© Strojni{ki vestnik 46(2000)5,302-308 © Journal of Mechanical Engineering 46(2000)5,302-308 ISSN 0039-2480 ISSN 0039-2480 UDK 629.3.013:656.13 UDC 629.3.013:656.13 Pregledni znanstveni ~lanek (1.02) Review scientific paper (1.02) Numeri~na analiza kazalnikov izkoristka nosilnosti cestnih vozil Numerical Analysis of the Capacity-Exploitation Parameters of Road Vehicles Jurij Kolenc - Ivan Smerdu - Stojan Petelin Za določanje učinkovitosti transportnega dela cestnih vozil obstajajo številni tehnično-tehnoloski in uporabnostni kazalniki, med katerimi imajo poseben pomen kazalniki izkoristka nosilnosti. V prispevku je analiziran način ugotavljanja koeficientov statične in dinamične izkoristka nosilnosti cestnih vozil ter njihove medsebojne primerjave. Numerična analiza je opravljena za primer izkoristka enega vozila v eni vožnji s tovorom, za eno vozilo v določenem časovnem obdobju, za homogeni vozni park ali skupino vozil iste nosilnosti in nehomogeni vozni park ali n skupinami vozil iste koristne nosilnosti. © 2000 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: vozila cestna, nosilnost vozil, učinkovitost transporta, modeliranje numerično) There are numerous technical, technological and exploitation parameters for determining the transportation work efficiency of road vehicles, among the most important are the capacity-exploitation parameters. In this paper, the determination of static and dynamic coefficients of the capacity-exploitation parameters of road vehicles and their mutual comparison is analysed. A numerical analysis is realised for the case of one vehicle in one ride with cargo, for one vehicle in a defined time period, for a homogeneous motor pool or a group of vehicles with same capacity and an inhomogeneous motor pool or n groups of vehicles of the same benefit capacity. © 2000 Journal of Mechanical Engineering. All rights reserved. (Keywords: road vehicles, vehicle capacity, transportation effects, numerical modelling) 0 UVOD Načrtovanje, raziskovanje in ocenjevanje učinkovitosti dela cestnih vozil v potniškem in tovornem prometu niso mogoči brez analize določenih kazalnikov za vrednotenje ustvarjenih rezultatov dela [1]. Obstajajo številni tehnološko-uporabnostni kazalniki dela cestnih vozil, npr. kazalniki časovne bilance dela vozil, kazalniki izkoristka prevožene poti, kazalniki pogojev pri opravljanju transportnega dela, kazalniki izkoristka zmogljivosti cestnih vozil ter prevozne zmožnosti cestnega voznega parka idr. Med vsemi temi kazalniki, posebej pa v skupini kazalnikov izkoristka zmogljivosti cestnih vozil, so najpomembnejši tisti, ki se nanašajo na nosilnost. Slab izkoristek cestnih vozil zmanjšuje njihov transportni učinek, izražen v tonskih kilometrih (tkm), prostorninskih kilometrih (m3km) ali potniških kilometrih (pkm), kar je posebej pomembno na večjih razdaljah [3]. 0 INTRODUCTION Planning, researching and grading the work efficiency of road vehicles in public and cargo traffic is not possible without an analysis of the determined parameters for grading the acquired results of work [1]. There are numerous technological and exploitation parameters for road-vehicle work, for ex-ample: time parameters of vehicle-work balance, exploitation parameters of the transportation route, condition parameters in realising transportation work, capacity exploitation parameters of road vehicles and the transportation capability of a road motor pool etc. Among all these parameters, especially in the group of capacity-exploitation parameters of the road vehicle, the most important are the parameters that refer to capacity. Under exploitation of road ve-hicles decreases their transportation effect in ton kilo-metres (tkm), volume kilometres (m3km) or passenger kilometres (pkm), which is especially important over longer distances [3]. grin^SfcflMISDSD ^BSfiTTMlliC | stran 302 J. Kolenc - I. Smerdu - S. Petelin: Numeri~na analiza - Numerical Analysis Izkoristek nosilnosti cestnih vozil se ugotavlja z numerično analizo modelov statične in dinamične izkoriščenosti koristne nosilnosti in njihovih medsebojnih odnosov. 