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# CALCULUS and BICYCLES.

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# CALCULUS and BICYCLES.

05-26-09, 02:36 PM
#1
mynameisryan
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CALCULUS and BICYCLES.

hi i am doing a calculus project, and I am planning on doing it on bicycle-related subjects, however I am finding it difficult to find such information on the internet. Therefore, I appeal to you to inform me of anything calculus-related you know bikes.
05-26-09, 05:21 PM
#2
HillRider
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This would apply to any vehicle but you could calculate the distance the bicycle traveled by taking veolcity (actually speed but close enough) data at fixed time intervals and integrate under the time/speed curve for distance.

How about the path a point on the tire traces as it rolls along on a hilly road?

Measure the pressure on a pedal at various points in its rotation and it's rpm and integrate for power input.
05-26-09, 05:28 PM
#3
jccaclimber
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Ryan,
You should be able to find ideas here:
http://lmgtfy.com/?q=bicycle+calculus+project
Also, saying "calculus" is like saying "car" and wondering why you get everything from a Porche to a Hundai. You could do something easy like look at the height change of a bicycle in relation to the number of molecules of air you put into the tires from flat to say, 150psi, or you could go in deeper and look at steering response. I'm guessing you're in high school, so something closer to the former would probably be good. Try searching as well?

As an additional one, the plotted path of the rear wheel in relation to front wheel steering input usually falls under calc. You would need some sort of goal to make it not a simple geometry problem, such as finding a non strait path where the front and rear wheels follow a strait line. The up side of that is that problem is VERY well documented online.
05-26-09, 06:06 PM
#4
z415
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What calc are you in? Depending on the calc sequence you are in, you can do different things - as jcca hinted at above.
05-26-09, 06:26 PM
#5
operator
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Originally Posted by mynameisryan
hi i am doing a calculus project, and I am planning on doing it on bicycle-related subjects, however I am finding it difficult to find such information on the internet. Therefore, I appeal to you to inform me of anything calculus-related you know bikes.
Yeah, let's just get random people on the internet to do your homework for you.
05-26-09, 06:47 PM
#6
silver_ghost
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Yep, that's almost as goofy as making fun of highschool students on the internet.
05-26-09, 07:02 PM
#7
DannoXYZ
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Yeah, take Hillrider's suggestion. Take power = (force * distance)/time and record force with power-meter. Use an accurate clock and record time and integrate to get resultant power. Re-calculate for different gears (distance your foot moves relative to road-distance traveled).

Of calculate power-required for various speeds given cross sectional area and coefficient of drag.
05-27-09, 01:33 AM
#8
sunburst
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There's a fantastic thread in the road forum about the physics of "why fat people go downhill faster" or something like that (it's fun to read the various theories being thrown out). And if there's physics involved, you can use calculus to solve and/or explain it, especially with things like acceleration.
05-27-09, 06:34 AM
#9
nitropowered
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spoke length calculation
05-27-09, 06:38 AM
#10
HillRider
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Originally Posted by nitropowered
spoke length calculation
That's just a geometry/trig. problem, although a messy one.
05-27-09, 08:31 AM
#11
jack002
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Buy a wal mart bike and take it to the top of a really tall building, throw it out the window, measure the terminal velocity as it hits the pavement below.
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05-27-09, 11:41 AM
#12
Booger1
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You could calculate excape velocity/trajectory to the Moon on your bicycle.....

Big people go down hills faster than small people for the same reason 747's fall out of the sky faster than ping-pong balls...gravity.

Last edited by Booger1; 05-27-09 at 11:45 AM.
05-27-09, 11:49 AM
#13
DannoXYZ
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Yeah, the force of gravity depends upon the mass. And the 747 has A LOT higher mass as well as mass-to-air-drag ratio than the ping-pong ball... Imagine Galileo dropping a 747 versus ping-pong ball off the leaning tower... heh, heh...

