Proposal for WLTP Tabulated Load Coefficients Thomas B. Wagner, 24.04.2013
Use of tabulated load coefficients Default load coefficients are used to handle high variety and small series. Today passenger cars (M1) are tested based on road load coefficients these parameters are lower than the default coefficients. Exceptions e.g. Sprinter coaches with 8+1 seats (about 4500 units per year). The default values of light commercial vehicles (N1) and 4x4 drivetrains are 30% higher (factor 1,3). This represents the payload of N1 vehicles. tabulated default values Coast down / road load data 2
Multistage vehicles high variety Reference mass = curb weight + default added mass (DAM) calculated by a 2 nd order polynomial function 3
Road load coefficients vs. tabulated load F[N] F[N] A 0, A 1, A 2 load adjustment F 0, F 1, F 2, F R, FTS V [km/h] - rolling resistance axles - drivetrain lossess V [km/h] Road load data rolling resistance aerodynamic drag drag torque drivetrain vehicle mass Dynamometer settings Tabulated load default aerodynamic Test Mass Widerstand bei 80 km/h a b c kg kw N N N/(km/h) N/(km/h)² 1000 5,9 264 30 0 drag 0,0367 1100 6,1 275 32 0 0,0381 1200 6,4 286 34 0 0,0395 losses 1300 6,6 297 36 0 0,0409 1400 6,9 308 37 0 0,0423 1500 7,1 319 39 0 losses 0,0438 1600 7,3 330 41 0 0,0452 1700 7,6 341 43 0 0,0466 1800 7,8 353 45 0 0,0480 F[N] 1900 8,1 364 47 0 0,0494 2000 8,3 375 49 0 0,0508 2100 8,6 386 51 0 0,0523 2200 8,8 397 53 0 0,0537 2300 9,1 408 55 0 0,0551 2400 9,3F 419 57 0 0,0565 0, F 2, F R, FTS 2500 9,5 430 59 0 0,0579 2600 9,8 441 61 0 0,0593 2700 10,0 452 63 0 0,0608 2800 10,3 463 65 0 0,0622 2900 10,5 474 67 0 0,0636 3000 10,8 485 V 69[km/h] 0 0,0650 3100 10,8 487 71 0 0,0650 3200 10,9 489 73 0 0,0650 3300 10,9 491 75 0 0,0650 3400 10,9 493 77 0 0,0650 3500 11,0 495 79 0 0,0650 3600 11,0 497 81 0 0,0650 3700 11,1 499 83 0 0,0650 3800 11,1 501 85 0 0,0650 3900 11,2 503 87 0 0,0650 4000 11,2 504 88 0 0,0650 4100 11,3 506 90 0 0,0650 4200 11,3 508 92 0 0,0650 4300 11,3 510 94 0 0,0650 4400 11,4 512 96 0 0,0650 4500 11,4 514 98 0 0,0650 default drivetrain default front axle Road load coefficients are significantly different from tabulated load coefficients. Due to load adjustment dynamometer settings are found. Dynamometer settings + rolling resistance driving axle + drivetrain losses By use of tabulated values there is no load adjustment. Rolling resistance and drivetrain losses are additional. 4
Dynamometer power @ 80 km/h [kw] Discussion of different default value proposals WLTP based dynamometer settings and target curve proposals No physical basis recognizable CO2 regulation M1/N1 ends at a reference mass of 2610 kg 2 nd TNO proposal, PSA tab. values WLTP reference mass: M1: Curb weight + 15% payload, N1: curbweight + 35% payload [kg] 5