1 RAČUNSKI MODEL STATIČNEGA IZKORISTKA NOSILNOSTI CESTNIH VOZIL Model statičnega izkoristka nosilnosti cestnih vozil predstavlja način ugotavljanja koeficienta statičnega izkoristka kot razmerja količine prepeljanega tovora in količine tovora, ki bi lahko bila prepeljana pri popolnoma izkoriščeni nosilnosti. Koeficient statičnega izkoristka cestnih vozil (g) dobimo z naslednjimi enačbami. The capacity exploitation of road vehicles is determined with the help of numerical analysis models of static- and dynamic-benefit capacity exploitation and their mutual comparison. 1 NUMERICAL MODEL OF STATIC CAPAC-ITY EXPLOITATION FOR ROAD VEHICLES The model of static-capacity exploitation for road vehicles represents the way of establishing the coefficient of static exploitation compared to the quantity of transportation goods and the quantity of goods that could be transported by complete capac-ity exploitation. The coefficient of static exploitation for road vehicles (g) is determined with the following equations. - Za eno vozilo v eni vožnji s tovorom: - For one vehicle in one drive with cargo: qx g= q (1), kjer sta: q - dejanska količina tovora, ki je prepeljana v eni vožnji s tovorom, qx - koristna nosilnost vozila. - Za eno vozilo v določenem časovnem obdobju: where: q - is the real quantity of cargo that is transported in one drive with cargo, qx -is the benefit capacity of road vehicles. - For one vehicle in a determined time period: kjer sta: Q1-količina tovora, ki je prepeljana z enim vozilom v določenem časovnem obdobju, Z - število voženj s tovorom v določenem časovnem x obdobju. - Za homogeni vozni park ali skupino vozil iste koristne nosilnosti v določenem časovnem obdobju: Q / j qxi / j qxi qZx x q (2), where: Q1-is the cargo quantity that is transported with one vehicle in a determined time period, Zx- is the number of drives with cargo in a determined time period. - For a homogenous motor pool or a group of vehi-cles with the same benefit capacity in a determined time period: x qx 2qxi qAZx qAZx x q (3), kjer so: Q -količina dejansko prepeljanega tovora, q -koristna nosilnost enega vozila, AZ - število voženj voznega parka s tovorom v določenem časovnem obdobju. where: Q - is the cargo quantity which is actually transported, q - is the benefit capacity of one vehicle, AZx- is the number of drives in a motor pool with cargo in a determined time period. - Za nehomogeni vozni park ali več skupinami vozil iste koristne nosilnosti: g' - For an inhomogeneous motor pool or more groups of vehicles of the same benefit capacity: n Y.Qi YaAZxi qigi n AZxi qigi n i=1-----= n--------= i=1 n------ (4), L,AZxiqi LAZxi qi qQLAZxi stran 303 glTMDDC g J. Kolenc - I. Smerdu - S. Petelin: Numeri~na analiza - Numerical Analysis kjer je: T.Qi = AZx1q1g1+Zx2q2g2 where: + AZxi qigi AZxnqngn oziroma skupna količina tovora, ki jo prevažajo vse in other words, the total cargo quantity which is trans- skupine vozil, ter razmerje količin, ki bi se lahko ported by all groups of vehicles and compared to the prepeljale, če bi nosilnost vseh vozil v vseh skupinah quantities that could be transported if the capacity of in pri vsaki vožnji s tovorom bila popolnoma all vehicles in all groups and in all drives with cargo porabljena. would be totally exploited. n E AZxi qi = AZx1q1 + AZx 2q2 +... + AZxi qi +...+ AZxnqn i _1 q’ - povprečna nosilnost heterogenega voznega parka za obseg prevoza. Iz enačbe za koeficient statičnega izkoristka nosilnosti cestnega vozila izhaja: q’Q - is the average capacity of a heterogeneous motor pool for transportation volume. This equation originates from the equation for the coefficient of static-capacity exploitation of road vehicles: n TQi=gTAZxi qi=gq'TAZxi (5), Ker so nosilnosti cestnih vozil po posameznih skupinah različne (q1 *q2*qi*q), se pojavlja problem določanja povprečne nosilnosti vozil v nehomogenem voznem parku. V praksi se najpogosteje uporablja razmerje celotne nosilnosti vseh vozil v voznem parku in števila vozil v voznem parku, ki se dobi po enačbi [5]: Because the capacities of road vehicles in individual groups are different (q1 *q2*qi*q), there is the problem of determining the average capacity