Bicycle Mechanics - Static vs Rotating Pounds

David Lamb, in his 1995 trans-America book "Over the Hills," talks about removing several water bottles to reduce weight. He claims "According to physics, every static pound is the equivalent of two rotating pounds." What does this mean? Does this have anything to do with unsprung weight?

As an engineer, I can confidently say that he doesn't have a clue as to what he's talking about. I can't even imagine how he could come up with such an opinion even based on personal observation. Would any other engineers care to agree?

So, if D.Lamb mounted his water bottles on his wheels they would weigh half as much.

Ok consider this:

Move 2 pounds from your frame and add it to your wheels. Then try and climb a hill, or accellerate from a stop. You will feel as though lots of weight has been added to your bike.

Please don't ask me to get out my textbooks to give proof.

I am an historian not an engineer, but I have always understood that rotating weight (wheels, cranks, pedals) costs more energy because of the fact that you have to overcome both its rotational inertia, as well as its static inertia. I think that is why they say rotating weight counts twice. But, I would imagine that you have to account for how far out from the axle the weight is placed--which would make any simple 1 + 1 = 2 statement only coincidentally correct.

Now, as I understand it, this only affects acceleration, not constant speed climbing. Once the wheel is moving, it will want to keep moving (Newton's law), and that doesn't change just because gravity is making life hard on you up that hill. So, SpotmaticF's test will be true for acceleration, but false for climbing (once a constant speed is reached).

For the same reason, on flat ground your weight makes no difference whatsoever in the energy you expend once you have reached a constant speed.

By the way, I bought new pedals this year that were about 1/2 the weight of my old ones. Although it was a difference of less than 200 grams (far less than carrying an extra water bottle), I really noticed the change--but only while accelerating.

The above is based on my meager memory of Physics 110. Any confirmations (or rebuttals based on physics) would be much appreciated.

Cheers,
Jamie

P.S. As an historian, I can confirm that this has always been true in the past--provided it is still true today! :P

"According to physics, every static pound is the equivalent of two rotating pounds."
Well, rotating mass (not the same as weight, BTW) does count both towards the total mass and also will require extra torque to spin, but that amount of torque is dependant on how far the mass is located from the polar moment of inertia, and the angular acceleration. So, in a non-scienticic way, perhaps the mass is counted "twice", but this in no way is the same as saying that Mstatic=2*Mrotating, which is essentially what this uninformed author is saying.

Perhaps what he meant was that Mrotating=2*Mstatic, which, although a fallacy in most circumstances, might at least make sense in very, very specialized circumstances. In other words, perhaps what he meant to say was "every rotating poung counts greater than a static pound", which is diametrically opposed to what you quoted.


I am an historian not an engineer, but I have always understood that rotating weight (wheels, cranks, pedals) costs more energy because of the fact that you have to overcome both its rotational inertia, as well as its static inertia. I think that is why they say rotating weight counts twice. But, I would imagine that you have to account for how far out from the axle the weight is placed--which would make any simple 1 + 1 = 2 statement only coincidentally correct


Jmlee: You missed the point that I was making. His facts were backwards. Did you actually pass your physics class? Do you have a degree in either physics or engineering? Stick to history-your lack of knowlege of physics is frightening-not to mention likely embarassing.


Move 2 pounds from your frame and add it to your wheels. Then try and climb a hill, or accellerate from a stop. You will feel as though lots of weight has been added to your bike.

spotmatic: Go back and read the original post. Now read your rebuttal. Notice your error? He was saying that static mass counted at TWICE what rotating did. Did you also flunk physics 101? I certainly hope you aren't an engineer!

What static weight? Most of us ride our bikes so everthing is moving (either translational only or both rotational and translational.)

