Moments of Inertia: Differences Between Wheelsets

[RollinOn27s]

So based upon the results published in the most recent Tour magazine wheeltest, I got to thinking about some of the various wheelsets that I've seen. One of the things that struck me as funny was the insistence of some people to use only extremely low profile wheels such as Zipp 202's for climbing purposes.

Now, after taking into account how the wheel is set up, with nearly all of the rotational weight at the extreme edge of the wheel, I would think that this would have a similar moment of inertia to a heavier wheel such as a 303. The difference being that while the 303 has a slightly heavier rim weight, the mass is also pushed more towards the center of the wheel (due to the structure of the rim, nipples closer to center of rotation, and shorter/lighter spokes), in turn reducing the MOI.

If this is logical, and two wheelsets are very close in weight with the same tires/spokes/nipples/hubs, wouldn't it make more sense to go with a wheel like the 303 over the 202? Not only very light, and more aero, but perhaps even possessing a lower moment of inertia?

Feedback appreciated, physicists.

[ProParadox]

Yes, it would.

The benefit of a wheelset like the 202, is just that: it's lighter.

[RollinOn27s]

But, and pardon my blasphemy with regards to this forum, what is the point of wheels that MIGHT put you at a disadvantage, all factors considered, when your bike is at the 6.8kg mark already?

[yourdaguy]

The 303's have more weight and their overall wheel inertia would be higher also. The amount of weight that is closer to the center is not significant in the overall scheme of things.

[STARNUT]

The 303's have more weight and their overall wheel inertia would be higher also. The amount of weight that is closer to the center is not significant in the overall scheme of things.

Thats what I was going to say, but after thinking about it, I think what the orginal post was asking was does the weight of the nipples and extra spoke legnth on the 202 negate the supposed MI advantage over the 303 because the spokes and the nipples are closer to the hubs? Does the extra weight of the 303 overcome the extra or outside weight of the nipple and spokes of the 202?

Further more can you get away with 2 less spokes front and rear on a 303 while maintaing the same stiffness of the 202 and getting rid of that much more weight to add to the MI of a 303?

Interesting question.............where are all the engineer guys with the big calculators.

Starnut

EDIT: How do you even meausure MI. I know what the units are but how do they get it?

[RollinOn27s]

Examples:
(Important figures in Bold)

Fulcrum Racing Speed 5.1/12.1/23.7 102 55/42 1350/no limit (recommendation 82kg)

FRM FL-R 23 SD Aerolight 5.3/12.6/24.6 105 53/32 1335/no limit (recommendation 80kg)

The first wheel is heavier, yet has a lower MOI.

Edit: These do not have descriptions of the total componentry of each wheel, so this must be taken with a grain of salt. Merely shows that a lighter wheel is not necessarily easier to lug up a hill.

[ProParadox]

Examples:
(Important figures in Bold)

Fulcrum Racing Speed 5.1/12.1/23.7 102 55/42 1350/no limit (recommendation 82kg)

FRM FL-R 23 SD Aerolight 5.3/12.6/24.6 105 53/32 1335/no limit (recommendation 80kg)

The first wheel is heavier, yet has a lower MOI.

Edit: These do not have descriptions of the total componentry of each wheel, so this must be taken with a grain of salt. Merely shows that a lighter wheel is not necessarily easier to lug up a hill.

A lower MOI never necessarily meant it was easier to lug up a hill. You could have a 20000g front wheel with 19999g completely in the axle. The MOI would be lower, but dragging the thing up hill would still be harder.

[username]

Examples:
(Important figures in Bold)

Fulcrum Racing Speed 5.1/12.1/23.7 102 55/42 1350/no limit (recommendation 82kg)

FRM FL-R 23 SD Aerolight 5.3/12.6/24.6 105 53/32 1335/no limit (recommendation 80kg)

The first wheel is heavier, yet has a lower MOI.