of vehicles in an inhomogeneous motor pool. In practice, the most frequently used relation is the total capacity of all vehicles in the motor pool and the number of vehicles in the motor pool. It is defined by equation [5]: n Ak1q1+Ak2q2+... + Aknqn i=1' Aq + A +... + ^ (6). Ko v enačbo za obseg prevoza vstavimo When we insert the average capacity of all povprečno nosilnost vseh vozil (q’ ), dobimo za vehicles in the equationn for the volume of transpor- n Qi: s tation (q’s), we obtain LQi : n n g 2-1 Akiqi 2-1 AZxi g T AZiqi = i=1= i =1 i=1 i =1 g'Y.AZxi oziroma or n Y.AZxiqi n,Aki qi Y.AZxi Dinamična povprečna nosilnost cestnih vozil za obseg prevoza heterogenega voznega parka (q’Q), ki se edina lahko uporablja pri preračunu, je v bistvu povprečna koristna nosilnost vozil pri vsaki vožnji s tovorom celotnega heterogenega voznega parka, izračunamo pa jo z enačbo: (7). The dynamic average capacity of road ve-hicles for the transportation volume of a heterogene-ous motor pool (q’Q), which can only be used for calculating, is really the average benefit capacity of vehicles in every drive with cargo of the total hetero-geneous motor pool. This equation defines it as: Y,AZxi qi TAZxi i=1 AZx1q1 + AZx2q2 + ...+ AZxiqi +...+ AZxnqn AZ + AZ +...+ AZ +...+ AZ qQ VBgfFMK stran 304 J. Kolenc - I. Smerdu - S. Petelin: Numeri~na analiza - Numerical Analysis qQ' = ZAZxi qi Š1 Q ~n (8). qQ*qS V posebnih primerih je povprečna nosilnost za obseg prevoza celotnega heterogenega voznega parka (q’) enaka statični srednji vrednosti (q’). To se dogaja Q ko sta izpolnjena naslednja dva pogoja [6]: - da je knjigovodsko število vozil v vseh n skupinah vozil enako, - da je vsaka skupina vozil heterogenega voznega parka opravila enako število voženj s tovorom. Ta pogoja lahko prikažemo na naslednji način: In special cases, the average capacity for the transportation volume of the total heterogeneous motor pool (q’Q) is identical to the static medium value (q’s). This happens when these two conditions are realised [6]: - that the bookkeeping number of all vehicles in all n groups is the same, - that all groups of vehicles of the heterogeneous motor pool realise the same number of drives with cargo. These conditions can be shown in this way: Ak1 = Ak 2 = Ak 3 = ... = Akn = ... = Ak i AZx1 AZ =AZ AZ AZ Če spoštujemo navedene pogoje, dobimo (q’s) po enačbi: n]A ki q i qs' nA If we consider the listed conditions, we obtain (q’s): A qi 7 qi i1 (9), s k (q1 + q2 + ...+ qn) nA nA kjer je: n - število skupin vozil heterogenega voznega parka qQ AZxq1 + AZxq2 +...+ AZxqn AZx(q1 + q2 +...+ qn) where: n - is the number of group vehicles in the heterogeneous motor pool nAZn nAZ nAZ Tako je dokazana enakost (q’ = q’ ) v primeru, ko sta izpolnjena navedena pogoja, kar pa se v praksi zelo redko pojavlja. 2 RAČUNSKI MODEL DINAMIČNEGA IZKORISTKA CESTNIH VOZIL Model dinamičnega izkoristka nosilnosti cestnih vozil oziroma koristne nosilnosti, pomeni način ugotavljanja koeficienta dinamičnega izkoristka kot razmerja med skupno opravljenim transportnim delom in mogočim transportnim delom. V nasprotju s koeficientom statične izkoriščenosti koristne nosilnosti cestnih vozil, ki upošteva količino dejansko prepeljanega blaga, vključuje koeficient dinamične izkoriščenosti koristne nosilnosti tudi razdalje, na katerih se tovor prevaža [5]. Koeficient dinamičnega izkoristka nosilnosti se določa po naslednjih enačbah. The equality is proven in this case (q’Q = q’s), when the listed conditions are met, however, this is rare in practice. 