘IABZI. 2

5PM "" '--D'.-.‘IISIT£ R117 '"I'Oi‘l’ WEETZCS

LAKE P.

 

 

 

..5 “2:: 93.11:; 5-7.1 4W PEI
I! 31 L1; "f5 “6‘4 ':’3 T3
'1' ’- ... ,. , ... .
a. 3.5.3 35,1 215.0 55.3 93.7 223.7

 

153.73

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

331/}: 41.125. 5150 43.2?1 .5310 3.32:3 “3.52:2? :
C “-1 5'3 ,5 37.2. 55.4; 1,; . .5 53. 3
_ 2» W 0.122 1.55 0.15131 142,35 1.75 1.33;

:2" 2.31 1. :2 2.03 1.5).; 22.5,; 31;)-
5 .95 L M

r ~0 .5553:- «35.1315 ' 4) . {31; -0 . 5;;3 -0 . {25-5 «3 . s , -

r5 0»3:’~:) 0.3313 0.22:; 0.2233 0.22;; 0 32:;

“IT/X. 1.2{2 153:1: 1.2: 1‘...‘i;.3, 3,5;3 1‘35

Sac/x2 1.515 33.3.2 1.24:5 :33 12.02 1.3-2

31' 0.61;;2 0.".‘1'3 1.3353 2.15;: 1.5.2 155
‘— 53 12”...“ 1 2.1.35.5 2.1.5 2&0 3.721;. 135

can? 55 5 5 5

 

 

 

 

\‘1
U1

'0)...

second. trial 1' .25}; 891-31011 cachLLa 1.1021. 2 :13 also was :egected by: the: Fe
leea2'i'FLy test. A 8:11:40. ‘inzfi. (:FilClfiA'LiQfl 1cm; 22:22:18 21:11:11: a, 8121:0233 a:
35 (35:1. The F-lineazi 1':;:,.* 1:88 ‘L 2:212: 388312301 Ls "big-8. The first trial
18 .....3 gum: calculLaLion *- ”'13:: lane 3 was 2.5218 1.1433233 9.5L éowiries but. was
reimt:.:<1. The 11:22:: trial was 3226.12 at. a cums: o.“ 5 3 231.3, which was
arcL 9.421211. the F linc 8318;; ”ta-23's.

,

Because lair-.2: 1's T112335

r

33;] and FTiJay (12:83 88:38 qui ta similar, it
was belt“ .23 that the" um: 3222:; data should also 511. v6 some malice. Lion

as to tt 8 possible critical $22.... ‘53 01‘ 55 mm. In the :-'.‘i “at calculni. ion
0:39.11 Line 231.23.: ‘13:. ' ics 1302:1838 1 on '31: 12623;], all of the 153:5». were med.
T111. maul .1ng F-linaeu-i by test was acacia-table“)... 2314 calcula. ..in with Lac
9351‘} level of ”septa-ace hem-3 Lu). {113.8 correladon co---1Li ..m‘; cal-
culated b.) be 2' =1"- -.QOT with r2 2 .329. When time data. was rte-used with
c c...o-: at 53 V1112 , 7:128 result: " were differs-re: 'L. '1" 1.. F-lfi: 88:. 1:}; test
yielucd an Weepable ”81.12 a O 121:”) vi'Lh 3. 95,11 level a: acceptazma
equal to 2.37. This result inflame-.3 531.13.. $13.5 :33 L9. 113... a. 33:823.th 2:18;, 1:82:
of linear: 33* than 211m all 6:21-7:13 were used. ibis fact 116-le8 ‘30 point. out
that $12,615 sag—22 change in the: relationship oi spa-61.. and density for

values above 55 rpm. However, the s tat 1:21:18 coefficient 0'. coz’r'ela Lion,

vixi cu usplaizls the ‘a'z‘iation of Y on X is less 9 for " we calcmLaLions using

the 53 5'95: cu‘bogfi‘ that: 1'10 ‘ 1:218 cal culaticms "1.1leij 9.11 11:10 clam. The
effic 19111: of cow“. elation for SS vpn mtofz'.‘ is r = -0. E1932 nth r2 = 0.1.31

’3 3‘ .,. . 1 .
”(1,3011 3]] 33-53, r a 40.533? with 1'“ = 0. 51-12. lame results ii'uhcate that

the 1.3mm ca of Y on X is explained more 11:31:33.8 sLll Lia La were used than

56

3.521.:82'13 (1.3.133. were cut 037‘: 8:”. 8 (3.4.3.8 03'3‘15'32. T118 '1. 33.39.383.38; thin;

that is indicatefi.by 888 calculations is that there 23 8088 reason to
88.1.1818 that 830:8 55 21:3 ti .18 3818818888179 0111' 8:38.28. 82.1.1 (1811.335 ‘1131‘1‘3123.
T1888 facts, along with tan 88813813 0: the chragological.plot, give

a mod indicacian that. ti:8 8': 81883. 85:88 0': 8.1;. 881331;; 7/ 18:: 5.1531 9331 'cat;':.

The 311.388 188.513: .; 331:“?! were “8128 standard (183338810138 of 8138 ed 8:13.
(3.2218183. The 68831133351 6.1? 13181883 of...p1;-'.-8d for lane 1 3.3838 0.6552",
3.32:2,2 and o. 73.3 2:581: cozzz'iL-zeme 12:282-181.. 0: - .525 < 83, < 0.836,

3.05 4 8.), < 5.222, and. 0.33:: (L s}. < o. 935', 3'8 581.: ~~.:5. 55::- first
two data 83:8 for Tum'sé‘uxy. Tue first 01" the—3:38 13:10 is for the cutoff
at 53 3.3.1.3 and is the 388-308 for 8818.3 so much mailer. The 5.13....«1 (3.888321
18 for Friday and. is 53311183 to Thursday as it was ca’imflawcl for a
cutoff of 53 2:321 5180.

The 888:: 8.89:1 881.131.10.33 of 38881-1? .1888 2 speeds are 1.126 and.
2J2 1171+ Li: 8811;118:388 1114:1315. .25 (a “ y< 1.73 and 2.0-3 < Sy<
2.39, “1;...1388 Lively. No cutoji‘o ‘dem 1’3" was used for tigers-.2 8818818818113.

T38 8.8331338 u”"‘.LatlJuJ of 3.388 3 31380.28 are 1.61? and 1.5" with
c ni‘iciance 13.5153 0:.“ 1.39 < 5;; < 1.93 9.21:1 1.35 < 3., < 1.35, respec-
tive ;. T118513 as. e 65.11163? 8 11-33:: tho ugh the 11.8 t 88:13:: is a pz'odact 01
8 auto?" at 5,"; 2.35.1. $15.23 is because the cutoff in'mlv'ed only one 688.221

being; cut 0:1‘.

138mm” "51 ("leviatials :03 1813 e l calculagiazm 31th (1811815183 c: t
oi‘i‘ at 55‘ @231.

.1.
“3588888 ("imdatium 1‘03: 1.13.88 1 calculation 12513.5 all :2... .

The 31.131559 3 219: - sting of. ”1311.35.13; orig-9 1.1;; 1.3.3 1.113;"... 12:21 ' oi.‘
8.131.323.2323 the reiatianamp of speed. and density and 82:22, the-933099, not.
co 99.12223 in this 98111159313

T119. standard error oi est... 2.9.1. as 132' the c‘zmed-dumity rem-.1321
range m 1.23 to 12.5.33. $1.123 10.11.91 5213193923 3 59211321912 8911311979. ' :3 o.“
paints 8.13 more “him likely 1.9.39. correlation 011' data.

