1. WLTP
Modelling of fuel consumption and detection of driveability problems for “borderline” cars with different maximum speed caps.
Heinz Steven 1

2. Aim
The latest discussions in the DHC and MCTF groups about the cycle allocation and vehicle speed caps led to the need of some modelling work in order to gather information about the influence on CO2 emissions and driveability.
The following approach was used in order to enable model calculations:
The gearshift calculation tool provides engine speed traces and estimates for the engine power for the WLTC cycles on a second by second base. 2

3. Approach
In a first step the tool was modified in that way, that it reduces the vehicle speed in cases where the required acceleration exceeds the available acceleration power and where the maximum speed of the vehicle is lower than the cycle speed.
This could even lead to max. speed reductions within the cycle in cases where the max. vehicle speed is slightly higher than the max. cycle speed.
The engine speed and load values could easily be combined with engine maps that are used for the calculation of emission factors for the Handbook of Emission Factors, a well established emission calculation tool in some EU member states. 3

4. Approach
Stefan Hausberger (TU Graz) provided normalised fuel consumption (FC) emission maps for an average Euro 5 Petrol and an avarage Euro 5 Diesel vehicle.
These maps provide specific FC emissions in g per h and kW rated power over the whole engine map in steps of 6% for the normalised engine speed and 7% for the normalised engine power.
The FC values are direct proportional to CO2.
The engine speed is normalised to the span between idling speed and rated speed and ranges from 0 to 120%. This is in good accordance with the gearshift calculation tool which covers the same engine speed range. 4

5. Approach
The engine power is normalised to the rated power and ranges from -40% to the engine speed dependend maximum, that is determined by a corresponding average full load power curve (see figures 1 and 2). 5

6. Engine map, average EU 5 Diesel, provided by S. Hausberger
Figure 1 6

7. Engine map, average EU 5 Petrol, provided by S. Hausberger
Figure 2 7

8. Vehicle specifications
The application of a maximum speed cap is only related to the maximum speed of a vehicle but does not take into account, how this maximum speed is achieved.
For a „normal“ car the the gearbox is designed in that way that the driving resistance curve crosses the full load power curve in highest gear near rated speed . In these cases the maximum speed id determined by the engine power (see figures 3 and 4).
But in some cases (e.g. for kei cars) the maximum speed is limited by the engine speed rather than by the engine power (see figure 5). 8

9. Wot power and driving resistance power vs vehicle speed
Figure 3 9

10. Wot power and driving resistance power vs vehicle speed
Figure 4 10

11. Wot power and driving resistance power vs vehicle speed
Figure 5 11

12. Calculations
Two important influencing parameters on FC and driveability are
the average normalised engine speed (n_mnorm_ave) and
the percentage of wot operation (p_wot)
p_wot is determined by
Prequired >= 0.9 * Pmax(n).
In order to demonstrate the effects of these parameters, variants of the same base vehicle (same engine power and vehicle mass) were defined. 12

13. Results
Calculations were performed for these variants for the class 2 version 2 cycle as well as for the class 3, versions 5.1 and 5.3 cycles and different speed caps.
The following tables show the results but only for one of these cycles.
Differences between cycle versions are not discussed here.
It must also be mentioned that the modelling is restricted to hot emissions only. Cold start contributions are not included. 13

14. Detailed results, example 1
Table 1 shows the results for a 45 kW Diesel vehicle with 3600 min-1 rated speed and a kerb mass of 1700 kg. This vehicle belongs to class 2 and the results are related to the class 2 cycle whose maximum speed is km/h.
This vehicle is able to reach a maximum speed of 135 km/h, but would not reach the maximum speed of the class 3 cycles.
For the 135 km/h version the speed caps of 5% or 10 km/h lead to higher speeds than the max. cycle speed and thus have no effect on the cycle trace. 14

