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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)

 02-06-06, 05:47 PM #1 Spor ROBOTS... Thread Starter     Join Date: Nov 2005 Location: Berkeley, CA Bikes: Posts: 169 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) 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?
 02-06-06, 05:58 PM #2 Moximitre dig dig dig     Join Date: Jan 2006 Location: Chicago Bikes: Full Fendered Bareknuckle, Faggin with 10spd Centaur, 1973 Raleigh 3spd Cruiser. Posts: 878 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) 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
 02-06-06, 06:00 PM #3 ZappCatt Back to being a Clyde....     Join Date: Oct 2004 Location: Santa Clara Bikes: Giant OCR1(specialized carbon seatpost,Terry Fly sadle, Syntace C2): Leader TT frame, Easton EC70fork, Aerolite bars, nashbar bullhorn, Titan Wheels: Fuji Track Pro(2003) Posts: 1,546 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) 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
 02-06-06, 06:00 PM #4 Moximitre dig dig dig     Join Date: Jan 2006 Location: Chicago Bikes: Full Fendered Bareknuckle, Faggin with 10spd Centaur, 1973 Raleigh 3spd Cruiser. Posts: 878 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) inches / minute * (1foot/12inches) * (1mile/5280feet) * (60minutes/hour) bam, mph
 02-06-06, 06:02 PM #5 Moximitre dig dig dig     Join Date: Jan 2006 Location: Chicago Bikes: Full Fendered Bareknuckle, Faggin with 10spd Centaur, 1973 Raleigh 3spd Cruiser. Posts: 878 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) 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.
 02-06-06, 06:03 PM #6 Moximitre dig dig dig     Join Date: Jan 2006 Location: Chicago Bikes: Full Fendered Bareknuckle, Faggin with 10spd Centaur, 1973 Raleigh 3spd Cruiser. Posts: 878 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) 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
02-06-06, 06:29 PM   #7
MacG
don't pedal backwards...

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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.

 02-06-06, 07:04 PM #8 Spor ROBOTS... Thread Starter     Join Date: Nov 2005 Location: Berkeley, CA Bikes: Posts: 169 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) 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.
02-06-06, 07:07 PM   #9
Spor
ROBOTS...

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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>

02-06-06, 07:35 PM   #10
Agent4573
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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.

and he probably comes out correct in the end most of the time....

 02-06-06, 07:40 PM #11 concernicus Senior Member     Join Date: Jan 2006 Location: Santa Cruz Bikes: doesnt matter. just ride. Posts: 425 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) sheldon brown has a cool gear calculator
 02-06-06, 08:05 PM #12 poopncow MADE IN HONG KONG   Join Date: Aug 2005 Location: Washington DC Bikes: some but not enough Posts: 1,763 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 1 Post(s) 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.
 02-06-06, 08:30 PM #13 Spor ROBOTS... Thread Starter     Join Date: Nov 2005 Location: Berkeley, CA Bikes: Posts: 169 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) 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.
 02-06-06, 11:49 PM #14 poopncow MADE IN HONG KONG   Join Date: Aug 2005 Location: Washington DC Bikes: some but not enough Posts: 1,763 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 1 Post(s) a fish
 02-07-06, 08:01 AM #15 geog_dash Senior Member   Join Date: Jun 2005 Location: Oklahoma Bikes: Pake fixie. Klein Reve (for sale, http://www.theveer.net/gordons_klein) Posts: 389 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) 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/
 02-07-06, 09:04 AM #16 jfmckenna Tiocfáidh ár Lá     Join Date: Dec 2003 Location: The edge of b# Bikes: A whole bunch-a bikes. Posts: 5,445 Mentioned: 1 Post(s) Tagged: 0 Thread(s) Quoted: 185 Post(s) 6 x 9 = 42
 02-07-06, 02:00 PM #17 r-dub likes avocadoes   Join Date: Nov 2004 Location: oakland, ca Bikes: heh, like that info would fit here... Posts: 1,125 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) 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.
02-07-06, 02:04 PM   #18
humancongereel
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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.

02-07-06, 02:28 PM   #19
geog_dash
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Quote:
 Originally Posted by jfmckenna 6 x 9 = 42
He's in base 13.

 02-07-06, 03:14 PM #20 humancongereel live free or die trying     Join Date: Oct 2005 Location: where i lay my head is home. Bikes: bianchi pista workhorse, cannondale r1000, mountain bike fixed conversion Posts: 6,999 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) ah. i have no idea how other base systems work, but i do understand the idea.