T19 902.299.191th 90933191119412 129.129 99.19.119.921 131* 527.1 data 81.- 122229
r 93.1.1193 1:12 .1931 3.19.11.31.22 the 12:29 229111 01 199.2131... 0." I vs 1.11.2193. 117....
V9139; of :- 13111-19 £12311 0.51)], 113 0.323? with 30:3.33913'1211135; r2 values of:
.351 8:13. 331. Tm latter 198,111.33 1.311129; ta 1922': 1'93: 35 to 31:14 of 211-9
13.93.913.132: in Y can be afigflsinai by the variation 01‘ X. ’his pro: raj-fly 1.3
a 3:929. .112; of 2319 [5223-2151912 2399;333:1ng of data. I 191;: 31319113" 3.3133 129.99
cart“. 0:31? at 55 19:1, the per cent of 2m: ' 1:19.11 of Y on X 313.3 1993421131 when
all 213239. 132.929 113.991. Appmxctzately J 16- o: the V8.1 131.1991 99.9 9'9plained
with a. cutoff at 55 vgn but up to 80?: could be ngamcd Using all data.
Table 3 gives all the 31121238 0:." r and Ali-3'3 the 35% level of mcepfmce
for: r. The 2:111:13 135.311 091 all the coefficients 122911991319 9. negative
2202291831011 beam: speed and firmsity. T2113 means that 88 6.921913};

11192993239 9.23, 23110921 (13c ..mus.

58

13.223.132.213 02" Volume 452312251151 ' 151.8 31.322313135

 

 

In the 272:: prar'd-zma 13022123223 of the analysis, 2.13:2: 32:33:32: was mafia
to 333013121 the variation of. 32;: :2 23. 1:3; 23222132331 :13 of .rt:l~.2.2a. and of 6.223.235.4332.
T1115: 312313313 will attempt 12032: 13122 the variabian of VOl‘JILC by the
variation 031‘ (122215 5.135.222 .

'2123 (33.122013010571331. plot of data was 2321.323 2:22.233; 55 3.9221 (2.23 2.1123 11.213
bettmen critical and non-c 1:121:33: flow. F112. 23 23, 212. 3:25. 25 are
plots. of 'mllm a-«immityd .2133 10:: lanes 1, 2., 3221 3, 22...?” 17.5.2313.

In the: plot of min-213 213:2:3 2122225123? 1101' 13.21:: 1'2" 2.232.337] (13.3, 1.112:
3335;: and 11225222331332: of (1.2231133: are 332221.21 an indication that the
1102! 0: 13:33:12: has a. diLf‘ 2222:2123 22.332.323.231" for 632-3233127233 alum 53 2.23:3.
The range in 6:321:3ity for non—critical flow is 3.2 vpzu 3:232 in 02:12in flew
5’! 21:23. 127.22 aver-age increme- anzi decrease in density changes are 10.15
and 13,125 mu, 2:331:32: tirzreLy, for critical flaw. For Imz—critical flaw,
tut: 81'81’36'36 are smallezsr' with val was of 7.713 and 7.6%» 2:113, reageciively.
The: difference in these $32,322.42. 312.2228 some inflation that the flow
crnaz~mta.-. iB‘CiCB are d1: .22.. ant £22322 3202:2231 1.3.924 See paramasrn tiara-a
of tire Azmlyris of fipacd~ ..nsity Relaifionslfips for affiitimzal clans. ty
3213153313 . Em: range-.23 0;" 2:11:31 2.2.3; and the appwant are-3:23.323 1:: 2233.433 322:].
decreases may be seen in Fig *8 23 which help: tr: «322332323 2.33. a 132.13 02‘
212317532121: 21917 c3223.. mun-11:2,“; prevailing 1.21 a: 2.1.23.1 flaw. Tm: £13.23»:
31.230 812.223 the 12:13:21.2: 11212322133? 0'; 2012230 2232.213 (tawny up to 53 23:23.

The 221.2232: in vo mm: is 21-32: too 6:11.233» 2 111 3:71? ical 11m! (3) 2: 3:2)

17.23:: 22034;: 1.2312331 flaw (2’4 2;. .3) , 2202‘ 322-3 23":«9328233012012222a 12123132223222: and

 

 

60

<3“. -';~:2‘88.~3:38 81133-2- 3; 12:1 7281183714... TELLJEEG a: 1'1. 2:- z3.;:=3 32111181211... 8.11.2. 13113132312111.2833 888,
28.2.3338: 3731:1213, 11.13 8.1.2. 15.9- mm 1523. 8121331881. 3711.38. 128 '38 133 31.333238:

1119.2" '11. crui: her-12‘ .18 tat a 8:8 :3 11:21:38 8-3 8:8 18:33: 1.3. 2-2.8 83-1: 1:813:12
12182388888 in critical £138 821318 '8':- 38 11111371123139 in (2.28321881 31.81; are
182-3132- than average deer-228.383 in non—82111311381 $1.332. T2318 “M11134; be 8813:: ed
‘8; 13228 5382211888 2218.812. 5.011 in con- 313:3 1.13 an . Mather '38:; 1301‘ 2..."; ‘38 1.2.8 11812813}
(2218;788:12’3 his 6.1235133123313120: non-critical i’imr 8:33. 83"}. ”3189.1 13.0212. The
21312 critigal flare-2...... 1'": ' 11. ':2 the 81:11.17; 13:) 8.1.1. ".3 1.33888 822381383 by drivers
8: 1:13:52 3.2;; 131.181.1181" 11128338.,8 3.338121 3*, '13:. (.31... 11.1 11.32, i... ‘Z‘C’; 2:38;." 31.32;

«q

u' '.‘1_— 1 1‘“ .I .~ J.-"- .n. f . '1 -. --. . - .
fifif’..,.ai~.j_:1 1112‘. 1%.{.Jfi~l 1? ‘53 {was 3.. 3 3311-319 ($55.71.... Jig. 1“...) ‘-'5.1i~" ’33 5.1L 31:1: '3‘): 01“ 3.1.3..-.9333

..«nl

_ 1
--
.,

v.

I

2.8.13.8 {2’8 1'83.'11238~¢1.21:3.23 p.181; 11:wa YALWS 18:18 8.3 '83 2-3.1); tn... 3:81.8-
1.13""319 83:; 18:38 1‘8 131.82., 1322'}; 2338313 18 a trait? 0'1? the ggcxmral tcnlzmcy.
E'lrj-ii'e 213 813.3213 "" 1.128 121.31”; 133' 18238 2 82.2.3. 11'. (2821 1'28 81:. 88 1.138.: shave e.

'11.: 2'1"; 02'? 5") 79": t...~.-.-1:-. is a *"M‘mfly 1'33" 1.28 8.3818321: of 3111:): w (32.8.1338.
The a '82." ‘8 313.12.: 3.12 858 3.8 C3 5.13:3. .81 23.338 6.112 4L.12 83.3.3 Vgfl fi'm mnocr‘ticai
£1128 1.32118 831938.31?! n-.r~d..1 13 1.3 1.1.385. 3.7 13.881.18.88 .2111 half 8. vs. 31¢ 18 2311.3
mil:..I'12'. 18:83: 8.18:) '12:: 1305213386. out 1182.178 that 1:8 3.233818 822 E: 128-; 3:82-18
F by 1.128 F-li'....:.m"1:1;r v1.81; , 1..-...1'.i12~. had to be "1.323 (2233" 8‘23 55 "23121.