15. Example 1, class 2, Diesel
Table 1 15

16. Detailed results, example 1
For all speed cap variants (including no cap) the vehicle versions with lower max. vehicle speed than 135 km/h have higher FC than the 135 km/h version.
The increase is related to an increase in average normalised engine speeds, which is caused by the fact, that the transmission ratios need to be increased („shorter“ gears) in order to achieve lower max. vehicle speeds.
Another parameter that influences the FC is the difference in engine load, especially in the wot percentage. At given average engine speeds higher wot percentages would lead to higher FC values. This effect can compensate the engine speed effect and thus makes the whole picture less clear. 16

17. Detailed results, example 1
This can explain why the FC values for the 126 km/h variant are higher than the FC values for the 106 km/h variant although the n_norm_ave values are lower.
For all speed cap variants (including no cap) the vehicle versions with lower max. vehicle speed than 135 km/h have higher FC than the 135 km/h version.
For all speed cap variants there is a trend towards higher FC with decreasing max. vehicle speed but this trend is not clear because of variances in n_norm_ave as well as in wot percentage. But, of course, there is a clear trend towards lower wot percentages with increasing speed cap. 17

18. Detailed results, example 1
Although the speed limitation to lower max. vehicle speeds than 135 km/h is not determined by the rated power of the vehicle rather than by the transmission design, an application of a speed cap of 10% would lead to reasonable FC values compared to the base version (135 km/h max. vehicle speed without speed cap.
A deletion of the extra high speed part would lead to significantly lower FC values, except for the 90 km/h variant. 18

19. Detailed results, example 2
Table 2 shows the results for a class 2 Petrol vehicle with rated power of 25 kW at 5000 min-1 and a kerb mass of 785 kg.
This covers max. vehicle speeds of 90, 106 and 126 km/h. A 26.5 kW version was added in order to include a max. vehicle speed of 130 km/h.
Also in this case no clear trends related to max. vehicle speed or wot percentage can be found, but for the same reasons (combined influence of average engine speed and wot percentage).
A deletion of the extra high speed part leads to lower FC values for the 130 and 126 km/h variants but to higher FC values for the variants with 106 and 90 km/h max. vehicle speed. 19

20. Example 2, class 2, Petrol
Table 2 20

21. Detailed results, example 3
Table 3 shows the results for a class 3 Diesel vehicle with 55 kW rated power at 4000 min-1 and a kerb mass of 1415 kg.
5 different max. vehicle speed variants could be modelled for this vehicle.
The results are related to the class 3 version 5.3 cycle.
The wot percentages are in all cases below 4%, so that no speed cap would be required for those cases where the max. vehicle speed is below max. cycle speed. 21

22. Example 3, class 3 ver. 5.3, Diesel
Table 3 22

23. Detailed results, example 3
Because of the low wot percentages, the engine speed influence dominates (see figure 6) and thus the trends with lower max. vehicle speed and higher max. speed cap are more clear than in the previous examples.
The lower the max. vehicle speed the higher the FC values.
The application of speed caps would reduce the FC values in relation to the „no cap“ variants, but would still lead to reasonable higher FC values than the base variant. 23

24. Example 3, class 3 ver. 5.3, Diesel
Figure 6 24

25. Detailed results, example 4
Table 4 shows the results for a class 3 Petrol vehicle with 26 kW rated power at 5500 min-1 and a kerb mass of 750 kg with a 4speed gearbox.
Because this vehicle is a borderline case (pmr = 34.7 kW/t) the wot percentage influence dominates (see figure 7) and thus deteriorates the correlation with max. vehicle speed significantly.
It must be mentioned that the maximum cycle speed of km/h is reached in no case, even the base case reaches only km/h.
But a 10% speed cap does not improve the situation, because it decreases the max. cycle speed only by 2.1 km/h compared to the base case. 25

26. Example 4, class 3, ver. 5.3, petrol
Table 4 26

27. Example 4, class 3 ver. 5.3, petrol
Figure 7 27

28. Detailed results, example 4
The use of the cycle version 5.1 instead of 5.3 is also no solution because the extra high speed part is identical.
A 15% cap would at least improve the situation for the wot percentage.
But the situation could certainly be improved if the 4speed gearbox would be replaced by a 5speed gearbox. 28