If he has static weight, then he's either a relly good trackstander or he sits still while the wheels and earth rotate under him. :D

Physics is great. We can say all kinds of wierd stuff. Like the contact point of the tire really isn't moving (instaneously anyway) as is moving around the circle at the same speed as the bike is moving, but in the opposite direction. Conversly, the top of the tire is moving twice as fast as you are! I guess I just contradicted myself as I said earlier that everything on the bike is moving, but oh well. :(

At this point I forgot who asked, but yes the distance of the mass from the point of rotation is important when calculating angular momentum and therefore the force required to accelerate something along a curved path.

Please correct me if I'm wrong as I'm a student with a test coming up soon.;)

Alex:

I did realize that the author had his logic backwards.



My first statement contained a measure of sarcasm which was not quite as obvious as I had thought.
So, if D.Lamb mounted his water bottles on his wheels they would weigh half as much.

By this perverse science we should consider moving all manner of ancillary equipment to our wheels. Maybe my tool kit could be strapped to my spokes to reduce its weight by half. :)

This is ludicrous, of course, though in over simplified terms, the opposite could be true as you pointed out.


Perhaps what he meant was that Mrotating=2*Mstatic, which, although a fallacy in most circumstances, might at least make sense in very, very specialized circumstances. In other words, perhaps what he meant to say was "every rotating poung counts greater than a static pound",

Boy this is fun.

D*Alex,

In your first post you made no other point than to say that the guy was clueless and that you were confident about that.

I, too, recognized the mistake in the quotation. But, I decided that I would try to answer what I assumed was the poster's actual question: what is the relationship between mass of rotating parts and total mass? I forwarded my understanding of the matter, appending several qualifications about my lack of expertise.

As I read your second post, I understand it as confirming the essence of what I said, including my point about the need to account for the distance of the mass from the center of the rotating object.

In short, based on the information you provide, I see nothing grossly wrong in my post, even if my language betrays a layman's understanding of the matter. Instead of insults, I would appreciate a demonstration of what is actually wrong in what I was trying to convey.

Furthermore, would you please enlighten us to the "very, very special circumstances" under which this is true, and confirm whether they apply to a bicycle.

Cheers,
Jamie

P.S. I, too, could make fools of most of the readers of this forum in several areas of historical, cultural, and linguistic knowledge. When a question that falls in my area of expertise pops up, I don't respond with, "hah, you don't know the importance of 1789 or how to spell peloton. Did you flunk both history and French?" Just as I have always done for my students, I accommodate myself to my readers and share with them what I know--which, of course, you started to do in your second post.

Ok, for those of us who dozed off in physics.

Is the reason rotational mass expends more energy on something like a bike, because the additional effort to get the wheels, cranks or peddles moving, must also be maintained, as well the energy required to maintain the bike at a constant speed?

(Mrs. Engle, I hope you cringe at that run on scentence!! Plus the punctuation and spelling!!!)

The real beast is air friction once you've gotten to the speed you want to maintain. (unless you ride a Huffy) All other forces are neglible by comparison. As far as the rest, I forgot the equations but for an example let us say you have a choice between 2 20lb bikes on the first the frame weighs 10 and each wheel weighs 5. On the second the frame weighs 15 and each wheel weighs 2.5. Now both bikes weigh the same but you'll be better off with the heavier frame and the lighter wheels. (Unless it's a Huffy)

Originally posted by jmlee
For the same reason, on flat ground your weight makes no difference whatsoever in the energy you expend once you have reached a constant speed.


In a perfect world, yes, but we have friction to overcome as well.

I remember someone saying on the forums that 4 lb on the bike was equal to 1 lb on the wheels, can't confirm or disprove this. I will ask my "fizziks" teacher monday about this and report back with a large formula with theta, pi, and a bag of other greek symbols so that we all may feel less of our selves :confused: . Anyways, taking weight off of anything rotational will improve your performance more than an equal amound removed from the non-moving parts of the bike. That said, what good would a formula do us? :beer:

Originally posted by D*Alex

Well, rotating [B]mass (not the same as weight, BTW) does count both towards the total mass and also will require extra torque to spin

D*Alex, but what happens as you approach the speed of light? Does a 17 pound bike even matter as one rides at the speed of light, or maybe even faster?

i think we can all agree that rotational mass is what we feel more when we ride as opposed to static mass. i spent the dollars buying a nicer set of wheels and the ride felt much lighter than with the cheap oem wheels.

jmlee, I think you've got it right and said pretty much what had to be said.

