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aostling
09-17-2007, 10:09 PM
Here is a puzzle which I've seen confound some of my rocket scientist friends, even those who ride bicycles to work. It's been around for years, so I'm sure some of you have seen it. But I don't think it is widely known.

The experiment involves a bicycle with its pedals in the vertical position as shown. Assume the bicycle is balanced (by side forces only) so that it doesn't fall over.

Tie a string to the lower pedal (14), and standing behind the bicycle, pull backward on the string. Which direction does the bicycle move?

http://i168.photobucket.com/albums/u183/aostling/bicyclepuzzle.jpg

hitandmissman
09-17-2007, 10:24 PM
If the bike is balanced side to side and no other forces involved I would guess it would move backwards. However if there were a small drag goin rearward it would tend to propel forward. This is just a dummy guess, ha ha.

john hobdeclipe
09-17-2007, 10:38 PM
My first thought was that the bike would move forward, but I just tried it, and the bike went backward. But I think it will depend on the gear ratio, and that if you had a ratio (measured in inches, the traditional method over here) that was less than the diameter of the driven wheel, the bike would move forward.

The bike in the picture appears to have a ratio of about 65 to 75 inches, so it will go backward.

Someone with a mountain or touring bike handy, try this, assuming your low gear is less than 26 inches.

dp
09-17-2007, 10:47 PM
The bike will move backward even faster than the string pulling it because the peddle, driven by the rear wheel and chain coupling to the sprocket, will move in the opposite direction (away from the string tugger).

Edit: clarification - the pedal moves forward relative to the bike, not the string tugger.

mochinist
09-17-2007, 11:34 PM
http://graphics8.nytimes.com/images/2006/12/11/technology/poguespan.jpg

A.K. Boomer
09-17-2007, 11:59 PM
My first thought was that the bike would move forward, but I just tried it, and the bike went backward. But I think it will depend on the gear ratio, and that if you had a ratio (measured in inches, the traditional method over here) that was less than the diameter of the driven wheel, the bike would move forward.

The bike in the picture appears to have a ratio of about 65 to 75 inches, so it will go backward.

Someone with a mountain or touring bike handy, try this, assuming your low gear is less than 26 inches.

I believe you are correct, to me it makes sense that its all up to the gearing, I cant imagine a bike still moving backwards with extreme gearing ----
think for a second on those wierd ass wind sculptures that someone posted, some of them walked directy into the wind -- they did this by means of gearing, the fan blades that were powered were at an extreme ratio and over rode the rest of the winds force on not only the blades themselfs but all the rest of the sculpture,,, the bike experiment is no different, My Mt. bike in high gear (48/11) gets pulled imediatly backwards BUT, in low gear (24/32) it grid locks, im a thinnin it would go forward with a 22/34 but realize as soon as the crank arc is a fair degree beyond BDC then the advantage would start to get taken away until gridlock is achieved once again.....

gmatov
09-18-2007, 12:06 AM
I may not understand this, but I would think it would move forward ( chain drive action) until the pedals were parallel to the ground. Then you are pulling on a fixed point, against a coaster brake.

Coasts, so it would come to the pulling force.

You put forward force on the pedal, you engage the clutches, it goes forward.

Cheers,

George

Evan
09-18-2007, 12:07 AM
The bike goes nowhere unless you pull hard enough to make it skid backward. It can't move forward because you are pulling it back. The pedal can't move backward farther than the bike moves forward since the driving sprocket is larger than the driven sprocket.

A.K. Boomer
09-18-2007, 12:32 AM
"The bike goes nowhere unless you pull hard enough to make it skid backward. It can't move forward because you are pulling it back. The pedal can't move backward farther than the bike moves forward since the driving sprocket is larger than the driven sprocket."

Nope --- the bike moves imediatly backwards with no skidding what-so ever, while doing it the pedal actually moves foreward whilst being tugged on in the reverse direction, but thats only with the illustration given,

Like J.H. stated, with the proper gearing the bike moves imediatly foreward and the pedal is drawn to the back and like I stated with a no advantage no dis-advantage gearing the bike will grid lock its drive system, Now and only now will you skid the rear tire to draw it backwards... EDIT: the picture of the bike in the illustration is in no way to be confused with gearing that could even aproach a gridlocked drivetrain as the front sprocket would have to be smaller than the rear...

darryl
09-18-2007, 12:34 AM
Evan has it, the bike doesn't move.

