Introduction
Nico Rosberg was the winner of the 2014 Grand Prix de Monaco, with an impressive time of 1:49:27:661. However, so as to continue winning on the race track, Rosberg and his team wanted to improve the performance of the vehicle on the track. To do so, Rosberg and his team must anylyse his performance and that of his vehicle at Monaco in 2014 to determine where improvements must be made. Using mathematical modeling, it is possible to tell where Rosberg and the vehicle performed at his peak and where performance fell. Using this information, appropriate improvements and alterations can be made to maximise the performance of Rosberg and the vehicle for his next event.
Interpretation
The point A (in Fig. 6) is the point of inflection on d(t), when Rosberg was travelling his fastest. At this moment, he was travelling at 225.0 kph and had travelled 122.7 km meaning he was towards the end of the 36th lap. Holding a solid average speed of 142.8 kph for the entire race, with an average lap time of 00:01: 24.203, Rosberg's fastest average speed for a lap spiked to 151.4 kph for his 36th lap. Rosberg completed the race in 1.824 hours, finishing with a time of 1:49:27.661. It was possible to determine the length of the race by multiplying the length of the track by the number of laps, which gave d(t) - 260.52 km. Using this value, it was also possible to determine the time Rosberg completed the track by rearranging the function d(t) to obtain an inverse function so as to give the time passed in hours for any distance travelled in km. Recommendation As determined (See Appendix C), Rosberg was close to the end of his 30 lap when he was travelling his fastest. As the drivers tend to go faster along straights, it can be determined that he was somewhere along Nouvelle Chicane when he was travelling at 225 kph. So as to improve performance, Rosberg should attempt to maintain speeds close to 225 kph along Beau Rtvage as well as Nouvelle Chicane, as this would increase his average speed and decrease his average lap time in turn decreasing his total time. Justification of Validity Using the model of d(t), a value with an error of 32.74% was calculated for the fastest lap time. …show more content…
This shows limitations in the ability of the model to determine accurate time intervals_ Al the official records of speed for the Grand Prix de Monaco are in mph while the function used to deter" -e the instantaneous velocity at a time in hours, is in kph. To accurately determine data, the origr model should be revised to give values in mph instead of kph. There are anomalies occurring the model though. The function d(t) gives an average velocity of 142.8 kilh which is incorrect as it should be 229.8 kph or 142.8 mph, but the the total distance travelled in 1,824 hours (Nico Rosberg's race Time) is given in km and is correct. The velocity function of the original model, v(t), suggests that Rosberg had a 74.40 kph rolling start, though the Grand Prix de Monaco doesn't have a rolling start showing an error in the function. The function also does not take into consideration pit stops where it should plateau, but instead is constantly increasing. The velocity function v(t) and the acceleration function a(t) do not take into consideration Rosberg decreasing and increasing his speed due to
Nico Rosberg was the winner of the 2014 Grand Prix de Monaco, with an impressive time of 1:49:27:661. However, so as to continue winning on the race track, Rosberg and his team wanted to improve the performance of the vehicle on the track. To do so, Rosberg and his team must anylyse his performance and that of his vehicle at Monaco in 2014 to determine where improvements must be made. Using mathematical modeling, it is possible to tell where Rosberg and the vehicle performed at his peak and where performance fell. Using this information, appropriate improvements and alterations can be made to maximise the performance of Rosberg and the vehicle for his next event.
Interpretation
The point A (in Fig. 6) is the point of inflection on d(t), when Rosberg was travelling his fastest. At this moment, he was travelling at 225.0 kph and had travelled 122.7 km meaning he was towards the end of the 36th lap. Holding a solid average speed of 142.8 kph for the entire race, with an average lap time of 00:01: 24.203, Rosberg's fastest average speed for a lap spiked to 151.4 kph for his 36th lap. Rosberg completed the race in 1.824 hours, finishing with a time of 1:49:27.661. It was possible to determine the length of the race by multiplying the length of the track by the number of laps, which gave d(t) - 260.52 km. Using this value, it was also possible to determine the time Rosberg completed the track by rearranging the function d(t) to obtain an inverse function so as to give the time passed in hours for any distance travelled in km. Recommendation As determined (See Appendix C), Rosberg was close to the end of his 30 lap when he was travelling his fastest. As the drivers tend to go faster along straights, it can be determined that he was somewhere along Nouvelle Chicane when he was travelling at 225 kph. So as to improve performance, Rosberg should attempt to maintain speeds close to 225 kph along Beau Rtvage as well as Nouvelle Chicane, as this would increase his average speed and decrease his average lap time in turn decreasing his total time. Justification of Validity Using the model of d(t), a value with an error of 32.74% was calculated for the fastest lap time. …show more content…
This shows limitations in the ability of the model to determine accurate time intervals_ Al the official records of speed for the Grand Prix de Monaco are in mph while the function used to deter" -e the instantaneous velocity at a time in hours, is in kph. To accurately determine data, the origr model should be revised to give values in mph instead of kph. There are anomalies occurring the model though. The function d(t) gives an average velocity of 142.8 kilh which is incorrect as it should be 229.8 kph or 142.8 mph, but the the total distance travelled in 1,824 hours (Nico Rosberg's race Time) is given in km and is correct. The velocity function of the original model, v(t), suggests that Rosberg had a 74.40 kph rolling start, though the Grand Prix de Monaco doesn't have a rolling start showing an error in the function. The function also does not take into consideration pit stops where it should plateau, but instead is constantly increasing. The velocity function v(t) and the acceleration function a(t) do not take into consideration Rosberg decreasing and increasing his speed due to