Vehicle Platooning Impact on Drag Coefficients and Energy/Fuel Saving Implications

V ehicle Plato oning Impact on Drag Co efficien ts and Energy/F uel Sa ving Impli cations Ahmed A. Hussein 1 , Hesham A. Rakha 2 Abstract In this pap er, empirical dat a from the literature a r e used to dev elop general p ow er mo dels that c apture the impac t of a v ehicle p osition, in a plato on o f homogeneous v ehicles, a nd the distance gap to its lead (and f o llo wing) v ehicle on its dr a g co efficien t. These mo dels are dev elop ed f or ligh t dut y v ehicles, buses, and hea vy dut y truck s. The mo dels we re fit using a constrained optimization fr a mew ork to fit a general p o w er function using either direct drag force or fuel measuremen ts. The mo del is then used to extrap o la te the empirical measuremen ts to a wide range of v ehicle distance gaps within a plato on. Using these mo dels w e estimate the p oten tial fuel reduction asso ciated with homogeneous plato ons of ligh t dut y v ehicles, buses, and hea vy dut y truc ks. The results sho w a significan t reduction in the v ehicle fuel cons umption when compared with those based on a constant drag co efficien t a ssumption. Sp ecifically , considering a minim um time gap b et w een v ehicles of 0 . 5 secs (whic h is t ypical considering state-of-practice comm unication and mec hanical system latencies) running at a sp eed of 100 k m/hr , the optim um fuel reduction that is ac hiev ed is 4 . 5%, 15 . 5%, and 7 . 0% for lig h t dut y v ehicle, bus, a nd hea vy dut y truc k plato o ns, resp ectiv ely . F or longer time gaps, the bus a nd hea vy duty truc k plato ons still pro duce fuel reductions in the order of 9 . 0% and 4 . 5%, wh ereas lig h t dut y v ehicles pro duce negligible fuel sa vings. 1 Post-Doctor ate F ellow, Center for Sustainable Mobilit y , Virginia T ec h T ranspo rtation Institute, 3500 T r ansp ortation Resea r ch Plaza (05 36) Blacksburg, V A 2406 1, USA. 2 Samuel Reynolds Pritchard Professor of Engineering, Cen ter for Sustainable Mobility , Virginia T ech T r ansp ortation Institute, 3 500 T ransp orta tion Resear ch P la za (05 36) Blacksburg, V A 2 4061, USA. Co r re- sp onding a uthor (hrakha@vt.edu). Pr eprint submitt e d to Elsevier Novemb er 30, 2021 1. In tro duction The ob jectiv es of this pap er are tw o -fold. First, w e dev elop general p o wer mo dels that capture the impact o f a v ehicle p osition, in a pla to on of homogeneous ve hicles, and the distance gap to its lead (and f o llo wing) v ehicle on its dr a g co efficien t. These mo dels are dev elop ed for lig h t dut y ve hicles, buses, and hea vy dut y truc ks. Second, we use these mo dels to estimate the p oten tial fuel reduction asso ciated with ho mo g eneous plato ons of ligh t duty v ehicles, buses, and hea vy duty truc ks. The contributions of the pap er is that it is the first effort t o dev elop analytical mo dels that relate the v ehicle’s drag co efficien t to a v ehicle’s p o sition, in a plato on of homogeneous v ehicles, and the distance gap to its lead (and follow ing) v ehicle on its drag co efficien t. 1.1. Liter atur e R eview and Backgr ound Plato oning is ga ining momentum as an efficien t appro ac h to increase roa dw a y capacity and reduce ve hicle fuel consumption, as sev eral studies ha v e suggested [1, 2, 3 , 4, 5, 6, 7, 8 , 9]. One o f the k ey factors b ehind this reduction in fuel consumption is the relatio nship b etw een the in ter-plat o on distance gap and the drag f orces. The drag force generated on a v ehicle consists of tw o main comp onen ts, namely: (i) the skin friction drag, and (ii) the form dra g. The skin friction dra g depends mainly on the roughness a nd the tot a l area of the ve hicle sub jected to the a ir flo w. This t yp e of drag is not affected b y the distance gap b et w een v ehicles. The most imp ortant ty p e of drag that is affected by driving in a plato on/con vo y is the form drag . The fo rm drag is a function of the ve hicle shap e and flow around it. This t yp e of drag is dep enden t on how quic kly and smo othly the a ir that separates from the v ehicle rejoins downstream of the v ehicle, i.e. w ak e shap e and turbulence lev el. In other w ords, the mor e the v ehicle shap e is streamlined, the less the form dra g is. This type of drag can b enefit the follow ing v ehicle b y reducing its frontal dynamic pressure when following another v ehicle at a closer spacing. This effect is observ ed in nature where birds fly in a 2 streamline/w ak e of each other [10 , 11] kno wn as slip-streaming or dra fting and was mimick ed in fighter aircraft [12 ]. Hence ha ving tw o v ehicles (one ahead and another b ehind) driving a t a close distance gap affects the pressure f o rces on the v ehicle, thus reducing the aero dynamic resistance f orce and pro ducing fuel sa vings. Ho we ve r, the effect at a v ery close distance ga p dep ends on some geometrical asp ects and the t yp e o f ve hicle plato ons [1, 13, 14, 7, 15, 16 ], i.e. ligh t dut y ve hicles (LD Vs), buses or hea vy dut y truck s (HDTs). In other words, the effect of drag forces at very close spacings encoun ter an adve rse b eha vior. Exp erimental w ork done b y Zabat et al. [17] on LDV plato ons w as used in this study . The experiment w as p erformed on 1 / 8 of the full scale mo del of a 19 91 General Motors Lumina APV in a wind-tunnel env ironment with drag measuremen t s up to distance gap of 3 and 2 ve hicle length fo r the tw o and three-LD V plato on resp ectiv ely . The results show ed a drag reduction of up to 15% for the lead v ehicle and up to 30% for the trail v ehicle in a t w o- LD V plato on at a distance gap of 0 . 5 of a veh icle length. F or distance gaps less than 0 . 5 of a v ehicle length, this effect w as rev ersed and the lead v ehicle pro duced a higher reduction in the drag co efficien t compared to the trail v ehicle. Hong et al. [18] ve rified this b eha vior at close distance gaps b y p erforming a full-scale road test, and it w as also observ ed in part of the wind tunnel test done by Marcu and Bro w a nd [19] in crosswind conditions. F or the bus pla to ons, an experimental study do cumen ted in Ref.