A.K. Boomer
09-18-2007, 12:39 AM
Evan has it, the bike doesn't move.

wrong answer dude, Hint --- listen to the mechanic!

That bike in the illustration gets pulled imediatly backwards without dragging its tire...

darryl
09-18-2007, 12:51 AM
Oops, you might be right. Evan's answer seemed right to me, but let me think this out again (without resorting to getting the bicycle out)

Ok, if you were actually pedalling, even though the bottom of the crank is moving backwards relative to the bicycle, it's actually always moving forward. Therefore it will actually move backwards if the bicycle is moved backwards, even though it would then be moving forwards relative to the bicycle itself. If you pull it backwards with the string, the force you apply is resisted only by the torque imparted to the tire against the ground. Because of the drive ratio, there will be less torque applied to the ground than that applied to the pedal. Right you are, Boomer, the bicycle moves backwards.

I'm going to post this bit of logic before I try it with the bicycle.

A.K. Boomer
09-18-2007, 12:58 AM
I got my bike out to prove I had enough of a low gear to propell in foreward motion, i dont but I know im still right about this, like I stated, its the exact same principle on how that guy got his mechanical wind machines to walk against the wind...

dp
09-18-2007, 01:00 AM
wrong answer dude, Hint --- listen to the mechanic!

That bike in the illustration gets pulled imediatly backwards without dragging its tire...

Yep - the mechanical advantage belongs to that big tire turning that tiny sprocket against that big sprocket. That tire and gearing ration will counter turn the sprocket which causes the lower pedal to move forward (counter clockwise).

Just to help clarify, imagine the rear tire is a gear in a rack and can't skid.

Evan
09-18-2007, 01:16 AM
I think we have a little problem here with the thought experiment. My concept of pulling it backward doesn't allow for the rope to move forward, only the bike. I am considering the problem as if the backward pull is applied by a rope taken up by a winch fixed in place.

dp
09-18-2007, 01:59 AM
I think we have a little problem here with the thought experiment. My concept of pulling it backward doesn't allow for the rope to move forward, only the bike. I am considering the problem as if the backward pull is applied by a rope taken up by a winch fixed in place.

The string never moves forward. The pedal moves forward relative to it's axle and the rest of the bike, but backward relative to the world. The string, pedal, and bike all move backward but at two different rates.

09-18-2007, 02:55 AM
I think it's the usual story:"it all depends".
If you consider that the pedal is at the end of a crank,then pulling the string will cause the sprocket,and therefore the bike,to move forward,but only for a quarter of a rotation of the sprocket.Once the crank is at the "9 o'clock" position,the bike will be dragged backwards,assuming the string is pulled hard enough.Pull harder still,and the bike will be dragged around a horizontal axis,since the string is attached to the right pedal,disturbing the longitudinal balance.Then again,maybe I'm talking through a hole in my head:D.

Evan
09-18-2007, 05:16 AM
I reverse my position, pun intended. It certainly does "depend".

The motion of the pedal on the crank arm relative to the ground describes what is called a form of Trochoid curve. The shape of that curve varies depending on the length of the arm and in this case the size of the rear wheel and the gear ratio. For any such ratio that works out to greater than 1 to 1 at the crank it is equivalent to attaching the string to the back wheel itself somewhere between the axle and the rim on the wheel. This is true for any ratio that results in the pedal making fewer rotations than the back wheel.

For any value that results in a ratio greater than 1 to 1 the cycle will move in the direction of pull. The pedal will describe a trochoid known as a curtate cycloid. The curtate cycloid always moves in the same direction as the wheel that carries the point that defines it.

http://vts.bc.ca/pics2/cycloidc.gif

The larger the ratio the closer the effective pull is to the back axle. If we decrease the ratio to 1 to 1 then the bike doesn't move and if it is less than 1 to 1 the bike moves in the opposite direction to the pull, slightly.

