Balancing on a Segway

[hodgepoj]

Posted - Sep 17 2002 : 7:43:54 PM
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> It should be noted that the weight is well above the axle. No doubt > getting the weight below the axle makes it much easier for the > Segway to keep a person upright. I wonder exactly how easy it would > be to balance on it without power. It would be a pretty shaky > pendulum, I think.

> Somewhere I read that in applications where the weight is above the > axle, the further away the weight is the easier it is to stabilize > it (As in balancing a stick on your palm. The longer the stick, the > slower the reflexes required to move under it.)

I just came across the dead thread above. Someone undoubtedly challenged the assertation on balance but I didn't see, in my cursory examination of the thread, an explanation of the physics of balancing.

Newton's laws apply to both linear and angular motion. He observed that in the absence of an applied force, all objects tend to retain their state of motion (what we now call velocity). If it's stationary, it will remain stationary. If it's moving, it will continue to move in a straight line at constant speed.

He further observed that when a force IS applied, the object's state of motion (velocity) will change, with the rate of change being proportional to, and in the same direction as, the applied force. This is expressed as "the rate of change of linear motion (now called acceleration) is equal to the applied force divided by the object's mass." In mathematical shorthand it is written "a = F/m."

We can apply this 2nd law to angular motion as "the rate of change of angular motion (called angular acceleration) is equal to the applied torque divided by the object's moment of inertia." (Any object's moment of inertia about a rotation point depends on how the object's mass is distributed about the point.)

The act of balancing an object on its end (a broomstick on your hand or you standing upright on a Segway) is simply a matter of applying the 2nd law for angular motion.

The torque being applied to the you/Segway combination that causes you to fall over is caused by the force of gravity pulling down on the combination's center of gravity. As long as you keep this center of gravity directly over the point of support (where the rubber meets the road), the torque will be zero because its moment arm is zero (any torque's moment arm about a point of rotation is the perpendicular distance from the rotation point to the extended line of force).

But as you begin to lose balance, the combination starts rotating about the point of contact, with the rate of rotation (angular acceleration) being proportional to the torque's moment arm about the point of contact.

To maintain your balance, you must quickly move the point of contact in the direction of rotation so it stays directly under your center of gravity. The speed with which you must move your point of contact depends on your angular acceleration away from the balanced position -- the less your angular acceleration, the easier it is to keep the point of balance under the center of gravity.

Since your angular acceleration is inversely proportional to your moment of inertia about the point of contact (remember that the applied gravitational force is constant), the greater the moment of inertia, the less the angular acceleration and the easier it is to stay balanced.

The farther from the point of contact your center of gravity is, the greater is your moment of inertia about that point.

The bottom line is, it's easier to keep your balance on a Segway if your center of gravity is higher. So tall drivers can balance easier than shorter drivers.




Dr. Paul O. Johnson
Senior Exhibit Developer
The Science Place
Dallas, Texas 75210

[n/a]

U seem to know what u are talking about Paul, way beyond my comprehension, but I can respond to your bottom line.

quote:The bottom line is, it's easier to keep your balance on a Segway if your center of gravity is higher. So tall drivers can balance easier than shorter drivers.

That could mean that we might eventually see pogostick versions of Segways and Segway ladders? What uses do u see such things?

[BruceWright]

Great Explanation Paul!

And that explains why it's easier to balance a broom on your hand than a pencil. I just thought the longer falling time gave you more mental time to react.

[GlideMaster]

Not saying it's impossible to balance a Segway without power, but I've tried it more times than I care to admit. No luck.

<center>REMEMBER:
Responsible Riders Ride Segway
and
Segway Riders Ride Responsibly

Segway, The Mind Changer</center>



quote:Originally posted by hodgepoj

Posted - Sep 17 2002 : 7:43:54 PM
---------------------------------------------------------------------
&gt; It should be noted that the weight is well above the axle. No doubt &gt; getting the weight below the axle makes it much easier for the &gt; Segway to keep a person upright. I wonder exactly how easy it would &gt; be to balance on it without power. It would be a pretty shaky &gt; pendulum, I think.

&gt; Somewhere I read that in applications where the weight is above the &gt; axle, the further away the weight is the easier it is to stabilize &gt; it (As in balancing a stick on your palm. The longer the stick, the &gt; slower the reflexes required to move under it.)

I just came across the dead thread above. Someone undoubtedly challenged the assertation on balance but I didn't see, in my cursory examination of the thread, an explanation of the physics of balancing.

