Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

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Dra.;-force Function. The most commonly used drag-force function in railroad engineering is the Davis formulation. 5 This relationship is usually presented as follows, applicable both to rail cars and locomotives; F d (v) = (1.3 + 29/w + by + SXv 2 /wa)wa, (5.13) in which F (v) = drag-force, or resistance of car or locomotive, d in pounds w = weight per axle of car or locomotive, in tons a = number of axles b = coefficient of flange friction = 0.045 for freight cars; 0.03 for locomotives S = drag coefficient of air = 0.0025 for locomotives; , 0.0005 for freight cars X = cross-sectional area = 105-120 square feet for locomotives; 85-90 square feet for freight cars. Frontal area could be determined for each particular locomotive and car, but since the subsequent analysis is to be applied to a large variety of cars and locomotives and since the range of variation of X is small,'it will be assumed to be equal to 112.5 for locomotives and 87.5 for freight cars (the arithmetic averages of the end points of the ranges of variation). Equation (5.13) may be put into a more useful form if the im- plied multiplication of the bracketed expression by wa is carried out. Note that wa is the gross weight of the vehicle. Substituting the values of b, S, and X, two drag-force functions are obtained, one for a locomotive and one for a .freight car, viz., FL (v) = 1.3w + 29a L + 0.03w L v + 0.28125v 2 (5.14) 1
and F(v) = 1.3w c + 29a 0.045w c v + 0.04375v 2 , (5.15) in which F(v) = drag-force of locomotive, in pounds F(v) = drag-force of freight car, in pounds w L = gross weight of locomotive, in tons w c = gross weight of freight car, in tons a L = number of axles of locomotive a number of axles of freight car v = velocity of locomotive or car, in miles per hour. The above formulas give resistance of only one locomotive and one freight car. Total train resistance is the sum of the locomotive resistance and the resistances of all the freight cars, or N N L c F (v) = V F d L (v) + 1: F c L...., d. - (v), 3. d. i=1 i=1 3. where F d (v) = total train resistance F d. (v) = locomotive resistance of ith unit N L = number of locomotive units in train F d. (v) = freight car resistance of ith car N c = number of freight cars in train. (5 16)
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c,q /kao, PROPERTY OF THF H S. GOVE
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INSTITUTE FOR WATER RESOURCES In 19
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NORTHWESTERN UNIVERSITY AN ECONOMET
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ACKNOWLEDGMENTS LIST OF FIGURES •
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Figure FIGURES Page 3.1 Two-Market
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Table Page 4.12 Rail Rate Regressio
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Table 4.A.5 Rate Regression Rail Qu
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This paper presents an economic mod
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All transport modes are designed to
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CHAPTER II REVIEW OF THE LITERATURE
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The first significant generalizatio
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artificially contrived solution met
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trannportnLion, thin neglect ham cP
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to the mode under consideration, cr
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that even if the reasoning is 'corr
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competition, that is where the qual
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His estimating process is divided i
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Table 2.1 COMMODITIES CARRIED ON TH
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- 15 In a recent volume on the de=a
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aggregation over regions for each c
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for each of the modes under the ass
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ail rates, and here he encountered
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had statistical significance; howev
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flows with actual shipments. 21 The
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CHAPTER III THE TWO-MARKET MULTI-MO
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the market price in A it is obvious
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P b P o P a T r 0 Fig. 3.4 -- Equil
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for all quantities, we conceive of
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0 (3.6.A) (3.6.B) Q 2 Fig. 3.6 -- T
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• Q2 Qi Q0 Fig. 3.7 -- Two-Mode M
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preference. He pays money today for
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Situation II: Producer Ownership. T
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little consideration will reveal th
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considered these costs in several f
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Then, to calculate the rate of chan
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(T1) (T2) The effect upon Q of an i
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(3.A.7) (3.A.8) APPENDIX A TO CHAPT
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(3.A.17) (3.A.18) ■FQ 5-(43-- -7,
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term more negative and, since it is
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and its inverse (3.B.8) T c • C(Q
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Now, going back to equation (3.3.7)
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APPENDIX C TO CHAPTER THREE The Two
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product to be transported, Q1 units
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(3.C. 3) ,(3.C.6) The monopolist's
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To obtain the greatest profits, the
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.1., OA The sign of — is only sli
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(4.11) (4.12) (4.13) (4.14) 111 Tc
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(4.26) (4.27) (4.28) (4.29) (4.30)
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The tons figure is the total tonnag
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Since the aim of this study is to e
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Distance ' Quantity Rate Eq. (4.33)
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Distance Quantity Rate Eq. (4.33) (
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Distance Quantity Rate Eq. , Source
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Distance Quantity Rate . Eq. Distan
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where R E average, revenue received
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• Table 4.8 332.42 808.54 478.58
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269.02 931.44 900.75 0.98 0.98 0.97
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Table 4.12 RAIL RATE REGRESSIONS FI
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1. date of the freight bill. 2. ori
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(4.41) Rik ■ 0 30 + 0 31 Mik + 0
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making is usually taken to refer to
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Total 728 79,603 Reduction due to m
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Source of Variance Total Reduction
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there is a wide difference between
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All Commodity Classes. Table 4.20 c
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Source of Variance Total 100 599,25
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Intercept Distance Quantity Density
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Intercept Distance Quantity Density
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stability and density showed very l
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groups into STCC commodity groups,
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The reduced form of this system is
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Exogenous , Changes(X) Transport de
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the quantity of commodity k transpo
