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1、400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (724) 776-4841 Fax: (724) 776-0790 Web: www.sae.org SAE TECHNICAL PAPER SERIES 2007-01-4297 Road Evaluation of the Aerodynamic Characteristics of Heavy Trucks Helmut H. Korst, Robert A. White and L. Daniel Metz University of Illinois at U
2、rbana Champaign Commercial Vehicle Engineering Congress and Exhibition Rosemont, Illinois October 30-November 1, 2007 Author:Gilligan-SID:1178-GUID:19091828-141.213.232.87 The Engineering Meetings Board has approved this paper for publication. It has successfully completed SAEs peer review process u
3、nder the supervision of the session organizer. This process requires a minimum of three (3) reviews by industry experts. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying
4、, recording, or otherwise, without the prior written permission of SAE. For permission and licensing requests contact: SAE Permissions 400 Commonwealth Drive Warrendale, PA 15096-0001-USA Email:permissionssae.org Tel:724-772-4028 Fax:724-776-3036 For multiple print copies contact: SAE Customer Servi
5、ce Tel:877-606-7323 (inside USA and Canada) Tel:724-776-4970 (outside USA) Fax:724-776-0790 Email:CustomerServicesae.org ISSN 0148-7191 Copyright 2007 SAE International Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE. The author is solely res
6、ponsible for the content of the paper. A process is available by which discussions will be printed with the paper if it is published in SAE Transactions. Persons wishing to submit papers to be considered for presentation or publication by SAE should send the manuscript or a 300 word abstract to Secr
7、etary, Engineering Meetings Board, SAE. Printed in USA Author:Gilligan-SID:1178-GUID:19091828-141.213.232.87 Copyright 2007 SAE International ABSTRACT Coast down testing with full-scale vehicles on level and inclined roads offers an inexpensive approach to road load determination and, in particular,
8、 aerodynamic force evaluation, provided that drag component extractions can be accurately achieved under random instrumental disturbances and biased environmental conditions. Wind tunnel testing of large vehicles, especially truck/trailers, to establish their aerodynamic drag is costly and also may
9、produce questionable results when the effects of the moving road, blockage, wake/diffuser interaction, and rotating tires are not properly simulated. On the road, testing is now conveniently and speedily carried out using GPS-based data acquisition and file storage on laptops, allowing instantaneous
10、 on-board data proc- essing. Specifically, this can be done by using a spread- sheet which allows parameter identification by fitting rou- tines applied to a “ user defined function” (the latter being obtained from the solution of the equation of motion for the vehicle, including properly defined bi
11、ased and ran- domly disturbed environmental conditions). Fitting rou- tines, such as given by Levenberg-Marquardt and others are part of some spreadsheets. Thus, information on tire drag and aerodynamic drag contributions can be promptly evaluated at the end of each coast down run. Special concern a
12、rises from the sensitivity of aerody- namic drag determination under- even light- prevailing winds. It is shown how to account for such disturbances by introducing the concept of “ effective” wind correction by conducting coast down runs in opposing directions. Additional difficulties arise due to t
13、he lack of separability of the drag parameters (speed dependency of tire drag); in which case one has to use information provided by tire manufacturers. The efficiency of different data processing methods is tested by the recovery of drag components from a gen- erating program, which simulates coast
14、 down subjected to biased and randomly disturbed conditions. Examples of actual coast down runs with 18 wheelers and their road load evaluations are given to demonstrate the ca- pability of the approach. Since heavy trucks and, especially 18-wheeler rigs come in a great variety of configuration, sel
15、ection of a refer- ence (frontal) area for extracting drag coefficients may produce misleading results; as one observes that all im- portant criteria for truck operation depend on the product A0 times CD, it is conventional to define this product as Drag Area, as the most appropriate criterion for a
16、erody- namic performance. INTRODUCTION Heavy trucks come in a great variety of configurations and, depending on regional definitions, are usually lim- ited in total weight, length and height. In the US heavy trucks are defined to be within the limits of gross weight (80000 lbs), length (70-80 ft), h
17、eight (13 6” ) and width (8 ), unless specially licensed. Of special interest here are so called semis or 18 wheelers and, in particular their aerodynamic performance. Conventionally, one expects a definition of reference (frontal) area and the establishment of an aerodynamic drag coefficient, which