Newton's laws apply to both linear and angular motion. He observed that in the absence of an applied force, all objects tend to retain their state of motion (what we now call velocity). If it's stationary, it will remain stationary. If it's moving, it will continue to move in a straight line at constant speed.

He further observed that when a force IS applied, the object's state of motion (velocity) will change, with the rate of change being proportional to, and in the same direction as, the applied force. This is expressed as "the rate of change of linear motion (now called acceleration) is equal to the applied force divided by the object's mass." In mathematical shorthand it is written "a = F/m."

We can apply this 2nd law to angular motion as "the rate of change of angular motion (called angular acceleration) is equal to the applied torque divided by the object's moment of inertia." (Any object's moment of inertia about a rotation point depends on how the object's mass is distributed about the point.)

The act of balancing an object on its end (a broomstick on your hand or you standing upright on a Segway) is simply a matter of applying the 2nd law for angular motion.

The torque being applied to the you/Segway combination that causes you to fall over is caused by the force of gravity pulling down on the combination's center of gravity. As long as you keep this center of gravity directly over the point of support (where the rubber meets the road), the torque will be zero because its moment arm is zero (any torque's moment arm about a point of rotation is the perpendicular distance from the rotation point to the extended line of force).

But as you begin to lose balance, the combination starts rotating about the point of contact, with the rate of rotation (angular acceleration) being proportional to the torque's moment arm about the point of contact.

To maintain your balance, you must quickly move the point of contact in the direction of rotation so it stays directly under your center of gravity. The speed with which you must move your point of contact depends on your angular acceleration away from the balanced position -- the less your angular acceleration, the easier it is to keep the point of balance under the center of gravity.

Since your angular acceleration is inversely proportional to your moment of inertia about the point of contact (remember that the applied gravitational force is constant), the greater the moment of inertia, the less the angular acceleration and the easier it is to stay balanced.

The farther from the point of contact your center of gravity is, the greater is your moment of inertia about that point.

The bottom line is, it's easier to keep your balance on a Segway if your center of gravity is higher. So tall drivers can balance easier than shorter drivers.




Dr. Paul O. Johnson
Senior Exhibit Developer
The Science Place
Dallas, Texas 75210

[hodgepoj]

[quote]Originally posted by weskifm

Not saying it's impossible to balance a Segway without power, but I've tried it more times than I care to admit. No luck.

[red][size=2][center][b]

I think it would be just about impossible, weskifm, if the wheels were free to roll. You might have more luck if you locked the wheels.

It's different maintaining the balance of a rod supported on your hand than it is when your body is the rod and is supported below you. In the first case, you have to quickly shift the support point to keep it under the rod's CG; in the second case, you must shift your CG to keep it over the support point.

It's much easier to balance the first way.


Dr. Paul O. Johnson
Senior Exhibit Developer
The Science Place
Dallas, Texas 75210

[GlideMaster]

Yes Hodgepoj you are right it would be easier to balance if the wheels were locked.

<center>REMEMBER:
Responsible Riders Ride Segway
and
Segway Riders Ride Responsibly

Segway, The Mind Changer</center>

[hodgepoj]

quote:Originally posted by Lawrence

U seem to know what u are talking about Paul, way beyond my comprehension, but I can respond to your bottom line.

That could mean that we might eventually see pogostick versions of Segways and Segway ladders? What uses do u see such things?


Yes, Segway could well offer the world's most expensive pogo stick or ladder, Lawrence. If fact, they could address any device that depends on balance -- including tightrope walking, stilts, unicycles, and crossing a stream by stepping on stones.

I'm grateful that you think I might know what I'm talking about. A lot of my compatriots don't share your feeling. My brief resume:

BS in math, 1950, MS in physics, 1952, PhD in physics, 1964.
5 years as engineering physicist in defense industry.
30 years as system development manager with Central Intelligence Agency.
10 years teaching physics and physical science at college level.
2 years as exhibit developer at The Science Place hands-on museum.


Dr. Paul O. Johnson
Senior Exhibit Developer
The Science Place
Dallas, Texas 75210

[n/a]

quote:Yes, Segway could well offer the world's most expensive pogo stick or ladder, Lawrence. If fact, they could address any device that depends on balance -- including tightrope walking, stilts, unicycles, and crossing a stream by stepping on stones.


