Post #208,295
5/23/05 5:39:32 PM
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Power required goes as cube of speed.
[link|http://www.getfaster.com/Techtips/Physics6.html|Linky] of required horsepower to overcome wind resistance using a hypothetical Corvette as an example:
[image|http://www.getfaster.com/BIS/Techtipdata/_8387_tabular103.gif|0|Power needed to overcome wind resistance for a car|63|409]
The force against the air varies as the square of the speed, but the horsepower required gives another factor v, giving the cube relationship.
HTH.
Cheers, Scott.
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Post #208,354
5/24/05 4:51:56 AM
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"cube of speed" - again, what units? km/h cubed != mph cubed
Be it cubes or squares or whateverthefuck, my point was: What we're interested in here is the cube [or square, etc] of the change in speed (or, IOW, the cube of the ratio of speeds) -- but NOT the "cube of the speed".
My original post was an attempt to correct [link|http://z.iwethey.org/forums/render/content/show?contentid=208144|Todd's "You must square your power to double your speed"]; that's why I talked about squares there. But what I am really trying to say is, it just makes no sense to talk about "squaring" -- or "cubing" -- one's speed or power or something like that; the very concepts of "speed squared", or "power cubed", etc, do not exist. One way to realize this is, try to explain them in plain words.(*)
And words are what I'm talking about: From da Todd's post, it was plain he was misusing them. De Scott, I'm not so sure about; if by "goes as" you're trying to imply that the rates of change on both sides of the equation are related, then you're right... But since you're not explicitly saying, "...goes as cube of speed goes" or "...varies as the square of the speed varies", I'm not so sure. Oh well, never mind...
In general terms, though, the whole category of laws -- "square law" (if that is the correct expression?) -- Todd mentioned means, not "you must square X to double Y", but "you must quadruple X to double Y"; likewise, "a cube law" would mean, not "you must cube X to double Y", but "you must multiply X by eight to double Y. (At least, if what you showed is called "a cube law", then this is how "cube laws" work -- because what you showed works exactly the way I've been saying.)
This is because quadrupling is "the square of doubling", so to speak, and multipling by eight is "the cube of doubling". It is the rate of change that is squared, or cubed or whatever; not the basic measurement itself.
Still clear as mud, or what?
(*): As an example, I can explain "speed": It measures how far you can go in a given amount of time, and therefore it is measured as "distance per time" -- km/h, mph, m/s, etc.
Acceleration: How much faster you're getting over time, hence (distance per time) per time -- (m/s)/s, or whatever units you use.
Area: How big a surface is, which grows linearly with both the length and the width; hence, distance times distance or square foot, square meter, etc.
But "speed squared"?!? WTF is that; it'd be measured in distance-squared per time-squared... So is it some kind of area-acceleration, then, or, uh...?
[link|mailto:MyUserId@MyISP.CountryCode|Christian R. Conrad] (I live in Finland, and my e-mail in-box is at the Saunalahti company.)
Your lies are of Microsoftian Scale and boring to boot. Your 'depression' may be the closest you ever come to recognizing truth: you have no 'inferiority complex', you are inferior - and something inside you recognizes this. - [link|http://z.iwethey.org/forums/render/content/show?contentid=71575|Ashton Brown]
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Post #208,357
5/24/05 8:26:00 AM
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The linky explains all that.
The constant factors in the equation take care of the units. Remember R, the Ideal Gas Constant? It's used in: PV = nRTIt has about eleventy-seven values depending on the system of units you're using - SI (kg, m, s, K) or cgs (g, m, s, K) or US ("lbs", ft, s, F) or ... Similarly, the power needed to overcome the friction due to air is proportional to the cube of the speed. If you measure power in HP and speed in mph, then constant factors in the equation will be different than if you measure power in KW and speed in m/s. But the functional relationship is the same no matter what units you choose - power required varies as the cube of the speed. If it's not clear, then think about finance. The amount of "money" you need to buy a bottle of whiskey at a particular duty-free store doesn't depen on what currency you use. It might be $100 or 10,728.57 Yen. It's the same amount of "money" - just the units change. (Assuming no transaction costs, of course.) Finally, you write: What we're interested in here is the cube [or square, etc] of the change in speed (or, IOW, the cube of the ratio of speeds) -- but NOT the "cube of the speed". No. Starting at 0 and going to 50 mph takes a lot less power than starting from 500 and going to 550 mph. The change is the same, but the power required is very different. The incremental change is much smaller in the latter case too (55/50 vs "50/0"), but the power required is much larger. It really just falls out of the [link|http://www.getfaster.com/Techtips/Physics6.html|equation]: [image|http://www.getfaster.com/BIS/Techtipdata/_8387_tex2html_wrap153.gif|0|Equation for HP to overcome air resistance|37|394] If v is the vehicle speed in miles per hour, then P is in horsepower. The constants in the equation will be different if the units of speed and power are different. Units can be very tricky. E=mc^2 and similar relationships in physics implies all sorts of interconnections between units that can be hard to get ones head around... HTH a bit. Cheers, Scott.
