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Is a scooter as stable in a straight line as a motorcycle?

My thinking is that the lower rotating masses of the smaller wheels means that it's not. But I don't have a motorcycle, so can't make a direct comparison.
But then there's center of gravity.

Just curious...
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I'm not an engineer but all I've read says the larger diameter wheels on motorcycles are more stabile at higher speeds due to the rotating mass (gyro effect). Other advantages of bigger wheels are pothole survival and, I believe, more miles per tire.
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I, on the other hand, am an engineer and the answer is...it depends.

The mass of the wheel has no direct impact. The moment, however, does, and the mass is one factor that goes into the moment (the other is how that mass is distributed around the axis). All things being equal, a large diameter but small sidewall tire can have a greater moment than an equally large but bigger sidewall tire, because moment also involves how much of the mass is furthest away from the axis (that's why you don't see bikes with solid wheels like a car; putting mass close to the axis adds useless weight but not useful moment).

All things being equal - same sidewall size, same tire weight per unit volume - the moment is approximately equal to mass times the square of the radius. Double the diameter of the wheel and you quadruple the moment. So a bigger wheel has four times the moment of a smaller wheel.

BUT, the force that's keeping the bike up is the moment times the centripetal acceleration, which is (v^2)/r. Obviously v stays the same regardless of the size of the wheel (if you're going 10mph the outside of the wheel is going 10mph no matter what it's size is). When you double the diameter of the wheel, you cut the centripetal acceleration in half. Net result, four times the moment times half the acceleration equals twice the stabilizing force.

So, again stressing "all other things being equal," a wheel twice as big provides twice the stabilizing force. But that's only true of a bike that has just flown off the end of a ramp and is airborne. The majority of the stabilization comes from the contact patch (which is mostly a function of tire width and inflation) and especially rake - a cruiser and a sports bike can have the same tires but they sure do have different stability profiles because of the different rakes. I believe I recall that rake itself has several components having to do with not only the angle of the front fork but the fork's placement relative to the handlebar turning axis, but I'm fuzzy on that.

The center of gravity thing is misleading, because it is important to have a low center of gravity (small wheels win) but it's also important to have a center of gravity that is a smaller percentage of the radius (big wheels win - a true sports car with a center of gravity below the axles cannot flip over).

As Raybur correctly points out, a larger wheel also handles all but the largest potholes better by riding over them rather than through them, and handles changes in road surfaces better by smoothly leveraging itself over the obstacle rather than bouncing over it - to picture this just imaging a tire a hundred feet tall rolling over a pothole.

Isn't it pretty amazing that people can stay upright on rollerblade wheels?
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rjeffb wrote:
I, on the other hand, am an engineer and the answer is...it depends.



All things being equal - same sidewall size, same tire weight per unit volume - the moment is approximately equal to mass times the square of the radius. Double the diameter of the wheel and you quadruple the moment. So a bigger wheel has four times the moment of a smaller wheel.
Interesting reading for someone who hasn't had much need to remember his limited physics education in the last 30 years or so. Correct me if I'm wrong that your simplifying the situation for our ease of understanding by "All things being equal" kept the mass of the wheel the same while doubling the radius which is doubled for the moment. Am I correct that the outer rim mass would also double? So even if you double the diameter without increasing the width the moment would go up by approximately 8 times?
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I bow to heinlein's very sharp eye.

Yes, I assumed that the smaller and larger wheels both had similarly sized sidewalls (to continue to use the same simplified formula for moment) but whose masses magically remained the same. In actuality if the two tires were the same construction except for different diameters, the weight of the tire would double and so the moment of inertia would quadruple. I proportional to (V^2)/2R x 2M((2R)^2) = V*V*2*M*2*R*2*R/2*R = V*V*M*4*R; the original I was (V*V/R) * M*R*R = V*V*M*R*R/R = V*V*M*R so the difference is

V*V*M*4*R
______________
V*V*M*R = 4!

(Sorry for the longhand but whenever I post algebra somebody challenges me on it).



If the tire was literally doubled in size - double the diameter, double the sidewall height, double the width, double the thickness of the rubber - then its mass would increase eightfold (2x2x2) and its resulting stability would increase something less than 16 times ("something less" because the mass would be distributed slightly closer to the axis and so the Moment would be affected).

Of course, there is most definitely such a thing as too stable - you also want to make turns once in a while...

