Wheel upgrade

[annirak]

If you don't like my assumptions, say so, change them to something more realistic and do the math. BTW, I've made the assumptions more realistic for you. Compare them to mine.

Let's take your scenario and refine it a little.

Two bicycles accelerate from zero to 30 kph in three minutes. Both weigh the same with their riders - 90 kg.
However, bicycle A has wheels that are lighter than bicycle B, by 400 grams for the pair. Obviously bicycle B has the 400 grams placed elsewhere.
That weight saving is shaven of all areas of the wheel, ranging from tyres (radius 368mm) to hub (radius 36mm).
Bicycle B's wheels have a mass of 2500 grams and the mass is evenly distributed from radius 368mm through 36mm.

Most bicycle wheels aren't discs, they're rims with spokes and hubs. There are a few iterations of refinement we can go through, but before we get too complicated, lets just go with a fairly simple model:
A hub, some spokes, a rim.
I'll assume that the rim, tyre, and tube have all their mass concentrated in a cylindrical strip, the radius of the wheel.
For the hub, I'll assume it is a cylinder of uniform density
I'll assume the spokes extend all the way from the centre (straight through the hub, yes) to the rim.

Hubs:
mass = 357g rear, 155g front
radius = 57.9mm

Spokes (32 per wheel)
length: 368mm
mass: 6g

Rim+tyre+tube:
radius = 368mm
mass = 435g (rim) + 105g (tube) + 200g (tyre) = 740g

Total wheel masses:
Front: 1.087kg
Rear: 1.289kg

Moments of intertia:
Cylinder: 1/2MR^2
Rod suspended at one end: 1/3ML^2
Cylindrical thin strip: MR^2

Numeric values (kg*m^2)
Front Hub = 0.000259812
Rear Hub = 0.000598405
One spoke = 0.000270848
Tyre = 0.0270848
Tube = 0.01421952
Rim = 0.05890944

Front Wheel: 0.109140708
Rear Wheel: 0.109479301
This seems to indicate that the moment of inertia of the hub doesn't matter, which is what we'd expect, since it's much smaller in radius than any of the other parts.

Since the inertia of the hub doesn't matter and spokes don't change much, we're going to concentrate that 400g weight savings in the rims.

So bike A has lead shot in the water bottle, and bike B has lead shot in the rims.

KE @ 30kph:
Bike A: 3830J
Bike B: 3844J

Bike B's extra energy requirement to get to 30kph: 14J => 0.36%

Like I said: I disagree with your assumptions, but I agree with your conclusion.

 

[Yellow Saddle]

Let's take your scenario and refine it a little.


Most bicycle wheels aren't discs, they're rims with spokes and hubs. There are a few iterations of refinement we can go through, but before we get too complicated, lets just go with a fairly simple model:
A hub, some spokes, a rim.
I'll assume that the rim, tyre, and tube have all their mass concentrated in a cylindrical strip, the radius of the wheel.
For the hub, I'll assume it is a cylinder of uniform density
I'll assume the spokes extend all the way from the centre (straight through the hub, yes) to the rim.

Hubs:
mass = 357g rear, 155g front
radius = 57.9mm

Spokes (32 per wheel)
length: 368mm
mass: 6g

Rim+tyre+tube:
radius = 368mm
mass = 435g (rim) + 105g (tube) + 200g (tyre) = 740g

Total wheel masses:
Front: 1.087kg
Rear: 1.289kg

Moments of intertia:
Cylinder: 1/2MR^2
Rod suspended at one end: 1/3ML^2
Cylindrical thin strip: MR^2

Numeric values (kg*m^2)
Front Hub = 0.000259812
Rear Hub = 0.000598405
One spoke = 0.000270848
Tyre = 0.0270848
Tube = 0.01421952
Rim = 0.05890944

Front Wheel: 0.109140708
Rear Wheel: 0.109479301
This seems to indicate that the moment of inertia of the hub doesn't matter, which is what we'd expect, since it's much smaller in radius than any of the other parts.

Since the inertia of the hub doesn't matter and spokes don't change much, we're going to concentrate that 400g weight savings in the rims.

So bike A has lead shot in the water bottle, and bike B has lead shot in the rims.