09-18-2007, 05:23 AM
http://graphics8.nytimes.com/images/2006/12/11/technology/poguespan.jpg

Is there a fly in there? If so I got another question!

IOWOLF
09-18-2007, 06:31 AM
Mo Has it, Another "One of Those Posts". :)

Benesesso
09-18-2007, 06:58 AM
Now that that's settled, anyone wanna talk about half-step gearing?

A.K. Boomer
09-18-2007, 09:23 AM
The string never moves forward. The pedal moves forward relative to it's axle and the rest of the bike, but backward relative to the world. The string, pedal, and bike all move backward but at two different rates.

Yes very important point to clarify, no matter the gearing extremes it will always be the case (unless complete gridlock -- then nothings going anywhere...)

A.K. Boomer
09-18-2007, 09:37 AM
You guys want a brain teaser? imagine there is no rear freewheel so its a track bike, direct drive in both directions, Now --- keep the string but pull from opposite direction (from front of bike), Has anything changed? does the bike have the exact behaviour except for the fact that it will move (or not move) in reverse instead of foreward, be careful -- this is a tricky one..

Edit; One of the bikes has the top of its chain loaded -- the other the bottom, does this have an effect on the way the crank bearings are loaded in relation to the pull? how about the rear wheel bearings in relation to the pull?
is this a hint or am i trying to throw you off track? gotta work today, bye..

BCtech
09-18-2007, 11:27 AM
Per the diagram,

http://img223.imageshack.us/img223/1878/bikesp3.jpg

- The mechanical advantage of the pedal to the driving sprocket is 7.70/4.31 or 1.78, however, the pedal is not perpendicular to the direction of pull so the actual perpendicular distance must be used which is 7.60. 7.60/4.31 = 1.76

- The mechanical advantage of the driving sprocket to the driven sprocket is 1.53 / 4.31 or 0.355.

- The mechanical advantage of the driven sprocket to the driven tire is 1.53/14.4 or 0.106

So the total mechanical advantage of the pedal to tire is 1.76 x .355 x .106 or .066.

This means that any force on the pedal would have to be multiplied by .066 to determine the force at the tire tread.

If I pull back on the string with a force of 1 pound, the tire will pull forward with a force of 1 x .066 or .066 lbs.

A vector diagram on the bike as a unit would show a 1lb force backward added to a .066 lb force forward so the net force would be in a backward direction of 1 - .066 = 0.934 lbs.

The bike will move backwards.

dp
09-18-2007, 11:31 AM
The only question unanswered is, what is holding up the bike? If a divine being or unseen force is involved, how does that impact the final vector? Inquiring minds need to know :)

aostling
09-18-2007, 11:41 AM
You guys want a brain teaser? imagine there is no rear freewheel so its a track bike, direct drive in both directions, Now --- keep the string but pull from opposite direction (from front of bike), Has anything changed? does the bike have the exact behaviour except for the fact that it will move (or not move) in reverse instead of foreward, be careful -- this is a tricky one..

A.K.,

A nice twist on the original puzzle. At first I thought you meant that the string is now tied to the upper pedal, but re-reading your post, I see you did not mean that.

aboard_epsilon
09-18-2007, 12:45 PM
depends on how heavy the bike is ...

if the bike is lighter than the force needed to turn the pedal ...
it goes backwards skidding the wheel..wheel not turning

if the bike is heavier than the force needed to turn the crank ..

it goes forwards

if the bike is the same weight as force needed to turn the crank, then it goes forward a bit ..but also the wheel turns and skids.

also a lot would depends on what surface it is stood on ...

a slippery surface would produce the above results ...

a grippy surface would alter them.

so question cant really be answered unless you account for the surfaces its stood on.

all the best.mark

andy_b
09-18-2007, 12:55 PM
http://graphics8.nytimes.com/images/2006/12/11/technology/poguespan.jpg

EXACTLY what i was thinking!!!!!

andy b.

aostling
09-18-2007, 05:56 PM
Most of you have concluded that the bicycle, as pictured, will move backward. That is correct. But as post #3 was the first to point out, it does depend on the gear ratio. The gearing can be made low enough so that the bicycle goes forward. A.K. Boomer in post #6 apparently has a mountain bike with a granny gear close to this.

