SolarDaveGreen
Active member
Brought to you by ChatGPT:
David asks:
My electric car has a 45 kWH battery, and I only use the charge between 20 and 80 percent of capacity. My car uses energy at the rate of 5 miles per kWH at 55 MPH and 3.5 miles per kWH at 70 MPH. I charge the car at a rate of 45 kW. For a 600 mile road trip, will I complete the trip faster if I drive at 55 MPH or 70 MPH? Please show your work.
ChatGPT answers:
To solve this problem, we need to calculate the time it would take to complete the 600-mile road trip at both speeds and then compare them.
First, let's calculate the amount of energy we have available for the trip:
80% of 45 kWH = 36 kWH (maximum usable charge)
20% of 45 kWH = 9 kWH (minimum usable charge)
Usable energy = 36 kWH - 9 kWH = 27 kWH
Now, let's calculate the distance we can travel with this energy:
At 5 miles per kWH, we can travel 27 kWH x 5 miles/kWH = 135 miles
At 3.5 miles per kWH, we can travel 27 kWH x 3.5 miles/kWH = 94.5 miles
Since the total distance of the trip is 600 miles, we will need to charge our car once during the trip. We can assume that we will charge the car from 20% to 80% during this stop, which means we will need to charge 27 kWH x 0.6 = 16.2 kWH.
Since we charge the car at a rate of 45 kW, we can calculate the time it would take to charge the car:
Charging time = 16.2 kWH / 45 kW = 0.36 hours = 21.6 minutes
Now, let's calculate the time it would take to complete the trip at both speeds:
At 55 MPH, we can travel 135 miles before needing to charge, which will take 135 miles / 55 MPH = 2.45 hours. Including the charging time, the total time for the trip will be 2.45 + 0.36 = 2.81 hours.
At 70 MPH, we can travel 94.5 miles before needing to charge, which will take 94.5 miles / 70 MPH = 1.35 hours. Including the charging time, the total time for the trip will be 1.35 + 0.36 = 1.71 hours.
Therefore, we will complete the trip faster if we drive at 70 MPH, which will take 1.71 hours compared to 2.81 hours at 55 MPH.
WAIT!
David spots an error in the calculations, and asks: Please adjust the calculations to account for a total trip length of 600 miles, which will require multiple charges.
ChatGPT answers:
To adjust the calculations for multiple charges, we need to calculate the distance we can travel on a single charge, including the charging time. We can assume that we will charge the car from 20% to 80% each time, as before.
Usable energy = 36 kWH - 9 kWH = 27 kWH
Distance at 5 miles per kWH = 27 kWH x 5 miles/kWH = 135 miles
Distance at 3.5 miles per kWH = 27 kWH x 3.5 miles/kWH = 94.5 miles
Charging time = 16.2 kWH / 45 kW = 0.36 hours = 21.6 minutes
Assuming we drive at a constant speed of either 55 MPH or 70 MPH, we can calculate the number of charges we will need and the total time for the trip as follows:
For 55 MPH:
Distance per charge = 135 miles
Number of charges = ceil(600 miles / 135 miles) = 5 charges
Total charging time = 5 charges x 21.6 minutes = 108 minutes = 1.8 hours
Total driving time = 600 miles / 55 MPH = 10.91 hours
Total trip time = Total charging time + Total driving time = 12.71 hours
For 70 MPH:
Distance per charge = 94.5 miles
Number of charges = ceil(600 miles / 94.5 miles) = 7 charges
Total charging time = 7 charges x 21.6 minutes = 151.2 minutes = 2.52 hours
Total driving time = 600 miles / 70 MPH = 8.57 hours
Total trip time = Total charging time + Total driving time = 11.09 hours
Therefore, even with multiple charges, we will complete the trip faster if we drive at 70 MPH, which will take 11.09 hours compared to 12.71 hours at 55 MPH.
WAIT!! WAIT!!
David remembers that there is "charging overhead" and asks for one final calculation:
David asks: Please redo the calculations assuming there is 15 minutes of "charging activity overhead" for each charging stop.