29. Detailed results, example 5
Table 5 shows the results of a 5th example, a Petrol vehicle with 32 kW rated power at 5500 min-1, a kerb mass of 800 kg and a maximum vehicle speed of 140 km/h in the base variant.
Although this vehicle is not a borderline case, it has also difficulties in reaching the max. cycle speed even in the base variant (see figure 8).
Also with a 10% speed cap the situation is not improved much, because the most demanding part of the extra high speed trace between 1560 s and 1585 s is not affected and remains unchanged (see figure 9). 29

30. Example 5, class 3, ver. 5.3, Petrol
Table 5 30

31. Example 5, vehicle speed trace, without speed cap
Figure 8 31

32. Example 5, vehicle speed trace, with 10% speed cap
Figure 9 32

33. Detailed results, example 5
In order to make the reason for the driveability problems more obvious, vehicle speed, acceleration and engine power traces are shown in figures 10 and 11 for the extra high speed phase between 1559 and 1585 s.
During the first 7 s the set acceleration is constant or slightly increasing.
This would require an increasing engine power, which is normally fulfilled in a gear where the engine speed is below rated speed.
For these high vehicle speeds this requirement would be fulfilled in 5. gear (highest gear), but the available power in this gear is not high enough. 33

34. Example 5, speed and acceleration trace
Figure 10 34

35. Example 5, speed and engine power trace
Figure 11 35

36. Detailed results, example 5
At the beginning of the time period, shown in figure 11, the required power is just provided in 4. gear, but it does not increase in accordance with the required power, because the engine speed crosses rated speed and the available wot power decreases with increasing speed (see figure 12).
This is the reason why the vehicle could not follow the trace and the vehicle speed drops below the tolerance (see figures 8 and 9).
And as already said, this situation would not be improved by a 10% speed cap, but does on the other hand not justfy a higher speed cap.
Another more appropriate solution should be found instead. 36

37. Example 5, engine power vs vehicle speed
Figure 12 37

38. Further model calculations
In order to confirm/verify the findings so far, additional calculations were performed for the following model vehicles:
Petrol engine with s = 6500 min-1 and n_idle = 850 min-1,
Petrol engine with s = 5000 min-1 and n_idle = 650 min-1,
Diesel engine with s = 4000 min-1 and n_idle = 700 min-1.
In all cases a 5speed gearbox was modelled. 38

39. Further model calculations
The kerb mass was set to 840 kg and the rated power was varied in 3 steps in order to achieve the following max. vehicle speeds:
170 km/h (51.4 kW), 150 km/h (35 kW) and 135 km/h (28 kW)
The last case defines a class 2 vehicle but the calculations were performed for the class 3, version 5.3 cycle. 39

40. Further model calculations
For each of these vehicles 3 variants with different transmission ratios (but based on a 5speed gearbox) were defined as follows:
v_max is reached in 4. gear only, the 5. gear is intended to drive economically also at high speeds. Such transmission design was found for 12% of the M1 vehicles in the in-use database.
v_max is reached in 5. gear but n_v_max < s. (29% of the M1 vehicles in the in-use database.)
v_max is reached in 5. gear but n_v_max > s. (31% of M1 and 79% of N1 vehicles in the in-use database.)
The technical data are shown in table 6. 40

41. Additional model vehicles, technical data
Table 6 41

42. Results for the additional model vehicles
The results for the case without any speed cap are shown in table 7.
The average n_norm and FC values increase from the variants with v_max in 4. gear over v_max in 5. gear but below s to v_max in 5. gear but above s.
The wot percentages show an opposite trend, except for the highest rated power variants, where the values are below 4%.
Due to the difference in the normalised wot power curves (see figures 1 and 2) the wot percentages for the Diesel vehicles are lower than for the Petrol vehicles. 42