We can discard almost all of the hardware of the bicycle without losing anything crucial to the puzzle. Here is a sketch of an equivalent system -- it is merely a dual-diameter disk rolling on a track, with a cord wrapped around one of the disks. The disk with the cord corresponds to the pedals -- its radius equals the radius of the pedal multiplied by the rear/front sprocket ratio.

http://i168.photobucket.com/albums/u183/aostling/wheels.jpg

Even in their lowest gear, most bicycles are geared to the geometry of sketch A. Pulling back on the cord will cause the wheel to rotate counter-clockwise, and backward. But a bicycle could be geared so low that it would correspond to sketch B. Then pulling back on the cord would cause the wheel to rotate clockwise, and forward.

Of course the pedals are not a disk, and the initial backward (or forward) movement of the actual bicycle will cease when the pedal moves to the horizontal.

darryl
09-18-2007, 09:42 PM
Hmm, I'm trying to picture the ratios required to achieve the no-motion criteria, or the 'pull the string backwards-bike goes forwards' situation. Seems like one very tall granny gear would be needed.

Another twist- what configuration of pedal to drive gear plus driven gear to tire diameter would give a situation where you could pull the string and it wouldn't move, but you could manually push the bike backwards or forwards a small amount without moving the string-

dp
09-18-2007, 10:10 PM
Most of you have concluded that the bicycle, as pictured, will move backward. That is correct. But as post #3 was the first to point out, it does depend on the gear ratio. The gearing can be made low enough so that the bicycle goes forward. A.K. Boomer in post #6 apparently has a mountain bike with a granny gear close to this.

The distraction of gearing answers a question that was never asked but yes, it is possible to create a gearing situation on a bicycle that will cause the bike to move forward by pulling backward on the pedal. Certainly it won't move very far - 1/4 turn of the crank is pretty much it. This gearing factor isn't applicable to the original question owing to the test conditions established by the image provided where the ratio of the sprockets clearly prevents forward movement.

Next time use a mountain bike image and allow selecting any gear ratios desired to demonstrate how forward and backward movement can be accomplished :)

A.K. Boomer
09-18-2007, 10:13 PM
Another twist- what configuration of pedal to drive gear plus driven gear to tire diameter would give a situation where you could pull the string and it wouldn't move,

-

I already covered that in post #6, this is a rough estimate as i did do it on carpet and stuff;

"My Mt. bike in high gear (48/11) gets pulled imediatly backwards BUT, in low gear (24/32) it grid locks, im a thinnin it would go forward with a 22/34 but realize as soon as the crank arc is a fair degree beyond BDC then the advantage would start to get taken away until gridlock is achieved once again....."

More specs; its a 7" crank arm , its a 26" wheel...

Evan
09-18-2007, 10:33 PM
Sorry Allan but I disagree. Your illustration is not equivalent. The trochoid motion of the pedal is all important if the ratio is such that the bike should move forward. If that is the case, the bike will move forward a small amount and then stall.

The equivalent illustration is this:

http://vts.bc.ca/pics2/wheel.gif

aostling
09-18-2007, 11:15 PM
Sorry Allan but I disagree. Your illustration is not equivalent.

Evan,

No arguments here. I thought of sketching something like that, but you get the prize for the best visual of the day.

 If you could supply a second illustration with a short crank, with the wheel moving backward, that would put it all in a nutshell.

kendall
09-18-2007, 11:33 PM
Hmm, I'm trying to picture the ratios required to achieve the no-motion criteria, or the 'pull the string backwards-bike goes forwards' situation. Seems like one very tall granny gear would be needed.
-

Not sure what ratio would be needed, but I have an unused 30 tooth chainwheel and an old freewheel with a 32 tooth sprocket on it.

Unused because it takes so little effort to turn that you wear yourself out just going fast enough to maintain balance, and that's on a bike with a 12-21 tooth spread on the 9spd cluster. Couldn't imagine riding it with the 32 in the rear.