121.388 '25 c.8818“ 1:13:38 132.83 03‘ 182113.31 .2-«1..:-.2. 33:; {223.238 for 18.21.18 3.
“£128 r1118": 1:183, usual ...;1 the 881.8818": 1:28 1:222 12’ 1:38:12: 1'2": data, 12813.80 128
out off at, 1.3 112:1 in 03:22:28 13;: (32138.18 8.: err-:2 "888.13... “~li'311." ritzy tent.
A 81.11.3128 113‘. 81.3331 5.22.." 81:32:. 3'1. 1.3.1“ 2.22.: 131.131.23.11281‘38 indium 88 8. .381 133.8 (213:

PI’LtTlaEilj 8233' .83 3'23 v.33 . Ii. 1.. £8.22 that; a 1.13;,3 12:25:: :8 8:“ 138113831 ‘53

 

 

 

 

 

65

cauld be attained 1f the: (301-...é1‘;3 14-1-3:- c-esi.‘ Q “3 1332:2230; 3'3 .111 3“ ‘."‘;T?..
T2113 belief 13 alga“) 811990.;‘te'x1 by tile? 83:13.30 3.: 01' 05:12:33.». 01:15.3 (1.03:1.
the: factor a1“; "ecti 0.3 0:." creating; this 101:0: (3:311:13: is the fact

that most of the tmm use this lane.

F0:- 0301‘; of the: 4021333 3.0100,: _,.. 0.33m... gut-.1. :3; war: 133-333 11‘.
03:10:: to 63$in an atmroical relauiaasii‘p 'rn;-....r.:v- 33.2.. = 011:1 dun-015;;
(:2’mtrac-égaristics .

Valuas far Um 510-930 03' the regs-1:321:30 1.1.30 30: 13:1: 1 we 0 . 3L1;
mi 0.633333!” 134.30 2, 5.33. and G 35‘? :-; 2:131 3': 1.2.31: 3 0.1;}? 0'03. 0. 5;).
Tim: "aLMLn**m £07: tzw‘ ‘2 .. m:1.‘1*m .0 15...: “ti 1", 0-. 53.01:: 1.0.1133: as: for
lane 1, 0. <1: <00£=3m11 0. 3+1 1<11< 0.2551; 330:" 13.30 2., 9.3135 <31<JJT31I3
and. 0..l43+-'3<m<0.70‘3; 811:1 for lane 3, 0.1533(3- (3. 551 err-i D.h9’5’<m<3.5;11.
Toe 1‘1. 8*; set 0.1" 15:110.: 1‘0": lane 1 is 1‘0: Kata tszizen 111100 15110103311";

was fully 003133000 and. with a cut-off 0: 5'3 1.13.1. T210 other limits are

37)

for data. 1:33-11:31 #10111" ..‘:..1 * .33.:111ty 1:80 000:0": :.1.; 1111513": 31002: 00:15..) 13.3:

J

not fully 0004;001:051 and, in most ca: 03, wish a 01m:- ‘3" 011.001" 53 1.11:1;
The exception my be nut-0:1 111 T3010 3. VT 1031 13:-.. l ”:1."qu (1:1. 0 m1
recalmflated for a 011w; .. 0 . 53 up: 1:31: 5133:: value was 0.3-1.3;353101 0::
1:01:35 0.612. 1110 0001130. 00 11.11.1255 230:: the slap-3 "031132: 33311 '01:...1 a
large but do not name-00207113 11101115.: all other (3303. ’11:: 139.1 :10 of (0)
also fits 03113 last. 331301.14; 1.11. that {11.0 Y 5.112.01- teas-3t: 1:1 1.1.1111 13:10 ' 8;:
very close, but this 13 mt. true when Camrm'; lane minim-b 1.111;.- min-m...
fore, ior lane 1 n 1031103100 cqufiian 13 V =2 0.61.2.2 D + 3.7, for 0:10 2

it. is V = 0.331 D + 7.5, 05:21 5:031:31: i"' 1.3 V "-1 0.11.9? D 4 3.3.

I?)

EXILE 3

V‘OII‘E 13-333mm ...3. 1"“1 1 “$113317! CHAIM .LS’I'ICS

 

 

1‘ 31‘3"}: " i '- 1'1?! ’3 K i-V'T‘ .
W1” {In at EL.) 1 1 LI'UUJ C. let‘lu 3
S‘dJ' .‘I ‘v-fi- ‘0‘ ... .9 ~.‘ AAin:a_-—-— u‘. r”- 9—‘su‘ ‘1'" .- P-.._-:I If:
t .4. an“) xvi-LL Lax-4.4 £431. '3; .1..I.'.'x

 

1 _ , . . .... ,.
N 31 9-5 61. 1 70 L0 60

 

X 36.2 35.9 . 30.2 {133.3 . 25.0 29.2

 

i233 1 133-? 3 293 323 15-3 7-0

 

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I"... l 2.3:: 2.313 3 2.2:". 1 2.3.9. 1.9; 2,09

 

:- i 0.956} 0.9;3i (3.955 I .931 0.9131 0.957

 

0.325. 0.291 0.250 0.23::- | 0.237 0.937

 

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337/“. O . :33 O . 923.3 0 , 771 l .. 3:43 0 J .334 0 . “5.,

 

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J. "

 

 

 

 

 

 

3:3- 2.13 2.513 3 1.99 2.55 1.6"." 1.5.7
is. 1.97 2.12 1.95 2.23 3.03 2.53
GULF-“.32."? 55 55 55 1 75 1.35 1.; 5

 

 

 

 

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52522231011 2151:9223 6.2.1" Luz-32.33:: 121 21.5.2 02' *I :2 six 2:22.19: 3'53 L22. :1:
‘L‘ZTIIz': 11220 of all (II-La “Ian-2.51.1 not 55.2.12 26.21 32:25:33 32.22.2122 F~li115~asiLy "Lest. Lanes:

1 arts. 2 1113.». cats—i 8. (1.11:. it; ester: of 53 x .31 hilt." 211.519 3 62:22:28. reqdrad

3 02.1933? at 1:5 2.11:2. LII-.5: l ‘1‘} 3. 3223:? 62.3.3 321:1 1.32132 him ("L-2mm.-

(1:22-4:11: j! Qua-...: 8:. 65 8.2.18. ?3 2.52-3.22, 16.,3L5211--.L-.J. It vex—2 believed that

a 1215;1102 clItz;;;:2c-2I9 of 1321:2321? ecu-1d be attained 12" time c2: ..o: f 99:52

13272-222523. 120 ‘53 2.11.21. 1-: I cal-212.152 ".1095 of Ila-Le. 1:222:22: 2:22:19 fair: 111223 8.23:; “4-7;" 51.121
82:82. “the 39522123 par-2.1 1'1; 111 all 1:51-2:95.ch $112.: C-uluulalcd F “94498 were

an.
a

0.;{75 113:: 13:2»:- 3} “r 22:: c ...-3-.. 8.13. 1.221. foI; 1:129 65 2.1222 cumi‘z‘. T2225 ecu;-
IIILLSLUL mama—I22 Lin: 5.2.133 2.1.13 {55 “an c2522.: .. m 0:. 12:21. 221 1:222:22. ’15." 1252323. :22.}
(...-.2... 2‘32: LL»: "22.3353 02' “L125: 35 V11:- i322ca;'3d7..y', tile LBOL‘L'IZ'lLJiCLQt of (attaina-
1212; for t‘ya 55 2:31:33 153:: 0 . 933 m 2:221:32..me 122:2 O . 5121 1‘01" film: .6 rpm.