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Post #208,449
5/24/05 7:09:40 PM
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Oh fer cryin out loud (new thread)
Created as new thread #208448 titled [link|/forums/render/content/show?contentid=208448|Oh fer cryin out loud]
"Whenever you find you are on the side of the majority, it is time to pause and reflect" --Mark Twain
"The significant problems we face cannot be solved at the same level of thinking we were at when we created them." --Albert Einstein
"This is still a dangerous world. It's a world of madmen and uncertainty and potential mental losses." --George W. Bush
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Post #208,649
5/26/05 5:02:00 AM
5/26/05 5:49:12 AM
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Yup.. *bloody* pounds! and feet! + Another formula:
and lbs-wt and lbs-force, ounces, drams, quarts!
(But I thoroughly enjoyed \ufffd/s/d, that octagonal 3-p? and the merchants' Machiavellian means for extracting an extra Shilling: the Guinea! Also.. doing the mileage calc with 5/4 for the 5 qt. Imperial gallon, km/mi vs litres at the pump -- BSF, Whitworth wrenches vs metric or US: all kept little grey cells doing stuff-in-head. Prevents mind-rot.)
I've often wondered if rampant Murican iggerance of the metric system (except in actual science courses; never mind computer-'science') accounts significantly for the current official Dumbth/sec\ufffd acceleration, plus most of the Innumeracy -?- for which we are also deFamed.
Why, even those non-UAV heathen countries -- at least among their whatever %educated -- do not saddle their tykes with Ridiculous archaic BS-units as lead to furlongs/fortnight and the other albatrosses hung about the scrawny necks of our now regularly drugged, I-podded tykes.
BTW, I recall a formula for estimating HP needed at any given speed (corrected for aforementioned Puritan units chaos). 'Twas the mechanical-drawing instructor -remember when ya drew stuff?- who tossed this one out to us freshmen (about the time he demonstrated How the el-cheapo Brownie movie camera outperformed its 'precision-Swiss' competition):
HP = 1.21 (MV/T)
HP = er HP
M = mass in kilopounds [fully Muricanized for assimilation]
V = Velocity of interest, in MPH (speed is scalar; velocity is vector - call it a straight line forward ;-)
T = time [d'oh] for following procedure:
A) Accelerate to (V+5) mph B) Clutch in (or auto in neutral) and start timer C) Stop timer when speedo reads (V-5) mph
No STP or rho corrections but reveals surprising things, like that little Corvette chart. Especially: how little HP is needed at modest speeds. Works on motorcycles, I found and as one would suppose. (There - you can change! your A frontal area; sit-up, crouch - note the Different readings - you too can Believe in physics.)
(I have to try this on my new sled in 30 mph increments between 40 and 130, on a next in-car-ceration on a boring Interstate; hmmm.. set cruise to V+5 and kill it, as switch to N and start timer)
Bon appetit
Edit: grey-cells are unsure of the "1.21" constant.. think it more likely than original '1.51' from visceral memory. Order of magnitude is right, and whatever the error in an HP point, the \ufffd law relationship should be ~ demonstrated. (Most are surprised at how little HP is needed at 30-40 mph.)
Edited by Ashton
May 26, 2005, 05:49:12 AM EDT
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Post #208,656
5/26/05 7:45:23 AM
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Neat.
There's probably a [link|http://www.journals.uchicago.edu/Isis/journal/demo/v000n000/000000/000000.text.html|nomograph ][1] of that out there somewhere. Those were amazingly handy at times.
Cheers, Scott.
[1] Found on Edward Tufte's site, [link|http://www.edwardtufte.com/bboard/q-and-a-fetch-msg?msg_id=0000Bc&topic_id=1|here].
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Post #208,766
5/26/05 9:53:39 PM
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Funny you should mention..
* John Scott Campbell also pushed samples of such into our tiny little nascent minds! I recall using one of his in several courses, and also making one.. for some silly purpose ot other. But then, when your Only calculator is a K&E log-log-Decitrig and log tables - this is no Big Deal. (Saw a 17-place log table once. Huge tome! Need Reo Speedwagon to cart around for surveying n'such)
Today, however - nomographs could well fill-in a bit, for necessary look-ups by the vastly-innumerate majority. If 'we' were smart enough to hand them out, that is. And if they were smart enough to realize they needed one. And - -
Hmmm - MPG at the gas pump? Naah.. take out the throwaway $3 4-banger.