Hey, that's another good calculus model. Compute terminal-velocity as a function mass-to-air-drag. Maybe model a piece of plywood falling on edge versus falling flat. Skydivers know all about this too well..
05-27-09, 12:19 PM
#14
merckx_rider
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differences in tires/wheels rolling resistance and air pressure, width, weight and diameters....
05-27-09, 12:36 PM
#15
exRunner
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You could prove that wheel weight makes no difference on bike performance (Lite wheels actually increases power requirements).
04-22-19, 09:35 PM
#16
triggerhappy403
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Yes ��
04-23-19, 07:25 AM
#17
JanMM
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I wonder how the calculus project turned out.............
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RANS V3 Ti, RANS V-Rex, RANS Screamer
04-23-19, 07:44 AM
#18
DrIsotope
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NecroPost® Report: 3,618 days

That's pretty good. Some points deducted for it being the resurrector's first post (search function still works!) but some added back on as the OP has not been here for 3,577 days, for an overall B+ effort.
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04-23-19, 08:04 AM
#19
CliffordK
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Originally Posted by DrIsotope
NecroPost® Report: 3,618 days

That's pretty good. Some points deducted for it being the resurrector's first post (search function still works!) but some added back on as the OP has not been here for 3,577 days, for an overall B+ effort.
So, what is the probability that a post will be bumped 10 years after the last reply?

Ok, more of a statistics issue, but many of the statistics equations have a strong calculus basis.
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04-23-19, 08:19 AM
#20
DrIsotope
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Ten years to the day seems unlikely, unless it was done intentionally. New posts 7-9 years (in the 3,000 day neighborhood) after the last thread activity are fairly common.

Posts in General Cycling Discussion go back to late 2002 (5,994 days) and those in Road Cycling to mid-2000 (6,927 days) so there's certainly room for some real necros.

BF gets new members every day, but loses active participants nearly as quickly. Of the total pool of registered members, around 98% are inactive. New folks use the search and never look at the dates.
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04-23-19, 08:26 AM
#21
WizardOfBoz
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Originally Posted by CliffordK
So, what is the probability that a post will be bumped 10 years after the last reply?

Ok, more of a statistics issue, but many of the statistics equations have a strong calculus basis.
Now that would be a good stats problem.

BTW, for those that are interested, the analysis of bicycle stability is pretty complex. A good overview is in Bicycling Science. The 2nd edition, imho, may be more clear than the 3rd, but both are good.
04-23-19, 09:17 AM
#22
CliffordK
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Originally Posted by WizardOfBoz
Now that would be a good stats problem.

BTW, for those that are interested, the analysis of bicycle stability is pretty complex. A good overview is in Bicycling Science. The 2nd edition, imho, may be more clear than the 3rd, but both are good.
Mmmm...

It would be interesting to look at a bunch of forces contributing to bicycle ride and stability.

HT angle,
Trail
Rake
Gyroscope Effect
Counter-steering

Etc. Perhaps one could answer the question once and for all, of how to ride a bike.

Over the last 10 years, since this thread was started, there has been a huge interest in materials science and modelling of a bicycle.

So, to a large extent, we've seen an end to round-tube bicycle frames, and everything is engineered tubing.

Big Tubes, Small Tubes, Fat Tubes, Skinny Tubes. Tapered Tubes, etc. In materials design, one not only has the bike in normal riding conditions, but extreme conditions. Running into parked cars (good acceleration problem), hopping up onto, and down off of curbs, etc.

Fatigue, and aging of components?
04-23-19, 09:45 AM
#23
WizardOfBoz
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Clifford, I think you'd like Bicycling Science. You are thinking of all the things Bicycling Science discusses. Amazon link here.

I sure hope that the math doesn't prove riding a bike is physically impossible.

I'm an engineer, so I look at sensitivity. That is, for commuting and shopping and bopping around town, how obsolete are round tubes? I have a fancy CF road bike, but that would not be my choice for a durable commuter. And engineered tubing requires molds, resin mixing systems with good QC, etc. Still easier to build a bike with round tubes. In other words the performance differential for bopping around service may not justify the 14 lb CF frame with DI2.

Last edited by WizardOfBoz; 04-23-19 at 09:48 AM.
04-23-19, 10:08 AM
#24
wphamilton
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HS stuff, just do something with acceleration equations. Or energy/power climbing a hill if you want to make it really easy. More advanced, try a line integral of the actual path that a bike takes, relate it to the period of inverted pendulum if you want a challenge.

Arg, tricked by a zombie!
04-23-19, 10:28 AM
#25
CliffordK
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[QUOTE=WizardOfBoz;20897071]Clifford, I think you'd like Bicycling Science. You are thinking of all the things Bicycling Science discusses. Amazon link here.[/url]

I think I have that book, but only read part of it. I was interested in an article about pedal dynamics and pulling up.

I should already dig it out again.

Originally Posted by WizardOfBoz
I sure hope that the math doesn't prove riding a bike is physically impossible.
You mean like bees can't fly?

https://www.snopes.com/fact-check/bumblebees-cant-fly/

Actually, the Snopes article is interesting. Apparently bumblebees aren't fixed wing aircraft.