1 ~25 ‘ ‘ ‘ 2

M 3...... co"..- -‘i’icicnn o; c:)2;2;2Is:lat.2o:1 g22.2c:a a2 :2 value aqua-'2 ‘ to 0.291",

‘ ”.13 “Bu-:.1..
It (251:1 1»:- 30.1231 5.3.2.5- 2.21 LhaL 31‘,» 2:22 £323 5223;212:1526: 0.? 901.1229 1:: 62291.11-

by the variance 2‘ 6:22.22: ’3}. 1'111221-117, the st Ina-1m dc“ -;2or 0; es tints

‘ 2"- ‘III- 9 v .1" t ”o ('2: wt 6' - -~:.' 2- ~ :5 - 1 5.1 0*
is 212-“;222 2‘.)- L125: 5,) an am the U," ‘-11J'2‘£c7;);).2:1-.«aut3;y one-Lbc-d as.

18:233. “Ia-.5552 £7 '21:: 1:222:22‘92 1.213;". the 53 22:93 cuboff 15.32213. be a ”De-"LL22:
9:33.062 20:2 .2262 line ..Ic 5.20.211 3114;221:1231 flaw 912-21 critic '1 flaw.

D13 to lam 3'3 2222.13.22.92 22.22221222223- oi' problem 021 a. cutoff line
it 13 1.42. 0.2.1 £2121": $1113-321:: mmlculatiam 21:31 a cub-32’1” at 35 51:11

9:21:13. 1252.22.21:- m an 12-. crease 12.: 1112935211329 mxi 22022225219212.2211 of (113.2192. '77-»

O

T1:2:.5:20..~:1Ir;lcal plot, Wick 211. 20 h 22:12:: ta 3201119 1112-53 O‘I'c, was 1..-3-...“2

'-. C. '- l‘v‘ .. . - ‘4'. 4' ~-
5.221.212.5222 111 ...-1.2;: ml 2.2....

.3
V

As in the 939.102.12.21 3.12 2:23:23, the coefficients 02' correlation were
detenfincd for all claim. These values are given in Table 3 along with
the 93:23 accchance mam-2 for :2 5:10. the values of re. T112236: Imam
range-3. fmm a. law of 0.1Ill far lane 1 to a high of 0. ‘2—1" for t: 12 same
lane. Tn 215 means LhaL for the Thuz 363;: LI: :2: 011131-3333 of the marl-amen:
of“ volLrI-me could I)... 623.313.3162.; ‘o-y‘ we V132; lance of (1.22.9135. 17113.3 was Rim
3 cs.“ 3:." of dens; 12-23;; values at I333 mm. Maw; with a cabal-‘3? of 53 V1131,
the 3:2 mlwe becams buggy-6.913 or 9153 of the valance o" the volume
hem; wgpImineIi by twirgme of ’cnsi'tj. This is close to the cflculatod
value 0:2 0.91.7 or 9:76 t’ar lane 1's 921:5; data which also used a
cuLofli' of 53 mm. The only 101: sci-.1396. comisla-Iion cos-‘i'ficicnt 1:3 for
lane 2 Fri: =2! dabglmL Lid-II was "i‘Lh a. density (-22.110312? . 11‘ 7‘3 warn and. not
Lhe 53 mm .mcuLoII' 1.13.6. for 22-23 LoLh-er data.

(densities), or

The stam‘mm deflation-'3 or.“ eithsr (ml-mm) , 8

fly 2:
the stwflmfl ezt‘or oi’ esLiuIa'Le 83’. x (3011.23.35 /UE‘:VLS 13182.1.) do not 3.1.1 in
eIrlaaming the re LaLLOIn of volme I: 222311.. flamity. Bowman it (Ines
give an 1416:1353: .Iirm cementing LIIe cut-oi? va. 2113.8. $273311 the cuter? values
are 3.330%! 55 m, the 33332233123 error of 3:23-12:33 is 25:32:; 9:133: than 1.0
u—izlle with cuLJffzs of $3 @3321 072.2 less, the eta-Mud arm:- oi‘ asthma

21136.25 are less leu 1.0.

(‘21:1 3:21:21 Aveme Data. $1183.33: 5.52.3.
2.23 cabins-d lanes anal; 223-223 ware made in the same: general mun-:22:
as the im’lividual Lane wWi-fl. In ac. .3331, the results of the

analysis and general trends are little afferent flu: Lhasa 01‘ the

67

miviimal lane results.
The chronological. plots of data indicate the same cutoff lines
far 513996. and dummy. These are shown in flames 8-5, 27, and 23.‘

The statistics for the mqumee are smwizal in Table 1;.

 

 

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012,191—1‘: -\ In :.1..) ’- 5-2: 2:“ on: ‘r 3)“?5. I. r in; 1,”.‘. s s-fir‘? :.'.,.- f9 “'3" 3.“ . in. I..7'—.,- 1"
1.- 1 2.4.4:}, V J AA. «an 1.ik..._x.-.v! 3.5. 1:;- Iluui. 3 ‘1‘~“.-“-".i All} :.‘3 r”:- t;..[
(In try-TD.“ a
in. An #JLIV _ .>_ " . ‘ V‘— ‘ A
(“V ’. ". "Q: ~ \f‘ rvT -v '6‘. ‘-"-."', If. rel-r, A '1' ..‘7-nf
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C} I :2) K) n 2-73 0 a 1:? .) (J a $.31.” 39 LE" 0 - 2.1"}

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:3-_ 3 1.115;. 1,131: j 3 . 33. 3 .15 r 53:3 1.31 -
__ :- - *“‘ _A .

55/312 1 . 2:3 1 ., ; 1:3. :93 1 11. 1.113 1. 3:3

133'. v 0 4 271) :3 u (1) ‘ 1 .. i}: b 1- Ci )3 l - _:'3 i 1 ~ C:

3' A. A A _T,

83: 1 .131 1. 43",? 2. f;- 3 33.; 3. 5‘; 1 2.1:)

 

 

 

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71

cwxw *
- "A o

r: “; 31’ . ”—9" ~ - $117.: a it. ’5’.“ ‘f'p-{sz-
'--.:\l ‘1' J’s-“uh a' «“1 flrul f.- I ‘ l
'a 1" i‘ "7"? ‘1‘»

..., xxx}; ._.? L." .... N 92'"?
pvo' :..- “K, *1 :At' L4" # 03.1.... .'.' ‘3'...

