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Old 02-24-14, 11:31 AM   #1
mikemargolis
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Mt Mount Washington Hillclimb Gearing (help with math!)

Hi All,

First post here, need a little help please.

I last rode this race in 1984, now 30 years later, at age 54, I am riding it again.

I am a rider, not a racer. The winners are sub one hour, I'll be VERY happy with sub two hours.

So here's the question: What is the gearing I need? Everybody and everything I read says I need 1:1 at a minimum. Equal teeth front and rear with 700C x 25 tires nets a 26.5" gear, so that means that every crank rotation moves the bicycle forward 26 and a half inches. (At least, that is what I understand, maybe my error is right there. Please read on.)

So, I am going to work gearing backwards.

I want to ride the 7.6 miles in under two hours. What is the AVERAGE gear I need to move forward 7.6 miles at an 80 cadence in two hours?

Here's my math, tell me where I am wrong, because the answer doesn't make sense.

63,360 inches in a mile (12 * 5280)
481,536 inches in Mt Washington hillclimb (63,360 * 7.6 miles)

80 cadence per minute
9,600 pedal strokes in two hours (80 * 120 minutes)

So divide 481,536 inches in the ride by 9600 pedal strokes, and you get 50 inches per pedal stroke.

The lowest gear on my bicycle now is 34 front and 30 rear which is 29.9", and I have am pushing hard to ride a 10% grade with that, being an old man and all. A 50" gear can not be correct, there is NO WAY I can climb that mountain, or any mountain for that matter, on my 34 tooth front and 18 tooth rear. On a 10% grade, I need my 28 or 30 tooth rear regularly.

Please tell me what I am doing wrong with the math. I already know I'm going to put a single 24 or 26 tooth chainring up front and leave the 11/30 in the rear, but want to understand the math.

And thanks in advance! (PS I can do this in four languages, but math is not my strong suit!
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Old 02-24-14, 11:48 AM   #2
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Well it's 80 revolutions of the chainring so two strokes per revolution and gear inches is the equivalent of a certain wheel diameter- not the same as development.

Try playing with this:
http://home.earthlink.net/~mike.sherman/shift.html
at the bottom for a particular gear combo it will give you the speed at a picked cadence so at 80 rpm you need to go 3.8 mph to get to the top in 2 hours

a 22/36 combo will give you 3.9 mph at 80 rpm. 16 gear inches.
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Old 02-24-14, 01:43 PM   #3
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Originally Posted by delcrossv View Post
Well it's 80 revolutions of the chainring so two strokes per revolution and gear inches is the equivalent of a certain wheel diameter- not the same as development.

Try playing with this:
http://home.earthlink.net/~mike.sherman/shift.html
at the bottom for a particular gear combo it will give you the speed at a picked cadence so at 80 rpm you need to go 3.8 mph to get to the top in 2 hours

a 22/36 combo will give you 3.9 mph at 80 rpm. 16 gear inches.
Well, after reading your reply, I did it the old fashioned way, put my bicycle in the 34/30 gear and measured rollout for one crank revolution, it was 95". So, honestly, I have NO idea what the gear ratio charts are measuring "in inches", but with an actual 95" of rollout, I can do the math.

First off, if I stayed in the lowest gear that comes standard on my bike (a Felt Z6 by the way) and maintained the 80 cadence that I want to maintain, the 7.6 miles would take me 5069 crank revolutions which is 63 minutes.

So, Mr. 54-year-old can not carry a stock gear to Mt. Washington, as I am NOT a 63 minuter.

Mike Sherman shows the rollout of a 34/30 at 93.9" so my 95" is pretty close. And now I can noodle with chainring size to get to a 50" rollout.

If I put a 22" up front and leave the back at 12/30, I get 60.8" rollout, so I might have to go bigger than 30 in the back.
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Old 02-24-14, 02:01 PM   #4
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Gear inches are based on wheel diameter, going back to the day of the large wheeled bicycles. So a gearing of say 26.5 is basically the same as riding an old high wheeler with a 26.5" wheel... not much of a high rider, but that is what it means.

So for a 26.5" wheel, if I remember my geometry right, the circumference (or roll out) would be 26.5 * pi (2 pi r)

So with a 34 x 30 on your bike (29.9 gear inches) the roll-out is approximately 93.9 inches...
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Old 02-24-14, 02:34 PM   #5
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Gear inches are based on wheel diameter, going back to the day of the large wheeled bicycles. So a gearing of say 26.5 is basically the same as riding an old high wheeler with a 26.5" wheel... not much of a high rider, but that is what it means.

So for a 26.5" wheel, if I remember my geometry right, the circumference (or roll out) would be 26.5 * pi (2 pi r)

So with a 34 x 30 on your bike (29.9 gear inches) the roll-out is approximately 93.9 inches...
Exactly. Gear Inches is equivalent wheel diameter. Development is how far you go in one revolution of the cranks. put a 22 tooth granny on the front and an 11/36 on the back and you'll make it up in 2 hours- in bottom gear.
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Old 02-24-14, 02:49 PM   #6
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Exactly. Gear Inches is equivalent wheel diameter. Development is how far you go in one revolution of the cranks. put a 22 tooth granny on the front and an 11/36 on the back and you'll make it up in 2 hours- in bottom gear.
Europeans do roll-out in meters. Americans do gear inches. Neither has much intuitive meaning until you've ridden a bike with similar gear range and have something to which to compare it.
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Old 02-24-14, 03:16 PM   #7
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Europeans do roll-out in meters. Americans do gear inches. Neither has much intuitive meaning until you've ridden a bike with similar gear range and have something to which to compare it.
Or ridden a penny-farthing.
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Old 02-24-14, 06:01 PM   #8
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Sheldon's gear calculator will make things easier. In the 'gear units' pulldown it has MPH at different RPM's.
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Old 02-24-14, 06:02 PM   #9
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Thanks everybody.

All these years of riding, and I always thought that a 100 inch gear (52 x 14) actually rolled out at 100 inches. Silly me...
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Old 02-24-14, 06:56 PM   #10
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Thanks everybody.

All these years of riding, and I always thought that a 100 inch gear (52 x 14) actually rolled out at 100 inches. Silly me...
The average bike-riding citizen has never heard of gear inches, and of those who have, a significant number would say it means what you thought.
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Old 02-25-14, 08:54 AM   #11
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All this discussion of gearing is maybe beside the point. Have you ridden enough sustained climbs to do this ride, or not? If not, you have to train in preparation, or you will suffer. 10% average grade represents a significant threshold value. Have you done the ride recently?

Your gearing is fine. How is your motor?
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Old 02-25-14, 09:55 AM   #12
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Your gearing is fine. How is your motor?
Hi Phil,

Thanks for the reminder. I am training and riding, inside and out. I've done the ride twice before, albeit a long time ago.

I well understand that it is three parts: mechanical, physical and mental.

I am well prepared mentally and physically, it it the mechanical that I came asking about.
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Old 02-25-14, 10:24 AM   #13
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Your mental part will be your strength. Save your energy when you can and ride patiently. I believe that your gearing is low enough. When is the ride?
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