P.S. why don't Modern Vespa bbcodes support superscript [/sup] and subscript [/sub]?
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SU-Mac-Dude: Aren't you glad you asked? I lost them the moment they started talking about the moment! Wha? emoticon
I was fine with the simple geometry of the rake and trail (well explained in Prof. MC) but my head exploded after that.
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I hope there won't be a pop quiz on this.
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Yes - "trail," that was the other component I was trying to remember, thanks.

Here's one to make your head explode a second time - how on Earth DOES a rollerblader stay upright with such a tiny Moment of Inertia? I find that fascinating.
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re: rollerblade: What makes that different from ice skates? My uneducated guess is the ANKLES keep them upright (which is why I suck at ice skating). Crying or Very sad emoticon
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Re. Ice skates: but in my experience it's about as difficult to stand still on ice skates as it is to actually skate, while standing still on rollerbaldes is damned near impossible. Doesn't that suggest that there's some sort of Moment of Inertia at play?

>I hope there won't be a pop quiz on this

Well, a pop quiz on stability seems a little off-topic but here goes: what was Madonna's longest relationship? Razz emoticon
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Well, there you go again! Talking about moments! I've had a few good ones and a few bad ones but most have been forgotten! Clown emoticon
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To take this back to the original question - yes, motorcycles will generally have more high speed stability than small wheeled scooters. Likewise true that larger wheeled scooters will generally have increased high speed stability compared to small wheeled scooters. That is not the end of the discussion, of course. Length of the wheelbase, fork rake, suspension, and many other factors affect handling and aspects of stability. Smaller wheeled scooters are well known for having very quick steering which can be an advantage in city riding. Also, heavy bikes with a high center of gravity (such as many motorcycles) will feel unstable at low speeds.
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And # of wheels?
Would not the number of wheels impact stability as well? Our 2 small front wheels would perhaps more than make up for one larger front wheel...
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I think that's what I like most about Piaggio - the people that drive them.
This reminds me so much of an early computer user group meeting.

Anyways...

I forgot all about rake and trail and how it effects stability.
The reason I was asking is to see if there was a correlation.

But I think the short of it is that a motorcycle with 16" or greater wheels is going to be relatively more stable in a straight line.
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welcha wrote:
And # of wheels?
Well, if you go through the calculation that rjeffb offers, two small diameter wheels do not provide the same stabilizing force as one large diameter wheel. But that is not the point of the two front wheels on the MP3, of course. The advantage of the MP3 front wheels is two patches of rubber on the road. That is to say, much increased road holding ability while cornering.
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as off-topic as it gets
(I just made this so I get all the credit or blame)

What property do physicists use to describe an 80-year-old acrobat?

A Senior Moment.
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Thank you, RJeffb
Dooglas recognized that I obviously did not go back and reference the previous formulas etcetera, and simply pulled it from a dark space directly behind me. Rjeffb was kind enough to draw attention away from my failings with his humor. Thanks for that.

Now back to the regularly scheduled topic already in progress...
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Wow... maths formulas... i thought i don't have to see those again.. Razz emoticon
but in general, having bigger wheels does have its advantage...

having said that, there are some bikes with big wheels by crappy handling and some sweet one despite smaller wheels... so end of the day it depends on the overall setup like what guys have spoken here... rake angle, wheelbase... etc...
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rjeffb wrote:
I, on the other hand, am an engineer and the answer is...it depends.

The mass of the wheel has no direct impact. The moment, however, does, and the mass is one factor that goes into the moment (the other is how that mass is distributed around the axis). All things being equal, a large diameter but small sidewall tire can have a greater moment than an equally large but bigger sidewall tire, because moment also involves how much of the mass is furthest away from the axis (that's why you don't see bikes with solid wheels like a car; putting mass close to the axis adds useless weight but not useful moment).

All things being equal - same sidewall size, same tire weight per unit volume - the moment is approximately equal to mass times the square of the radius. Double the diameter of the wheel and you quadruple the moment. So a bigger wheel has four times the moment of a smaller wheel.

BUT, the force that's keeping the bike up is the moment times the centripetal acceleration, which is (v^2)/r. Obviously v stays the same regardless of the size of the wheel (if you're going 10mph the outside of the wheel is going 10mph no matter what it's size is). When you double the diameter of the wheel, you cut the centripetal acceleration in half. Net result, four times the moment times half the acceleration equals twice the stabilizing force.

So, again stressing "all other things being equal," a wheel twice as big provides twice the stabilizing force. But that's only true of a bike that has just flown off the end of a ramp and is airborne. The majority of the stabilization comes from the contact patch (which is mostly a function of tire width and inflation) and especially rake - a cruiser and a sports bike can have the same tires but they sure do have different stability profiles because of the different rakes. I believe I recall that rake itself has several components having to do with not only the angle of the front fork but the fork's placement relative to the handlebar turning axis, but I'm fuzzy on that.

