## 3 Results and Discussion
### Overall Performance of Odd/Even Evaluations and Low Sample Rate Effects  
Given the results found in the previous sub-section, the two methods (rpm and spark duration) were implemented and scrutinized for all five load points. Only the overall rate of successful firing TDC ID will be discussed, without showing detailed results in terms of distribution. Figure 10 shows the results obtained by applying the rpm and spark duration-based methods. An excellent performance was recorded for the first procedure, with 100% reliability when evaluating firing TDC phasing based on measured rpm. Directly comparable results were also obtained with the spark duration method as well, with the lowest success rate at 99.8%. This translates in only two false IDs in a set of 1000 cycles. When hypothesizing port fuel injection control as in [37], this would mean that the benefits of phased fuel delivery would only be lost for two cycles out of 1000. This does not mean, however, that these two cycles would misfire (injection would still occur, but during the 'other' crankshaft turn, total injection time permitting), and therefore, for fuels such as gasoline, it would be of no real influence. For other energy sources, such as hydrogen, it could lead to backfire phenomena [35]. Further development to include fuels with such different properties with respect to gasoline could be an interesting line of research; the fact that H\({}_{2}\) features much lower ignition energy may result in lower coil charge (and spark duration), and therefore, certain applicative aspects of the algorithm may have to be adjusted. Nonetheless, actual applicability should not be significantly influenced by fuel properties. At a first glance, it would seem that the best option is to choose the rpm-based method. In the odd/even mode, it ensured 100% successful detection of the firing TDC for all five load points that were investigated. One possible drawback is that it requires high sampling rate for correct measurements. At 5200 rpm, the 50 kHz rate ensures an accuracy better than 0.17%, translated into a sensitivity of detecting engine speed variations of around 10 rpm; if instead a sample rate of 10 kHz would be used (still relatively high, but comparable to that usually obtained with a 58/60 tooth crank gear sensor at 6000 rpm), the sensitivity would be around 45 rpm. This would be at the very limit when considering the in-cycle rpm variation shown in Figure 7 at the 1.0 kW load; things would be even worse for the idle case, for which an achievable sensitivity of over 26 rpm would completely miss a large part of variations recorded at 4000 rpm. For this reason, it was decided to test whether the spark duration method could work with lower sampling rate, such as 10 kHz. Figure 11 illustrates the difficulty of actually implementing duration measurements with such a low readout frequency (acquisition points are highlighted with cross symbols; they were randomly distributed to emphasize the effect of time-based data acquisition). Indeed, even with interpolation, the starting  
Figure 10: Success rate of firing TDC identification for the rpm and spark duration methods in odd/even mode. point of the spark event would be difficult to be determined; things are even worse as engine speed increases (note the wider crank angle spacing between 10 kHz symbols). On the other hand, the specific triangle shape of the secondary current during spark discharge can be correlated to the actual duration of the event. More to the point, short sparks will feature a steeper slope of the falling current profile. In this way, the odd/even sparks can be compared by reading the index location and the value of two points and then calculating the correlated slope. As shown in Figure 11, the third point after the instance in which the secondary current exceeds 2 mA was chosen as the first reference for the slope (to make sure it will read the falling side), while the second location was taken after another four acquired samples.