2 NUMERICAL MODEL OF THE DYNAMIC EXPLOITATION OF ROAD VEHICLES The model for the dynamic-capacity exploitation of road vehicles, or benefit capacity, presents a way of establishing the coefficient of the dynamic exploitation in relation to the totally realised transportation work and the possible transportation work. As distinguished from the coefficient of static exploitation of benefit capacity of road vehi-cles that considers the quantity of actually transported goods, the coefficient of dynamic exploitation of benefit capacity also includes the distance over which the cargo is transported [5]. The coefficient of dynamic capacity exploitation is determined with the following equations: - Za eno vozilo in eno vožnjo s tovorom: - For one vehicle and one drive with cargo: qL qL q x stx xtx x qLs stx qLt q tx (10), gfin^OtJJIMISCSD 00-5 stran 305 |^BSSITIMIGC d J. Kolenc - I. Smerdu - S. Petelin: Numeri~na analiza - Numerical Analysis - za eno vozilo v določenem časovnem obdobju: - for one vehicle in a determined time period: S / , (qxLtx )i 2-i (qx Ltx )i x (qLtx)i q x Ltx (11). kjer so: S - opravljene transportne storitve, S ak - največje število možnih storitev, n - število voženj s tovorom v določenem časovnem obdobju, q - količina tovora, ki se prepelje v posameznih x vožnjah, L -razdalja s tovorom v posameznih vožnjah, Lstx - srednja razdalja ene vožnje s tovorom. - Za homogeni vozni park ali skupino cestnih vozil iste nosilnosti: where: S - are the realised transportation services, Smaks - is the maximum number of possible transportation services, n - is the number of drives with cargo in a deter-mined time period, qx- is the cargo quantity during individual drives, Ltx- is the distance with cargo for individual drives, Lstx - is the medium distance of one drive with cargo. - For a homogenous motor pool or a group of road vehicles with the same capacity: d S ALtq / , (qxLtx )i 2-i (qx Ltx )i 2-i (qx Ltx )i x (qLtx )i q x Ltx qALt (12), kjer sta: AZx - število voženj s tovorom vsega voznega parka, AL - razdalja s tovorom vsega voznega parka. where: AZx - is the number of drives with cargo for a motor pool, ALt - is the total distance for the whole motor pool with cargo. - Za heterogeni vozni park: n Si n Si - For a heterogeneous motor pool: n Y.ALtiqiöi n ALti qiA ES maxi z2ALti qi Y,ALtiqi q'z2ALti (13), kjer je vsota opravljenega transportnega dela vseh skupin vozil v voznem parku: where the amount of realised transportation work for all groups of vehicles in the motor pool: ESi = ALt1q1A+ ALt2q2S2+ ...+ ALtiqiSi+ ... + ALtnqnÖn in razmerje možnega transportnega dela vsega heterogenega voznega parka: n Y.ALti qi=ALt1q1+ALt2q2 3 PRIMERJAVA STATIČNEGA IN DINAMIČNEGA IZKORISTKA CESTNIH VOZIL Za eno cestno vozilo v nekem časovnem obdobju ali za homogeni vozni park oziroma skupino vozil iste nosilnosti je ugotovljeno, da je koeficient dinamičnega izkoristka nosilnosti večji ali manjši od koeficienta statičnega izkoristka za tolikokrat, kolikokrat je srednja razdalja transporta ene tone tovora večja ali manjša od srednje razdalje vožnje s tovorom, to je: and the relation of the possible transportation work heterogeneous motor pool: ... + ALti qi .+... + ALtn qn 3 COMPARISON OF STATIC AND DYNAMIC EXPLOITATION OF ROAD VEHICLES For one road vehicle in a determined time period or for a homogenous motor pool or a group of vehicles of the same capacity it is determined that the coefficient of dynamic-capacity exploitation is bigger or smaller than the coefficient of static exploitation. This coefficient is bigger or smaller by the number of times the medium distance of the transportation of one ton of cargo is bigger or smaller than the medium distance of the drive with cargo: VBgfFMK stran 306 d J. Kolenc - I. Smerdu - S. Petelin: Numeri~na analiza - Numerical Analysis d= d g S g = Q ALtq qAZx S ALtq SAZx Q Q-ALt qazx S Q AZx 1 = = Lst in/and ALt Lstx ter/then dL st1 = gL stx (14), kjer je: Lst1 - srednja razdalja prevoza ene tone tovora. To razmerje ne velja za ves heterogeni vozni park. Pri koeficientu dinamičnega izkoristka koristne nosilnosti (d) je težni faktor povprečne nosilnosti število kilometrov s tovorom, pri koeficientu statičnega izkoristka (g) pa je število voženj s tovorom [3]. ali/or d-Lstx=g-Lst1 where: L - is the medium distance travelled with one ton st of cargo. This relation does not consider all of the heterogeneous motor pool. The coefficient of dynamic exploitation of benefit capacity (d) is an estimated factor of the average capacity of the number of kilometres with cargo. The coefficient of static exploitation (g) is the number of drives with cargo [3]. Ker je: n Y.ALtiqi di ^AZxi qi g i d'=i =1------------; g=i=1 Since: n Halti qi i=1 ;L' = i =1 n stx n n TALti qid ;L'.