43. Results for the additional model vehicles
The lowest rated power variants reach wot percentages between 9% and 14%, which is still reasonable, since it is a class 2 vehicle. The values are in the same order than for the example 4 class 3 vehicle (see table 4).
In table 16b can be seen that the petrol vehicles with v_max = 150 km/h, reached in 4. gear do not meet exactly the maximum cycle speed.
Figures 13 to 15 show that the problems described for the example vehicle 5 could already start to occur at a max. vehicle speed of 150 km/h and pmr values around 40 kW/t. This risk is not very high for European vehicles, because the acceleration performance would hardly be acceptable. 43

44. Additional model vehicles, results
Table 7a 44

45. Additional model vehicles, results
Table 7b 45

46. Case 379, vehicle speed trace
Figure 13 46

47. Case 379, speed and acceleration trace
Figure 14 47

48. Case 379, speed and engine power trace
Figure 15 48

49. Results for the additional model vehicles
The acceleration problem between 1560 s and 1585 s is even higher for the transmission design, for which v_max vehicle is reached in 5. gear but below rated speed (see figure 16).
As expected the variant with v_max vehicle = 135 km/h has significantly higher driveability problems, partly due to the pmr value of 33.3 kW/t and which specifies it as a class 2 vehicle (see figure 17).
The other part is related to the transmission design, what can be proven by a comparison with figure 18.
Figures 19 and 20 show, that a speed cap of 10% would not solve the driveability problems. 49

50. Case 380, vehicle speed trace
Figure 16 50

51. Case 388, vehicle speed trace, no speed cap
Figure 17 51

52. Case 390, vehicle speed trace, no speed cap
Figure 18 52

53. Case 388, vehicle speed trace, 10% speed cap
Figure 19 53

54. Case 390, vehicle speed trace, 10% speed cap
Figure 20 54

55. Draft Conclusions
The fuel consumption and thus the CO2 emissions are influenced by the following parameter:
Average normalised engine speed (n_norm_ave),
Engine load, represented by the wot percentage,
Transmission design with respect to v_max vehicle.
The average normalised engine speed is dependent on the shape of the wot power curve and decreases with increasing power to mass ratios (pmr).
Diesel engines have normally advantageous power curves compared to Petrol engines.
Also the wot percentage decreases with increasing pmr. 55

56. Draft Conclusions
The transmission design influences the FC values as follows:
Designs where v_max vehicle is reached in the 2nd highest gear lead to low n_norm_ave but relatively high wot percentages.
Designs where v_max vehicle is reached in highest gear at engine speeds above rated speed show opposite results (higher n_norm_ave values but lower wot percentages), but are advantageous with respect to driveability for low powered vehicles.
Designs where v_max vehicle is reached in highest gear at engine speeds below rated speed lead to n_norm_ave values and wot percentages between those cases. 56

57. Draft Conclusions
Driveability problems in the extra high speed phase of the class 3 cycle can already start at max. vehicle speeds of 140 km/h and pmr of 40 kW/t.
Since they are related to the acceleration potential, they can only be reduced but not eliminated by speed caps up to 10%.
But higher speed caps would be less effective than cycle modifications, because the problems are related to 3 distinct sections of the extra high speed phase.
For class 3 vehicles (pmr > 34 kW/t) max. vehicle speeds below 130 km/h can normally only be achieved by specificly „short“ transmission designs. 57

58. Draft Conclusions
This leads normally to higher n_norm_ave values and higher FC/CO2 values.
Since the design is obviously intended to get a better performance at lower speeds and the speeds of the extra high phase are not intended to be frequently used in real traffic, the application of a speed cap of up to 10% could be justified.
But since the driveability problems in the extra high speed part are less related to max. vehicle speed rather than to transmission design and the shape of the wot power curve, more effective solutions based on key parameters of the transmission and the wot power curve should be found. 58

59. Draft Conclusions
The downscaling of the speed trace of the extra high speed phase in the time section between 1533 s and 1762 s might be a promising approach to elaborate such a solution. 59