..J. 5! -~ "‘»0. ,..‘.- -’ ...-bf

.0 -. 1 u -" ' .' . f .‘l I M\.u ,0 , a: 0‘ . ‘t . .- ~ .- -_._—~.- .. u. 11!.“ v ('3. ' 1‘ .' 1 ~ ‘. ‘
.c 1" xix-‘Wk’1;'£ 0-... Ldbl- 2" 1.1.?3‘.‘ \LBK. Ira-t1 ‘&3 ‘15:) (1‘? w'.‘ ; ‘ @2151: 44;: A 4:» jun-:1 ‘tw1331-
_.- fl 3 .1 g - . .:-. . f. o ,. - ... . _' .- . 1 t - s r o .... ... ..-. ‘ q .3 .
3331.1..1zzs--.1271£= o- : pea-... \- .: :3 “.3 10.1.1113 , 51"....1 11:. 17.1113 3.11.11. .33 3:... 1%11133
I - ‘— .‘I‘1 ‘ -- 0- --I 3" _‘ p 'I .3 I" ‘1‘ \ ‘ “ \
11%"? .13 ’2 ' 131.131»; '1: .11: 3115:3113). 0t; .21; '31 '3 "CC. 12.: '11.} 3:21;: 9-11.18 11111.13 r6111!-

1.1311331193 c3 Mere-«:1 on the-:1 use of 3. (2111111131191331 7.9131: of 13.113 311:1 the

Raine-3111;? bis-st .

19531321311: hip c :i' 511:- :3. 1:3; 3:11: 2' “Egg:

Ih‘malgfil 3 00111111313100 11191:. of 63.1.1! 3:1-:1 1313115111131 testing, it
11311 r1: :..111131 1.2.1133 0.11.931? 1.1113 [‘31: 39:23:13 31: 130 11121 11-1-3311 be 3:31 ta
1113313311313 1.23" vac-11 min “11:13]. £101: (aid-'3 L10 119.1) 3:1-:1 cri .101]. 13.7.1
(2131.01: L2) mph) . T213 F-linear 13133111. 3313 11336. 111111.13} 1:111: the 31:19.37 in
5.35731 15.12133; the 0‘11 off 11.131: .

.1113 (111133191311331 plot of data 1111133335. 3 am: 53: :1 age 121 - .2311:
in err-3931.31.31: 3313-11 f0? non-1 riticsfl. 11011—41 ugh n 11-. “1:3 511.: mph-w
1:311:11 a 13113 6131310113 (2311. mstlcm (33. lane 1) 1 11.13 plot; 3.1.5 o 5113'? “1:.
that. the 6.333 in the» critical 11:3 311111111. be 112111113: 13-1-11. 133-11: 311:1 113:;
111 Lb " 2:3 baa-er “b-1131 :13 .3. If 1:113 «131:3 mare mi: km 111241 33;:13331313,

‘c; 3 2 33211123 (2071313. 113 q 11. 1'12 17113133111115 . Riff-3.1917333)??? 1:114: Cat-1:1 in 0.31 £11113.
flow 0171313 1111113 1111.33 3.1:;13L31’13't113r1 of 11.3 123.311.111.12.) --.-.13" 1%:- ..
37:33:11: 3111 1313011.. 1.31.3115. Tim 0113- 131ng 1.713;: is punted out in 3.11 1113
plots: 13 12119.? cons-3r: 11.11111 £11133 11191: 17.11:: 31:11 .111)“ 0:11:13." 1‘310113‘1313’ f 01-

1017111.: 13.311.11.11 1131117111 111 1113-3113. {:31 1101*. 11113 13 1111332134; can E1315:

72

 

75

1223 the: rela: 5.0213 the. . have "21:222.: pic-{3.17.1 12;“ 1:32:22 9213214215212: 22‘12.“-22.2 232‘." 1.9::
853222214 1311.. ‘22 131:)... $313: perr‘aéiaflic 2‘... :12: 21:”! F‘i..;.‘.‘~.z $2 3.1;. 332:3 2.22.3.3 2.12:3...121:
20113.8 occur sjust 11:20.1“: 221;:an ‘1 or 22331712121. 3171‘... 2:. “2:12.52 1:. mt 3:2
323201232221“; to the cinnmloafiagi 91.0121 222132.21 ‘12:. * 3..." 1.22:2“: 1.3312. 32.;
bellmw ti st’ 13.3 3.2: 6&2: aft :3 r 1.2121 2304. 21112.1 "Liszt-‘2: 21.21.12.321 01' slawfimmm
‘ifllich “it: occm‘red 1.3"1.."“£:.. 1.1131 15‘: 23 21:11“ 1333.223.
The tm planes of maeei—mlum 21211211233:- 1111-32: (-2 22:12“: 3 are :23: 21:2:

mha‘ix‘lc about the relai; 1112 322.113 9.2: 12:13:: 1132322 1 121.31., bib. 111-; 2213111 1.22.1.1

sia‘ilnr awry. All lam: 1215121372: 8:: ‘ 113:2 $221121“. 3311.; .....2-21 are la.‘?:‘;:‘3‘-‘t'
3.71 m-cri‘tical £3.01: 12111.13 average 51.12231 decrease: are 1211‘“: in
cm Mica]. 10v. T1123 M312}. 2‘.” .' 133.118 13 that; in maize-2:313 33-1-5.1 1 L ., 03.113513;
are 1:11! and can a.~co...:-:»..:-c. 1.22: 21932221 11.192.113.231: 22:.“ 1.1.39.1 3:13;: 1:2

...,- ‘a. 'i-- .4. .."_ ‘. ., ‘ .“". n;- 0‘ ,. ‘m n .4.-.. 0 .. 53-“,ng 1",”‘a‘
849 a £00.3- OX; “£1 e $1-18....e 1.5 Lari" bis—a Lg)»; no 1'ng P 8030‘ '31::35 pf sci-R .- 0541’ '. Inga-L ;J‘3 Ci uw11.,_‘,:.;8

‘ :..31“.('i. 113226129 -2‘ , 21:22:22.3. 5222:2229-1122:233 2.3. 21:32 «0.3.1.1111 £10128. :‘2 23.131.122.22

.

‘l'!

‘ -‘u a _ ,9 5-4 ... 1v 4 ' 9-. ‘ ».'~ . I." s v‘ gm. .. g: ‘ ..
bet-212.2226 male 13 11:10.8 13.21.2121. .1: 21.93 12.3.1123 a. ...- ”12:21:12 1-1 0.2.2.1198; 12.3..
3.3211. 3 the 1132121122222“ 311:3 too 21:22:31 852.. “ .30“ 3.21.9321: <“‘~‘“‘22.....c.2 1.1132

