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 #268195  by Bill Putney
 
I had to look it up (Fluid Dynamics was not my cup of tea in college, and I've not worked with it since):

You do have to be careful about applying any one equation without knowing certain things having to do with laminar and turbulent flow (see http://en.wikipedia.org/wiki/Reynolds_number and http://en.wikipedia.org/wiki/Drag_equation).

From: http://en.wikipedia.org/wiki/Drag_(physics):

The drag equation calculates the force experienced by an object moving through a fluid at relatively large velocity (i.e. high Reynolds number, Re > ~1000), also called quadratic drag. The equation is attributed to Lord Rayleigh, who originally used L2 in place of A (L being some length). The force on a moving object due to a fluid is:

Image

where:

Image is the force of drag,
Image is the density of the fluid,[3]
Image is the speed of the object relative to the fluid,
Image is the drag coefficient (a dimensionless parameter, e.g. 0.25 to 0.45 for a car)
Image is the reference area,

. . .

The power required to overcome the aerodynamic drag is given by:

Image

Note that the power needed to push an object through a fluid increases as the cube of the velocity. A car cruising on a highway at 50 mph (80 km/h) may require only 10 horsepower (7.5 kW) to overcome air drag, but that same car at 100 mph (160 km/h) requires 80 hp (60 kW). With a doubling of speed the drag (force) quadruples per the formula. Exerting four times the force over a fixed distance produces four times as much work. At twice the speed the work (resulting in displacement over a fixed distance) is done twice as fast. Since power is the rate of doing work, four times the work done in half the time requires eight times the power.

. . .

The equation for viscous resistance or linear drag is appropriate for objects or particles moving through a fluid at relatively slow speeds where there is no turbulence (i.e. low Reynolds number, Re < 1). Note that purely laminar flow only exists up to Re = 0.1 under this definition. In this case, the force of drag is approximately proportional to velocity, but opposite in direction. The equation for viscous resistance is:

Image

where:

Image is a constant that depends on the properties of the fluid and the dimensions of the object, and
Image is the velocity of the object


Did anybody's eyes not gloss over when reading that - especially if you started digging deeper into the Reynolds number? Now you know why I wasn't too excited about fluid dynamics. :)
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 #268250  by 300maximilien
 
my eyes rolled back in my head right after the first equation! But thanks for sharing BilL!
 #268307  by isrb710
 
Bill Putney wrote:Note that the power needed to push an object through a fluid increases as the cube of the velocity.
Bill,

You're right about that causing one's eyes to glaze over!!

I think the phrase above is the key phrase in your explanation.

So comparing 70 mph to 60 mph:

60 x 60 x 60 = 216,000
70 x 70 x 70 = 343,000

343,000 / 216,000 = 1.59. In words, that says to me it takes 59% more power to go 70 mph than to go 60 mph.

Does that sound right, Bill?

Thanks, Ron
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 #268326  by Bill Putney
 
isrb710 wrote:...In words, that says to me it takes 59% more power to go 70 mph than to go 60 mph.

Does that sound right, Bill?

Thanks, Ron
Your welcome.

It says that of the power required to move "the object" thru the air, yes - 59% more power. The moving-thru-the-air power is one part of the power required of the engine and fuel. There are other inefficiencies (engine efficiency (which may actually increase at 70 depending on how it's tuned, gearing, etc.) bearing friction, etc.) that may not increase at the same rate. I only say that to caution not to start saying that the *total* power increase goes up 59% from 60 to 70 mph. It would be something less than 59% increase because the wind resistance increase gets diluted somewhat, again, by those other things that may not go up as rapidly.
 #268338  by isrb710
 
Bill,

I agree aerodynamic drag can NOT be the only factor, as we don't see a 59% decrease in mpg when going from 60 to 70!

Thanks again for taking the time to re-visit something that you obviously didn't like too much back in your college days!

Ron
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 #307632  by Chrome
 
Truckers are ecodrivers best friend



If you don't believe Mythbusters this man is Superman
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 #377533  by EasyRider300M
 
Concerning the 300M Special, it has a difference shift setup compared to base M. If doing driving on local roads where you rarely get over 35 mph, you might save a bit of gas by using autostick and when at 30mph, shift it into 4th gear. If you rely on the automatic transmission to do the shifting, it doesnt get into 4th gear till about 40mph.
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 #377595  by LUNAT1C
 
Part of why I prefer to use autostick in my Special is the extra long second gear. The computer holds it, so driving around town I'll use autostick to shift up into 3rd faster. On the highway it doesn't matter, unless crawling along in a traffic jam.

And I've noticed the sweet spot is about 65mph, as I get my bet MPG there. I tend to stay around 75. In my Jeep, I gave up and typically do 80 (following the flow of traffic!). I'm lucky to get 14.5 if I hypermile it.