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Why my Prius is faster than my old Audi RS4

Discussion in 'Gen 3 Prius Fuel Economy' started by cit1991, May 6, 2010.

  1. cit1991

    cit1991 New Member

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    ...when driving long distances.

    The old Audi got about 22 MPG at 60 MPG. The Prius gets about 55 MPG at 60 MPH.

    Assuming:

    Usable fuel is 75% of the tank volume (Audi, 16.6 gal tank; Prius 11.9)
    Fuel flow burn rate (GPH) goes as the cube of speed (due to air resistance)
    Time to stop, fill up, and return to cruise speed is 15 minutes

    I set up an excel sheet to try various cruise speeds to see when the extra fuel burn from high speed is offset by the need for more refuelings. It worked like this:

    1. Choose a cruise speed (x)
    2. Calculate fuel burn rate = (x/60)^3 * fuel flow at 60 MPH
    3. Find how long you can cruise = usable gallons / fuel burn
    4. Calculate how far you will go = x * time-in-cruise
    5. Calculate average speed = how-far / (time-in-cruise + 15 minutes)
    6. Run solver to maximize the average speed by changing the cruise speed.

    For the Audi, the optimal cruise speed is 125.4 MPH, which is less than the top speed of 155 MPH. 125.4 MPH in cruise nets 83.6 MPH when fuel stops are taken into account (having burnt 3/4 of it's tank).

    The Prius optimal cruise speed is 152.3 MPH, but of course that's above the top speed, so the optimal answer is top speed, or about 100. At 100, the average speed (including 15-minute fuel stops after 3/4 of it's tank is burnt) is 87.6 MPH, or 4 MPH faster than the Audi.

    If the Audi were to go faster, it would burn more fuel and have to stop more often, offsetting the faster speed. If it were to go slower, the slow speed would overcome the less frequent stops...there's no way to win, except to install a bigger fuel tank.

    Interestingly, no matter what the fuel tank size is, or what the fuel economy is at 60 MPH, the best speed is always found by burning the usable fuel in twice the time it takes to fill up...if you can. If not, then top speed.

    So, that's why my new Prius is faster than my old Audi RS4 with 420 hp.

    P.S. Then again my Chevy 2500HD 4WD Diesel is faster still (average speed of 94.7 MPH, cruising at 105 MPH) since it has a 45 gallon fuel tank.
     
    #1 cit1991, May 6, 2010
    1 person likes this.
  2. cit1991

    cit1991 New Member

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    I checked to see how far I would be able to go on the remaining 1/4 tank the the above scenarios.

    In the Audi, I'd have 21 miles left, which is a little tight. In the Prius (even at 100 MPH), I'd have 59 miles, and wouldn't stop that early.

    So, I changed the fillup criteria. Instead of filling up at 1/4 tank, I'd fill up at 25 miles remaining (at whatever cruise speed). Then the Audi's best cruise speed drops to 114 MPH at an average speed of 83, while the Prius (still at 100 MPH) averages 89.4 MPH. So, with the new fillup criteria, the Prius is now 6.4 MPH faster than the Audi.
     
    #2 cit1991, May 6, 2010
  3. a_gray_prius

    a_gray_prius Rare Non-Old-Blowhard Priuschat Member

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    I thought it was the (very important) difference between thse two scenarios that made the Prius faster than most sports cars:

    Cop sees speeding RS4:
    1. Hits car with laser radar gun
    2. Readout: 110 mph. In a 55 zone.
    3. Ticket.

    Cop sees speeding Prius:
    1. Hits car with laser radar gun
    2. Readout: 110 mph. In a 55 zone.
    3. Cop whacks side of radar gun, grumbles "I gotta get this thing checked out, it's a PRIUS, no way this thing is right"
     
    #3 a_gray_prius, May 6, 2010
    2 people like this.
  4. GWhizzer

    GWhizzer not so Senior Member

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    Of course this all assumes that you run to the end of the tank before stopping. My personal experience is that either of the two vehicles will exceed the bladder capacity of my wife and/or kids and we would be stopping before the tank is dry anyway!!! But it's a nice thought....
     
    #4 GWhizzer, May 6, 2010
  5. patsparks

    patsparks An Aussie perspective

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    You need to speed up so you run out of fuel before they run out of bladder space!

    Where can you drive at 110mph and petrol stations are at 25 mile intervals? You wouldn't find that here in Australia.

    Here is a real world situation, this actually happened. All vehicles were the same.
    I think the trip distance was about 1000km from Marla to Adelaide.
    I was driving at 118km/h from Marla to my home in Adelaide 2 other cars were "with" me but they drove at 130+km/h.
    We all set off at the same time after fuling up at Marla. At the first fuel stop the other 2 cars finished filling before I arrived but were ordering a coffee and food when I finished filling, paid for the fuel on credit card and left them there. They both passed me a way down the road. They refueled again about 100km from home, but I didn't need to so I kept going and got home before they did. I used 10 litres less fuel on the first leg of the trip and I don't know how much less on the second leg and got home sooner and more relaxed.
     
    #5 patsparks, May 6, 2010
  6. racer

    racer New Member

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    I hear that. Just finished a road trip and didn't even make it 40 miles before we already stopped 2 times for my little one to pee.
     
    #6 racer, May 8, 2010
  7. thatguychristian

    thatguychristian New Member

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    LOL. I bet my friend wishes this was true.

    He got a ticket for going 60, in a 35. In his defense, it was downhill and he had just sped up to pass a car. It was also a speed trap. He'll be fighting the ticket obviously.
     
    #7 thatguychristian, May 8, 2010
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