Conclusion There is a discussion initiated on tabulated load settings because of the assumption they don t represent the reality in a appropriate way. This wrong interpretation is supported by wrong statements and analyses. Facts: Passenger cars as well as small and medium vans (M1 + N1) use road load coefficients because the default tabulated settings are worse. In the segment of large vans (M1 + N1) there are a lot of variants, therefore tabulated values are helpful to optimize the homologation complexity. (Examples: 3 roof heights, roof-a/c, different tire types, single and twin axles, different drivetrains, manifold platforms, multistage type approval, ) Today payload of N1 vehicles is represented by an load increase of 30% (factor 1,3). If payload is added to the reference mass, there is no physical basement for this factor anymore. 6
Conclusion Today the M1 and N1 CO2-regulation is not exceeding a reference mass of 2610 kg we recommend a discussion about the payload of 35% and the load increase of 30% (factor 1,3). In the available proposals of PSA and Ford (2 nd ) we look for a physical basis to legitimate a polynomial growth with increasing weight and for the jump in the function at 1810 kg. After analysis of the todays tabulated default values we conclude that they represent the vehicle landscape in a appropriate way. The WLTP dynamometer settings large vans, such as Sprinter, are clearly under the 30% curve. Based on our proposed default values we expect a better physical approach than the todays load increase of 30%. We invite you to draw your dynamometer settings of passenger cars and vans in the diagram on slide 5 by using the calculation in the backup. 7
Backup
Tabulated Load Values (proposal MB Vans) There is no general correlation between aerodynamic resistance and Test mass of the vehicle. So it makes sense to limit the factor c at the worst case of the Large Van categorie The factor c is based on the actual measured aerodynamis cw x A from our Small-, Midsize- and Large Vans. This will be the worst case in the future when the new table values will become effectiv. The Factor a corresponds to the quotient A0 (Coast down test)/f0 (Load adjustment on the test bench). rolling resistance =A0/F0 a = 7 kg/t*9,81*tm/4 + 10 N vehicle test mass brake losses (nondriving axle) c = 0,5*cw*A*1,2/(3,6²) 9
Correlation between table values and road load data Driving resistance at the roller test bench= Resistance of the braked dynamometer (F0, F1, F2) + rolling resistance driving axle (FR) + drivetrain losses: driving axle, joint shaft bearings, gearbox and bearings (FTS) =required engine power With road load data Load adjustment (F0, F1, F2) = Road load data (A0, A1, A2) FR 1 FTS 1 With table values Required engine power= Road load data(a0, A1, A2) = Load adjustment (F0, F1, F2) + FR 1 + FTS 1 Required engine power= Table values (F0, F1, F2) + FR 2 + FTS 2 By using the same car (FR 1 = FR 2 and FTS 1 = FTS 2 ) for measuring with road load data and table values, it is correct to compare load adjustment and table values. FR.. rolling resistance driving axle FTS.. drivetrain losses: driving axle, joint shaft bearings, gearbox and bearings 10