The center of gravity thing is misleading, because it is important to have a low center of gravity (small wheels win) but it's also important to have a center of gravity that is a smaller percentage of the radius (big wheels win - a true sports car with a center of gravity below the axles cannot flip over).

As Raybur correctly points out, a larger wheel also handles all but the largest potholes better by riding over them rather than through them, and handles changes in road surfaces better by smoothly leveraging itself over the obstacle rather than bouncing over it - to picture this just imaging a tire a hundred feet tall rolling over a pothole.

Isn't it pretty amazing that people can stay upright on rollerblade wheels?
Thanks for the explanation. Just curious, though: did you really mean "centripetal" force, or should it be "centrifugal" force?
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Centripetal force is the correct term.
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Sidecutter wrote:
Centripetal force is the correct term.
Ah, yes. Thanks.
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rjeffb wrote:
Re. Ice skates: but in my experience it's about as difficult to stand still on ice skates as it is to actually skate, while standing still on rollerbaldes is damned near impossible. Doesn't that suggest that there's some sort of Moment of Inertia at play?
Don't know much about the Moment of Inertia but I can tell you rollerblades get more stable as you go faster, until a point. I am comfortable on blades till about 30mph. Above that, they start to get a bit shaky.
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To totally trash any pretense of staying on topic: there is no such thing as centrifugal force. Centrifugal force is an illusionary, non-existant force (although one with very real consequences). When you make a turn in a car, it appears that the car is pushing against you (centrifugal illusionary force). In reality, it is you who is pushing against the car (very real centripetal force) as your body attempts to track a straight line and the car prevents you from doing so.

A similar illusion is Coriolis force. Stand in the middle of a merry-go-round and throw a ball straight out. You will "experience" Coriliolis force (more accurately described as Coriolis effect) as it appears to force the ball to curve away in the direction opposite to the ride's rotation. An observer standing outside on the ground will see the ball do exactly what it must, which is track a perfectly straight line. But that illusionary, non-existant "force" is also responsible for most of the weather on our planet.
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rjeffb wrote:
To totally trash any pretense of staying on topic: there is no such thing as centrifugal force. Centrifugal force is an illusionary, non-existant force (although one with very real consequences). When you make a turn in a car, it appears that the car is pushing against you (centrifugal illusionary force). In reality, it is you who is pushing against the car (very real centripetal force) as your body attempts to track a straight line and the car prevents you from doing so.

A similar illusion is Coriolis force. Stand in the middle of a merry-go-round and throw a ball straight out. You will "experience" Coriliolis force (more accurately described as Coriolis effect) as it appears to force the ball to curve away in the direction opposite to the ride's rotation. An observer standing outside on the ground will see the ball do exactly what it must, which is track a perfectly straight line. But that illusionary, non-existant "force" is also responsible for most of the weather on our planet.
And gravity isn't a force either.

I wonder if "The Force" is a force.
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>And gravity isn't a force either.

That seemingly simple statement has so many nuances that it borders on the metaphysical. Wanna start a fight? Say that in a room full of physicists.

(Some of whom are still looking for "gravitrons" after more than 40 years and $10 billion worth of trying and over 100 years after Einstein said, in effect, that there ain't no such thing...)
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rjeffb wrote:
>
(Some of whom are still looking for "gravitrons" after more than 40 years and $10 billion worth of trying and over 100 years after Einstein said, in effect, that there ain't no such thing...)
Scientific careers are made on trying to prove Einstein wrong. In fact, isn't that the definition of a scientist - working hard to disprove what the last guy said?
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Point taken. It's nevertheless interesting that a century after general relativity, we literally still haven't agreed on what makes an MP3 fall over.

Oh wait a minute, it's that tilt-lock button. Nobel Prize!
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In my most recent couple of drops I have yet so see a gravitron.
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rjeffb wrote:
>And gravity isn't a force either.

That seemingly simple statement has so many nuances that it borders on the metaphysical. Wanna start a fight? Say that in a room full of physicists.

(Some of whom are still looking for "gravitrons" after more than 40 years and $10 billion worth of trying and over 100 years after Einstein said, in effect, that there ain't no such thing...)
Actually, there is no such thing as gravity...





...just an unnamed force with the identical properties.



Oh, and it's graviton - like proton or tachyon.
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I rode up beside a graviton once. Not so interesting, so just pulled on past... Razz emoticon
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