Normally ride on the 53 and range between the 12 and 15 on the cluster, can't use the small wheel.

rode from kentwood to bitely taking the scenic route a few weeks ago, 100+ miles each way, and tried one hill in basement gears, got a quarter up top and
-HAD- to hit the 53, that small wheel's a killer.

ken.

A.K. Boomer
09-19-2007, 09:15 AM
http://i146.photobucket.com/albums/r249/AK_Boomer/Carloshorsethiefridge.jpg

Granted -- if I turned my bike around and try to climb this I can only get about 60% of it because its so technical, but Iv been out to the "slickrock" in Moab Utah many a time and been on gradiants that make this look flat --- and humped up every inch of them, And although awhile back --- I can still attest that im the 1991 durango colo. hill climb champ:D

If you have anything larger than a 24 tooth front your goose is cooked on stuff like this unless you go very - very large in the rear --- sooooo, it all depends on the type of riding you do;)

What many people dont realize about climbing (including many of the guys who consider themselves "climbers") is that when you approach angles like this it takes just as much if not more upper body strength as it does legs... (and lots and lots of lung and heart to boot)...
In the steeps it is imperative to remain "fluid" with your power strokes, if you dont you will imediatly stall out at TDC/BDC, so much of your effort is trying to create power in the so-called "dead spots" ---- this equates to trying to rip your handlebars off of your machine...

Edit; that pic is called "horsethief ridge" in fruita colo. ---- if you guys look real close just ahead of me you will see the blood on the rocks from many of the poor slobs that very morning who were in over their heads (that is not motorcycle oil drops or anything like that as their not allowed) --- not that I havent been a poor slob from time to time, One of the worst feelings is completely stalling-out on a steep while climbing and not catching both your brake levers a millisecond after ---- its no fun riding down crap like that backwards at 20 mph+ with the "twins" being compressed onto the top tube of your bike frame...

That very day before that pic was taken we watched a kid show up on a fancy full-suspension, he rode down and it seemed like nobody ever told him where the brake levers were, it was one of the most ugliest crashes Id seen in awhile, he tore the crap outa one of his kee's, I think some of the blood was his...

aostling
09-19-2007, 12:51 PM
I thought of sketching something like that, but you get the prize for the best visual of the day.

Here is an unanimated short-crank version of Evan's visual, sketched in Word, then photographed and uploaded. (There must be an easier way!).

http://i168.photobucket.com/albums/u183/aostling/trochoid.jpg

dp
09-19-2007, 12:54 PM

A.K. Boomer
09-19-2007, 02:13 PM
although I should stay away from stuf like that its now a bookmark, maybe i'll get the hang of it after awhile...

kendall
09-19-2007, 04:45 PM
read an artical this afternoon, (yahoo news) regarding the meteorite that supposedly made people sick in Peru. but one quote kind of made me say huh?

quote:

Because no one actually saw anything impact at the crater site, it's hard to say whether a space rock was involved because they are often deceptive as to where they will land. Many times, people swear a meteor landed nearby when in fact it was so far away that it dipped below the local horizon but never actually struck the ground.

"Sometimes these things land hundreds of thousands of miles away from where [people] think they will land," Grossman said.

end quote
the first sections ok, but the last line got me wondering, considering that the earth is approximately 8000 miles through, which would give a max distance of roughly 25000 miles in any one direction, could something that lands 'hundreds of thousands of miles away' actually be said to land at all?

back on subject though, I ride road bikes, and I have no idea why that 30 tooth chainwheel is on this bike it's way too low for any hill I've ever been on.
I could see it on mountain bikes, but for a street bike it's overkill, I'd be happy with a 48 or therebouts.

Ken.

Alistair Hosie
09-19-2007, 05:01 PM
I think Evan will be getting invited to the Google staff dance he's obviously their no 1 customer:D:DAlistair green with envy:D

kendall
09-19-2007, 06:12 PM
back on subject though, I ride road bikes, and I have no idea why that 30 tooth chainwheel is on this bike it's way too low for any hill I've ever been on.
I could see it on mountain bikes, but for a street bike it's overkill, I'd be happy with a 48 or therebouts.