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Regression Distance < 200 mi. Rail
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Regression Distance Rail Motor Dist
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increase with distances. This is ra
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Table 4.33 contains the derived rat
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Sample Regression Size Intercept M2
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Mode Int. Mode Sample Size Rate Tab
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Mode Sample Size Table 4.38 STCC 32
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Sample Regression Size Intercept Di
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Table 4.42 STCC 37 - TRANSPORTATION
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the three-mode model. Table 4.43 di
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Summary of the Empirical Results In
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Table 4.45 FREIGHT RATE DATA ANALYS
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Commodity Group II III IV V Total C
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Group Mode . I Truck Rail Water /I
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shipments. After a lengthy analysis
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for Group III is positive, large an
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of the underlying structural parame
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Table 4.49 DEMAND REGRESSIONS FINAL
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• supply The model assumes that t
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Commodity Group Table 4.50 DEMAND A
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APPENDIX A TO CHAPTER FOUR The Effe
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Table 4.A.2 RATE REGRESSION RAIL QU
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Table 4.A.4 RATE REGRESSION RAIL QU
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The overall tendency appears to be
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CHAPTER V SUMMARY AND CONCLUSIONS R
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theoretical basis for their empiric
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competitive industries. Applying th
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in the appendix to that chapter. Th
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BIBLIOGRAPHY Baumol, W. J., "Calcul
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United States Department of Commerc
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NORTHWESTERN UNIVERSITY A MODEL OF
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CHAPTER IV EMPIRICAL RESULTS . Page
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. INTRODUCTION Our goal is to study
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Other studies have been done by the
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. Recently air freight has grown aw
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• For instance, suppose a firm ha
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eceive the same criticisms as above
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Per Cent WA Decrease From Current L
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• Cargo . Brewer's analysis depen
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A different type of approach, is ta
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These substantial estimates of elas
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and the consumption points. These a
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Initially, the determinants of a fi
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axis. Q is the quantity the firm wo
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Arc elasticity of the associated tr
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• same A*es (-p)/-11 Skto 4441.
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Suppose that the range of one choic
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is better than getting P 2 tomorrow
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A, At the kink P . Any_further rais
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market price; or inventory costs ma
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The shipper must pay a transport bi
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quantity transported of Z decreases
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The analysis yields a downward slop
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of each market and calculates each
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If more consumption points ,are add
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or ( 5 1) . 1. Q-14.)4 `("P)EXarg (
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4. 0 -A? 040- Net MR 1 0 so. Ira."
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To determine the demand curve for t
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I • The above equations (1-4) wer
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(I). 1■1 (7). Id. (8). •a 0.0.1
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• goods arrive (so that Q A+Q S g
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k The optimal amounts of QA and Q s
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it has been used in economics. Basi
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An analogous relationship exists fo
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• • (11). Now a probability dis
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--_.—..---...........AawmarA D SA
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, (1). APPENDIX TO CHAPTER III SENS
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decreases. Proper choice of P rA (X
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products, have different cost funct
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The above data falls short of the q
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lower than air rates. It rises more
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One of the objectives of the study
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a. Regression equation TABLE IV-1 r
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significant. 8 It was, therefore, d
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in large tonnages tend to have a lo
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T .A T ° S Highest value per pound
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. In addition, only the smallest qu
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Here the deviations are zero. The r
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certain range, the demand estimates
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expected as goods in the discrimina
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• BIBLIOGRAPHY [1] Air Cargo Maga
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[24] 2 Study of the Possibilities f
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[42] Dawson, Michael, "A Technique
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[62] Gorham, G., Sealy, K.R. 1 and
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■•■•■■•••••
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[100] Richards, Anthony, The Role o
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[120] Traffic World Marketing Study
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! i \ NORTHWESTERN UNIVERSITY FREIG
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While working on this dissertation
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BIBLIOGRAPHY Anderson, T.W. "An Int
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VITA MICHEL VINCENT BEUTHE Born in
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of cost iv iazroduced at once along
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In the present theoretical formulat
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It is possible to generalize this m
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however, because of their nature, t
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ij xo ij ,Diagram 3, . 0 X ij of th
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equal to+ where E is the median of
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CHAPTER II Discrimination With One
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which is,.in this case, the only q
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Notc that the first subscript of a.