[20, 21] was p erformed on 1 : 20 scale of a cylindrical bus-shap ed b o dies (equiv a lent to Mercedes-Benz S 80 mo del) in a wind-tunnel en vironmen t with drag measuremen ts up to distance gap of 5 bus length. The results sho w a drag reduction of up to 1 0% fo r the lead bus a nd up to 60% for the second bus in a tw o-bus plato on at a 10 m distance gap. F or HD T plato ons, most of the a v ailable data w ere fuel measuremen ts for differen t in ter-plato on distance gaps [22, 4, 5, 6, 23] on a full-scale truck in a roa d test environmen t with fuel measuremen ts up to distance g ap of 2 truc k length. T o compute the equiv alen t drag co efficien t, one ma y use the fuel mo del dev elop ed in R ef. [24] to relat e the fuel consumption to the drag for ces. In additio n, 3 one of the other sources in the literature [16] has the fuel measuremen ts resulting fr o m road test fo r empt y truc ks at v ery close spacing o f 5 − 20 m whic h is equiv a lent to time gap of 0 . 23 − 0 . 9 secs . As w e will show later, we are not interes ted in these ve ry close spacings since they are not realistic for implemen tation and the fuel savings fo r t he truck s encoun ter a reve rse b ehavior a s mentioned earlier. The same b ehavior has b een rep orted in the wind tunnel drag measuremen ts of Ref.[25, 17] and b een p oin ted out in differen t sources [1, 13, 14, 7, 15]. Ho w ev er, w e consid er all the data [16, 26] to v a lidate the model for the t w o- HDT plato on. In general, the dep endence of t he drag co efficien t on the in ter-plato on distance gap acts in fav o r o f reduction of the resistance fo rces but ma y a dd complexit y to the plato o n car-following con troller design [27, 28] through the non- linearit y intro duced b y coupling the v ehicle-plato on mo del, i.e. the drag co efficien t is now dep endan t on the distance gap b etw een v ehicles in the plato o n, C D = f ( G = x i − x i − 1 ). The a ccurate mo deling o f the drag interaction b et w een v ehicles make s the con troller design more efficien t when it comes to finding t he optimal control action using either robust or mo del predictiv e tec hniques [29, 3 0, 31, 28] and reduces the uncertaint y in the mo del [32]. In other w ords, the mo deling of t he drag co efficien t improv es the efficiency a nd accuracy o f the optimizatio n problem and in turns impro v es the con tro l a ction needed as mentioned in Ref.[2 8]. In addition, for optimization problems that explicitly optimize fuel sa vings, mo deling the f uel consumption accurately requires an analytic relationship b et we en the drag co efficien t and the pla to on distance gap. Finally , mo deling the impact of plato oning on the drag co efficien t is critical to quantifying the fuel/energy consumption impacts of plato oning strategies. F urthermore, in quan tifying the fuel reductions asso ciated with vehic le plato oning strategies, the drag co efficien t of all vehic les in a plato on fo r t he full ra ng e of distance gaps is needed, which is not a v ailable from measurem ent/n umerical da t a . Hence, the need for an ana lytic function that describes the relation b et wee n the drag co efficien t and the inter-plato on distance gap to extrap o late the dat a b eyond the measuremen t/n umerical sp ectrum is inevitable. 4 1.2. Pap er Contribution and L ayout The t wo main contributions o f this pap er are: (1) w e dev elop and presen t a unified mo del that c haracterizes the impact of the in ter-vehic le distance gap and p osition in a plato on on the v ehicle’s drag co efficien t; and (2) w e use this mo del to quan tify the energy/fuel sa vings asso ciat ed with homog eneous plato o ns o f LD Vs, buses, a nd HDTs. Sp ecifically , this dev elop ed drag mo del is used to provide an analytic function that describ es the relatio n b et we en t he drag co efficien t and in ter-plato on distance gap: (i) quan tify the p o ten tial fuel consumption sa vings for differen t homo g eneous plat o ons at a wider r a nge of distance g aps b ey ond existing empirical measuremen t s, ( ii) quantify the p oten tial f uel consumption sa vings for differen t homogeneous plato ons for a new ve hicle t yp e without the need to p erform an exp erimental/n umerical study , (iii) t o be used when the fuel consumption in the ob jectiv e to b e minimized [3 3] and for designing the con troller asso ciated with this ob jectiv e [33] or other ones, i.e. maintaining time-headw ay for stabilit y [34] or minimizing the error for v ehicle follow ing control [28]. In this pap er, w e examine the effect of the inter-v ehicle pla to on distance gap on the p oten tial of fuel reduction for LDV, bus, and HD T plato ons. The outline of the pap er is as follo ws. In Section 2 , w e presen t the empirical data a v ailable for eac h t yp e of plato o n. F or LD V plato ons [25, 35, 17], the av ailable data are the drag measuremen ts on a 1 : 8 v ehicle in wind tunnel testing. F or bus plato ons [21], t he av a ila ble data a re dra g measuremen ts through wind tunnel tests on 1 : 20 scale cylindrical bus mo del [20]. F or t he HDT plato o n mo deling [22, 23], the data av ailable for the t w o- and three-HDT plato ons is fuel measuremen ts through full-scale road testing. The fuel data for the truc k plato on is used to compute the equiv alen t drag co efficien t using the fuel mo del deve lop ed in Ref.