Ken.

I rode about every hill in SF, and never used lower than a 43, but ran into this link over on bike forums, Maybe my bike came from one of these areas:

http://deputy-dog.com/2007/09/18/the-steepest-streets-in-the-world/

couple of those streets I wouldn't even want to ride -down-
ken.

dp
09-19-2007, 06:25 PM
I rode about every hill in SF, and never used lower than a 43, but ran into this link over on bike forums, Maybe my bike came from one of these areas

couple of those streets I wouldn't even want to ride -down-

On my recent tour by Harley around Italy we came upon a section of road the dropped down very steeply to a lake. Of the three bikes, two of them locked up the front brakes at low speed and crashed, sliding the rest of the way down the hill on the crash bars. I was riding one of them and have never seen a street that steep. None of us felt the bikes could make it back up but fortunately we didn't have to. My wife is still sore from that crash - my first real crash since I quit racing motorcycles in 1977.

A.K. Boomer
09-19-2007, 06:40 PM
back on subject though, I ride road bikes, and I have no idea why that 30 tooth chainwheel is on this bike it's way too low for any hill I've ever been on.
I could see it on mountain bikes, but for a street bike it's overkill, I'd be happy with a 48 or therebouts.

Ken.

Depends where you live, 30 or 32 is very small for the small front gear on a road bike I'll give you that but there are certain "roads" in colorado that would require it, skyline drive (about three blocks from where i live) is one of them, you may not be in your largest of the cluster in the rear (depending on what your running back there) but I guarantee you will be close...

It all equates to effort expended in a certain time frame, preferably close to 90/100 reps per minute, unless sprinting all the time (this has its own set of cadence rules but usually much lower) you want to stay within certain RPM guidelines, I was rated about 5th in the state for awhile in the sports class in Mt. bike racing so was no slow-poke, yet Iv been on long long hills (usually they hold Mt bike races UP the sides of ski slopes) that had me bogged down in 24/32 (thats 24 front 32 rear) yet was grinding out 100 rpm's and its all i could do (at 10,000 ft:) ) --- if I threw a shift into 28 or 30 in the rear it was too much and not only could i not hold 90/100 rpm's but my heart rate would skyrocket if I tried... while this is an extreme example I can assure you that there are many many paved places in this state that would make you cough up your liver if the smallest you had was a 30 or 32 front and the largest on your rear cluster was a 21, road bike or not ---------- a 21 rear for your largest is actually flat landers gearing unless of course you make the front even smaller... but now were getting into a high tension drivetrain inefficiency that I try to avoid --------- not only do you increase bearing friction between the crank and the rear wheel --- You increase frame flex on every power stroke, you also increase chain link friction whilst the chain is having to bend around a smaller arc while under this friction, (the smaller sprocket) better to go large on large and keep the drivetrain under less tension, even though you have the same ratio there is a power savings ----- the drawbacks with big on big is you have to carry a few extra links of chain and the chain has more speed but with todays super efficient derailure bearings the testing grounds have proven that big on big is an energy saver...

aostling
09-19-2007, 06:58 PM
http://deputy-dog.com/2007/09/18/the-steepest-streets-in-the-world/
couple of those streets I wouldn't even want to ride -down-
ken.

I drove up Baldwin Street, pictured here, in 1995. It is in Dunedin, and it's the steepest street in the world. I didn't know that at the time. I just knew it was the steepest street I'd ever seen. My 1980 Datsun ("Super Kea") just barely had enough steam to get to the top. I wasn't intending to go back down Baldwin, but at the top I found I'd arrived at a cul-de-sac, so had no choice. The descent was decidedly scary.

A.K. Boomer
09-19-2007, 07:00 PM
I rode about every hill in SF, and never used lower than a 43, but ran into this link over on bike forums, Maybe my bike came from one of these areas:

http://deputy-dog.com/2007/09/18/the-steepest-streets-in-the-world/

couple of those streets I wouldn't even want to ride -down-
ken.

