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Singlespeed & Fixed Gear "I still feel that variable gears are only for people over forty-five. Isn't it better to triumph by the strength of your muscles than by the artifice of a derailer? We are getting soft...As for me, give me a fixed gear!"-- Henri Desgrange (31 January 1865 - 16 August 1940)

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Old 02-06-06, 05:47 PM   #1
Spor
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What's wrong with my math?

OK,
trying to do some gear-inch/rpm math and the numbers aren't coming out right.

I'm imagining something that should be really fast and has nice even numbers, i.e. spinning a 90 inch gear at 120 revs/minute
how many miles/hour is that?

so:
90 inches/rev ÷ 12 inches/foot = 7.5 feet/rev
7.5 feet/rev X 120 rev/min = 900 feet/min
900 feet/min X 60 min/hour = 54,000 feet/hour
54,000 feet/hour ÷ 5,280 feet/mile = 10.227 miles/hour

intuitively i feel that this answer is off by a factor of at least three, what's wrong with this math? Is my comprehension of gear inches off, or am I just doing something really stupid?
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Old 02-06-06, 05:58 PM   #2
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lets see, do, 120 rpm * #front teeth / # rear teeth = rpm of tire.
then, go, rpm of tire * pi * diameter of tire = inches per minute, then do the other conversions
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Old 02-06-06, 06:00 PM   #3
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According to the gear calculator I downloaded from FixedGearfever.
A 90.35(44x13{but elsewhere on the SAME spreadsheet he calls 44x13 a 91**) gear inch, spun at 120rpm =32.25 mph

I don't know the math...so I use a spreadsheet
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Old 02-06-06, 06:00 PM   #4
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inches / minute * (1foot/12inches) * (1mile/5280feet) * (60minutes/hour)

bam, mph
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Old 02-06-06, 06:02 PM   #5
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yeah, I'm sure my calculations work the same, and don't you have to take rear tire diameter in to account? wait, why am I asking, the answer is yes.
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Old 02-06-06, 06:03 PM   #6
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not to be an ass, but yes, your comprehension of gear inches is off, it is just used as a reference, It really has no physical value, at least from what I can see
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Old 02-06-06, 06:29 PM   #7
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Quote:
Originally Posted by Spor
OK,
intuitively i feel that this answer is off by a factor of at least three, what's wrong with this math? Is my comprehension of gear inches off, or am I just doing something really stupid?
I think you answered your own question without realizing it. You're indeed off by a factor of (roughly) three.

Gear inches are a unit conceived when people needed a way to compare the gearing of safety bicycles (a new invention) to penny farthings (the existing standard). Since a penny farthing's wheel travels exactly one turn per turn of the cranks, getting a taller gear meant getting a bigger wheel. Safety bikes had chains and sprockets, so you could get different gear ratios depending on what size sprockets were used. If you were in the market for a safety bike and wanted to know what the gearing was like, the salesman could tell you that it was just like riding a penny farthing with an 80 inch wheel (or whatever the case may be).

Quote:
I'm imagining something that should be really fast and has nice even numbers, i.e. spinning a 90 inch gear at 120 revs/minute
how many miles/hour is that?

so:
90 inches/rev ÷ 12 inches/foot = 7.5 feet/rev
7.5 feet/rev X 120 rev/min = 900 feet/min
900 feet/min X 60 min/hour = 54,000 feet/hour
54,000 feet/hour ÷ 5,280 feet/mile = 10.227 miles/hour
your 90 inches per rev is actually a 90 inch diameter wheel. Multiply by pi (3.141592...) to get how many rolling inches you would get. Everything from there on looks fine to me.

Amusingly enough, your observation that your numbers seemed off by a factor of three was more accurate than you realized.
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Old 02-06-06, 07:04 PM   #8
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Ah-ha,
So gear inches references diameter, not circuference.
Cheers to MacG for pointing out my error. If this were a math forum, I would feel like an ass, but instead this is bffgss, and I don't really feel all that bad.
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Old 02-06-06, 07:07 PM   #9
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Quote:
Originally Posted by MacG
Amusingly enough, your observation that your numbers seemed off by a factor of three was more accurate than you realized.
Yeah, I have an engineer friend who whenever his calculations are off, just assumes it's by a factor of pi.
</nerd>
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Old 02-06-06, 07:35 PM   #10
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Quote:
Originally Posted by Spor
Yeah, I have an engineer friend who whenever his calculations are off, just assumes it's by a factor of pi.
</nerd>

and he probably comes out correct in the end most of the time....
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Old 02-06-06, 07:40 PM   #11
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sheldon brown has a cool gear calculator
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Old 02-06-06, 08:05 PM   #12
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yup, gear inches is for diameter, so multiply by Pi!!!

++++'s! you are performing a very good exercise by working the calculations out yourself! spread sheets are useful for making lots and lots of calculations, but understanding the math behind the cal's makes you smarter. There's that engineer in me coming out again.
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Old 02-06-06, 08:30 PM   #13
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Wait,
Isn't pie, the dessert, some sort of meme-ish in-joke on this site? Could I have un-wittingly crafted some sort of meta-bike-nerd-math-nerd super-joke?

Not that it's even that funny, just sayin.
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Old 02-06-06, 11:49 PM   #14
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a fish
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Old 02-07-06, 08:01 AM   #15
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90 * pi * 120 * 60 / 12 / 5280 = 32 mph

in / rev * rev / min * min / hr / (in / ft) / (ft / mile) = mile / hr

Gear inches = wheel diameter of an equivalent high wheeler.
See:
http://sheldonbrown.com/gloss_g.html#gearinch
http://sheldonbrown.com/gears/
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Old 02-07-06, 09:04 AM   #16
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6 x 9 = 42
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Old 02-07-06, 02:00 PM   #17
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A few years ago I was helping a friend with some math for his thesis (caltech astrophysics.) I asked him to define some constants for me that I had never heard of and he laughed. He said they just assume all constants are one, and then work it out in the end if they really need to.
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Old 02-07-06, 02:04 PM   #18
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Quote:
Originally Posted by jfmckenna
6 x 9 = 42

6x7=42 (also the answer to the ultimate question of life, the universe, and everything).

any math more complex than that, and i'm lost.
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Old 02-07-06, 02:28 PM   #19
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Quote:
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6 x 9 = 42
He's in base 13.
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Old 02-07-06, 03:14 PM   #20
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ah. i have no idea how other base systems work, but i do understand the idea.
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