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Re: Doing The Math

melgish said:
Using figures posted earlier in the thread.
Code:
MPH   MPG   TIME   FUEL   Y  
 25    79   4.00   1.27  5.27
 30    80   3.33   1.25  4.58
 35    78   2.86   1.28  4.14
 40    75   2.50   1.33  3.83
 45    71   2.22   1.41  3.63
 50    67   2.00   1.49  3.49
 55    62   1.82   1.61  3.43
 60    57   1.67   1.75  3.42  <= the sweet spot
 65    53   1.54   1.89  3.43
 70    48   1.43   2.08  3.51
 75    44   1.33   2.27  3.61
 80    41   1.25   2.44  3.69
Looking at these values, it appears to indicate that 60 MPH is the best balance between fuel consumption and travel time. Which oddly enough seems to substantiate an earlier claim in this thread that the prius has been 'optimized' for 63 mph. Obviously the meaning of this value is subjective. If I'm late for work, time has more value, and if my wallet is empty fuel consumption is more important. But this is the speed where I get the best of both worlds.
How are you calculating "Y"? What is the formula? And what are the units of "Y"? Inquiring minds and all that.
 

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I thought we'd covered that ;)

Y = TIME + FUEL, and has no tangible meaning outside the graph.
 

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melgish
Y = TIME + FUEL, and has no tangible meaning outside the graph.
I don't understand how you can add 2 different units of measurements together. :?

To illustrate my point, try to convert all the hours to minutes and calculate your Y again.

Now, convert all the hours to days and recalculate.

Alternatively, you may also convert the fuel to other units of measurements.

Are there any difference? :?:

Vincent
 

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melgish said:
I thought we'd covered that ;)

Y = TIME + FUEL, and has no tangible meaning outside the graph.
Ok, I just ran your numbers again. But first I converted the time numbers given to minutes, then ran them again with the time measured in fractional days. Same exact amount of time, but different "Y" minima result. Here:

MPH MPG TIME FUEL Y
25 79 4 1.27 5.27
30 80 3.33 1.25 4.58
35 78 2.86 1.28 4.14
40 75 2.5 1.33 3.83
45 71 2.22 1.41 3.63
50 67 2 1.49 3.49
55 62 1.82 1.61 3.43
60 57 1.67 1.75 3.42<==If time in hours
65 53 1.54 1.89 3.43
70 48 1.43 2.08 3.51
75 44 1.33 2.27 3.61
80 41 1.25 2.44 3.69

Same data, time in Minutes

25 79 240 1.27 241.27
30 80 199.8 1.25 201.05
35 78 171.6 1.28 172.88
40 75 150 1.33 151.33
45 71 133.2 1.41 134.61
50 67 120 1.49 121.49
55 62 109.2 1.61 110.81
60 57 100.2 1.75 101.95
65 53 92.4 1.89 94.29
70 48 85.8 2.08 87.88
75 44 79.8 2.27 82.07
80 41 75 2.44 77.44<==If time in Minutes

Same data, time as fractional days.

25 79 0.1666 1.27 1.436666667
30 80 0.1387 1.25 1.38875 <==If time Measured in Days
35 78 0.1191 1.28 1.399166667
40 75 0.1041 1.33 1.434166667
45 71 0.0925 1.41 1.5025
50 67 0.0833 1.49 1.573333333
55 62 0.0758 1.61 1.685833333
60 57 0.0695 1.75 1.819583333
65 53 0.0641 1.89 1.954166667
70 48 0.0595 2.08 2.139583333
75 44 0.0554 2.27 2.325416667
80 41 0.0520 2.44 2.492083333

(edited to correct cut and paste error)

If the "Y" factor had any meaning, its location in the graph would not change based on units chosen. Its value would change, but the lowest point would fall at the same place.

Or to place it differently: 60 Miles per Hour, 1 mile per Minute, 1440 Miles per Day are all the same speed, they will all get me to my destination in the same amount of time. 30 Miles per Gallon, 7.5 Miles per quart, and 1260 Miles per Barrel all are the same consumption rate and get you the same distance for the same amount of fuel.

Because the relative value of "Y" changes with the unit of measure, it really does not have a real meaning.

Make sense?
 

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Your evaluation of my calculations is correct. I will not argue the point further. I will suggest, however that we've both missed something obvious. :)
 

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melgish said:
Your evaluation of my calculations is correct. I will not argue the point further. I will suggest, however that we've both missed something obvious. :)
I will concede that point. Tell you what, I'll meet you in a bar someday and we can wave our arms around and spill drinks and generally make a nuscience of ourselves until we both understand perfectly.