[24]. In Section 3, w e presen t the optimization framew ork used to fit t he data f or the drag co efficien t and to extend the data for a rang e of distance gaps bey ond that in the wind tunnel and road tests. In Sec tio n 4, w e in v estigate t he effect of the drag co efficien t function on the p oten tial fuel reduction for 5 differen t vehic le t yp es. In addition, w e v alidate the tw o - HDT plat o on mo del using the CFD [7] and fuel data [26]. In Section 5 , w e summarize the results and discuss the impact o f the curren t w ork. 2. Drag and F uel Measu rements for LD V , B us, and HDT Plato ons The data for the drag measuremen ts v ersus the in ter-plato on distance ga p for eac h v e- hicle in t wo- and three-LD V plato ons fro m Refs. [25, 35, 17] are sho wn in Figure 1. The distance gap, denoted b y G in all the figures and sections, is the distance measured from the rear bump er of the lead v ehicle to the front bump er of the sub j ect v ehicle, i.e. for 2+ v ehicle plato ons, the distance g a p is symmetrical for b oth the front and rear of a v ehicle within the plato on. F or the lead v ehicle measuremen t s, the difference in the drag co efficien t, C D , for b oth tw o - a nd three-v ehicle plato o ns is negligible. The lead vehic les exp erience a 15% reduction in the drag co efficien t at a distance gap of 2 . 5 m . F or the second v ehi- cle measuremen ts, the drag co efficien t for the second v ehicle in the three-ve hicle pla to on, exp eriences more reduction compared to the second veh icle in the t wo-v ehicle pla t o on for distance g aps less than 5 m . When the distance gap is larger than 5 m , the b eha vior of the drag co efficien t of t he second vehic le is reve rsed, i.e. t he drag co efficien t of the second v ehi- cle in the three-v ehicle plato o n experiences less reduction compared t o the second vehic le in the t w o-vehic le plato o n. Comparing t he last veh icle in the three-v ehicle plato on, the drag co efficien t experiences more reduction ov er the full range of distance gaps compared to the second v ehicle in the tw o - v ehicle plato on. This is attributed to the effect of reducin g the pressure on the last v ehicle because of driving in the slipstream of more than one v ehicle. Based on the r esults in Ref.[17], we assume tha t t he drag r eduction for the third v ehicle in the plato on is almost the same as the remaining v ehicles in the plato on, i.e. C D | 3 ≈ C D | 3+ . This result is also applied to Bus a nd HDT plato ons. 6 2 4 6 8 10 12 14 16 G(m) 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 Lead Vehicle, Two-LDV Platoon Lead Vehicle, Three-LDV Platoon 2 nd Vehicle, Two-LDV Platoon 2 nd Vehicle, Three-LDV Platoon 3 rd Vehicle, Three-LDV Platoon Figure 1: Drag Co efficient ratio for empirical data, C D /C D ∞ , for each vehicle in t wo- and three-LDV plato ons versus distance gap, G , b etw een vehicles fr om the ex per imental work done in Ref.[17]. The dr a g co efficient is no rmalized rela tive drag co efficient of a single vehicle, i.e. C D ∞ . The data for the drag measureme nts for eac h bus in t w o- and three-bus pla t o ons from Ref. [21] are show n in Figure 2. Similar to the LDV plato ons, the last bus in the three-bus plato on experiences more reduction in the drag co efficien t compared to the last bus in the t w o- bus plato on. This is attributed to the same reason discussed earlier. 0 10 20 30 40 50 60 70 G(m) 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Lead Bus, Exp, Two-Bus Platoon 2 nd Bus, Exp, Two-Bus Platoon 3 rd Bus, Exp, Three-Bus Platoon Figure 2: Drag Co efficient ratio for empirical da ta, C D /C D ∞ , for each bus in t wo- and three-bus plato o ns versus the distance ga p, G , betw een buses from the exp erimental w o rk done in Ref.[21]. The dra g co efficien t is nor malized b y the dr ag co efficie n t of a sing le bus, i.e. C D ∞ . 7 The fuel data [22] fo r the tw o- HDT pla to on is sho wn in Figure 3(a). The road test in done in Ref.[22 ] examined a range from 3 − 1 0 m whic h is considered a small rang e compared to the other data considered in this w ork. F or the three-HDT pla t o on [23], the data av aila ble also were the fuel measure ments , show n in Figure 3(b). As men tioned earlier, we are not in terested in this small range of distance gaps, ho we ver, we used these data as opp osed to the CFD results of Ref.[7] b ecause of their consistency with other mo dels that are either based on wind tunnel or road test measuremen ts. F or b oth HDT plato o ns, the equiv a lent drag co efficien ts for the data in Figures [3(a),3(b)] a re o btained through the fuel mo del dev elop ed in Ref. [24], whic h relates the fuel consumption to the v arious forces via the exerted p ow er. The pro cedures used to conv ert from fuel consumption to the drag co efficien t are sho wn in Eqs. [8-10]. 8 2 3 4 5 6 7 8 9 10 11 G(m) 0 5 10 15 Lead Truck - Fuel Data 2 nd Truck - Fuel Data (a) F uel reduction r atio, ( F − F ∞ ) /F ∞ , for tw o -HDT plato ons from Ref.[22]. The fuel co nsumption is no r- malized with r esp ect to a s ingle truck fuel consump- tion, i.e. F ∞ . 15 20 25 30 35 40 45 G(m) -2 0 2 4 6 8 10 12 14 Lead Truck - Data 2 nd Truck - Fuel Data 3 rd Truck - Fuel Data (b) F uel re ductio n ratio, ( F − F ∞ ) /F ∞ , for three- HDT pla to ons from Ref.[2 3]. The fuel consumption is normalize d with resp ect to a single truck fuel con- sumption, i.e. F ∞ . 0 5 10 15 20 25 30 35 G(m) 0.5 0.6 0.7 0.8 0.9 1 1.1 Lead Truck, CFD Data 2 nd , CFD Data (c) Empirica l data Drag Co efficient ra tio , C D /C D ∞ , for ea ch vehicle in a tw o-HDT pla to on fro m the CFD work done in Ref.[7]. T he drag co efficient is norma l- ized with resp ect to the drag coefficie nt of a single truck, i.e. C D ∞ . Figure 3: Drag co efficient and fuel ra tio versus dista nc e gap, G , for tw o- a nd three-HDT plato ons, re s pe c- tively . The para meters of the v ehicles used to obtain the data in the previous F ig ures are giv en in T able 1. In the next section, w e discuss the fitt ing pro cedure used t o dev elop analytical mo dels f or LDV, bus, and HDT plato ons. 9 T a ble 1: V ehicle characteristics used to o btain the CFD/exp erimental data in Fig ur es [1-3] for LD V, bus, and HDT plato ons. V ehicle T yp e V ehicle Mo del P arameters m ( k g ) leng th ( m ) w idth ( m ) h eig ht ( m ) C D ∞ LD V Chevy Lumina APV 1,70 0 4.952 1.877 1.663 0.367 Bus Mercedes - Benz S 80 16 ,000 12.0 00 2.865 2.865 0.650 HDT V olv o - VNL 6 7 0 29,400 2 2 .710 2.48 9 3.353 0.570 3. Fitting Drag Measurem ents for LD V, B us, and HDT Plato ons In this section, w e fit mo dels to the empirical data for LDV, bus, and HDT plat o ons using a general p ow er function as giv en in Eq.