Another good perspective,

Originally posted by tFUnK
i think we can all agree that rotational mass is what we feel more when we ride as opposed to static mass. i spent the dollars buying a nicer set of wheels and the ride felt much lighter than with the cheap oem wheels.
This is why I don't obsess over the weight of the frame too much (does anyone ever say anything about the weight of the rider?).
I ditched some heavy (sigh, high mass) OEM wheels & sprang for a nice pair of Bontrager Racelights for my hybrid, with cool Conti GP 3K tires and lightweight tubes. That was all it took to take my ride from milquetoast to megafun!

It is nearly 40 yrs since I got my engineering degree, and I cant remember the formulae. However I once did the calculations and I think they told me that 1 oz on the rim of a 27" wheel was equivalent to 1.3 oz on the frame when accelerating. The joy of riding light rims is all in the mind and these formulae dont apply there.

i dont know how you jokers sleep @ night with all that stuff buzzing round in your heads???:D i dont think cycling is the exact science some think it is. ;)

Beer

I once ran a set of very heavy (but aero) Aerospoke wheels. They would never do for sprinting or climbing, but on the flats they would require ridiculously minimal effort to keep at speed. Perhaps angular momentum working in my favor?

Isn't it true that when something is rotating... that it's weight is 3 times as much as it was standing still ? ...


(excuse my ignorance).

I do however know that when something weighs more it is:

harder to get going (accelerate)
slower to stop
harder to push against when trying to maintain a speed
harder to pull wheelies, endo's, etc


The wheel idea is to keep it light, as you'll accelerate faster, and corner quicker because there is less mass & force attempting to act against your actions.... (if I'm getting this BS right... lol).

(just think F-1 Car )

My best guess at where this alleged rule of thumb come from is the formulas for potential energy, and kinetic energy. Very basic physics. Potential energy is that energy possessed by virtue of the objects configuration, for example weight. Kinetic energy is the is that energy possessed by virtue of the the objects motion.

Specifically Potential energy Ep = Wh
where W = Weight and h = hieght

Kinetic energy of rotation Ke = 1/2I*w2
Where w2 + the angular velocity squared
I = the moment of inertia (mass) of the item.

So if one applies the formulas at face value and assumes that I = W which it does NOT then you may think that 1 pound of rotation wieght = 1/2 pound of static wieght.

However this is a dramatic oversimplification of a very complicated engineering problem. One really needs to consider aerodynamics, friction, average gradient of the route, and overall design efficency to really figure out what the right combination is.

All that said. It is my opinon that a loss of body weight does not contribute as much to an increase in average speed over distance as much as a reduction in wieght of the bike. I have done both and the bike seemed to make a bigger difference. This is based on my training log. However I really do not know why.

before someone points out my typo. w2 = angular velocity squared

lighter wheels also require more energy to keep at constant speed. so it's a trade off (exagerated) between quicker acceleration and maintaining constant velocity.

it had never ocurred to me that there might be a momentum advantage to a heavier wheel. i have always assumed that removing an ounce of wheel weight had an equivalent affect on performance as removing two or more ounces of frame weight. i know that lighter wheels certainly feel more lively and faster. much more so than a lighter frame.

it would be nice if someone could say definitively. are there no physicists/engineers who know?

Conservation of angular momentum, if i remember my physics classses. Angular momentum is proportional to the rotating mass. and the distance away from the center of rotation. It requires energy to overcome the inertia of the wheels when starting from a dead stop; it also requires the same energy energy to slow the wheels down once they are rotating. This energy (to slow the bike down) comes from wind resistance, friction of wheels over pavement, internal friction of hubs, etc.
Any advantage of more massive rims is quite dependent on the number of start/stops and hills you have to climb. They would only help on a relatively flat course, say a TT course with no sprints or quick acceleration/deceleration, maintaining a fairly consistent speed.
Maybe a REAL engineer or physicist could chime in.