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I .' 1) (22) P 1 (X) = (25) Therefo
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(34) P 2 (X) (36) 1 = 1 a b c ' and
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CHAPTER III An Application - Corn T
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time the draft is honored by the co
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2. Critique of the Data. We must no
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made through questionnaires to coun
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we can still hope to obtain satisfa
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common and contract carriers are co
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Table II. Rail Time Regressions: Ti
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3. The Statistical Results. After t
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Table IV gives the discriminant fun
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February non-weighed July weighed T
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the binary problems, when the choic
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Table VII Probabilities that an obs
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Table VIII, Probability of Correct
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significantly different from the 'n
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-X _21 5.15 L4.45 TRUCK RAIL lalm
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CHAPTER IV. A Predictive Model of R
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C ab /C a is smaller than one, the
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II. Rail-Water Competition: One Por
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Until now, no attention has been pa
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9 ) (Z a - kZ b ) = C w /C r Zab +
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shipper. In the reality of competit
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DIAGRAM 5 For the most interesting
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DIAGRAM 7 waterway may be numerous.
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Note the restriction of Y to its ab
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the road-water route. In (24) C t (
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Squaring both sides, one obtains an
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interesting expressions. However, t
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CHAPTER V. This chapter attempts to
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TOTAL . COST D = -(L r - L t ) 2 Th
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2. Two Markets Model. subject --co
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X 0, X 2 - 0. It can readily be see
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the river does not have any --, but
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:sLY: x rail 0 truck 0 rail and tru
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'NLY: K rail 0 truck 0 rail and tru
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Table XI. Rail Rates Regressions: C
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mileages. The reason why this ratio
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Table XIII. Boundary Equations. Wat
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DIAGRAM 21 Figure T shows the actua
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truck sample is small ( 148 origins
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In this application of the spatial
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NORTHWESTERN UNIVERSITY LIBRARY Man
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in the dissertation. In addition, h
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Analysis of Tow in Motion 66 Introd
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Table • TABLES Statistical Result
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deepening or widening the channel,
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lines and isoquants. This locus is
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limited to the cost and production
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problem because engineers also atte
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are ignored. Making sure that the r
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variables, the form of the basic re
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family of cost curves obtained in t
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economies of scale exist in ihe tra
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in which R = resistance, in taw-rop
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(2)marginal productivity of the boa
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conditions are not always met in pr
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production relationship, e.g., a ma
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Howe's production and planning mode
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of the barge coefficient seemed to
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1962 counterparts. However, only (1
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A 10 peicont increase in all inputs
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proportion of constant costs. Typic
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In short, cost was estimated as a f
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o f cars, etc.). Each is then multi
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haul. The variable (Z/X) was used i
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In the switching process--which con
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defined to be the percentage change
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other production analysis of rail i