ChatGPT
If we assume an additional 15 minutes of "charging activity overhead" for each charging stop, the total charging time for each stop would be 36 minutes instead of 21.6 minutes (36 minutes = 21.6 minutes + 15 minutes). We can then recalculate the total trip time as follows:
For 55 MPH:
Distance per charge = 135 miles
Number of charges = ceil(600 miles / 135 miles) = 5 charges
Total charging time = 5 charges x 36 minutes = 180 minutes = 3 hours
Total driving time = 600 miles / 55 MPH = 10.91 hours
Total trip time = Total charging time + Total driving time = 13.91 hours
For 70 MPH:
Distance per charge = 94.5 miles
Number of charges = ceil(600 miles / 94.5 miles) = 7 charges
Total charging time = 7 charges x 36 minutes = 252 minutes = 4.2 hours
Total driving time = 600 miles / 70 MPH = 8.57 hours
Total trip time = Total charging time + Total driving time = 12.77 hours
Therefore, with an additional 15 minutes of "charging activity overhead" for each charging stop, we will still complete the trip faster if we drive at 70 MPH, which will take 12.77 hours compared to 13.91 hours at 55 MPH.
END OF CHAT
David adds: While it may seem like driving faster wins, the time needed for leaving the freeway, finding the charger, paying for, starting and stopping the charge, then re-entering the freeway, can sometimes take as long as half of the charging time - or more - depending on charger location and how uncooperative the charger is. Consequently,adding the "charging overhead" closes the time difference between the two speeds a bit.
Personally, I much prefer driving slower. It's less strain on my battery and inverter and it's less stressful for me too. I also only need 5 working chargers to make my trip instead of 7. Also, I'd rather be driving at any speed than charging, and the faster trip has me spending 4.2 hours for the charging instead of 3.
These calculations line up very well with the monthly trip I drive in my RAV4 EV between Santa Barbara, CA and San Jose CA.
If you haven't played with ChatGPT, this is the kind of thing that can make it a lot of fun to use.
What do you think of ChatGPT's calculations? Do you see the remaining error?
David asks:
My electric car has a 45 kWH battery, and I only use the charge between 20 and 80 percent of capacity. My car uses energy at the rate of 5 miles per kWH at 55 MPH and 3.5 miles per kWH at 70 MPH. I charge the car at a rate of 45 kW. For a 600 mile road trip, will I complete the trip faster if I drive at 55 MPH or 70 MPH? Please show your work.
ChatGPT answers:
To solve this problem, we need to calculate the time it would take to complete the 600-mile road trip at both speeds and then compare them.
First, let's calculate the amount of energy we have available for the trip:
80% of 45 kWH = 36 kWH (maximum usable charge)
20% of 45 kWH = 9 kWH (minimum usable charge)
Usable energy = 36 kWH - 9 kWH = 27 kWH
Now, let's calculate the distance we can travel with this energy:
At 5 miles per kWH, we can travel 27 kWH x 5 miles/kWH = 135 miles
At 3.5 miles per kWH, we can travel 27 kWH x 3.5 miles/kWH = 94.5 miles
Since the total distance of the trip is 600 miles, we will need to charge our car once during the trip. We can assume that we will charge the car from 20% to 80% during this stop, which means we will need to charge 27 kWH x 0.6 = 16.2 kWH.
Since we charge the car at a rate of 45 kW, we can calculate the time it would take to charge the car:
Charging time = 16.2 kWH / 45 kW = 0.36 hours = 21.6 minutes
Now, let's calculate the time it would take to complete the trip at both speeds:
At 55 MPH, we can travel 135 miles before needing to charge, which will take 135 miles / 55 MPH = 2.45 hours. Including the charging time, the total time for the trip will be 2.45 + 0.36 = 2.81 hours.
At 70 MPH, we can travel 94.5 miles before needing to charge, which will take 94.5 miles / 70 MPH = 1.35 hours. Including the charging time, the total time for the trip will be 1.35 + 0.36 = 1.71 hours.