"v I” ’1 ‘ p n w 1'. 9‘ .‘~ ..1‘ ...
1219111121213 an 0“‘e:.‘al 1 5:223:21? r3... ‘2‘:- 913...: :22.-La- 12.11... 1.2.23.1. 11:21:14.2.-. L. 2 22.1
flow . This 1:18.212): 8.12:0 22351,,;1;.;3 131 ‘2‘“ 11- 3:222:23122‘ 2:2: $22.1 awry-:22.. .
. .r- .. I. I 1 .. t 2'!" . .3 .‘ ‘ v "‘A' "’ r V.; a .' ‘3'" ‘
The 112.22.13.22 re .2111“. :3. :39 3.122 2.1211 1133....-- 1.2 21111-2 11'... 2.9.3. .13.: 1,.
va‘. :0 c-D- ----- ,-~r‘v- "p -'-~."!‘ I? ' I kw -' I. ‘n “‘
Eva Jiiv 318M! 113.2% Q11; '1‘»; ...“ .. 1‘ LC" L; .‘I‘ {990:7 a “.LLL -uLl J” 335-. :7, $9113.11}.
172131.131 "232.123 (29:11.153132 c.1....'.’.. " 1-..‘ 1212.93 1‘32: (...) 1.1 ....r‘”. 312.612.3925.
”‘11.” .. u " ‘lfia" ' "’ ‘. W . ...?!- ‘; (v"“~s‘. ”win" .‘- ..a. 5. :Cu '2 1 M" "‘ ".-"' “‘1’ 7 -‘.-‘. 3‘
*t a 1A,” cfiLWu ‘JJ‘Q‘J la ‘11:“ 33L a "i" ‘1)“ flow.) Lab- '9. I- ‘fl‘;t‘~~'-I 'Nvl (Jon 9- ‘K‘ IN $3.111; ..‘L ‘ ‘F'L. :1 :I: _I'.F‘1
h ”M . .2 4.11,." -.¢-.. . ¢ .~ :nA-a " M -,~ ,9 : ..., 91.7..
cor‘trcLa. 1:111 (#32) 132.12.13.13 :22.-:93. ...-.1 gem-.11; 52:153. 1 33. .2“: 23.21.. 2.921..i--~.
T123: re“: . 2211231021 19.21;”. 3:31;: :1.’ s .41 Let‘s-.1223 (“1..-‘1; 3.12. H..."-C‘.. .1223}. 1.; 1:1
.. .'-. . n Y - 'a- n. w :.«og‘:~ In ‘ '.'. .‘ 'r 3’1, . ‘ “ Ag»: .- 1' -_-...
112239.219}. :23 in R221. 2»... v3.13 :22 1’31... 02., 22.92.31 £1222. 2.12%. I: 2.5.1.9311

11131., “we tar‘ezfi 3.3 for: $922233 ":0 £233.12: 22 1:2. L711 W121. 115.2". 201-122;, 1222“:

€6.23 :13 v! 1.21 9, 821122: 1:21:13 ‘19.. . 3.22312221231: 1:). 22%.: r.

 

 

7‘!

file remmm ecmatimz For we ararmjée of the: film-fee lanes 1::
S I: 43.2}? V + 50.2. Cmmwlfielfis infidcaived a mJleagion of S E: 4:309
+ 1:3 which is quite "i‘erent fan this aimlysia . 111.3 81096 doe-c. not
fit the 9:55!) cwfiémce limits either and his Y intercegt is 1?); less.
It woulrl 3112.0 mam that the: 61399 of GI'-'e.~;m-.~3hielfis ' regewion equation
would not test sigdficantly nan-zero which wan Meets: the line to
be almost hori :sn’cal mid not in accordame with the. garmral trend.

The calculations do not tulle-ate too much diffamnce between
lame rely; isnaifips , but th- chassis; 1:1 cal plats (is mum-1:9 a. Eiffel-cam
baimeen lane 3 and laws 1 or: 2... A osmium-ism m? Figare 15 with Figures:

12 and. 2.3 will a‘nmr the d: f‘ference (mite remtily.

F! ’1 aixiflrzsthig of “im'iA't-az" ““3"

The cat-off lines for? we EWuJ-Gwlm‘i ty relation were flatmmaa
by bath aha F-linwdty test and the cfimrzological 131m; of da‘oa..'1’;:e
clans My C’I'Wi‘f line is 53 7.43973 for lanes 1 and 3 and not. span; il‘ivsfi. far
lane 2.

Tile range in 5930.5 53mm in the chmmhaical plat of data we
the was: as far the spmi~wluaa analysis. Tug plot 03? lane .1 alas
mum-ta tfzmt the 6mm in tha critical area 321313.41 be M1341 avegan:en's.2.1ys
This ; Emma-er, coula mt be verified. by the humanity test winch did
not mjsct the Imus thesis of linearity of data. when all dCLEi‘t-icfi 3:1-c

mas-r1. Lane 2 did mt auba‘tantiat-e the rejectian of linearity at dan-

aitiea mow. 5-5 mg. lane 3 , Ema-31“; is linear may for values; less.

0

F.

1

man '53 v1): lane 1 83101113131335 for all 63m yiellai an mcwtatlv

75

1111...}...1 tea; “.1123 a ~.;;.}"1 (2:. “321327131 5111.--...1'1...“ 13.2: raven the )1;
1.32.1 c3313.“? calculat-ian 3.1013293 £331.31- 1.13:3: '."":,"5.' u: :3 Vim a walla...
(2:1. 1-131.111 eve. 1‘1 1.21mi), as; 5.138 atextl-rhzfl 91.2.): 0'1 12.5.13: e is
alas 8:13.113; which means a. 13 3:: sea“. $3.135 of €3m«1.2'1’2 cmmefl to
the 111921 5. 9'? 1‘02“ all 6:131:41.

T3 clmnaolsgiaal plots; 3.3213 to 831333311313 3.... (1314131 13.323 of

00:12. 832351 and (Emmi-ea . 1'3... 2‘3 “3.39 inert-r: 333.3 3115. Literal-mas of 3.2031

Jami 1.11.11 :1 Purdue; awn. 3;. the pow. £121.33. 0.; the 03130352 line 33 filmy ad
in ti 1‘: 3123;132:012wa 1221331133..

Gina 2133:? 11313232“. 0'1" 21391 511:1 c.1121 Ly 1:1 3.13%.. “2.1233. 11.2%: 1‘11":
33". 1.322131134 1221:3111 quite 32:: 1:91.; 11:: {£23. I? «1.1.2.13121'133 1.3!; ‘5. $3.13

4 a " 'w'v-n—u "r -': " ‘ -1\.' 2"- 5" “'u ' "v
2:01“- a; 111.3... (213.1. 1...-..“ 1..-.- 13..,«.-:: 1.3:“ :..1..-. . .53 is ...- ’19 1..-.121. .01 12.1.:

..- ...: .H "l., . ,_ -. .. :3.- '8. -. ‘1, .. . 1‘1. .
5379522..-.31333 wish 1:32.13. 5.1.1:.) 1.1.13; 33 b1. 1‘ ...-3 313.123.1011 01 (31.9..

P's}. J

u. r 1, .- - 5 , . a, ‘3: r - -”:~\_ fit me- ', . J‘.‘ 41‘ g «1' . -. cl 1.‘ o" .{1 «fir-l «.O
1.12: 1 22311133 1%..(23 1.3 i... .11.. L1: 1.2“. 1 221,. o. ...-.13 .3. 13...-.. 0.. 32.1» “at... c: :31: La;-
‘u' ‘ i P “Q It " TIT +3 ~ ‘ a “Y". 5 ."4 ..‘o ."' N .Ef 1"” 3‘: ‘,"'1 'H
\r.-n._f:v.L£X-Ll&. .. . ] aux J31. Alt-LL bl. &L&.J.L'J.L ~1J J

9"“ ‘- A '1“ n ‘ "tr '“ ‘1 .. F ‘I ’4'": °'~ - ' "' " ‘7

1.3. ragga-'15.. 1cm 12111131131033 1..“..- :1. 81M. ’1 {...-.10 11.23:: 1.3.1.3.. 1.,

t- v‘“, lkt'v'h 2. ,;‘ K "”13. 1 ‘5’ 2"‘*V. * f " fl". V‘

8- «(LB 5 D * 1'1." Gra 115.315.153.311 1 12.: -.~c.“..‘:.io.1 o. f: -

3.
...- i

l -'r 0.91“. 1') which '“* “.1223 8. 3111111.“ curve “be: me line. but. 12:: +413: 31:12.... .11.
Sinai; a 11:13 7’“ 12:133133 ma. be: 2511:1535 3.2101: 1..-11.11 only Elia-1t mm):

01:: but, 111213.152“, £0,233. 3 89.11.1131 3313,»; :33: «2535121 101' tmml £1.23 r “

S :2 «0.1.13 DI 331.7 10: :.13113411’245901fl 13218 mad 8 .5. £33.33 D ‘r 2"“.