(1). y = ax b + c (1) The adv antage o f using a p ow er rather than a p olynomial function is : (i) the p o w er function v aries monotonically with resp ect to the independent v ariable [36], i.e. y either con tinuous ly increases or decreases ov er the en tire x doma in dep ending on the signs of the co efficien t s a and b , and (ii) the p ow er function has a horizon tal asymptote, i.e. the distance b etw een the p ow er function and the horizon ta l axis reac hes zero as x approac hes infinit y . The second prop erty of the p o w er function represen ts an inherent prop erty of the drag co efficien t. F or our case here, our ob jectiv e is to ha ve the drag function monotonically increase with the distance g ap up to the drag co efficien t of a single v ehicle ( C D ∞ ). The dra g coefficien t ov er a broad range of distance gaps can b e defined as: C D C D ∞ =            aG b + c, 0 < G ≤ G o 1 , G ≥ G o (2) 10 where G o is the critical distance gap ab ov e whic h the drag fo rce on a v ehicle is not affected b y the presence of other v ehicles either in fron t or behind it, i.e. C D /C D ∞ ( G o ) = 1. C D ∞ is the dra g co efficien t of a single v ehicle in the absence of an y other v ehicles in its vicinit y . The ob jectiv e of the curve fitting is to find the pa rameters of the p ow er function that b est represen t the empirical data for eac h case in Fig ures[1,2,3], i.e. the optimal parameters that minimize the error b etw een the function and the measuremen ts. The p ow er function w as used b efore in Ref. [3 6] to construct the drag co efficien t reduction of a v ehicle in a plato o n as a function of its maxim um deficit v elo cit y rate inside the w ak e. Since w e do not ha v e measuremen ts b ey ond certain distance g a ps, the p oint G o is obtained by extrap o la tion. This is due to the na ture of the underlying experiment or computational resources for each case that allow ed only to span a short sp ectrum of the v ehicle distance gap. Ho we ver, for a set of initial conditions, a different lo cal optimu m solution could b e obtained with differen t v alues of G o when extrap o la ting the curve . Hence, to determine the v alue of the critical distance gap, G o , the G o v alue was assumed to b e unkno wn a nd was estimated through the optimization pro cedure. The nonlinear least square data fitting is defined as follo ws min z N p X j =1  C D C D ∞ ( G j ) − C D C D ∞ ( G j ) | M  2 (3) sub jected to t he b ound constrain t on G o G o l ≤ G o ≤ G o u (4) where z = { a, b, c, G o } T is the v ector of the design v ariables, N p is the n um b er of empir- ical observ ations a v ailable for eac h case, and the subscript M stands for measuremen ts. W e used the nonlinear least square function lsqnonlin in Matla b with either Lev en b erg- Marquardt [37] or trust-reflective-region [3 8] algor it hms. The latter algorithm is used 11 when a b ound constraint on G o is needed. In a ll the cases, t he nonlinear least square o pti- mization is used without constraints on G o except for the case of the trail truck for the tw o - [22] and three-HD T plat o ons [23] where an unconstrained fitting giv es an unreasonable v alue for G o , i.e. G o tr ail ≈ 1000, whic h is equiv alen t to 40 truc k lengths. This is attributed to the high uncertain ty in the data for the trail truck s [22, 23]. The constraints for these t w o cases are c hosen such that it satisfies the relativ e v alue of G o deriv ed from the results of LD V and Bus plato ons. The optim um para meters for each v ehicle ty p e and plato on configuration a re summarized in T a ble 2. In all cases considered, t he drag co efficien t rat io of the lead v ehicle reac hes unity v ery quic kly compared to t he middle and the last veh icle, i.e. the critical distance gap at whic h the lead v ehicle is no longer influenced b y the rear ones. T a ble 2: Drag co efficient par ameters for each vehicle in LD V, bus, and HDT plato on. V ehicle T yp e Plato on Size V ehicle Pos itio n P arameters a b c G o ( m ) LD V Tw o Lead -0.7575 - 1 .5225 1 .0 325 - T rail -1.7834 - 0 .0672 2 .3 614 55.72 Three Lead -0.8906 - 1 .6679 1 .0 185 - Middle -0.8985 - 0 .5126 1 .1 393 39.62 T rail -0.5953 - 0 .1197 1 .1 393 79.75 Bus Tw o Lead 0.0506 0.4527 0.8280 - T rail 0.2921 0.1862 0.1724 268.7 9 Three Lead 0.0506 0.4527 0.8280 - Middle 0.2622 0.2104 0.2728 127 .6 8 T rail 0.2250 0.2159 0.1722 416.9 8 HDT Tw o Lead 0.7231 0.0919 0.000 3 4.0181 T rail 0.2241 0.1369 0.5016 320 Three Lead 0.0035 0.5997 0.9662 - Middle 0.1522 0.2111 0.5260 217 .2 7 T rail 0.0726 0.2842 0.5794 480.0 0 T o illustrate the b enefits of including the G o parameter in the fitting pro cedure, a com- parison b et w een the t w o cases is conducted for the tra il vehic le and truck in the t w o- LDV and tw o- HDT plato ons, respective ly , as illustrated in Figure 4(a). F or the case o f the LDV, 12 where G o is no t a pa r ameter, its v alue is computed as 47 . 0; m b y extrap o lating the curve to the unit y v alue of the dra g co efficien t ratio . F or the case where G o is included in the fitting, its v alue is 55 . 7 m . The residual error is 0 . 6387 × 10 − 8 and 0 . 7 734 × 10 − 8 for the inclusion and exclusion of t he G o in t he optimization, resp ectiv ely . Not only do es the inclusion of the G o parameter in the optimizatio n yield a b etter optimal solution, but it also provides a natural formalism for obta ining the v alue of G o whic h (it s relative v a lue inside the plato on) should b e consisten t fo r differen t plato on sizes as will b e discussed in the next Figures. Similarly for the case of the trail truck in the t w o- HDT plato on in Figure 4(b), the inclusion of G o as a v ariable in the o ptimization yields m uch b etter results, with the residual error decreasing from 54 . 89 × 10 − 8 to 6 . 