=i=1----------- ^azxi qi ZAZxi TAZxiqig i je/is d'L'stx = g'Lst1 nlALtiqidi llALti Y.ALtiqidi i=1 i=1 EALti qi Y.AZxi ^AZxiqi i=1 i=1 Ž ALtiqidi X ALti Y AZxi qi = Y ALtiqidi Ž ALtiqi L AZx i=1 i=1 n Y.AZxiqi n ALti qi YAZxi YALti (15). Ta enakost ni točna in tudi razmerje (d-Ltx=g-Lstx) This equality is not correct and the relation ne velja, ker je: (d-Lstx = g-Lstx) is not valid, because: n YAZxi qi YALti qi in/and n ALti ter/and qQ * qS TAZxi i=1 i=1 razen v primeru, ko so izpolnjeni pogoji, velja enakost: except in the case when the conditions are met: qS' =qU' =qQ' grin^diJjpsflDsijai 00-5 stran 307 |^USSSIrlMlGC J. Kolenc - I. Smerdu - S. Petelin: Numeri~na analiza - Numerical Analysis 4 SKLEP Numerična analiza kaže način ugotavljanja statične in dinamične izkoriščenosti nosilnosti cestnih vozil ter njihov vpliv na transportni učinek. Statični in dinamični izkoristek cestnih vozil je pri tem analiziran z vidika števila voženj z cestnimi vozili, časovnega obdobja in sestave voznega parka. S primerjavo numerične analize statične in dinamične nosilnosti cestnih vozil je ugotovljeno, da je za eno vozilo ali skupino vozil iste nosilnosti za določeno časovno obdobje koeficient dinamičnega izkoristka večji ali manjši od koeficienta statične izkoriščenosti za tolikokrat, kolikokrat je srednja razdalja transporta ene tone ali m3 tovora večja ali manjša od srednje razdalje transporta s tovorom. Za heterogeni vozni park to ne velja, temveč je pri koeficientu dinamične izkoriščenosti koristne nosilnosti utežni faktor povprečne nosilnosti število kilometrov s tovorom, pri koeficientu statičnega izkoristka pa je to število voženj s tovorom. 4 CONCLUSION The numerical modelling shows a way of es-tablishing the static- and dynamic-capacity exploitation of road vehicles as well as their influence on the transportation effect. The said exploitation of road vehicles is analysed with respect to the number of drives by road vehicles, time period and the structure of the motor pool. By comparing the static and dynamic capac-ity of road vehicles it has been established that for one vehicle or a group of vehicles of the same capacity for the determined time period the coefficient of dynamic exploitation is bigger or smaller than the coefficient of static exploitation. The difference is found to be proportional to the difference between the medium distance of the transportation of one ton or m3 of cargo and the medium distance of the transportation with cargo. For a heterogeneous motor pool this does not work, therefore the coefficient of the dynamic exploitation of benefit capacity has the estimated fac-tor of the average capacity number of kilometres with cargo, whereas the coefficient of static exploitation presents the number of drives with cargo. 5 LITERATURA 5 REFERENCES [1] Shave, V., VA. Michel (1998) The impact of driver and flow variability capacity estimates of permissive movements. Transportation Research, Part A: Policy and Practice, Vol. 32.A, No. 7, 509-527. [2] Grubbstrom, R. W. (1998) Transportation inventory optimisation - A note. Proceedings of the 2 rd International Conference on Traffic Science ICTS’98, Trieste-Patras, 125-129. [3] Kolenc, J. (1999) Modeling of the transportation route in the processes of transporting goods. Proceedings of the 3 rd International Conference on Traffic Science ICTS’99, Portorož, 17-28. [4] May, A.D. (1990) Traffic flow fundamentals. Prentice-Hall, New Jersey. [5] Vuchic, V. (1981) Urban public transportation. Prentice-Hall, New York. [6] Kolenc, J. (1998) Organization and technology in the road traffic, Faculty of Maritime Studies and Transportation, Portorož. Naslov avtorjev: profdr. Jurij Kolenc dr. Ivan Smerdu profdr. Stojan Petelin Fakulteta za pomorstvo in promet Univerze v Ljubljani Pot pomorščakov 4 6320 Portorož Authors’ Address: Prof.Dr. Jurij Kolenc Dr. Ivan Smerdu Prof.Dr. Stojan Petelin Faculty of Maritime Studies and Transportation University of Ljubljana Pot pomorščakov 4 6320 Portorož, Slovenia Prejeto: Received: 23.3.2000 Sprejeto: Accepted: 2.6.2000 grin^SfcflMISDSD ^BSfiTTMlliC | stran 308