J
for £223 alO‘d-‘JIP’in 11-11:: v3.1.1“. 115. z para-2.331;: 04 (20.21 3:23... ‘3- VM “3'13"" W

Elite 13.331331 3.3110 on fine Fox :1 has a reg/23.3 1101‘ S == --0 137‘ ... + 553.6

 

 

76

and a. slow-... 1.2:}. 191.19 ra:;.'~ecsi-2n of S -.. 45.1221 D + 23.3. ‘5 1.3211111,
therefore, @1309: that tunnel 1" 10“.; is 110‘s r019. $.95. to freeway flow 110:
is the flow analyzed by 6.393501321113153. 1.10.19 13 the possi‘s 111’. 1"} 53a 1“. the
cs '59. of slope by 01-20:. t would. be acceptable but. there 13 a need 101:“
a. different I intercept. hither mlysis on Y intercepts 2211 31“.: lead
in a set of 5009131331113 0051;113:108 limits for 9:11.. ‘07.? 111'. agnecd
control-.3 on facilities .

It was madam]; point-9.53. out that the speesi-dmfity :93: "“1101.
'01-:1‘6 for 213.J‘.;«r, 952.55. 135253 011:1 Ina-"'9...‘ 1:113“. TELLS 111175110:
333011.; ”1.9 5202253051321 1:33.19 :1 that tze main 1" 133159 in r919“;imwh.‘ps

is ...-1': can 9030': or. 11191333111 81153963.

Lip}: >2 '2 -."3 o " "301.2. “-' .“r '03 3'12. I‘wfz2'31'ii

Tim c.1503: 13.133 for m “01:51-9~.d3;'.:.ity relatian ware 9.150 3.2m:-
1110.01 by 11:21.11 humanity beat and. the 3313311031191 plot 03‘ data.
17.9 1.0.15.3 c2150? $112139 are 55 192:. for 13099 1 ma 2 912:1 145 m 102'
1011:. 3. {Ex—2123 1:3 :.1.-30 a. 33:15.11 h‘sLicafiiou that the 19.30 3 cutoff W'uli
be better“ a": 33 1.31.2. 1120 magma 111012333023 9531151512 99993 in (1.31313;
0- an; 2 for lane 1 support the @1003? art 55'.

The c11wamlogical plot of data is more a gul'zatic about. the chance

in charact 2.- of‘ f “m 1.12 ‘19. cm’. 1.10.9.1 r3100 312.31 15 mfimtantiated by the

F~lmcazdtjg beetv - ’ch rejec‘: s Enact-2y aim-‘9 ,‘3 3.7:.
53519:. 0'... 49.300 009.01.333.53 far this 99.1.1110... 11115.15. 99 111,5.

6.3253390 of comm- lation--f.he a. “crane is 0. 9L1. The Im'iance 0‘: (11:11.35. by ,

7-“- «’77-.» fi,‘ '
1‘9}; 84-] . . .

mgr *2"!
1’. '13:?" ' r:

Irv-'7-

‘ in, 'PT,“-"

[...-i QLuJLL'- 'auJ 1..-!“- ...;ch

 

 

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3:3... S7-3.2,"..’i§€3.2 1 83.0.3.3):233 v «o 1+"2m..)-=.5 7
it: 3" “J I 3th 3-1 s l L 33-“9 I 3:. 13‘ 5r 0 1” iii-O I L54‘D‘ I“?- ‘3

 

 

 

 

77

78

:2, accounts for about 83!. or the variance in volume. The scatter of
points is small as the stemmed error of estimate, in general, is less
then 1.0.

The regression eqmtim for the three-lane average is V = 0.1rr2
D + 5.7 for non-critical flow up to the critical flow line. This is not
competed to Greenshielde‘ or Olcott'e relation as they did not use the
linear relation. Olcott did discuss the area of critical flow which he
and. m it a density of 65 V1131 and a speed. of 2.1 mph. The dmmity of
65 vpm and a. speefl of 9.1 mph indicate a. volume or? 135.35 vph which would. be
helm! the design “puny of 1300 vph need. when the Ford was planned.
Hie results do alffer consixim‘ably free this malyeis in that critical
flow 13 55 1.11:1 at a aimed of 2&0 mph and this is almost twice that of the
tml flaw. Greens‘hlelde indicated that mime volume is 21330 mph
which does mare with the Wren Of 2230 nah for this melysis.
Ligxtmll, Mexwr, undated the warm to be only 1500 vph.
Emmett macaw; that pee... flaw Occurs at. a. volume of 2300 V931 and at
a. speed of 1+3 mph which vould agree with the results of this analysis .
The general mane-m is , therefore, fer a nae-mam flow of 2.2390 Vph at
a. epeed of #0 mph it}; a critical density of SS vgm.
gamma Qorrelutiog Pptentigi

It we pointed. out in the speed-volume analysis the correlation of:
speed and mime m Intro-r 3 -0.59; in the speed almity analysis about
median-q --= -0.72: and in the volmae-deneity the comlation was high—-

r a 0.914. Them would seen to be u pattern in 431115 set of fishes.

79

A possible act-whim 0:? 1.15.2 1.232213. be t...:.:": one 2.1:? he Cim'trif-
111.152.223.012.- (112' 22 rant italic-axe 222329173712: flaw as 122.41.]. 5123 t"; 2.1.». 0+ 127. :22.-2 , I ,7: 23.
12121311223221 11112.13 were given 113 smefl (3), 220112.... 3‘22 (1"), 3.12.1 C...1:.1-3‘E.ty(3}

weanling 1:23 the corral-21313:: "917012125251, ..he d123mtmriv'e “at 7 "‘1 1310531033

JV. -ln~ ”-13-

\

1.3.8 3122141122221; wijwted 2:31:12.» 5123-21151 than be the (21122 viz-.1132; 1cm t r- 212--

«I u n-

rel. "23:32.11: pet-112.13.21.11. The table below {time the 1131;113:223. val-.233 32:2 1:1: 2-..»...
to 21:12.2 233:1"; labia-:21 13.712123. 21236. 1:1 the 8211.32.13. ..22r.: Chammfl tic of he
2.223.121" ‘3 12.111 with the 1231-2232521; mare 311131.212: wee given a weight of i .- 1 Tm
{2:1-rvmfteirn mate Lew 2:21: :4 22 low 1.11 high was 22 1.222211222131311. of "‘

a...

T122 mint -321 with the L1, :‘zeet c "rt-22.2.1. tier-:1 was {33.72221 :1 1.2.1.531; a.“ 3.

. .«- I
'73" 1:1

... '”'-Ag 0

l eu.‘

11712231222 2...: v3.2: 3' $1393 10““2'12.