It is an honour to have a man of your caliber here Paul. We Ginger/Segway fans have been doing a lot of speculating about the potential applications of Kamen's DS technology.
I would like to hear more from u what u would consider the most promising applications apart from what we have already seen. The ones u mentioned so far, apart from unicycles do not seem particularly usefull.

[Blinky]

Weskifm writes,
quote:Not saying it's impossible to balance a Segway without power, but I've tried it more times than I care to admit. No luck.
What made you think the Segway would work with the power off? I just thought that was funny Wesk,..

[Blinky]

hodgepoj writes,
quote:BS in math, 1950, MS in physics, 1952, PhD in physics, 1964.
5 years as engineering physicist in defense industry.
30 years as system development manager with Central Intelligence Agency.
10 years teaching physics and physical science at college level.
2 years as exhibit developer at The Science Place hands-on museum.
This is nearly twice as many years as I have been alive, looking forward to hearing and learning things from you Paul.

[hodgepoj]

quote:Originally posted by Lawrence

It is an honour to have a man of your caliber here Paul. We Ginger/Segway fans have been doing a lot of speculating about the potential applications of Kamen's DS technology.
I would like to hear more from u what u would consider the most promising applications apart from what we have already seen. The ones u mentioned so far, apart from unicycles do not seem particularly usefull.


Thank you, Lawrence. I appreciate your kind words. Now I must disappoint you by admitting that I am not familiar with Kamen's DS technology. I know that he invented the HT but where can I read about this DS technology? And while we're at it, what the hay is Ginger/Segway?

Dr. Paul O. Johnson
Senior Exhibit Developer
The Science Place
Dallas, Texas 75210

[Brooster]

Dr. J, you may remember that almost a couple of years ago now, a book proposal was leaked ... about a new invention by Dean Kamen that would sweep over and change the world. Referred to alternately as "Ginger" and "IT," it ignited a firestorm of speculation on the Web and in other media.

The book will be released this coming May 23rd. Titled "Codename: Ginger," it's available for pre-order on Amazon.com. The product, as we now know, is Segway.

Edit: Paul, that's quite a CV you have there. With your contacts, I'm a bit surprised that you asked about Ginger.

Brooster
Northwestern University Class of 2000

[Blinky]

quote:The book will be released this coming May 23rd. Titled "Codename: Ginger," it's available for pre-order on Amazon.com. The product, as we now know, is Segway.
A book that seems to have been taking forever to write, LETS GET IT TOGETHER PEOPLE!

[hodgepoj]

quote:Originally posted by Brooster


The book will be released this coming May 23rd. Titled "Codename: Ginger," it's available for pre-order on Amazon.com. The product, as we now know, is Segway.

Edit: Paul, that's quite a CV you have there. With your contacts, I'm a bit surprised that you asked about Ginger.

So now I know that Ginger was the codename for the HT. Thank you.

My next question is, What is this CV that I have? And why should I have known about Ginger?


Dr. Paul O. Johnson
Senior Exhibit Developer
The Science Place
Dallas, Texas 75210

[charmed]

CV-Curriculum Vitae-Resume.

Are you serious that you had not heard of Ginger or 'IT' during the pre-reveal hype/hysteria? Wow. It was all over the news, 60 minutes, papers, magazines....starting in Jan. 2001 up through the reveal last December.

I'm impressed!

[hodgepoj]

quote:Originally posted by charmed

CV-Curriculum Vitae-Resume.


Since it is obviously Latin, I looked up curriculum vitae in "Amo, Amas, Amat and More - How to Use Latin to Your Own Advantage and to the Astonishment of Others," one of several books on correct word usage on my shelf.

It said, "Using the Latin expression instead of the mundane, albeit once-glamorous, word Resume avoids association with the world of commerce and pegs the user as an academic." Well, I've been in both worlds and even the universities where I taught asked for my resume, not my CV.

quote:
Are you serious that you had not heard of Ginger or 'IT' during the pre-reveal hype/hysteria? Wow. It was all over the news, 60 minutes, papers, magazines....starting in Jan. 2001 up through the reveal last December.

I'm impressed!


Sure, I recall reading some of the IT hype but I don't recall ever reading about Ginger. I tend to avoid all advertising hype, especially when there is little or no indication of a scientific or engineering breakthrough.

I'm not a hermit but I have been called a curmudgeon.

Are you impressed good or bad?

Dr. Paul O. Johnson
Senior Exhibit Developer
The Science Place
Dallas, Texas 75210