All walks in the park,,, nothing will ever compare to the stuff iv climbed at slickrock, for one you cant hook up on pavement like you can on slickrock, its like super porous 30 grit sandpaper, you save your old tires to run because they hook up better than knobs, you run scary low tire pressure and excert so much force that you pray to god you dont snap a chain because you know it would cause you to hyperextend your knee... its insane --- You almost cant stand on it safely....

john hobdeclipe
09-19-2007, 10:45 PM
Allan, your drawings make it obvious what would happen in different circumstances, thus, assuming a crank fixed directly to a wheel: If the wheel is larger radius than the crank, the wheel will roll back when you push back on the crank. If the wheel is smaller than the crank, the wheel will move forward when you push back on the crank.

Now, assuming a bike with a 6-1/2 inch crank, directly connected to a wheel, if the wheel were larger than 13" diameter, it would roll backward; if the wheel were 13" diameter, it would not roll at all, and if it were less than 13" diameter it would roll forward.

Am I right so far?

Now, if we use gearing to connect the crank to the wheel, we can use any size wheel and gear it to be the equivalent of any other size wheel (this is the basis of our "gear inches" system anyway.)

So if we now assume a 26" diameter back wheel, we can arrange the gearing to make it represent a larger or smaller wheel. If we use the same size sprockets front and back, for a 1/1 drive, we have the equivalent of a direct drive 26" wheel (duh) which is larger than the crank, and the bike will move backward.

If we put a sprocket on the back that is twice the size of the one in front, for a 2/1 ratio, we have the equivalent of a 13" wheel, which is the same size as the crank, and the bike will not move at all.

And if we arrange the gearing to get a ratio of, say, 3/1, we would have the equivalent of an 8.7" diameter wheel, which is less than the crank, and the bike will move forward when you push back on the peddle.

Right?

We can't really test this on a real bike, since I don't think anyone has a bicycle set up with a gear of 13 inches or less, nor could you ever spin that fast enough to keep your balance.

A.K., on your bike with 7" cranks, you would need a 14" gear to make it not move at all. With your 34 tooth small chainring, you would need a 64 tooth back sprocket to get a 14 inch gear.

As for methods of stating bicycle gear ratios, I much prefer the European method, where you add some pi into the mix and see what develops.

aostling
09-19-2007, 11:47 PM
We can't really test this on a real bike, since I don't think anyone has a bicycle set up with a gear of 13 inches or less, nor could you ever spin that fast enough to keep your balance.

John,

I'll take your word for this. My only adult bicycle was stolen in 1978.

I live in the foothills of South Mountain Park in Phoenix. At 16,000 acres, this is claimed to be the largest city park in the USA. It's a wilderness with over 50 miles of trails which are very popular with mountain bikers.

A friend of mine has a mountain bike with only one speed. He takes it everywhere, recently to Fruita, Colorado. What ratio would you choose, if you were limited to one?

dp
09-20-2007, 12:15 AM
A friend of mine has a mountain bike with only one speed. He takes it everywhere, recently to Fruita, Colorado. What ratio would you choose, if you were limited to one?

My Schwinn beach cruiser had one speed and I used to ride it everywhere. When I moved from Newport Beach, CA to Bellevue, WA I added a 5-speed derailure rear sprocket and Sturmey-Archer drum brakes front and rear, and a genuine Schwinn springer front fork to it because we have hills here. I still rode it everywhere until I blew out a disk in my spine. It needs tires and I'm having trouble finding white wall balloon tires and tubes for it, but when I do I'm going to go riding again. It's a cool old bike.

A.K. Boomer
09-20-2007, 10:49 AM
A.K., on your bike with 7" cranks, you would need a 14" gear to make it not move at all. With your 34 tooth small chainring, you would need a 64 tooth back sprocket to get a 14 inch gear.

.

My 34 tooth is not my chainring, its on the back and is my largest gear on my freewheel, my 24 tooth is my small chainring and is up front, my bike did gridlock but it had two flats and was on carpet:p the rims size is an 11 1/2" radius, so this leverage decrease along with the added friction and the more i tugged did roll backwards but took some effort and was also skidding...