Therefore, we will complete the trip faster if we drive at 70 MPH, which will take 1.71 hours compared to 2.81 hours at 55 MPH.
WAIT!
David spots an error in the calculations, and asks: Please adjust the calculations to account for a total trip length of 600 miles, which will require multiple charges.
ChatGPT answers:
To adjust the calculations for multiple charges, we need to calculate the distance we can travel on a single charge, including the charging time. We can assume that we will charge the car from 20% to 80% each time, as before.
Usable energy = 36 kWH - 9 kWH = 27 kWH
Distance at 5 miles per kWH = 27 kWH x 5 miles/kWH = 135 miles
Distance at 3.5 miles per kWH = 27 kWH x 3.5 miles/kWH = 94.5 miles
Charging time = 16.2 kWH / 45 kW = 0.36 hours = 21.6 minutes
Assuming we drive at a constant speed of either 55 MPH or 70 MPH, we can calculate the number of charges we will need and the total time for the trip as follows:
For 55 MPH:
Distance per charge = 135 miles
Number of charges = ceil(600 miles / 135 miles) = 5 charges
Total charging time = 5 charges x 21.6 minutes = 108 minutes = 1.8 hours
Total driving time = 600 miles / 55 MPH = 10.91 hours
Total trip time = Total charging time + Total driving time = 12.71 hours
For 70 MPH:
Distance per charge = 94.5 miles
Number of charges = ceil(600 miles / 94.5 miles) = 7 charges
Total charging time = 7 charges x 21.6 minutes = 151.2 minutes = 2.52 hours
Total driving time = 600 miles / 70 MPH = 8.57 hours
Total trip time = Total charging time + Total driving time = 11.09 hours
Therefore, even with multiple charges, we will complete the trip faster if we drive at 70 MPH, which will take 11.09 hours compared to 12.71 hours at 55 MPH.
WAIT!! WAIT!!
David remembers that there is "charging overhead" and asks for one final calculation:
David asks: Please redo the calculations assuming there is 15 minutes of "charging activity overhead" for each charging stop.
ChatGPT
If we assume an additional 15 minutes of "charging activity overhead" for each charging stop, the total charging time for each stop would be 36 minutes instead of 21.6 minutes (36 minutes = 21.6 minutes + 15 minutes). We can then recalculate the total trip time as follows:
For 55 MPH:
Distance per charge = 135 miles
Number of charges = ceil(600 miles / 135 miles) = 5 charges
Total charging time = 5 charges x 36 minutes = 180 minutes = 3 hours
Total driving time = 600 miles / 55 MPH = 10.91 hours
Total trip time = Total charging time + Total driving time = 13.91 hours
For 70 MPH:
Distance per charge = 94.5 miles
Number of charges = ceil(600 miles / 94.5 miles) = 7 charges
Total charging time = 7 charges x 36 minutes = 252 minutes = 4.2 hours
Total driving time = 600 miles / 70 MPH = 8.57 hours
Total trip time = Total charging time + Total driving time = 12.77 hours
Therefore, with an additional 15 minutes of "charging activity overhead" for each charging stop, we will still complete the trip faster if we drive at 70 MPH, which will take 12.77 hours compared to 13.91 hours at 55 MPH.
END OF CHAT
David adds: While it may seem like driving faster wins, the time needed for leaving the freeway, finding the charger, paying for, starting and stopping the charge, then re-entering the freeway, can sometimes take as long as half of the charging time - or more - depending on charger location and how uncooperative the charger is. Consequently,adding the "charging overhead" closes the time difference between the two speeds a bit.
Personally, I much prefer driving slower. It's less strain on my battery and inverter and it's less stressful for me too. I also only need 5 working chargers to make my trip instead of 7. Also, I'd rather be driving at any speed than charging, and the faster trip has me spending 4.2 hours for the charging instead of 3.
These calculations line up very well with the monthly trip I drive in my RAV4 EV between Santa Barbara, CA and San Jose CA.
If you haven't played with ChatGPT, this is the kind of thing that can make it a lot of fun to use.
What do you think of ChatGPT's calculations? Do you see the remaining error?