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of transportation, the inputs contr
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It will be convenient to define T f
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vchicles, is considered to be a poi
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F t (v) = B/v. 6 Therefore, the equ
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The graphical expression of Equatio
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And the distance traveled, D c , du
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CHAPTER IV LINEHAUL PROCESS FUNCTIO
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Form of Process Function The proces
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particular . trip', that tonnage ma
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ostimated from a capacity cable for
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The function was originaliy fit by
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were greater than 11 miles per hour
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effective-push functions will be ex
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ilotilla. These assumptions will no
Page 513 and 514:
Upon testing the hypotheses indicat
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for in the first case tows were sem
Page 517 and 518: a 0 / V I HP 3000 - 12 - 225 • H
Page 519 and 520: 3.5 3.0 1.5 5.. 2.0 7, 4.0 ■•
Page 521 and 522: A final note concerning the effect
Page 523 and 524: predict the time required for trave
Page 525 and 526: Given the tonnage, 0, to be carried
Page 527 and 528: existence. For example, the locks o
Page 529 and 530: If all locks on the waterway arc tr
Page 531 and 532: loaded ones in 1950; therefore p is
Page 533 and 534: T L -2; Single Double Locking Locki
Page 535 and 536: u T L 1 Table 4.7 INDIVIDUAL AND SY
Page 537 and 538: it would leave the system. Alternat
Page 539 and 540: The government should incur the cos
Page 541 and 542: I si,:e was 3.1 bares. The small av
Page 543 and 544: To simplify the analysis all delay-
Page 545 and 546: characteristics and delays. Therefo
Page 547 and 548: Equation (4.37) divides the total :
Page 549 and 550: Xore confidence may be attached to
Page 551 and 552: Recapitulation of Tow Linehaul Proc
Page 553 and 554: function. The difference beiween th
Page 555 and 556: S -, speed of water, in miles per h
Page 557 and 558: y the above analysis, but for more
Page 559 and 560: econoinic analysis of the rail linc
Page 561 and 562: deceleration, Equation (3.8). Moreo
Page 563 and 564: Then the cargo weight of the ith ca
Page 565 and 566: (4, 6, or 8), the weight of the loc
Page 567: Analysis of Train in Motion Introdu
Page 571 and 572: Adiustment for Grade and Curvature.
Page 573 and 574: Curve resistance, like grade resist
Page 575 and 576: F . 0 VI Fd(v) F (v) t Fig. 5.1 --
Page 577 and 578: and (5.26), and 2-miles-per-hour sp
Page 579 and 580: per trip into several components, e
Page 581 and 582: N t = number of trains on a given r
Page 583 and 584: Table 5.1 STATISTICAL ANALYSIS OF T
Page 585 and 586: Each of the terms V f and C represe
Page 587 and 588: nowever, in the case of the rail li
Page 589 and 590: -, 1 9, D 0 ,- ._ 200 ! i 175 '—
Page 591 and 592: Horsepowe r ( in t hou sa n ds ) 3
Page 593 and 594: exceeded 6,000 horsepower, for at p
Page 595 and 596: Curvatures of greater than 5 degree
Page 597 and 598: hohavior of rail costs. First, the
Page 599 and 600: eing charged at the higher rate. Th
Page 601 and 602: 2. If train speed is greater than o
Page 603 and 604: maximula attainable horsepower of t
Page 605 and 606: price for each locomotive unit from
Page 607 and 608: I L' is given by (0.5)($94HP L - $4
Page 609 and 610: Figure 5.4 displays a set of short-
Page 611 and 612: Economics of scale, in fact, seem t
Page 613 and 614: Tab1e 5.8 LONG-RUN MARGINAL COST OF
Page 615 and 616: obtained this way may then be added
Page 617 and 618: The estimating methods for each of
Page 619 and 620:
Cos t per ton -mi le (m ;1 1s ) 7.2
Page 621 and 622:
CHAPTER VI SUMMARY AND CONCLUSIONS
Page 623 and 624:
eached for acceleration, which take
Page 625 and 626:
wide range of output would have to
Page 627 and 628:
Isoquants between car and locomotiv
Page 629 and 630:
eported in the dissertation will in
Page 631 and 632:
10. M. Bronfenbrenner and P. H. Dou
Page 633 and 634:
13. A. V.ctor Cabot and Arthur P. H
Page 635 and 636:
7. There are in fact three differen
Page 637 and 638:
26. Eric Bottoms, "Practical Tonnag
Page 639 and 640:
19. Hay, An Introduction to Transpo
Page 641 and 642:
BIBLIOGRAPHY American Railway Engin
Page 643 and 644:
Howe, Charles M... "Methods for Equ
Page 645 and 646:
Soberman, Richard. "A Railway Perfo
Page 647 and 648:
NORTHWESTERN UNIVERSITY ESTIMATION
Page 649 and 650:
TABLE OF COIMETS Page Chapter I. In
Page 651 and 652:
CHAPTER I INTRODUCTION AND REVIEW O
Page 653 and 654:
On the other hand, the statistical
Page 655 and 656:
and capital Outlays are also treate
Page 657 and 658:
TABLE 1 SUMMARY ESTIMATES OF RAILRO
Page 659 and 660:
C (X) FIGURE • ■ 9
Page 661 and 662:
The effects of two types of classif
Page 663 and 664:
egression equations will produce bi
Page 665 and 666:
S = speed in miles per hour W = wid
Page 667 and 668:
(6) S = h(HP, L, B, H, D, W) The ac
Page 669 and 670:
stock which remains idle. Under the
Page 671 and 672:
The planning function also exhibite
Page 673 and 674:
Of the production functions, (13, 1
Page 675 and 676:
sources of data. Despite the use of
Page 677 and 678:
The reader should note several them
Page 679 and 680:
from variations in rates based on v
Page 681 and 682:
service the firm would want to set
Page 683 and 684:
oat output, or effort, is not propo
Page 685 and 686:
this level of disaggregation are ex
Page 687 and 688:
CHAPTER III A STATISTICAL PRODUCTIO
Page 689 and 690:
A second way of generating data inv
Page 691 and 692:
variables, even if it is not accura
Page 693 and 694:
Three major inland waterway firms p
Page 695 and 696:
from changing depth or stream flow.