Im with you on all your deductions, its simple leverage -------- to keep things real simple say my cranks are 6 1/2" instead of 7" (in all reality my cranks are 175 mm) --- this is perfect cuz my tires pumped up are exactly a 13" radius, so yes whatever gear is up front times it by two for the rear, the way i look at it is try to imagine a lever right at where the tire meets the ground , pull on it and nothing will happen, this is the ratio you need to achieve for gridlock, A realated trick you can use --------- it works opposite for the other end of the tire --- No matter the wheels size of diameter -- be it a 1" wheel or a 55" wheel, when rolling foreward the top of the tire is always doing double speed of the vehicle, if your going 65mph, the top of your tire is doing 130mph,,,, this is how I single handedly get cars that wont run into my gargage even though its up hill at a fair angle, what do I do? I push the car in by useing the top of the tire, two to one ratio, my neighbors all think im a gorrilla:D

A.K. Boomer
09-20-2007, 10:52 AM
What ratio would you choose, if you were limited to one?

Please dont make me have to make that decision...

Swarf&Sparks
09-20-2007, 11:00 AM
"two to one ratio, my neighbors all think im a gorrilla:D"

parbuckling :D

A.K. Boomer
09-20-2007, 11:01 AM
I rode about every hill in SF, and never used lower than a 43, but ran into this link over on bike forums, Maybe my bike came from one of these areas:

http://deputy-dog.com/2007/09/18/the-steepest-streets-in-the-world/

couple of those streets I wouldn't even want to ride -down-
ken.

I have a question about gradient, I never really judged it by % so i get a little mixed up ,,, I seen in these pics of the steepest streets in the world that they were using percent and like 34 or 37 percent or something,

From what me and the people iv rode with can judge - im getting very close if not more than 45 degree's, is this 100 % gradient?

if gradient is judged by how much vert gain is achieved in a pre-determined horizontal length then 45 degree's should be 100% no?

Evan
09-20-2007, 11:54 AM
I think Evan will be getting invited to the Google staff dance he's obviously their no 1 customer:D:DAlistair green with envy:D

Whatever are you speaking about?

I created the wheel animation myself using JASC Animation Shop 3. I also frequently refer to Wolfram Mathworld, one of the best resources for mathematical information.

http://mathworld.wolfram.com/

dp
09-20-2007, 12:02 PM
Whatever are you speaking about?

I created the wheel animation myself using JASC Animation Shop 3. I also frequently refer to Wolfram Mathworld, one of the best resources for mathematical information.

http://mathworld.wolfram.com/

Wolfram has a lot of very interesting and innovative websites. Wolfram Tones is a hoot to experiment with.

dp
09-20-2007, 12:03 PM
I have a question about gradient, I never really judged it by % so i get a little mixed up

http://www.faqs.org/faqs/bicycles-faq/part4/section-39.html

kendall
09-20-2007, 02:01 PM
I have a question about gradient, I never really judged it by % so i get a little mixed up ,,, I seen in these pics of the steepest streets in the world that they were using percent and like 34 or 37 percent or something,

From what me and the people iv rode with can judge - im getting very close if not more than 45 degree's, is this 100 % gradient?

if gradient is judged by how much vert gain is achieved in a pre-determined horizontal length then 45 degree's should be 100% no?

pretty much rise to run like a roof, 12/12 would be a 45, it's however high you climb in relation to the horizontal distance converted to a percentage.

Back when I was younger, we used to race up the stairways in the transamerica pyramid and the hilton hotel in SF, get to the top of them and your legs would be jelly
For the guys that used to run with us hills were described as 'floors' 1st floor was an easy rise, with each increasing floor meaning steeper hills, till you got to 'top floor' which generally meant over 100% grade, for us that meant riding the drain channels next to the steeper stairways on some of the hills out there. (pre-mountain bike days)

Ken.

Evan
09-20-2007, 02:17 PM
Back when I was younger, we used to race up the stairways in the transamerica pyramid and the hilton hotel in SF, get to the top of them and your legs would be jelly

Reminds me of when I was a kid. Friend of mine and I once raced to the top of the Washington Monument. I think it has 999 steps but could be wrong.