5218 × 10 − 8 . Consequen tly , for the case of the trail truc k in the t w o- and three-HD T plato ons, a constrain t on G o has to b e enforced since p erforming the optimization with G o un b ounded yields unrealistic v a lues ( G o ≈ 1000 m ). The selection of constrain t b ounds on G o are detailed in the next section. 0 10 20 30 40 50 60 G(m) 0.7 0.75 0.8 0.85 0.9 0.95 1 Data Approximation with G o Approximation without G o (a) Drag Co efficie nt ratio, C D /C D ∞ , for the second vehicle in a tw o- L DV pla to on. 0 50 100 150 200 250 300 350 400 450 500 G(m) 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 Data Approximation with G o Approximation without G o (b) Drag Co efficient ratio, C D /C D ∞ , for the second truck in a tw o-HDT plato on. Figure 4: Drag Co efficient ratio, C D /C D ∞ , for the s e c ond vehicle in a tw o- LDV and tr uck pla to on v er sus the distance g ap, G , for tw o c a ses where the parameter G o is excluded and included in the fitting r esp ectively . In Figure 5, the data fitting results are sho wn for t w o- and t hr ee-LDV plato ons. T he exp erimental data a re extracted fro m the w ork of Zabat et al. [25, 35, 17]. As illustrated 13 in the Figures [5(a),5(b)], the mo dels for the lead v ehicle in b oth the t w o- and three-LDV plato ons are v ery similar. Notew orthy is the fact that the distance gap needed for the dra g co efficien t ratio of the follow ing ve hicle to reac h unit y after the drag co efficien t of its lead reac hes unit y are close for the tw o differen t pla to ons, i.e. the difference b etw een the critical distance gap of each v ehicle in t w o - and three-LD V plato ons, G o i − G o i − 1 is small. F or t he t w o- LD V plato on, the relativ e distance gap is G o tr ail − G o lead ≈ 45 m . F or the three-LDV plato on, the relative distances b etw een the lead and the middle and middle and the trail are G o middle − G o lead ≈ 30 m and G o tr ail − G o middle ≈ 40 m , resp ectiv ely . This is a nat ura l result from the optimization, whic h agrees with the ph ysical meaning of the parameter G o . No t only obtaining this agreemen t for the v alue of G o w ould b e hard using trial and error but enforcing it through the inclusion of constrain ts would bias the optimization. Dep ending on the accuracy of t he measuremen ts, the pa rameter G o will b e closer to reality . The inclusion of the parameter G o in the optimization impro ve s the accuracy of the extrap olation of the data to a wide range of distance gaps and is considered as a predictor for the no-influence p oin t b etw een v ehicles in the plato on. The G o parameter should th us b e considered as an upp er b ound for the distance gap betw een v ehicles when designing the plato on con troller [27, 28] since the ob jectiv e is to k eep the vehic les within a plato on as close as p o ssible to maximize their fuel sav ings. 14 0 10 20 30 40 50 60 G(m) 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 Lead Vehicle - Data Lead Vehicle - Approximation 2 nd Vehicle - Data 2 nd Vehicle - Approximation (a) Drag co efficient ra tio, C D /C D ∞ , v er sus dis ta nce gap for tw o-LDV plato on. 0 10 20 30 40 50 60 70 80 G(m) 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 Lead Vehicle - Data Lead Vehicle - Approximation 2 nd Vehicle - Data 2 nd Vehicle - Approximation 3 rd Vehicle - Data 3 rd Vehicle - Approxiamtion (b) Dra g co efficient ratio, C D /C D ∞ , v er sus distance gap for three- LD V plato on. Figure 5: Drag Co efficient ra tio , C D /C D ∞ , for tw o- and three-LDV platoo ns. The drag co efficient is normalized with resp ect to the single vehicle dra g co efficien t, i.e. C D ∞ . In Figure 6, the results fo r the tw o and three bus plat o on are sho wn. The fitting is based on the exp erimen tal measuremen t in Fig ure 2 collected from Ref. [21]. Based o n the measuremen ts for the lead car in Figure 1, the curv e fo r the lead bus in the presence of one o r mo r e buses b ehind is assumed the same. Hence the data and the appro ximation curv es in Figures [6(a),6(b)] are iden tical. The data sho wn in Figure 6(b) for the case of the second bus in a three-bus plato on is obtained b y assuming tha t the dra g coefficien t fo r the sec o nd bus in a tw o- bus plato on is the av erage of the result of the last bus in a t w o- and thr ee-bus plato on. This appro ximation is based on the observ a tion of the car results in F igure 1. Similar to the LDV plato on in Fig ur e 5, the relative distance ga p b etw een the trail and the lead bus in the tw o-bus pla t o on is close to the relativ e distance g a p b et w een the middle and the t r ail bus in the three-bus plato on, i.e. G o tr ail − G o lead ≈ 25 3 m and G o tr ail − G o middle ≈ 2 8 5 m . 15 0 50 100 150 200 250 300 G(m) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Lead Bus - Data Lead Bus - Approximation 2 nd Bus - Data 2 nd Bus - Approximation (a) Drag co efficient ra tio, C D /C D ∞ , v er sus dis ta nce gap for a tw o-bus plato o n. 0 50 100 150 200 250 300 350 400 450 G(m) 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Lead Bus - Data Lead Bus - Approximation 2 nd Bus - Data 2 nd Bus - Approximation 3 rd Bus - Data 3 rd Bus - Approxiamtion (b) Dra g co efficient ratio, C D /C D ∞ , v er sus distance gap for a three-bus plato on. Figure 6 : Drag Co efficient ra tio, C D /C D ∞ , for t wo- and three-bus plato ons. The drag co efficient is no r- malized with the v a lue of a single bus drag co efficient, i.e. C D ∞ . The data in the Figure is ba sed on the exp erimental measurements in Re f. [21]. In F igure 7, the results for tw o - a nd three-HDT plato o ns are sho wn. The drag co efficien t for the t w o and three-HDT plato ons in Figures [7( a ),7(b)] a re based on the measuremen ts in Ref. [23]. The drag co efficien ts a re calculated from the fuel measuremen ts via the relations defined in Eqs. [(5)-( 7 )]. Notew orthy is t he fact that fo r the case of the trail truc k in the tw o- and three-HDT plato ons, the b ounding constrain t on G o is needed giv en the uncertain ty in the data. The constraint w as c hosen to yield similar G o v alues