Tabulated Load Values (proposal MB Vans) Test Mass Widerstand bei 80 km/h a b c kg kw N N N/(km/h) N/(km/h)² 1000 5,9 264 30 0 0,0367 1100 6,1 275 32 0 0,0381 1200 6,4 286 34 0 0,0395 1300 6,6 297 36 0 0,0409 1400 6,9 308 37 0 0,0423 1500 7,1 319 39 0 0,0438 1600 7,3 330 41 0 0,0452 1700 7,6 341 43 0 0,0466 1800 7,8 353 45 0 0,0480 1900 8,1 364 47 0 0,0494 2000 8,3 375 49 0 0,0508 2100 8,6 386 51 0 0,0523 2200 8,8 397 53 0 0,0537 2300 9,1 408 55 0 0,0551 2400 9,3 419 57 0 0,0565 2500 9,5 430 59 0 0,0579 2600 9,8 441 61 0 0,0593 2700 10,0 452 63 0 0,0608 2800 10,3 463 65 0 0,0622 2900 10,5 474 67 0 0,0636 3000 10,8 485 69 0 0,0650 3100 10,8 487 71 0 0,0650 3200 10,9 489 73 0 0,0650 3300 10,9 491 75 0 0,0650 3400 10,9 493 77 0 0,0650 3500 11,0 495 79 0 0,0650 3600 11,0 497 81 0 0,0650 3700 11,1 499 83 0 0,0650 3800 11,1 501 85 0 0,0650 3900 11,2 503 87 0 0,0650 4000 11,2 504 88 0 0,0650 4100 11,3 506 90 0 0,0650 4200 11,3 508 92 0 0,0650 4300 11,3 510 94 0 0,0650 4400 11,4 512 96 0 0,0650 4500 11,4 514 98 0 0,0650 Citan Viano/Vito Successor Sprinter Successor worst case 11
History new table values 1. Proposal PSA (14.10.2012) Test Mass (TM) Power and load absorbed by the dynamometer at 80 km/h Coefficients a b c Kg kw N N N/(km/h) N/(km/h)² 1400 10,6 478 114,0 0,1 0,0556 1500 10,7 484 120,0 0,1 0,0556 1600 10,9 492 126,0 0,1 0,0559 1700 11,2 502 132,0 0,1 0,0566 1800 11,4 515 138,0 0,1 0,0577 1900 11,8 530 144,0 0,1 0,0591 2000 12,2 547 150,0 0,1 0,0608 2100 12,6 567 156,0 0,1 0,0629 2200 13,1 588 162,0 0,1 0,0654 2300 13,6 612 168,0 0,1 0,0682 2400 14,2 638 174,0 0,1 0,0713 2500 14,8 667 180,0 0,1 0,0748 2600 15,5 697 186,0 0,1 0,0787 2700 16,2 730 192,0 0,1 0,0829 2800 17,0 765 198,0 0,1 0,0874 2900 17,8 803 204,0 0,1 0,0923 3000 18,7 842 210,0 0,1 0,0975 3100 19,6 884 216,0 0,1 0,1031 3200 20,6 928 222,0 0,1 0,1091 3300 21,7 974 228,0 0,1 0,1154 Factor a is much too high, elevated values for rolling resistance and break losses There is no need for a factor b: drive train losses are included on the test bench. Factor c is much too high, and a correlation between weight and aerodynamics is wrong 12
History new table values 2. 1. Proposal Ford (13.02.2013) Test Mass Widerstand bei 80 km/h a b c kg kw N N N/(km/h) N/(km/h)² 1000 5,7 259 5,902 0 0,0395 1100 6,1 273 6,226 0 0,04166 1200 6,4 286 6,538 0 0,04374 1300 6,7 300 6,838 0 0,04574 1400 6,9 312 7,126 0 0,04766 1500 7,2 324 7,402 0 0,0495 1600 7,5 336 7,666 0 0,05126 1700 7,7 347 7,918 0 0,05294 1800 7,9 357 8,158 0 0,05454 1900 8,2 367 8,386 0 0,05606 2000 8,4 377 8,602 0 0,0575 2100 8,6 386 8,806 0 0,05886 2200 8,8 394 8,998 0 0,06014 2300 8,9 402 9,178 0 0,06134 2400 9,1 409 9,346 0 0,06246 2500 9,2 416 9,502 0 0,0635 2600 9,4 422 9,646 0 0,06446 2700 9,5 428 9,778 0 0,06534 2800 9,6 433 9,898 0 0,06614 2900 9,7 438 10,006 0 0,06686 3000 9,8 442 10,102 0 0,0675 3100 9,9 446 10,186 0 0,06806 3200 10,0 449 10,258 0 0,06854 3300 10,0 452 10,318 0 0,06894 3400 10,1 454 10,366 0 0,06926 3500 10,1 455 10,402 0 0,0695 3600 10,1 456 10,426 0 0,06966 3700 10,2 457 10,438 0 0,06974 3800 10,2 457 10,438 0 0,06974 3900 10,1 456 10,426 0 0,06966 4000 10,1 455 10,402 0 0,0695 4100 10,1 454 10,366 0 0,06926 4200 10,0 452 10,318 0 0,06894 4300 10,0 449 10,258 0 0,06854 4400 9,9 446 10,186 0 0,06806 4500 9,8 442 10,102 0 0,0675 13 These are the old table values (83:06), expanded to higher weights The aerodynamics (factor c) doesn t show the worst-case in the future when the new table values will become effective and has to be updated Factor a becomes smaller with a weight over 3800 kg. This is illogical.
