Re: 1973 Honda CB350 - how much power?

Mark Olson wrote:

Rick Cortese wrote:

Mark Olson wrote:


http://en.wikipedia.org/wiki/Drag_%28aerodynamics%29#Power


The important bit is the v^3.


OK, I think I am going to disagree with their numbers and analysis.

"Since power is the rate of doing work, four times a work in half the time requires eight times the power."


That's quite clear, (except for "times a work" should be "times THE
work") and I see nothing wrong with it.

I think this is wrong because of the distance component they add. I mean this is important for mileage. If your car is burning 4 times as much gas to go 60 miles per hour then at 30 miles per hour then you will be using gas at 4 times the rate but for 1/2 as long or mileage would be 1/2 instead of 1/4. IMO: It should factor out in something stationary, wind tunnel for instance.


All I will say is in my experience, cars don't typically burn 4x as much
gas at 60 mph than they do at 30 mph... but it does indeed take 8x as
much power _to overcome aerodynamic drag_ at 60 mph as it does at 30 mph,
_assuming their equation holds true_ at those sorts of speeds.

First I want to make it sure you know exactly where I am coming from. Should just take a second.

I say power by square, that Wiki guy says power by cube with a fudge factor. They have the approximately the same results over the interval tested.

The truth may be somewhere in between.

I don't think his numbers fit well. Let's say a ~5hp scooter goes 35-40 mph which has been my experience. By his method you would need 40 hp to do 70-80 mph which I think is high. Three times the speed or 105-120mph would be 27x the hp or 135 hp. I think we all pretty much ack a 60-70hp machine like a 750cc Honda will approach that. It gets even crazier when you start going to 320 hp for 160 mph. I mean remember that guy in a speedo laying down on a Vincent?

http://en.wikipedia.org/wiki/Rollie_Free

He approached that speed and a vintage Vincent puts out NOTHING like 320hp! My method is much closer to my own experience in that I would go 5, 20, 45, 80 hp respectively for 40ish, 80ish, 120ish, 150ish mph. My estimate method may be bad but it certainly isn't worse. Who knows? Maybe v^2.237 would be a better fit.

I just question why he uses that cube thing and the reasons he gives. It isn't obvious to even a person that did it for a living at Boeing.

On to your statement about mileage, true the reason being at which RPM an engine is designed to be most effiecent, but I can think of one example off hand. On the series Mythbusters when they revisited one of their mileage tests they used a flow meter to check mileage. As I recall the numbers were very close to what I described if you calculated them out. i.e. ~.7 gal/hour at 30 mph and ~2.6 gal/hour at 60 mph. I remember thinking my square energy thing worked for their speed range => 4 times the energy to move at twice the rate, but they covered twice the distance in that time so ~50% of the mileage. 30/.7 => 42 mpg, 60/2.6 => 24 mpg. It was an SUV IIRC. It could have been 45 and 70 mph, it could of been .9 and 2.4 gals, I really don't remember, just approximations.

I *think* it was on their show after being challenged about method where they were testing with the air conditioner vs. windows rolled down to see which produced the better milage. If I see the show again I will get some hard numbers and/or tell you when it comes on.

But this factors out when we use top speed for a measurement. That is the engines in question are running at their maximum output. A lot of assumptions such as the gearing is right to produce maximum speed too.

I did see my Boeing ChemE friend and took exception to the cube in Wikipedia. He went so far as to pull out one of his reference books and show me the sections on flow. I glanced through it and didn't come across any equations for flow that used the cube vs. the square. He said that there are some models that use the cube and even some that use the 4th power but they are only used in flow through a small orifice/nozzle.

He suggested I look into 'Reynold's Number as that is what they used in the wind tunnel at Boeing when he was there for testing models.

http://en.wikipedia.org/wiki/Reynolds_number

So engineer who worked at Boeing who said Reynolds is what they used, he questioned cube in anything other then a nozzle/special case, chemical engineering handbook, along with a Wikipedia reference that shows Reynolds square vs. cube, I am sticking to my guns. I think the Wiki Cube guy made a mistake if not several.

http://auto.howstuffworks.com/question477.htm

Uses square and cube with fudge factors. Once again, with fudge factors that probably end up with approximately the same number as I use. Just another hyperbola.

Once you've seen one hyperbola you've seen them all. Over a narrow range there just isn't a big difference between the three [^2, ^3, av^2+bv^3] forms.
.

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