to those deriv ed for LDV and bus plato ons, as illustrated in Figures [5,6]. In other words , the b ounds are c hosen suc h that t he optimization yields a relativ e distance ga ps b et w een the trail and the lead truc k in the tw o - HDT plato on similar to t he relative distance g ap b et we en the middle and the trail truc k in the three-truck plato on, i.e. G o tr ail − G o lead ≈ 2 63 m and G o tr ail − G o middle ≈ 2 87 m . If the constrain t w as not in v ok ed, the optimization w ould yield a v a lue of G o ≈ 1000 m for these cases. This is the only case where constrain ts on G o w ere in v oke d and is based on t he ph ysical in tuition concluded from the results of t he LDV and bus plato ons. 16 0 50 100 150 200 250 300 350 G(m) 0.75 0.8 0.85 0.9 0.95 1 1.05 Lead Truck - Data Lead Truck - Approximation 2 nd Truck - Data 2 nd Truck - Approximation (a) Drag co efficient ra tio, C D /C D ∞ , v er sus dis ta nce gap for a tw o-HDT plato on bas ed on the data in Ref. [22]. 0 50 100 150 200 250 300 350 400 450 G(m) 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 Lead Truck - Data Lead Truck - Approximation 2 nd Truck - Data 2 nd Truck - Approximation 3 rd Truck - Data 3 rd Truck - Approxiamtion (b) Dra g co efficient ratio, C D /C D ∞ , v er sus distance gap for a three-HDT plato on based o n the data in Ref. [23]. Figure 7: D r ag Co efficient ratio, C D /C D ∞ , for t wo- and three-HDT pla to ons. The drag co efficient is normalized with the v alue of a single truck drag coe fficie nt, i.e. C D ∞ . The data in parts 7 (a) and 7(b) is obtained by tra nsforming the fuel meas urements from Ref.[22] and Ref. [23] to dra g data using Eqs. (5)-(10). 4. F uel Curv es for LD V, B us, and HDT Plato ons In this Section, w e examine the effect of using the drag mo del dev elop ed in Section 3 on the plato on fuel consumption. The fuel mo del is dev elop ed b y Rakha et a l. [24] to calculate the instantaneous fuel consumption. The instantaneous p o w er in k W is calculated as P ( t ) =  R ( t ) + 1 . 04 ma ( t ) 3600 η d  v ( t ) (5) where m is the v ehicle mass in k g , a ( t ) is v ehicle acceleration in m/s 2 at instant t , v ( t ) is the v ehicle speed in k m/h at instan t t , η d is the drive-line efficiency , and R ( t ) is the resistance force in N at instan t t . The resistance f orce R ( t ) is calculated as R ( t ) = ρ 25 . 92 C d C h A f v ( t ) 2 + g m C r 1000 ( C 1 v ( t ) + C 2 ) + g mG ( t ) (6) 17 where ρ is the air densit y at sea leve l and 15 o c , C d is the vehic le drag co efficien t, C h is the correction factor of elev ation, A f is the v ehicle frontal area in m 2 , g is the gravitational acceleration, G ( t ) is the roa dwa y grade, and C r , C 1 , and C 2 are the rolling resis ta nce pa- rameters. The fuel consumption is then calculated using p ow er computed using Eq. (5) as F ( t ) =            α 0 + α 1 P ( t ) + α 2 P ( t ) 2 , P ( t ) ≥ 0 α 0 , P ( t ) < 0 (7) where the co efficien ts α 0 , α 1 , and α 2 are calculated using the p o we r and fuel consumed using the En vironmental Protection Agency (EP A) fuel ratings [24]. T o obta in the equiv alen t drag co efficien t for trucks that is sho wn in Figures [7(a),7(b)] from the fuel measuremen ts in Figures [3(a),3(b)], the fuel ratio is defined as F ∞ − F F ∞ = ∆ ⇒ F = F ∞ (1 − ∆) =  α 0 + α 1 P ( t ) + α 2 P ( t ) 2  n (8) where F ∞ is the fuel consumption ra te of the v ehicle when no other v ehicles are presen t either in-fr o n t o r b ehind it, n is the amoun t of fuel consumed f o r the same condition. The p ow er is then calculated f rom Eq. (7) as P = − nα 1 + p n 2 α 2 1 − 4 nα 2 ( nα 0 − F ) 2 nα 2 (9) Hence the drag co efficien t from the force relation in Eq. (6) as C D = P × 3600 η v − R ∞ ρ 25 . 92 A f C h v 2 (10) 18 where R ∞ is the resistance f o rce of t he v ehicle at no other v ehicles presen t either in-front or in rear. T a ble 3: Parameter s r equired for each vehicle in LDV, bus, a nd HDT plato o n for the fuel mo del defined in Eq. (7). V ehicle T yp e V ehicle Mo del P arameters m ( k g ) η d C D ∞ A f ( m 2 ) α 0 α 1 α 2 LD V A 1469 0.80 0.325 2 .30 6.00e-4 1.90e-5 1.00e-6 B 1550 0.80 0.24 2.20 5.00e-4 4.41e-5 1.00e-6 Bus M 8505 0.95 0 .80 7.59 1.33e-3 6.33e-5 1.00e-8 N 13486 0.95 0.80 7.38 8.31e-4 1 .90e-5 5.3 4e-7 HDT X 7239 0.88 0 .78 8.90 1.56e-3 8.10e-5 1.00e-8 Z 12864 0.88 0.78 8.80 1.66e-3 8 .60e-5 1.0 0e-8 McAuliffe et al. 8 500 0.94 0.5 7 10.70 1.5 6e-3 8.10 e-5 1.00e- 8 In Figure 8, t he fuel reduction rat io is sho wn fo r the case of tw o and three-car plato o ns for t w o differen t car types: A and B. The parameters f o r the t w o t yp e of cars are giv en in T able 3. F or the t wo-v ehicle pla t o on in Figure 8 ( a ), the second vehic le exp eriences f uel reductions more than the lead v ehicle; up to 6 % fo r the second one with no sa vings for the lead one at a distance g a p of 10 m . Similarly for t he three-car plato on in Figure 8 (b), the third, the second, and the lead exp erience up to a n 8%, 5%, a nd 0 % fuel reduction, resp ectiv ely . The differen t car parameters ha v e a negligible effect o n the fuel reduction curv es. It should b e noted that these results agree with what is rep orted in Ref.[39] with regards to fuel sav ings deriv ed from wind t unnel measu rements . Sp ecifically , they suggest that other parameters should b e included in wind tunnel-based mo dels (e.g. the turbulence lev el), when comparing to fuel estimates from on-road tests. 