Optimum Driving Speed

The analysis of optimum driving speed includes a detailed comparison of various speeds, fuel efficiency, travel time, and associated costs.

In the parameters section, a mileage of 100 miles is established, with a fuel price set at $3 per gallon. The value of time is calculated at $15 per hour, which is suggested to reflect a broader perspective than just salary or working hours. The cost of injury from car accidents is noted at $48,900, while the value of a life lost in an accident is estimated at $10 million.

When examining driving speeds, the data reveals that at 30 miles per hour, the vehicle achieves 43.1 miles per gallon, requiring approximately 3.33 hours of travel time, resulting in a fuel cost of about $6.96. When considering the opportunity cost of time, which amounts to $50, the total cost without accounting for accident risk is $56.96. The odds of an accident occurring are noted at 0.00018662, with injury odds at 0.1313%, and the death odds at 0.001286%. The expected loss from accidents at this speed is around $3.60, leading to a total cost including accident risk of approximately $60.56.

As speed increases to 35 miles per hour, the fuel efficiency remains relatively high at 43 miles per gallon, with a travel time of about 2.86 hours and a fuel cost of approximately $6.98. The opportunity cost of time drops to about $42.86, bringing the total cost without accident risk to $49.83. The accident odds increase slightly to 0.00020528, with injury and death odds at 0.1510% and 0.001543%, respectively. The expected loss from accidents at this speed is around $4.68, resulting in a total cost including accident risk of about $54.52.

At 40 miles per hour, the fuel efficiency is slightly lower at 42.9 miles per gallon, with a travel time of 2.5 hours and a fuel cost of approximately $6.99. The opportunity cost of time is $37.50, leading to a total cost without accident risk of $44.49. The odds of an accident are 0.00022580, with injury odds at 0.1736% and death odds at 0.00185185. The expected loss from accidents is approximately $6.10, culminating in a total cost including accident risk of $50.59.

As the speed increases to 45 miles per hour, fuel efficiency remains at 42.8 miles per gallon, with a travel time of about 2.22 hours and a fuel cost of roughly $7.01. The opportunity cost of time is $33.33, which results in a total cost without accident risk of $40.34. Accident odds rise to 0.00024839, with injury odds at 0.1997% and death odds at 0.00222222. The expected loss from accidents is about $7.95, leading to a total cost including accident risk of $48.29.

At 50 miles per hour, the vehicle achieves 42.7 miles per gallon, with a travel time of 2 hours and a fuel cost of approximately $7.03. The opportunity cost of time is $30, resulting in a total cost without accident risk of $37.03. The accident odds are 0.00027322, with injury odds at 0.2296% and death odds at 0.00266667. The expected loss from accidents is around $10.35, resulting in a total cost including accident risk of approximately $47.38, which indicates this speed as the most cost-effective option.

As speeds increase beyond 50 miles per hour, the total costs begin to rise. At 55 miles per hour, fuel efficiency drops slightly to 42.6 miles per gallon, with a travel time of 1.82 hours and a fuel cost of about $7.04. The opportunity cost of time is $27.27, leading to a total cost without accident risk of $34.31. The accident odds increase to 0.00030055, with injury odds at 0.2641% and death odds at 0.0032%. The expected loss from accidents is approximately $13.50, resulting in a total cost including accident risk of about $47.81.

At 60 miles per hour, fuel efficiency drops further to 39.4 miles per gallon, with a travel time of 1.67 hours and a fuel cost of around $7.61. The opportunity cost of time is $25, leading to a total cost without accident risk of $32.61. Accident odds rise to 0.00033060, with injury odds at 0.3037% and death odds at 0.00384%. The expected loss from accidents is about $17.61, bringing the total cost including accident risk to approximately $50.22.

As speeds continue to increase, the costs keep rising. At 65 miles per hour, the vehicle achieves 36.2 miles per gallon, with a travel time of 1.54 hours and a fuel cost of about $8.29. The opportunity cost of time is $23.08, leading to a total cost without accident risk of $31.36. The accident odds are 0.00036366, with injury odds at 0.3492% and death odds at 0.004608%. The expected loss from accidents is approximately $22.97, resulting in a total cost including accident risk of about $54.33.

At 70 miles per hour, fuel efficiency is further reduced to 33 miles per gallon, with a travel time of 1.43 hours and a fuel cost of around $9.09. The opportunity cost of time is $21.43, leading to a total cost without accident risk of $30.52. The accident odds increase to 0.00040003, with injury odds at 0.4016% and death odds at 0.0055296%. The expected loss from accidents is about $29.98, culminating in a total cost including accident risk of approximately $60.50.

At 75 miles per hour, fuel efficiency drops to 29.8 miles per gallon, with a travel time of 1.33 hours and a fuel cost of around $10.07. The opportunity cost of time is $20, leading to a total cost without accident risk of $30.07. The accident odds are 0.00044003, with injury odds at 0.4619% and death odds at 0.00663552. The expected loss from accidents is approximately $39.14, resulting in a total cost including accident risk of about $69.20.

Finally, at 80 miles per hour, the vehicle achieves 27.35 miles per gallon, with a travel time of 1.25 hours and a fuel cost of around $10.97. The opportunity cost of time is $18.75, leading to a total cost without accident risk of $29.72. The accident odds rise to 0.00048403, with injury odds at 0.5311% and death odds at 0.00796262. The expected loss from accidents is about $51.11, culminating in a total cost including accident risk of approximately $80.83.

When examining the impact of a rooftop box on fuel efficiency, at 55 miles per hour, the mpg before the addition is 42.6, while after the rooftop box is added, it drops to 39.4 mpg. At 60 miles per hour, the mpg before is 45.9, and after, it decreases to 39.4. At 65 miles per hour, the mpg is 36.2, and at 70 miles per hour, it drops to 33 mpg. At 75 miles per hour, the mpg is 39, which further decreases to 29.8 with the rooftop box. The mpg at 80 miles per hour is 27.35, and at 85 miles per hour, it is 29 before dropping to 24.9.