KE @ 30kph:
Bike A: 3830J
Bike B: 3844J

Bike B's extra energy requirement to get to 30kph: 14J => 0.36%

Like I said: I disagree with your assumptions, but I agree with your conclusion.

I think we are on the same page. I stated that the only place where the mass differs is at the rim (or tyre) i.e. the wheel was a thin strip. I didn't want to complicate the scenario by calculating the moment of inertia of the hubs and spokes, only to have then cancel each other out in the two similar wheels with one having more mass in the thin strip.

I don't know why you disagreed with that assumption. Mathematical pedantry? This only serves to confuse more people. Keep it simple.

 

[RedRider]

I think this discussion is about human nature and human perception as much as it's about objective reality. I'm sure that people do experience something different, although IMO the difference only exists in their minds. If that perception makes them happy, that's a real gain!

My understanding of the physics/maths in this thread is there's a measurable benefit from lighter wheels (as opposed to a lighter bike or rider) at the moment one accelerates from a standing start but a heavier wheelset will carry more momentum suggesting there's no difference in terms of energy expended over a ride.

I agree perception is important and I think one is more likely to clock the ease of moving off compared with the ongoing momentum as it's concentrated into a small moment. Therefore the same wheel with a more lightweight tyre for example, 'feels' like an energy saver. I agree this can make a psychological difference.

But in terms of energy expended by the rider and depending on the ride itself surely there could be a real difference. What if the ride is stop/start eg a typical traffic-bound urban commute with eg traffic lights and junctions? Any momentum from a heavier wheelset would be 'wasted' as heat generated from brake on rim would it not?

FWIW I've never upgraded wheels to save weight but have done for strength and serviceability. This gives me the confidence to ride faster being somewhat less worried about the damage likely to be caused by a pot hole for example.

 

[annirak]

I think we are on the same page. I stated that the only place where the mass differs is at the rim (or tyre) i.e. the wheel was a thin strip. I didn't want to complicate the scenario by calculating the moment of inertia of the hubs and spokes, only to have then cancel each other out in the two similar wheels with one having more mass in the thin strip.

I don't know why you disagreed with that assumption. Mathematical pedantry? This only serves to confuse more people. Keep it simple.

I didn't understand that was what you meant...

Obviously bicycle B has the 400 grams placed elsewhere.
That weight saving is shaven of all areas of the wheel, ranging from tyres (radius 368mm) to hub (radius 36mm).
Bicycle B's wheels have a mass of 2500 grams and the mass is evenly distributed from radius 368mm through 36mm.

That sounds like a rotating disc, rather than a thin strip. The results would be quite different if it were a disc, rather than a thin strip, but still probably irrelevant.

So, the long and the short of it is:

• Yes, you save some energy by using lighter wheels. It's more significant than weight anywhere else, but even still, it's almost not measurable (0.4%)
• Additional acceleration energy is absolutely NOT balanced out over the course of a ride. Any energy you put into getting those wheels moving is energy you NEVER GET BACK. At least it's not much energy and probably not worth worrying about.
• Heavier wheels give you more inertia, which smooths out your speed, but that will also be almost not measurable.

Personally, I am not sure about feel. I would have said it was a placebo until two weeks ago. I rode a CAADX (tiagra) and a Synapse (sora) one after the other. I went in *wanting* to like the CAADX. It felt sluggish. Even though the Synapse was a lower groupset and slightly too big for me, it felt dramatically better. It just jumped when I leaned on the pedals. I'm not willing to say this is definitely down to wheels without more data, but it seems plausible.

 

[Citius]

My understanding of the physics/maths in this thread is there's a measurable benefit from lighter wheels (as opposed to a lighter bike or rider) at the moment one accelerates from a standing start but a heavier wheelset will carry more momentum suggesting there's no difference in terms of energy expended over a ride.

I agree perception is important and I think one is more likely to clock the ease of moving off compared with the ongoing momentum as it's concentrated into a small moment. Therefore the same wheel with a more lightweight tyre for example, 'feels' like an energy saver. I agree this can make a psychological difference.

But in terms of energy expended by the rider and depending on the ride itself surely there could be a real difference. What if the ride is stop/start eg a typical traffic-bound urban commute with eg traffic lights and junctions? Any momentum from a heavier wheelset would be 'wasted' as heat generated from brake on rim would it not?