19 0 10 20 30 40 50 60 G(m) 0 2 4 6 8 10 12 Lead Vehicle - A 2 nd Vehicle - A Lead Vehicle - B 2 nd Vehicle - B (a) F uel reductio n ratio , ( F − F ∞ ) /F ∞ , versus dis- tance g ap for tw o-LDV plato on. 0 10 20 30 40 50 60 70 80 G(m) 0 2 4 6 8 10 12 14 16 Lead Vehicle - A 2 nd Vehicle - A 3 rd Vehicle - A Lead Vehicle - B 2 nd Vehicle - B 3 rd Vehicle - B (b) F uel r eduction ratio, ( F − F ∞ ) /F ∞ , versus dis - tance g ap for three-LDV plato o n. Figure 8: F uel r eduction r atio, ( F − F ∞ ) /F ∞ , for tw o- and three- L DV plato ons of type A and B . The fuel consumption is norma liz e d with resp ect to a single vehicle fuel consumption, i.e. F ∞ . In Figure 9, the fuel reduction ratio is sho wn for the case of t w o - and three-bus plato ons for tw o differen t bus t yp es: M and N. The similar trend of fuel reduction in car plato ons is observ ed here. F or the t w o-bus plato on in Figure 9(a) , the second bus exp eriences fuel reductions mor e than the lead bus with up to 1 5% reductions for the second one with no sa vings for the lead o ne at a distance g ap of 50 m . Similarly for the three-bus plato on in Figure 9(b), t he third, the second, and t he lead exp erience up to 20%, 10%, and 0 % fuel reductions, resp ectiv ely . The maximum payload used for the buses in these figures are 500 0 k g and 2500 k g for t yp e M and N, resp ectiv ely . This could b e found on the man ufacturer w ebsite. 20 0 50 100 150 200 250 300 G(m) 0 5 10 15 20 25 30 35 40 45 Lead Bus - M 2 nd Bus - M Lead Bus - N 2 nd Bus - N (a) F uel reductio n ratio , ( F − F ∞ ) /F ∞ , versus dis- tance g ap for tw o-bus pla to on. 0 50 100 150 200 250 300 350 400 450 G(m) 0 5 10 15 20 25 30 35 40 45 50 Lead Bus - M 2 nd Bus - M 3 rd Bus - M Lead Bus - N 2 nd Bus - N 3 rd Bus - N (b) F uel r eduction ratio, ( F − F ∞ ) /F ∞ , versus dis - tance g ap for three-bus plato on. Figure 9: F uel reduction ratio, ( F − F ∞ ) /F ∞ , for t wo- and thr ee-bus plato ons of bus types M and N . The fuel c onsumption is nor malized with resp ect to the v alue of a single bus fuel consumption, i.e. F ∞ . In Figure 10, the fuel reduction ratio is sho wn for the case of tw o- and three-truc k plato ons for tw o differen t t r uck types: X a nd Y. The fuel reduction curve s follow the same b eha vior in the car and bus plat o ons. F or the tw o- truc k plato on in Figure 10 (a), the second truc k exp eriences fuel reductions more t ha n the lead truc k b y up to 8% at a distance gap of 50 m . The lead one exp erience 0% at this distance gap using b o th of the t w o drag mo dels. Similarly for the three truc k plato o n in F igure 10(b), the third, the second, and the lead exp erience up to 9 %, 6%, and 0 % resp ectiv ely at distance gap of 50 m . W e used the equiv alen t pa yload from R ef. [23] to mak e sure the different truc k are ha ving the same w eigh t, i.e. W pay load = 22161 k g for truc k X, and W pay load = 16536 k g for truc k Y. The w eigh t of the truc k used in the road test exp erimen t in R ef. [23] is 29400 k g . 21 0 50 100 150 200 250 300 350 G(m) 0 2 4 6 8 10 12 Lead Truck - Data - Browand et al 2 nd Truck - Data - Browand et al Lead Truck - X - EXP 2 nd Truck - X - EXP Lead Truck - Y - EXP 2 nd Truck - Y - EXP (a) F uel reductio n ratio , ( F − F ∞ ) /F ∞ , versus dis- tance gap for t wo-HDT plato o n. The fuel data is from Ref.[22]. 0 50 100 150 200 250 300 350 400 450 G(m) -2 0 2 4 6 8 10 12 14 Lead Truck - Data - McAuliffe et al 2 nd Truck - Data - McAuliffe et al 3 rd Truck - Data - McAuliffe et al Lead Truck - X 2 nd Truck - X 3 rd Truck - X Lead Truck - Y 2 nd Truck - Y 3 rd Truck - Y (b) F uel r eduction ratio, ( F − F ∞ ) /F ∞ , versus dis - tance gap for thr e e-HDT pla to on. The fuel data is from Ref.[23 ]. Figure 10: F uel reduction ra tio, ( F − F ∞ ) /F ∞ , for tw o- and three-HDT pla to ons of t yp e X and Y . The fuel c onsumption is nor malized with the v alue of a s ing le truck fuel co nsumption, i.e. F ∞ . In Figure 11, the fuel reduction ratio is sho wn fo r the case LDV, bus, and HD T plato o n as a function of time g a p for different v ehicle sp eeds. Since it is more appropriate to sp ecify gap b etw een veh icles in terms of time ( headwa y) in pro cess of the v ehicle plat o on con tro ller design [27, 28, 34, 40] , w e tra nsfor med the Figures in terms of the time gap b etw een v ehicles. Accoun ting for comm unication, con troller and mec hanical latency , the minim um time ga p that could b e achie ved will b e lo wer b ounded a s Gap ≥ 0 . 5 secs (see Refs. [41, 42]. Hence the optim um fuel reduction that could b e att a ined is 4 . 5 %, 15 . 5%, and 7% for LD V, bus, and HDT plato on resp ectiv ely running a t sp eed of 100 k m/hr . These results a gree with what hav e b een found in the n umerical sim ulation by Alam et al [3] for the HDT plato on. In addition to the f uel reductions, the low er time gap has the b enefit of increasing the roadw ay capacit y . F or instance, based on the v ehicle lengths in T able 1 and a trav elling sp eed of 10 0 k m/hr , the headw a y of the LD V, bus, and HDT is 0 . 678 s ecs , 0 . 9 32 secs , and 1 . 317 secs , r esp ective ly . These are equiv alent to saturat io n flow rates o f 5 , 309, 3 , 862, and 2 , 733 v eh/hr /lane , resp ectiv ely . These v alues provide significan t impro v emen ts ov er typic al base LDV saturation flo w rates of 2 , 450 v eh/hr /l ane (High wa y Capacity Manual). 22 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Gap(s) 0 5 10 15 V = 70 km/hr V = 80 km/hr V = 90 km/hr V = 100 km/hr (a) Av er age fuel reduction ra tio , ( F − F ∞ ) /F ∞ , for three-LDV plato on a nd different sp eeds as a function of time gap for t yp e A vehicle. 0 5 10 15 20 25 Gap(s) 0 5 10 15 20 25 30 35 V = 70 km/hr V = 80 km/hr V = 90 km/hr V = 100 km/hr (b) Average fuel r eduction ratio, ( F − F ∞ ) /F ∞ , for three bus plato ons and different spe eds as a function of time g ap for type M bus. 0 5 10 15 20 25 Gap(s) 0 2 4 6 8 10 12 14 V = 70 km/hr V = 80 km/hr V = 90 km/hr V = 100 km/hr (c) Average fuel r eduction ra tio, ( F − F ∞ ) /F ∞ , for three-HDT plato o ns and different sp eeds as a func- tion of time gap for type X truck. Figure 11: Average fuel reductio n ratio for different plato on and different speeds as a function of the time gap. T o elab orate more on the fuel sa vings b et w een differen t plat o ons, the fuel reduction for the three differen t type of plato ons is sho wn in Figure 12 as a function of distance ga p/ t ime gap at v elo city o f 100 k m/hr . The distance gap and time gap are provide d on the same x axis for clarity . As men tioned earlier, to account for the time dela y in t he v ehicle mec hanical resp onse and comm unication b etw een v ehicles, the lo w er b ound of the attainable time g ap 23 b et we en v ehicles is b ounded b y 0 . 