History new table values 3. Proposal MB Vans (19.02.2013) Test MassWiderstand bei 80 km/h a b c kg kw N N N/(km/h) N/(km/h)² 1000 5,9 264 30 0 0,0367 1100 6,1 275 32 0 0,0381 1200 6,4 286 34 0 0,0395 1300 6,6 297 36 0 0,0409 1400 6,9 308 37 0 0,0423 1500 7,1 319 39 0 0,0438 1600 7,3 330 41 0 0,0452 1700 7,6 341 43 0 0,0466 1800 7,8 353 45 0 0,0480 1900 8,1 364 47 0 0,0494 2000 8,3 375 49 0 0,0508 2100 8,6 386 51 0 0,0523 2200 8,8 397 53 0 0,0537 2300 9,1 408 55 0 0,0551 2400 9,3 419 57 0 0,0565 2500 9,5 430 59 0 0,0579 2600 9,8 441 61 0 0,0593 2700 10,0 452 63 0 0,0608 2800 10,3 463 65 0 0,0622 2900 10,5 474 67 0 0,0636 3000 10,8 485 69 0 0,0650 3100 10,8 487 71 0 0,0650 3200 10,9 489 73 0 0,0650 3300 10,9 491 75 0 0,0650 3400 10,9 493 77 0 0,0650 3500 11,0 495 79 0 0,0650 3600 11,0 497 81 0 0,0650 3700 11,1 499 83 0 0,0650 3800 11,1 501 85 0 0,0650 3900 11,2 503 87 0 0,0650 4000 11,2 504 88 0 0,0650 4100 11,3 506 90 0 0,0650 4200 11,3 508 92 0 0,0650 4300 11,3 510 94 0 0,0650 4400 11,4 512 96 0 0,0650 4500 11,4 514 98 0 0,0650 These values are based on actual MB Vans Series, and this will be the worst case at the entry into force of the new table values. 14
15 History new table values 4. 2. Proposal Ford (19.02.2013) Test Mass Widerstand bei 80 km/h a b c kg kw N N N/(km/h) N/(km/h)² 1000 5,2 235 5,9151 0 0,0358 1100 5,5 246 6,2361 0 0,03754 1200 5,7 257 6,5391 0 0,03916 1300 5,9 267 6,8241 0 0,04066 1400 6,1 276 7,0911 0 0,04204 1500 6,3 284 7,3401 0 0,0433 1600 6,5 292 7,5711 0 0,04444 1700 6,6 299 7,7841 0 0,04546 1810 6,8 305 7,99761 0 0,0464434 1810 10,4 466 10,61153 0 0,0712222 1900 10,6 475 10,8107 0 0,07252 2000 10,8 485 11,0377 0 0,074 2100 11,0 495 11,2707 0 0,07552 2200 11,2 505 11,5097 0 0,07708 2300 11,5 515 11,7547 0 0,07868 2400 11,7 526 12,0057 0 0,08032 2500 11,9 537 12,2627 0 0,082 2600 12,2 548 12,5257 0 0,08372 2700 12,4 560 12,7947 0 0,08548 2800 12,7 572 13,0697 0 0,08728 2900 13,0 584 13,3507 0 0,08912 3000 13,2 596 13,6377 0 0,091 3100 13,5 609 13,9307 0 0,09292 3200 13,8 621 14,2297 0 0,09488 3300 14,1 635 14,5347 0 0,09688 3400 14,4 648 14,8457 0 0,09892 3500 14,7 662 15,1627 0 0,101 3600 15,0 675 15,4857 0 0,10312 3700 15,3 690 15,8147 0 0,10528 3800 15,6 704 16,1497 0 0,10748 3900 16,0 719 16,4907 0 0,10972 4000 16,3 734 16,8377 0 0,112 4100 16,6 749 17,1907 0 0,11432 4200 17,0 764 17,5497 0 0,11668 4300 17,3 780 17,9147 0 0,11908 4400 17,7 796 18,2857 0 0,12152 4500 18,1 812 18,6627 0 0,124 This is a combintion of the old table values (83:06), above 1810 kg with multiplication of the factor 1,3