Edit: These do not have descriptions of the total componentry of each wheel, so this must be taken with a grain of salt. Merely shows that a lighter wheel is not necessarily easier to lug up a hill.

A lower MOI never necessarily meant it was easier to lug up a hill. You could have a 20000g front wheel with 19999g completely in the axle. The MOI would be lower, but dragging the thing up hill would still be harder.

Yeah, I think he's missing the point that it still makes for the complete weight of the setup.

[STARNUT]

Examples:
(Important figures in Bold)

Fulcrum Racing Speed 5.1/12.1/23.7 102 55/42 1350/no limit (recommendation 82kg)

FRM FL-R 23 SD Aerolight 5.3/12.6/24.6 105 53/32 1335/no limit (recommendation 80kg)

The first wheel is heavier, yet has a lower MOI.

Edit: These do not have descriptions of the total componentry of each wheel, so this must be taken with a grain of salt. Merely shows that a lighter wheel is not necessarily easier to lug up a hill.

A lower MOI never necessarily meant it was easier to lug up a hill. You could have a 20000g front wheel with 19999g completely in the axle. The MOI would be lower, but dragging the thing up hill would still be harder.

True, but I think your mixing theorys or formulas or something here. Where are the engineers. I took some of this in college, but only to satisify a science credit. I'm an economist and business guy.

I think the 20000g wheel with 19999g at the hub refers to the amount of work needed to move the object up the hill. Like horsepower in physics 101. I found a bunch of links for MI and a bunch of formulas that are hib-e-dibity to me.

check it out:
http://hyperphysics.phy-astr.gsu.edu/HBASE/mi.html

I think MI refers to the amount of resistance a body gives to rotating around its axis. High MI=more resistance to rotating around the axis and a Low MI=less resistance to rotating around its axis.

Think about the skinny figure skater chicks. At the beginning of the spin, the skater extends her arms and the rotation speed is slow. As the skater pulls her arms in closer to her body, the speed of the spin greatly increases. Thus when the arms are extended, the skater’s Moment of Inertia is very high, and the result is a slower spin because the high MOI of the skater is resisting the speed of rotation.

This would explain why a disk is fast, its easy to keep going, less resistance to rotating around an axis. But does not explain why Eddy used weighted wheels in Mexico City to set his hour record. They were hard to get going but acted like cruse control once at speed.

Starnut

[alienator]

I think MI refers to the amount of resistance a body gives to rotating around its axis. High MI=more resistance to rotating around the axis and a Low MI=less resistance to rotating around its axis.
Starnut

No, inertia is a measure of a body's resistance to a change in it's motion. Example: a wheel with a relatively high moment of inertia requires more torque to spin up, but it also requires more torque to spin down.

[STARNUT]

I think MI refers to the amount of resistance a body gives to rotating around its axis. High MI=more resistance to rotating around the axis and a Low MI=less resistance to rotating around its axis.
Starnut

No, inertia is a measure of a body's resistance to a change in it's motion. Example: a wheel with a relatively high moment of inertia requires more torque to spin up, but it also requires more torque to spin down.

True, but Moment of Inertia is different.

http://en.wikipedia.org/wiki/Moment_of_inertia
Moment of inertia, also called mass moment of inertia and, sometimes, the angular mass, (SI unit kilogram metre squared kg m2) quantifies the rotational inertia of an object, i.e. its inertia with respect to rotational motion, in a manner somewhat analogous to how mass quantifies the inertia of an object with respect to translational motion. The symbols I and sometimes J are usually used to refer to the moment of inertia.

The moment of inertia of an object about a given axis describes how difficult it is to induce an angular rotation of the object about that axis. For example, consider two wheels of the same mass, one large and one small in radius. The smaller wheel is easier to accelerate into spinning fast, because its mass is concentrated close to the axis of rotation. Conversely, the larger wheel takes more effort to accelerate into spinning fast, because its mass is spread out further from the axis of rotation. Quantitatively, the smaller wheel has a smaller moment of inertia, whereas the larger wheel has a larger moment of inertia.