* (Aforementioned ept, vastly curious and widely read 'drawing' instructor.) JC possessed a Novachord ~ like a synthesizer; long before there was a decent techno, or even transistors. Had a prof. Ampex tape recorder - I accompanied it and him to LA Philharmonic to tape the debut of a new pianist. He also wrote an opera for local performance: Spooks in the Basement (..of the Physics Building) (!!!).
Who Says -?- being.. engineerish means: ya gots to be a one-dimensional dork? (Well, the envious do, but then...)
Dynamic nomograph: 2 nails in a board, with a string around: make ellipses! Sometimes I miss analyt. geom. - I mean, who ever today has the foggiest what a Latus Rectum might be?
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Post #208,670
5/26/05 10:18:29 AM
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every redneck with a wrench knows that 14mm=* 9/16ths
All tribal myths are true, for a given value of "true" Terry Pratchett [link|http://boxleys.blogspot.com/|http://boxleys.blogspot.com/]
Any opinions expressed by me are mine alone, posted from my home computer, on my own time as a free american and do not reflect the opinions of any person or company that I have had professional relations with in the past 48 years. meep questions, help? [link|mailto:pappas@catholic.org|email pappas at catholic.org]
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Post #208,684
5/26/05 11:08:41 AM
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Bah; old-Volvo fans know 14mm wrench will NOT fit 9/16 bolt!
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Post #208,708
5/26/05 2:09:09 PM
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horses duervers! fits just fine
which is what I use all the time as the 9/16th wrenches are dissapeared by the IDunno Bike fixing fairy. thanx, bill
All tribal myths are true, for a given value of "true" Terry Pratchett [link|http://boxleys.blogspot.com/|http://boxleys.blogspot.com/]
Any opinions expressed by me are mine alone, posted from my home computer, on my own time as a free american and do not reflect the opinions of any person or company that I have had professional relations with in the past 48 years. meep questions, help? [link|mailto:pappas@catholic.org|email pappas at catholic.org]
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Post #208,731
5/26/05 4:24:53 PM
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Funny. Either your bolts or your wrenches are off measure.
Since 9/16ths of an inch is about 14.3 mm.
Or maybe your bolt heads aren't 9/16ths at all, but 14 mm.
[link|mailto:MyUserId@MyISP.CountryCode|Christian R. Conrad] (I live in Finland, and my e-mail in-box is at the Saunalahti company.)
Your lies are of Microsoftian Scale and boring to boot. Your 'depression' may be the closest you ever come to recognizing truth: you have no 'inferiority complex', you are inferior - and something inside you recognizes this. - [link|http://z.iwethey.org/forums/render/content/show?contentid=71575|Ashton Brown]
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Post #208,769
5/26/05 10:09:20 PM
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try 13.8 mm if larger than, it would fit on would it?
most tools of men with children are made in china with the resultant tolerance differences. thanx, bill
All tribal myths are true, for a given value of "true" Terry Pratchett [link|http://boxleys.blogspot.com/|http://boxleys.blogspot.com/]
Any opinions expressed by me are mine alone, posted from my home computer, on my own time as a free american and do not reflect the opinions of any person or company that I have had professional relations with in the past 48 years. meep questions, help? [link|mailto:pappas@catholic.org|email pappas at catholic.org]
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Post #208,791
5/27/05 8:20:07 AM
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No, IF 13.8 mm were larger than 14 mm then a 14 mm wrench...
...would STILL not fit on a "13.8 mm" bolt-head. Or what the FUCK were you trying to say?!? For once, your body text was much clearer than the headline. Too bad the headline was total gibberish...
Yeah, sure, it COULD be that your el-cheapo Chinese tools(*) have such humongously sloppy "tolerance differences" that a nominally "14 mm" wrench would fit on a 9/16" (14,2875 mm) bolt-head. Or maybe your bolts are Chinese too -- WTF do I know (or care)...
Anyway, that's what I frigging SAID -- "Either your bolts or your wrenches are off measure" -- before, isn't it? So, uhmm... What the fucking fuck are you objecting to here???
(*) BTW, haven't you ever heard the old saying, "the poor man can't afford to buy cheap"?
[link|mailto:MyUserId@MyISP.CountryCode|Christian R. Conrad] (I live in Finland, and my e-mail in-box is at the Saunalahti company.)
Your lies are of Microsoftian Scale and boring to boot. Your 'depression' may be the closest you ever come to recognizing truth: you have no 'inferiority complex', you are inferior - and something inside you recognizes this. - [link|http://z.iwethey.org/forums/render/content/show?contentid=71575|Ashton Brown]
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