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Disc vs Rim Wheel Inertia
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If you remember from high school physics, when thinking about rotating objects “ie…wheels” what matters is inertia not mass. The two are related of course, but different.

Inertia = the resistance of any physical object to any change in its state of motion p=m*v

Mass= resistance to acceleration or the amount of matter in an object F=m*a

We always think of wheels in terms of mass but inertia matters more. (setting aside aerodynamics) Inertia will is a better measurement of how fast your wheel "accelerates".

Has anyone ever done any math/measurements of how the inertia of disc brake wheels compares to the inertia of rim brake wheels?

I wouldn’t imagine there is much difference because most of the extra mass of disc wheels is close to the hub, not affecting inertia much.
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Re: Disc vs Rim Wheel Inertia [xcskier66] [ In reply to ]
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xcskier66 wrote:
If you remember from high school physics, when thinking about rotating objects “ie…wheels” what matters is inertia not mass. The two are related of course, but different.

Inertia = the resistance of any physical object to any change in its state of motion p=m*v

Mass= resistance to acceleration or the amount of matter in an object F=m*a

We always think of wheels in terms of mass but inertia matters more. (setting aside aerodynamics) Inertia will is a better measurement of how fast your wheel "accelerates".

Has anyone ever done any math/measurements of how the inertia of disc brake wheels compares to the inertia of rim brake wheels?

I wouldn’t imagine there is much difference because most of the extra mass of disc wheels is close to the hub, not affecting inertia much.

Well, I'm not sure you can say categorically that moment of inertia matters more than mass when it comes to wheels. You have to consider what you are using the wheel for to decide what is more important to you. If you are a climber, mass probably matters more. For a sprinter, inertia. Since for the most part, wheels are constructed very similarly, moment of inertia will track pretty similarly with mass, unless the changes are done primarily to the hub. (Mass near the center of the wheel has little effect on rotational inertia).

So.... For a disc brake wheel the question is how much weight, if any, can you remove from the rim, how much do you add with the disc and what is the diameter of mass of the disc from the center? Additionally you have to account for the additional spokes required for disc brakes.

-------------
Ed O'Malley
http://www.motivengines.com
@EdwardOMalley
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Re: Disc vs Rim Wheel Inertia [RowToTri] [ In reply to ]
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Inertia always matters. Wheels are never rotating at a constant velocity; they are always "micro accelerating" in response to your pedal strokes. I would think that a climber would care about both!

The things you brought up are exactly the kind of thing I want analyzed!

I'm guessing wheel designers consider both inertia and mass and have done this kind of analysis.

Where are you guys?
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Re: Disc vs Rim Wheel Inertia [xcskier66] [ In reply to ]
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Tom A. will be very helpful here.

Powered by All Out MultiSport - http://www.aomultisport.com/
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Re: Disc vs Rim Wheel Inertia [xcskier66] [ In reply to ]
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Quote:
they are always "micro accelerating" in response to your pedal strokes

Yes, wheels with more inertia would micro accelerate slower, but they would also micro decelerate slower as well so all it wouldn't change the power requirements, it would just make the bike feel a bit different. (Climbing on super high inertia wheels would probably just feel more like riding on a flat)


Honestly if it wasn't for the weight penalty required to have a super high inertia wheel, I might want high inertia wheels since it would allow you to smooth out your power more. ***


***taken to an unreasonable extreme amount of inertia
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Re: Disc vs Rim Wheel Inertia [AngrySaki] [ In reply to ]
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AngrySaki wrote:

Yes, wheels with more inertia would micro accelerate slower, but they would also micro decelerate slower as well so all it wouldn't change the power requirements, it would just make the bike feel a bit different.