‘T” 22'”"I 032131: 51-1.3": 127316112733 17.21.1353

*‘W‘
1 :2 5-:- 2.-' n
M
22/? (rs-.532) e

v
8/1) (f1'=.?2) s D 2 .-
n

 

l 1- -

I'D

s
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WU;

123
.377-
V1

Sir-.3 1" 622.227.1432: of the 22911211221 31:12:; 11:13.: 2.22.2 “21122.“: 22:32. 3.23. has :22.-.3.

102 2-3.24:- 302321'2 tim: pot-22:11:13]. :12." 15219 ‘hrW2 (2112-2311103 with enmity

{5'33“ "22‘3““ 21377 . ecu-21.83. of 22221122261331 :.1. I." ":..2. (mix). 1:22- i'z... "2“ 2-.-
...ia..2..-, :..12211 it 1111." .2 s. be has t to 111.2: the 2.1311 ne*-....~1.i.1;-1 0"" t2

o-""l_ = '3' ., ‘ '..s ' ~ -' a '4' 1 '9‘
...-.312! 2:13 the «3.1.2:: 22342.1; 131 3'2 1131...: 1. "1 1*

4‘. D
by

l.

mu

CCEECHJS 10233

There is a good. mention that the cutoff lines 'be‘mmm critical
and non-critical. flow are 9.3 follows:

A. 1&0 mph 1'02: the speed-mime relation.

B. 55 mu for the spew-density relation.

C. 55 *rgm for lanes 1 and 2 and 1'5 m for lane 3

for the volmxxe-«tzns ty relatim.
The F-nnwity tmt imiicates that a linear relation is mceptcfiale
below the above cutoffs for the speed-values! , speed-dens 11:7; , and
volume density relatiomhips .
The cfimwlogical plot of Gate substantiates the need for separating
ritieal flow ram non-critical flow and 13 generally very useml

in the es-rplanation of: relutiunships.
The correlation of data. is not the same for all relationships:

A. Speed-twinge com Alstion cocfi‘icimt rs «0.671:-

B. Speed-deawity cor-re tion coefficient r= «0.335

C. Volume-damn}! correlation c «‘L'ficieht r= 0.372
There is reason to believe that apt—mi has a 1m! pot-mum. for cor-
r tion with mime and dwity. The bet-2t indicated correlation
is tint 3‘." vohme and items ity .
There is a. cliff: zence in siege of the regression equations for high.-

space-1 lanes and law-speed lanes .

80

c3

81

Under full congestion, the spot-x". ra 13:3 in (:31 ' it a]. flow is several
2.12.2133 the I‘Me 21.13. m11<.'a'i'5.ir.:r3.1 £037.

A mate 890051 1:1c;.u.32;s we Lu'r'cz' than dBCl. cams in non-c7: bical
fin“. Average :35 L:.» bani (it-3r. "capes 8239132219? J 3.. 1112383325 in
critical flow. A rem.- 1:: 5 mm «342cm 20.9. of a: 3.2.1:: mflow at (2
13:11:21” EJ£3 spew. increases 01' non-L's“: deal. £1311.

Fmfim 2-9.2.1..-.) 3.297.323. be puriforncd. L1 U121: axes. in: :21 samples
mum {“931 congestiml, :11er peak flow 22.1.; v}. .2. no congestion,

of 12.93.9113 a 3*".22 3222-2131 03):: seal. 3,; cimzthterietics, eta-1 with more

Cate on 20:3 sides oi‘ his peas: period 91‘ fem-r.

1.

10.

12.

13.

BIBLIOG RAP?!

Arkin, H. and Colton, R.R., Tables for tatisticians. Barnes and
Noble, Inc . , 1950 .

Barnett, J. , Operation of Urban E. .resswagro. Journalo fthe
Highway Division, American Society of Civil Enginmz
Vol. 83, No. HHL, Sept., 1957.

U!

Crow, E. L., Davis, F. A., and Wield, M. 24., Statistics Manual.
Dover Publications, Inc. , 1950.

 

Edie, L. C. and. Foote, R. 8., Traffic Flow in T'mnels. Highway
Research Board, Jan. , 1953’.

Forbes, '1‘. $1., Speed, 216221.de and Volume Rola“ 1011813125 on a. Freevai.
Institute of 'lrai“ 1:. En: ineezs, 1951,13}. 103-126.

Greonshields, B. D. and. Haida, F. M., Stati .tics With Ajpglicasions
to 5131:2815" Trmpfic Analyses. The lino loaniaworl lo; Eighmy
Traffic Control, 1952.

 

Halsey, M., Traffic Accirlent. and Con; “es..ion. l9Ll.

Ilijmay Cagaoity Manual, U. S . Deom'ment of Camera, Bureau of
Public Koala, 193:).

Keese, C. J. and Sc‘nleioor, R. 8., Egrelation of Design and.
Qperational Characters of Efigsigks in “foxes . Eigmay
Research Board, B131. 170. 195-3.

Liv-ht} , M. J. and Whitman, G. B., gimmntic Havana-Part II.
A Emory of Traffic Flow on Long; Crowoofi 2:03:12. Proceedings
:2 the Roi-'33. Society of London, Series A, Vol. 229, 1.955,
PP- 317-316.

Moroney, M. J., Facts. From Figures. Perm-air). Books, 1953.

MOS"O¥"1+Z, K., Research on Open: atln‘ Chagacte ristics of hoax-rays.
Institute 01‘ 'l‘rai'iic fiuulueozb, 1;);3.

Olcott, E. S., The Influence of Vehic ila'r Soeell 92::18 gaging on
Eggnol Capo”... ,1. Sjt()po2:'es. ions Bageaccn for .....ar #:3138115, .L'ne

Walker, Helen M. and Lev, Joseph, gtotistioal 121531335953.
Henry Holt and Co. , 1953.

 

82

a:

X
M‘i’fiml

SETS-L £17273 £.EB"’.E"€I.‘.’IICE¥ SILELT

The symbols and abbreviations listed bolow are mad throughout tho report.

£3 . ouxfideneo limit: for slope “32/1:
0 g I 11in intercept
D 3 density of vehicle:
a distance spacing of vehicles
F 3 P-linearity teat calculated valuo

F.95 :- 95 poroent 19791 of neocotmoo valuo

clan interval in X direction

class interval in Y direction
k c mambo:- of paired data
m or “Ii/1 . slope of tho regression Y on )7.
mph or IIH ; miles per hour .... speed
H g the umber of sample-
: a the correlation ooefficiord‘.
Sb «... tho standard error of regression coefficiom b
8 a speed --- miles per hour
‘ : 81.13.“de deviation in the X direction
5,2 a variance in the X direction
83" . standard deviation in the I direction
ya I variance in the Y direction
. 8y], 3 standard error of estimate
team-2 c the 1. distribution, two-toiled test ...-11.1. 1.42 d.f.

V : voluno of vehicles

rpm

vph or VBH
vm

x

1'

é x

é 3:2

2 xx

ad

21:2

55

vehicles per mile -- density
vehicle: par hour

vehicle: per minuto -- volume
variable in the X direction

moon of date in the x direction

sum of the values in the K direction
nun of the x3 Vulne-

num of the x times I Values

variable in the I direction

mean of data in the Y direction

sum of the values in the I direction

cum of the 12 values

86

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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