Originally posted by Poppaspoke
Conservation of angular momentum, if i remember my physics classses. Angular momentum is proportional to the rotating mass. and the distance away from the center of rotation. It requires energy to overcome the inertia of the wheels when starting from a dead stop; it also requires the same energy energy to slow the wheels down once they are rotating. This energy (to slow the bike down) comes from wind resistance, friction of wheels over pavement, internal friction of hubs, etc.
Any advantage of more massive rims is quite dependent on the number of start/stops and hills you have to climb. They would only help on a relatively flat course, say a TT course with no sprints or quick acceleration/deceleration, maintaining a fairly consistent speed.
Maybe a REAL engineer or physicist could chime in.

I'm a real engineer (sort of:p) at uc berkeley and i don't see reason to not agree with you

DORKS! :D
Go ride sheesh!

Dorks?? Maybe, But without us Dorks there would be alot more building collapes and Bridges falling down and cars without proper steering and brakes.

Yup.

Some of this Shiznit is right over my head... but I'm trying to understand it.

My worst subject has always been MATH! ahhhh. Oh well.

:beer:

lots of info (much over my head), but thanks.

there is always the racing litmus test. i know of no racing teams that bolt on wheel weight to help maintain momentum in flat, windy stages. as best as i can tell, the teams go to great lengths to make bikes as light as they can. also, you don't see any 250-pound guys winning time trials (although tiny guys do best in the mountains).

so it seems to me that it's safe to assume that the advantages of a heavier wheel in maintaining momentum do NOT overcome the disadvantages of requiring more energy to accelerate.

the discussion raises a question that's been on my mind. what's the best wheel set that provides both light weight and ruggedness. i wouldn't mind dropping some wheel weight but not at the expense of having to replace spokes and true the wheel every week.

i weigh 215 lbs and ride (commute) 150 miles/week.

Light wheels are not only easier to accelerate, but also more responsive to steering inputs. It doesnt take any energy to keep a wheel rotating at a constant speed, so there is no advantage to a heavy wheel when riding at a constant speed.

I think double butted spokes will give slightly less weight, but since they can stretch more they will provide an equivalent strength wheel with a lighter rim.

Bandit,

Look at the Mavic Classics SSC. They are on sale at Excel Sports. www.excelsports.com for 400 a pair. They are relatively light and very rugged. I have about 1000 miles on mine so far and have not had any problems with them. I weight 190 so I'm no lightweight either, I also ride on some poor roads. Also any handbuilt wheel with 36 spookes built on a good hub with Mavic open pros would be fine as well.

don ... thanks a lot for the tip, but it sounds similar to what i already have ... 36-hole mavics with tiagra hubs, laced together with heavy duty spokes. i was just wondering if those new, modern wheels with low spoke counts are as strong. probably not. no free lunch, eh?

Bandit,

People say the Mavic Ksyrium's are strong the elites are lower priced than the SSC's, the Bontrager Racelites are said to be strong too. As for the Mavic Classics I switched to those from a 32 hole mavic CXP 21 rim laced to a RSX hub. Pretty much the same as what you now have, I noticed a difference in wieght right away, also in my average speed. The hub actually has alot to do with the wieght of the wheel set, the rim does too but most higher end wheels use light rims. Also consider the type of roads you ride on if they are rough and bumpy the low spoke wheel may give you a harder ride than you want. If I had to do it again, and there is a story behind why I bought the Classics, which I will not bore you with. I would probably go with the a Mavic CXP 33 laced to a ultegra hub with 32 14/15 db spokes. If done right that is all the wheel I would need. Keep in mind the low spoke wheels are sort of in vouge now, conventional wheels are not, so you may get a much better deal on a conventional wheel. Also the build quality is more important that the componenets when it comes to durability. IMHO.

much obliged for the tips, don.