If it's accelerating slower, then it's changing the power requirements. Because reaching the desired velocity will either require more power or more time vs. a lower-inertia wheel. It might not change average power over a long period of time

Your super high inertia wheels as flywheel might be OK on a pure constant-power time trial. But they wouldn't be any fun in a criterium or technical road race. Or even a technical TT. You'd get killed coming out of every corner. And and much of that energy wouldn't be recovered - you'd brake it away coming into the next turn. It'd also make braking more intensive.
Last edited by: trail: Mar 20, 17 8:06
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Re: Disc vs Rim Wheel Inertia [xcskier66] [ In reply to ]
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xcskier66 wrote:
If you remember from high school physics, when thinking about rotating objects “ie…wheels” what matters is inertia not mass. The two are related of course, but different.

Inertia = the resistance of any physical object to any change in its state of motion p=m*v

Mass= resistance to acceleration or the amount of matter in an object F=m*a

We always think of wheels in terms of mass but inertia matters more. (setting aside aerodynamics) Inertia will is a better measurement of how fast your wheel "accelerates".

Has anyone ever done any math/measurements of how the inertia of disc brake wheels compares to the inertia of rim brake wheels?

I wouldn’t imagine there is much difference because most of the extra mass of disc wheels is close to the hub, not affecting inertia much.

You need to think of it at a more system level...Since the rotational inertia of wheels is an exceedingly small percentage of the TOTAL inertia of the rider+bike system, any reasonable variances in wheel rotational inertia don't really matter performance-wise. So, it really is more about just the mass of the wheels than the rotational inertias.

There's an article I did on this subject here on ST that I'm having a hard time finding right now...



http://bikeblather.blogspot.com/
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Re: Disc vs Rim Wheel Inertia [Tom A.] [ In reply to ]
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Quote:
You need to think of it at a more system level...Since the rotational inertia of wheels is an exceedingly small percentage of the TOTAL inertia of the rider+bike system, any reasonable variances in wheel rotational inertia don't really matter performance-wise. So, it really is more about just the mass of the wheels than the rotational inertias.

There's an article I did on this subject here on ST that I'm having a hard time finding right now...

http://www.slowtwitch.com/...nd_Inertia_2106.html


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Re: Disc vs Rim Wheel Inertia [P McCatty] [ In reply to ]
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P McCatty wrote:
Quote:
You need to think of it at a more system level...Since the rotational inertia of wheels is an exceedingly small percentage of the TOTAL inertia of the rider+bike system, any reasonable variances in wheel rotational inertia don't really matter performance-wise. So, it really is more about just the mass of the wheels than the rotational inertias.

There's an article I did on this subject here on ST that I'm having a hard time finding right now...


http://www.slowtwitch.com/...nd_Inertia_2106.html

Thanks! That's it.



http://bikeblather.blogspot.com/
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Re: Disc vs Rim Wheel Inertia [xcskier66] [ In reply to ]
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xcskier66 wrote:
Inertia always matters.
Not so fast...


xcskier66 wrote:
Wheels are never rotating at a constant velocity; they are always "micro accelerating" in response to your pedal strokes.

Well that may be true but:

i. inertial load of a wheel won't affect the steady state speed one can sustain for a given power output

ii. the level of velocity variation is tiny* but in any case all that happens is the variations in velocity are of an ever so slightly different magnitude, and importantly

iii. this does not imply a different level of energy demand since conservation of energy applies and of course as has been pointed out:

iv. a wheel with higher moment of inertia also requires more energy to slow down at the same rate, so any energy put into the system to accelerate also helps to reduce the rate at which it slows down. IOW see point ii.


* For anyone that cares to look, I took a deeper dive into the issue of micro accelerations during steady state pedalling in this post:
http://alex-cycle.blogspot.com.au/...-crank-velocity.html

For a rider on flat ground at 90rpm / 250W, the normalised velocity variation during a pedal stroke is +/-0.15%

I went further, examining the velocity variations during hard accelerations:
http://alex-cycle.blogspot.com.au/...-crank-velocity.html


As the overall impact of additional wheel mass (or a higher moment of inertia) on one's ability to accelerate, well I examined some scenarios where acceleration on a bicycle is at its maximum, and hence where such differences in wheel moment of inertia would potentially matter the most.