The moment of inertia has two forms, a scalar form I (used when the axis of rotation is known) and a more general tensor form that does not require knowing the axis of rotation. The scalar form I for any axis can be calculated from the tensor form using the double dot product




where the summations are over the three Cartesian coordinates. The scalar moment of inertia I is often called simply the "moment of inertia".

The moment of inertia is sometimes called the mass moment of inertia (especially by mechanical engineers) to avoid confusion with the second moment of area, which is sometimes called the moment of inertia (especially by structural engineers) and denoted by the same symbol I.

http://en.wikipedia.org/wiki/Inertia
The principle of inertia is one of the fundamental laws of classical physics which are used to describe the motion of matter and how it is affected by applied forces. The concept of inertia is today most commonly defined using Isaac Newton's First Law of Motion, which states:


Every body perseveres in its state of being at rest or of moving uniformly straight ahead, except insofar as it is compelled to change its state by forces impressed. [Cohen & Whitman 1999 translation]


The description of inertia presented by Newton's law is still considered the standard for classical physics. However, it has also been refined and expanded over time to reflect developments in understanding of relativity and quantum physics which have led to somewhat different (and more mathematical) interpretations in some of those fields.

[alienator]

True, but Moment of Inertia is different.

Gee, no kidding? Thanks for the lesson, Mr. Wizard.......I wondered when my physics degree was going to come in handy. I guess I should have skipped all the classes and just counted on Wikipedia for all requisite knowledge.

[STARNUT]

True, but Moment of Inertia is different.

Gee, no kidding? Thanks for the lesson, Mr. Wizard.......I wondered when my physics degree was going to come in handy. I guess I should have skipped all the classes and just counted on Wikipedia for all requisite knowledge.

Maybe you can use Wikipedia for other stuff. Like this: http://en.wikipedia.org/wiki/Tact.
Tact is a careful consideration of the feelings and values of another so as to create harmonious relationships with a reduced potential for conflict or offense. Tact is considered to be a virtue.
An example of tact would be relating to someone a potentially embarrassing detail of their appearance or demeanor without causing them distress.
Tact is a form of interpersonal diplomacy. Tact is the ability to induce change or communicate hurtful information without offending through the use of consideration, compassion, kindness, and reason.
A tactful person can tell you something you don't want to hear and you will be thankful for the information when they are finished.

Use that fancy physics degree and let us know the difference. All I and the orginal poster asked was a fairly or not so fairly straight foward question. I don't recall anything in there about 'tude

[2 wheels]

Moment of inertia only matters when you accelerate. If you climb with a steady pace, moment of inertia doesn't matter. That's also what Tour's test says, it's a measure to tell how much energy it requries to acellerate (and decellerate) the wheel.

I think MI refers to the amount of resistance a body gives to rotating around its axis. High MI=more resistance to rotating around the axis and a Low MI=less resistance to rotating around its axis.

To quote Wikipedia:

Conversely, the larger wheel takes more effort to accelerate into spinning fast, because its mass is spread out further from the axis of rotation. Quantitatively, the smaller wheel has a smaller moment of inertia, whereas the larger wheel has a larger moment of inertia.

A body rotataing at a steady state gives no resistance to rotation, it only gives resistance to changes in speed (acceleration and deccelration).

Moment of inertia to a rotating body is like mass to a linear moving body.
The mass in a linear moving body gives no resistance to movement, it only give resistance to changes in movement (acceleration and decelleration).

Becuse of graivty, the mass (but not the moment of inertia) also adds resistance to moving upwards however. But moving in a horizontal line, the mass only matters while accelerating and decellrating, but not moving in a steady pace.

[foxracer826]

So now that you say this all matters just for acceleration/deceleration, what would be the best climbing wheel, best aerodynamics, lightest weight, or most weight close to hub, or most weight on outside edges?