18、 together with information on tire drag, will allow calculating road load under given driving conditions. Due to the great variety of trailer configura- tions (see Figures 1 especially if the trailer configuration is aerody- namically cluttered, see Figure 3. Figure 1 2007-01-4297 Helmut H. Korst, R
19、obert A. White and L. Daniel Metz University of Illinois at Urbana Road Evaluation of the Aerodynamic Characteristics of Heavy Trucks Author:Gilligan-SID:1178-GUID:19091828-141.213.232.87 Instead, and not discarding CD concepts, it is preferable to consider the product of area times CD, Drag Area, (
20、ft2) as a true measure of aerodynamic performance. In order to evaluate aerodynamic drag of heavy trucks, one can perform wind tunnel tests, which for full scale testing are costly and may require empirical corrections to account for size limitations of available tunnel facilities 1,2. Even then, th
21、e expected accuracy of results is not As an alternative, one may depend on coast down test- ing. While rigorous mathematical tools can be used to extract aerodynamic and tire rolling resistance under ideal environmental and data acquisition conditions, for- midable problems have to be overcome in or
22、der to iso- late the aerodynamic drag. Substantial improvement in establishing velocity vs. time recording has been achieved by utilizing GPS records during coast down which can be directly stored and immediately processed on board by laptop computers. However, environmental conditions must be known
23、 and disturbances due to (even low speed prevailing) winds must be accounted for properly. Even then, any speed dependency of tire rolling resistance over the speed range of the test leads in most cases to difficulties due to the mathematical separatabilty problem of individual drag components. In t
24、his case, information on the speed dependent rolling resistance must be obtained from the tire manufacturer, or properly estimated. A theoretical analysis establishes the basis for data processing and parameter identification through optimi- zation of experimental results by the use of the theoreti-
25、 cal “ user defined function” and the extraction of relevant coefficients (in particular the Drag Area) from those pa- rameters). Processing of coast down records by utilizing a spread- sheet and the parameter optimization method of Leven- berg-Marquardt will be illustrated in two ways: First on the
26、 basis of coast down records for two given 18 wheel- ers under well defined test conditions in order to demon- strate the expected precisions of coefficient evaluation and second, by comparing the present approach to an earlier coast down program with the new wind correction applied. In the Appendix
27、, it is shown how correctly obtained per- formance parameters can be utilized to predict run-away behavior on downhill roads or (with the use of motor test stand information) estimate fuel consumption of vehicles under various road and environmental conditions. Figure 2 THEORETICAL ANALYSIS The diff
28、erential equation of motion for coast down (here in absence of wind disturbance) is as follows: Equation 1 G0)/(2VCDA0? 1000)V/(G0GM0F1 H%/100G/G0)(M01000)G/(G0M0F0MF)/G0(M0(dV/dt) 2 ? ? ? The symbols are represented as follows: ? M0 is the vehicle mass (lbm) ? MF is the virtual mass of rotating par
29、ts (mainly tires) (lbm).1 Figure 3 ? G0 is the gravitational constant (32.174 lbm- ft/lbf-sec2). ? F0 is the tire rolling resistance (lbf/1000lbf). ? G is the local gravitational acceleration (ft/sec2). ? U is the (small, disturbing) Wind Velocity (ft/sec). ? is the wind vector angle (deg), see Figu
30、re 4. ? H% is the road slope (%, positive if uphill). ? V is the vehicle velocity, in absence of wind dis- turbance (ft/sec). ? t is the time during coast down (sec). ? F1 is the linear tire drag term (lbf-sec/1000lbf-ft). ? is the density of the air (lbm/ft3). ? A0 is the vehicle frontal area (ft2)
31、. ? CD is the drag coefficient (-), accounting also for the effect of the aerodynamic down force on car frontal area and tire resistance increase. ? with M1= (M0+MF)/M0 is the effective mass fac- tor. Equation 1 is integrated after separation of variables, according to: 1 The virtual mass of rotatin
32、g part (mainly tires) is. for each tire = Io / R2 where Io is the polar moment of inertia (lb. ft2) and R (ft) is the tire rolling radius. necessarily reliable. Author:Gilligan-SID:1178-GUID:19091828-141.213.232.87 consttAVBVCdV? ? )2/( 2 (for 0) CAB? 2 2 yielding: 22121 /)/)()/)0(BCABCAVCBTANBCAVCB
33、TANt? ? where V0 is the velocity at the start of coast down at t = 0. It is preferable to select the velocity V as the dependent variable since it will be subject to instrumentation error while the time is recorded correctly, hence, solving for V(t), one arrives at Equation 2 CBBCABCAtBCAVCBTANTANV/