Have a look at how tiny the impact of real world wheel mass (moment of inertia) differences are when considered, as Tom Anhalt says, as part of the entire system:

http://alex-cycle.blogspot.com.au/...sum-of-parts-ii.html



http://www.rstsport.com
http://www.aerocoach.com.au
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Re: Disc vs Rim Wheel Inertia [xcskier66] [ In reply to ]
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xcskier66 wrote:
Has anyone ever done any math/measurements of how the inertia of disc brake wheels compares to the inertia of rim brake wheels?

I wouldn’t imagine there is much difference because most of the extra mass of disc wheels is close to the hub, not affecting inertia much.
You are correct in that the mass being closer to the hub than rim reduces the increase in moment of inertia of the wheel compared with say adding the same mass all to the rim.

It is possible to calculate the moment of inertia of wheel with various test methods e.g. acceleration tests using a string around the rim + hanging weight + video motion sensor, or torsional pendulum tests.

As previously said though, wheels' different moments of inertia have a negligible impact on performance, especially steady state cycling performance.

http://www.rstsport.com
http://www.aerocoach.com.au
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Re: Disc vs Rim Wheel Inertia [xcskier66] [ In reply to ]
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Here's a real oldie - one of the first articles I wrote for bike.com back in the day:


http://biketechreview.com/...63-wheel-performance





=================
Kraig Willett
http://www.biketechreview.com - check out our reduced report pricing
=================
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Re: Disc vs Rim Wheel Inertia [AlexS] [ In reply to ]
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Thanks guys!

I knew there would be people who would be able to answer this stuff.

Turns out total inertia of the system is what matters most.
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Re: Disc vs Rim Wheel Inertia [BikeTechReview] [ In reply to ]
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BikeTechReview wrote:
Here's a real oldie - one of the first articles I wrote for bike.com back in the day:



http://biketechreview.com/...63-wheel-performance




Yes, I provided a reference to that older item in the first of my The sum of the parts posts:
http://alex-cycle.blogspot.com.au/...he-sum-of-parts.html

Quote:
Now this question has already been examined by others, including a good item on wheel performance by Kraig Willett at Bike Tech Review. In that item, Kraig runs through the physics and demonstrates how (in)significant a difference in wheel rotational inertia during accelerations is, relative to the other primary resistance forces encountered on a bike. In another, more simplified look, Tom Anhalt also examined this and illustrates the same finding in this article on Slowtwitch.

http://www.rstsport.com
http://www.aerocoach.com.au
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Re: Disc vs Rim Wheel Inertia [AlexS] [ In reply to ]
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AlexS wrote:
BikeTechReview wrote:
Here's a real oldie - one of the first articles I wrote for bike.com back in the day:



http://biketechreview.com/...63-wheel-performance




Yes, I provided a reference to that older item in the first of my The sum of the parts posts:
http://alex-cycle.blogspot.com.au/...he-sum-of-parts.html

Quote:
Now this question has already been examined by others, including a good item on wheel performance by Kraig Willett at Bike Tech Review. In that item, Kraig runs through the physics and demonstrates how (in)significant a difference in wheel rotational inertia during accelerations is, relative to the other primary resistance forces encountered on a bike. In another, more simplified look, Tom Anhalt also examined this and illustrates the same finding in this article on Slowtwitch.

cool - thanks for that! ...glad to see that old article still has some legs.

=================
Kraig Willett
http://www.biketechreview.com - check out our reduced report pricing
=================
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Re: Disc vs Rim Wheel Inertia [BikeTechReview] [ In reply to ]
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Never let physics get in the way of marketing. The fatal flaw of engineers is we think everyone else thinks like engineers.

http://www.trainingbible.com/...1/active-spokes.html

From a purely theoretical standpoint, if you could efficiently capture energy going down a hill, and release it going up the next hill, you could come out ahead because you have less aerodynamic loss in total. I think this was what they were trying to do with activespoke, but for sure there are too many other losses that overcome any minor benefit. Forgetting about wheels and rotational inertia, if you assume starting from a charged battery + motor maybe you could create a system worth it's weight penalty to capture and release energy.
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