Now, as I understand it, this only affects acceleration, not constant speed climbing. Once the wheel is moving, it will want to keep moving (Newton's law), and that doesn't change just because gravity is making life hard on you up that hill. So, SpotmaticF's test will be true for acceleration, but false for climbing (once a constant speed is reached).



As I understand it, constant speed climbing will be affected, but not as much as acceleration. Here's why.

Resistance.

You have both wind resistance and rolling resistance (between tires and road). These 2 will slow you down.

Either way, whether you are accelerating or maintaining speed, you are still applying force (which is what it is really all about) towards some type of acceleration.

This is why tubulars are popular. They can maintain a high tire pressure, which minimizes rubber contact with the road, which minimizes rolling resistance. Couple that with riding in a peloton where you can draft. Barring any difficult climbs, your biggest challenge is saddle soreness.

Originally posted by Poppaspoke
I once ran a set of very heavy (but aero) Aerospoke wheels. They would never do for sprinting or climbing, but on the flats they would require ridiculously minimal effort to keep at speed. Perhaps angular momentum working in my favor?

All this angular momentum talk. I understand the concept.

Speaking from personal experience, I have found it easier to maintain a slower speed with heavier wheels than lighter.

However, I wonder if the truth lies outside the weight. Lighter weight wheelsets tend to have lesser spoke counts. The lighter wheels I have had were somewhat inexpensive; meaning they were poser wheels. I probably had more flex in them as opposed to my heavier 32 hole, 3 cross, 14ga spoked wheels. And as we all know, flex takes away from pedaling force.

If anything, I found that my heavier wheels were easier to accelerate than the lighter ones. However, once I got above 20 mph, the lighter wheels seemed to be more accomodating. Maybe the rotating force offsets the flex. Maybe I'm just full of s&!t.

Just a few thoughts. Feel free to tear me up.

As I understand it, constant speed climbing will be affected, but not as much as acceleration. Here's why.

Resistance.

You have both wind resistance and rolling resistance (between tires and road). These 2 will slow you down.

Either way, whether you are accelerating or maintaining speed, you are still applying force (which is what it is really all about) towards some type of acceleration.

Danr, You are certainly correct that the cyclist has to overcome wind resistance, rolling resistance, and (when climbing) gravity. If you want to think of it that way, he/she is then always trying to accelerate against the forces that are working to decelerate him/her.

But, the issue is whether mass in the wheels contributes more resistance than a non-rotating mass. The idea is that "getting the wheel" turning--all that stuff about angular momentum, etc.--does require more effort than if the weight were added to a non-rotating part of the bike. But, once that wheel is rotating at a constant speed, it will want to keep doing so. (This is where some will wax prolific about the "flywheel" effect--although its proponents always forget that the energy attained from it had to be put there by the cyclist in the first place.)

In order to apply your logic (of the constant need to accelerate against decelerating forces) you'd have to show that the rolling, wind, or gravity resistances are decelerating the wheel (due to the rotating mass) more they are decelerating the rest of the bike. With the possible exception of rolling resistance (which is tiny anyway), none of them are acting on the angular momentum of the wheel in the way necessary for that to happen. The whole "wheel weight" question really only matters for acceleration.

Thus, once a constant speed is attained, the mass in a wheel counts the same as mass anywhere else in the bike. A lot have written about "good climbing wheels," but at a constant speed they get no more benefit from lighter wheels than from tossing their water bottle into the ditch.

As I have said before, I am not a physicist. I am more than happy to be corrected. But, at this point in the thread, we need someone willing to give arguments and equations and so forth that will teach us the way to physical wisdom and bliss.

Cheers,
Jamie

P.S. as to the question of your heavier wheels being easier to accelerate, this will depend on where the weight savings comes from. Weight saved at the rims makes a much bigger difference than weight saved at the hubs, since it all has to do with the distance from the center. (This is why an ice skater will twirl faster when she pulls her leg in close to her body. Try this in a spinning chair--stick your legs out, spin, then pull them in. It's fun, if you have nothing better to do.)