Page 697 and 698:
made for each. (In the log-linear r
Page 699 and 700:
•Ps Variable Name Riven Districts
Page 701 and 702:
Variable Name River Districts Port
Page 703 and 704:
La Variable Name River Districts TA
Page 705 and 706:
Variable Name River Districts TABLE
Page 707 and 708:
t..n .....1 TABLE 6 . . VARIABLE ME
Page 709 and 710:
A. Linear Regression (Arithi.etic M
Page 711 and 712:
are roughly comparable across all c
Page 713 and 714:
termed "labor embodied technologica
Page 715 and 716:
TABLE 8 COMPANY ONE LINEAR REGRESSI
Page 717 and 718:
the other monthly coefficients indi
Page 719 and 720:
CHAPTER IV AN ANALYSIS OF DIRECT TO
Page 721 and 722:
with the use of dummy variables. To
Page 723 and 724:
A more direct method, and the one e
Page 725 and 726:
. cost In using; for example, , cro
Page 727 and 728:
• ,,, • .. -Excluded Variables
Page 729 and 730:
200,000 EBM per year) comes to abou
Page 731 and 732:
Form C weights have limited accurac
Page 733 and 734:
study as to the level of output to
Page 735 and 736:
The firm in the sample operates a l
Page 737 and 738:
would tend to be slightly higher co
Page 739 and 740:
3. other bulk 4. petroleum products
Page 741 and 742:
In addition, river districts with s
Page 743 and 744:
where: Cost = annual total direct b
Page 745 and 746:
1964 1965 Variable Name Barge Type
Page 747 and 748:
TABLE 13 F-TESTS FOR BARGE COST REG
Page 749 and 750:
tend to rise with increases in barg
Page 751 and 752:
ing is quite consistent with a prio
Page 753 and 754:
TABLE 16 PERCENT COMMODITY REGRESSI
Page 755 and 756:
arge was to ship one more commodity
Page 757 and 758:
1 are the costs of operating and ma
Page 759 and 760:
preparation of barges is necessary
Page 761 and 762:
estimated was the same for all thre
Page 763 and 764:
TABLE 17 DIRECT BARGE EXPENSE r 2 =
Page 765 and 766:
Variable Name TABLE 19 TERMINAL EXP
Page 767 and 768:
considerable growth in the past twe
Page 769 and 770:
also be used in conjunction with di
Page 771 and 772:
to an already scheduled tow). Two k
Page 773 and 774:
The terminal results are quite tent
Page 775 and 776:
The five firms in the sample repres
Page 777 and 778:
sure the extent of this activity, a
Page 779 and 780:
1 linear form of- the functions hav
Page 781 and 782:
C. Net Tons of Barge Capacity TABLE
Page 783 and 784:
Indirect cost is the same for towbo
Page 785 and 786:
A. Total Horsepower TABLE 22 CROSS
Page 787 and 788:
1 .‘ A. Total Horsepower TABLE 23
Page 789 and 790:
to scheduling. In addition, we obse
Page 791 and 792:
:CHAPTER VII SUMMARY AND CONCLUSION
Page 793 and 794:
the coefficients of the dummy varia
Page 795 and 796:
. The coefficients of the dummy var
Page 797 and 798:
Supporting results for neutral tech
Page 799 and 800:
port agencies. A considerable amoun
Page 801 and 802:
I to inland waterway operators, sin
Page 803 and 804:
Footnotes--Continued 7 Howe, Jan.,
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Footnotes--Continued This is also w
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Bibliography--Continued Interstate
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UNCLASSIFIED Security Classificatio
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Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

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