5 secs . As we see fro m Figure 12, the 0 . 5 secs is equiv a len t to a distance gap of 25 m . T his may b e c hallenging in the case of bus and HDT plato ons, where the lo w er b ound of the time gap need to b e higher than that of LD V plato ons. If w e g o to the v alue o f time gap of 2 secs , w e can see that the bus and HDT pla to ons still pro duce a significant amount o f fuel reduction, with sa vings up to 9% and 4 . 5%, resp ectiv ely while the LDV plato o ns is a lmost 0 . 6 %. 0 50 100 150 200 250 300 350 400 450 Distance Gap(m) 0 5 10 15 20 25 30 35 LDV Bus HDT 0 2 4 6 8 10 12 14 16 Time Gap(s) Figure 12: Average fuel reduction ratio , ( F − F ∞ ) /F ∞ , for three vehicle plato ons a s a function of distance gap/time ga p at sp eed of V = 100 k m/ hr . The mo del for tw o- HDT plato on [22] is v alidated b y comparing its estimates to the CFD data of Ref.[7]. F or the case o f the lead truc k, the drag co efficien t mo del offers a ve ry go o d fit with the CFD data o v er the full range of plato on distance gaps. As seen from Figure 3(c), the drag co efficien t is asymptotic to a v a lue less than 1.0 whic h is inconsis tent with the measuremen ts for either LDV, bus or HDT plato ons. This finding agrees with Ref. [9], in whic h t hey concluded that the CFD data for the non-lead v ehicles is inconsis tent with empirical data at shorter distance g aps. Hence we did not use the CFD data for the trail truc k to v alidat e the prop osed mo del. 24 0 5 10 15 20 25 30 35 G(m) 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 Lead Truck - Data Lead Truck - Approximation Figure 1 3 : Drag co efficient ratio , C D /C D ∞ , versus distance g ap for tw o-HDT plato on. The prop ose d mo del versus the CFD results from Ref.[7]. In F ig ure 14, the mo del estimates f or the tw o-HD T plat o on are compared to the exp er- imen tal measuremen ts pro vided in Ref.[26]. As is eviden t from Figure 14(a ), the dev elop ed mo del pro vides a v ery go o d agreemen t with a ll the empirical data for the lead truc k. On the con tra ry , the mo del estimates for the trail truc k is consisten t with part of the dat a (set A), as show n in Figure 14(b). The deviation in the other data set (set B) in Figure 1 4(b) is attributed to the adv erse b eha vior at low distance gaps discussed earlier whic h depends on differen t factors. e.g. the geometry of t he truck . 25 0 5 10 15 20 25 Gap(m) 0 1 2 3 4 5 6 7 8 9 10 Lead Truck - Confidence Report Lead Truck - Present (a) F uel r eduction r atio, ( F − F ∞ ) /F ∞ , for the lea d truck as a function of dista nce gap. 0 5 10 15 20 25 Gap(m) 0 5 10 15 20 25 Trail Truck (set A) - Roberts et al Trail Truck (set B) - Roberts et al Trail Truck - Present (b) F uel reductio n ratio, ( F − F ∞ ) /F ∞ , for the trail truck as a function of distance g ap. Figure 1 4: F uel r eduction ra tio , ( F − F ∞ ) /F ∞ , versus distance g ap for t wo-HDT plato on. The curves represent the pr op osed mo del and the data are from the confidence repo rt o n tw o-HDT plato oning [26]. 5. Conclusion In this pap er, the effect of in ter-plato on p osition and distance gap strategy on the v ehicle drag co efficien t and fuel consumption for ligh t dut y vehic le, bus, and hea vy dut y truck plato ons w as in v estigated. F or the ligh t dut y v ehicle a nd bus plato ons, the data a v aila ble w as direct force measuremen t . F or the hea vy dut y truc k plato ons, the data av aila ble was fuel measuremen ts. The fuel measuremen ts were used to compute the drag forces using the VT-CPFM mo del. Subsequen tly , mo dels were deve lo p ed t ha t capture the impact of the v ehicle in ter- plato on p osition and distance gap on the drag co efficien t using a general p ow er function. The critical distance gap, the gap at which the drag co efficien t is not affected b y the v ehicle ahead of it, is determined through o ptimization. It w as demonstrated that the inclusion o f this para meter in the optimization reduces the residual erro r ( increases the fit accuracy) and yields a v alue that is consisten t with empirical data. The mo del for the tw o- HDT plato on w as v alidat ed against the drag co efficien t from the n umerical sim ulation results and fuel sa vings a gainst in-field exp erimen tal measureme nts from the literature. F or the dra g 26 co efficien t, a high lev el of agreemen t w as observ ed for the lead tr uck with some deviation for the trail truck . This disagr eemen t is consisten t with other literature concluding that the nume rical sim ula t io n of the fluid flow is not suitable for mo deling the drag in teraction b et we en ve hicles. F or the fuel sav ings, go o d agr eemen t w as observ ed with the field data in the literature while the tr a il truc k mo del w as consisten t with the empirical data that exhibited a decreasing trend o ver the full range of the distance gaps. The dev elop ed dra g mo dels w ere used to quan tify the a verage fuel sa vings fo r differen t types o f plato ons. The results show a p o ten tial decrease in the fuel consumption directly prop ortio na l with the inter- plato on distance gap/t ime g a p. F or safet y considerations, and data and con trol la tencies suc h as v ehicle mec hanical system resp onse and latency in communication b et we en v ehicles, the bus and heavy duty tr uc k plato ons sho w more p o ten tial in the plato on energy sa vings at longer time g a ps when compared to the light dut y v ehicle plato ons. This highligh ts the need for plato o ning control to b e directed to wards buses and truc ks. Ac knowled gments This effort w as funded b y the Office of Energy Efficiency and Renew able Energy (EERE), V ehicle T echn o lo gies Office, Energy Efficien t Mobility Systems Program under aw ard n um b er DE-EE0008209. References [1] C. B onnet, H. 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