34、 )/ )0( 2221 ? ? The parameters A, B, C are now, expanding the terms shown in (equation 1) to include the effects of (small) wind disturbances (see vector diagram Figure 4): Equation 3a CCOSUMGHFA? 2 )() 11000/(%)100(? Equation 3b CCOSUMGFB?)() 12000/()1(? Equation 3c ) 102/()0(MMCDAC? which have to
35、 be determined by optimized fitting of the “ user defined function” , equation 2, V(t) from the coast down record. Since (even slightly) random distur- bances (instrument error, slight wind conditions) will not allow convergence in determining all three parameters A, B and C simultaneously (lack of
36、sepa- rability), an iterative procedure, to- gether with available tire performance information may be required. The lat- ter is in the form of a speed depend- ence record for the tire rolling resis- tance. Dealing with non-ideal environmental conditions (wind) requires special at- tention. It is ob
37、vious that any off-track wind information will not necessarily be directly useful in the form in which it appears in a vector diagram, Figure 4. Instead, one develops a concept of an “ equivalent head/tailwind“ based on practical observations. Indeed, at high vehicle 2 If , case of (down) hill coast
38、ing see the Appendix 0( 2 ?BCA speed ranges, dominating in the extraction of aerody- namic drag, the yaw angle ? will be small enough to re- place the relative velocity vector within the region of di- rection-independency by V+Ucos(?). The angle ? is defined as angle between the “ prevailing wind di
39、rection” and the vehicle path. However, as the value of U is yet to be determined, one has to find a satisfactory approximation in form of an “ effective wind.” This can be accomplished in the following way: Avoiding strict side wind, one utilizes three coast down runs, say “ south” - “ north” and “
40、 south” made over a relatively short time span. If the two “ south” runs are in close agree- ment, it is easy to develop a simple iterative procedure to determine the “ effective wind” magnitude as dis- cussed in section 4, “ Spreadsheet Utilization-Data Proc- essing” . DATA ACQUISITION Two test cas
41、es are here treated; dealing with an aero- dynamically faired rig as in Figure 1, contrasted by the case of an aerodynamically unfavorable configuration, as in Figure 3. TEST CASE 1: Coast down test with an International 9400 tractor and 48 ft trailer, loaded to a total weight M0, of 61400 lbs. On N
42、ovember 1, 2006, three runs were carried out on IN HWY 101. In the following order: 1. Run 2, direction south, at 9:30, prevailing wind 4 mph, NW. 2. Run 3, direction north, at 9:40, prevailing wind 6 mph, NW. 3. Run 4, direction south, at 9:50, prevailing wind 6 mph, NNW. Air temperature 40 F, baro
43、metric pressure 30.12 inches, steady, relative humidity 62%. Based on this data one obtains, using humidair.bas 3density ? = .07965 (lb/ft3). Vehicle speed vs. time was recorded by a VBOX III speed sensor (GPS) at a 20 HZ sampling rate and stored in a laptop as runs CD_S_2.asc, _CD_N_3.asc and S_CD_
44、4.asc, respectively. In addition, the following specifications were available: Frontal Area A0= 97 ft2, effective mass factor M1 = 1.02. Unfortunately, no tire speed dependency data (F0 and F1) were available. Since the speed dependency of the tire rolling resistance is needed for extracting the cor
45、rect Aerodynamic Drag, (separability); a value of F1= .00518 was here selected as typical for a low aspect Figure 4 3 Programs identified by italics run on DOS/BASICA. Author:Gilligan-SID:1178-GUID:19091828-141.213.232.87 ratio radial truck tire based on manufacturer supplied tire data. Also, if any
46、 wind tunnel data for the aerodynamic per- formance were obtained by the Company, they were not released as proprietary. Under these restricting conditions, data processing was carried out using a spreadsheet 3 and additional com- puter programs. As can be seen in Figure 5, all three runs show a ver
47、y close agreement; however a closer examination of the high speed portion of coast down, Figure 6, clearly demonstrates the differences caused by the head/tailwind. Figure 5 Figure 6 TEST CASE 2: Aerodynamically unfavorable configura- tion, see Figure 3, tank trailer, (no aerodynamic fairings). On J
48、anuary 17th 2007, 3 coast down runs were carried out with a 18 wheel tanker on the 36th Street near Lis- bon, WI on a level road (ft over 1.22 miles). Test times were within 9-11am, environmental conditions were steady at 16 degree Fahrenheit, barometric pres- sure 30.46 “ Hg and 61% humidity. Yield
49、ing ? = .08497(lb/ft 4(? 3). Wind was below 10 MPH, southerly and steady. 1. Run 5 was run with headwind. 2. Run 6 was run in opposite direction (tailwind). 3. Run 7 was run into headwind. As can be seen in Figure 7, all three runs were in good agreement (indicating that wind conditions were steady). Yet, enlarging the scales (see Figure 8) showed the dif- ference between head and tailwind runs, while confirm- ing the steadiness of the wind disturbance. Vehicle speed was recorded by
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