Skip
 

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Next time I flee a hurricane to Hotlanta, you're on! :)
 

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Discussion Starter #88
Labrat's dynamometer test numbers are not helpful.

Since they don't include wind or (likely) front tire rolling resistance, they don't have much to do with the driving fuel economy.

A big flat front van might look surprisingly good on the dynamometer, but in real driving, the air resistance and tire losses would whack it bigtime.

Whereas the extraordinary low drag of the 2004 Prius and the low rolling resistance of its tires helps make the real mileage exceptional.

'PriusPhysics' and 'Ken1784' have the most useful data and scientific reasoning--look their posts up in the older 'Technical' posts. PriusPhysics calcs closely approximate what I'm getting day to day.

Ignoring air resistance is silly...
 

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When using a chassie dynamometer to simulate driving conditions thier are factor that need to be taken in to consideration.
Such as the drag coefficient vehicle being tested.
This is used to simulate the airodynamic drag on the vehicle.
The mass of the vehicle.
Mass is needed to properly simulate acceleration and de-acceleration.
The air tempature must also be regulated.
This to maintain the same air density for the engine.(Warm air is less dense)
Also the rolling resistance of the rear tires.
 

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melgish said:
Your evaluation of my calculations is correct. I will not argue the point further. I will suggest, however that we've both missed something obvious. :)
The obvious thing that you have missed is your own personal trade-off between time and fuel economy. I.e., you need an additional input in order to find a unique "sweet spot" here.

For example, let's say I can work harder and earn more money or work less hard and earn less but have more free time. So, the question is, where is the sweet spot? Well, that depends how much I value my free time. I could convert my free time to an effective monetary unit. Then I could add the money I earn for working a given number of ours plus the amount of free time converted to dollars by multiplying by the value I place on the free time. And, I could try to maximize this value. If I value it at $1000 per hour, I'll get the result that I should lounge around all day. If I value it as $1 per hour, I'll get the result that I should be working like a madman!

Likewise for your case: If you are really into fuel economy, perhaps using a gallon less of gas is worth it taking an extra hour of drive, but if you are really tight for time, perhaps using a gallon less of gas would only be worth it if it meant just an extra 10 minutes.
 

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By the way, I should point out that my idea of coming up with one simple conversion factor between gallons and time based on your own personal preferences is still an oversimplification...Because, in reality your conversion factor is not likely to be a constant. I.e., there will be a non-linear relationship between the two quantities.

To see this, go back to the time-money example. If I am unemployed and contemplating how I am going to eat, I may be willing to give up an hour of free time for the possibility of earning $10. But, if I am already working 60 hours weeks and feeling burned out, I may need to be offered an extra $100 to give up an hour of free time.
 

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Mpg

What if you installed an engine block heater and used it all year round? Would this eliminate the approx. 15min engine warmup that decreases mpg?
 

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Re: Mpg

SyZyGy said:
What if you installed an engine block heater and used it all year round? Would this eliminate the approx. 15min engine warmup that decreases mpg?
Reduce, not eliminate. Probably wouldn't even reduce it in the summer. At least, I don't think block heaters keep the engine anywhere near 85 deg. C. I suspect they just keep it somewhat over 0 deg. C. (But I've never used one myself.)
 

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Perhaps a dumb question, but here it is anyway... isn't part of the initial period used to warm up all the emission control components, including the catalytic converter? I don't think an engine block heater would help that item.
 

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Engine Block Heater

8) All 04 and 05 Prius are equipped with a thermos type bottle located under the left front fender. It holds approx. 3 liters of hot coolant and will maintained the coolant for three day at near boiling tempter. So it will take very little time to heat up your Prius in the winter.

Here in Omaha we had a lot of days below 32 degrees an lower. My 04 Prius warmed up in less than 5 minutes.

Ben
 

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jshore said:
By the way, I should point out that my idea of coming up with one simple conversion factor between gallons and time based on your own personal preferences is still an oversimplification
Take all my figures a few messages back, and instead of adding TIME + FUEL to find the minimum point, use TIME * FUEL. You'll find it works out to around 65 for all the combinations of units. Even SkipHuffman would be satisified ;-) I discovered my oversigt last week, but figured the thread had enough of my postulating :)

Note that money hasn't been entered into either side of the equation at all. It's simply a relation of speed vs fuel vs time.

What everyone seems to be missing, is this point does have an importance of its own. When you are AT this speed, accellerating will burn gallons faster than you save hours, and decellerating will burn hours faster than you gain gallons.

One (inacruate but analogus) way to think of it is that at this speed, Horse Power per gallon is maximixed.
 
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