FWIW I've never upgraded wheels to save weight but have done for strength and serviceability. This gives me the confidence to ride faster being somewhat less worried about the damage likely to be caused by a pot hole for example.

I think that's a good summary - and you may well be right about the traffic/commute thing. The only thing I would say is that (with respect to commuters) they are probably less concerned about miniscule performance gains, and more concerned about getting to work safely

 

[Yellow Saddle]

I didn't understand that was what you meant...


That sounds like a rotating disc, rather than a thin strip. The results would be quite different if it were a disc, rather than a thin strip, but still probably irrelevant.

So, the long and the short of it is:

• Yes, you save some energy by using lighter wheels. It's more significant than weight anywhere else, but even still, it's almost not measurable (0.4%)
• Additional acceleration energy is absolutely NOT balanced out over the course of a ride. Any energy you put into getting those wheels moving is energy you NEVER GET BACK. At least it's not much energy and probably not worth worrying about.
• Heavier wheels give you more inertia, which smooths out your speed, but that will also be almost not measurable.

Personally, I am not sure about feel. I would have said it was a placebo until two weeks ago. I rode a CAADX (tiagra) and a Synapse (sora) one after the other. I went in *wanting* to like the CAADX. It felt sluggish. Even though the Synapse was a lower groupset and slightly too big for me, it felt dramatically better. It just jumped when I leaned on the pedals. I'm not willing to say this is definitely down to wheels without more data, but it seems plausible.

NO, my original wheel was thin strip. After your invitation to do the math, I was sure you would not like the thin strip, hence the rotating disk model. The two sets of assumptions are not the same (but just to not confuse the lurkers, the results are the same).

I disagree that the energy stored in a wheel is never returned. It has been pointed out there that just accelerating and then coasting will provide a better coasting result with heavier wheels. That is real benefit that's not wasted. If you squander it with injudicious braking, that's another matter.

If you think you can feel it, ask yourself if you can feel a 0.4% difference. If you still think you can, place the 0.4% elsewhere - like in a small increase in gradient or a small increase in headwind, for instance. I think you fool yourself if you say you can feel a difference. Your examples above don't have magnitude so I can't comment but as I've noted before here, I had a friend who thought he could "Feel" just about any difference and naturally therefore clock it on a stopwatch. I filled his wheels with water without him knowing and left it like that for weeks. He never noticed. I then ended the charade by asking him if he's noticed anything over the last few weeks and he said he didn't. I then let the cat out of the bag and removed the egg from his face.

One bike felt sluggish? Think about this: we have extremely weak engines and accelerate very, very slowly on a bicycle. Just try and get up to 30kph one day and time how long it takes you - ages. The reason is that our engines are weak and bodies heavy. A little bit of extra or less weight on the bike makes such a small difference that you will not be able to say one bike is more sluggish than another. Sluggish is defined as slow to accelerate in this case.

 

[Yellow Saddle]

cut cut cut cut

Therefore the same wheel with a more lightweight tyre for example, 'feels' like an energy saver. I agree this can make a psychological difference.

I doubt you can feel it, See post above. However, lightweight tyres make a different sound than a heavy tyre. The pitch is higher and I think this sounds faster than a lower-pitched sound. I bet the "feel" can be killed with earplugs. The perception is due to acoustics.

But in terms of energy expended by the rider and depending on the ride itself surely there could be a real difference. What if the ride is stop/start eg a typical traffic-bound urban commute with eg traffic lights and junctions? Any momentum from a heavier wheelset would be 'wasted' as heat generated from brake on rim would it not?
.

Yes, we can find all sorts of scenarios to make the statement fail. I've addressed the braking scenario but not the multiple stop-start one yet. Add up the stops and starts (just starts actually) on your commute and come up with a figure - say 100. 100 times a few Joules is still nothing. A commuter will benefit more (I.e. get to work quicker averaged out over the year) from heavy puncture resistant tyres and durable heavier wheels. But again, read the preamble I keep on pointing to and see where this argument comes from.

The problem with these things is bike magazines. I've yet to come across a magazine that communicates the truth about lighter wheels. People read something twice, and it is stuck in their minds and becomes reality.

I never fell for the audio thing Giles talks about, but I have seen gold-pated oxygen-free speaker cables in hi-fi shops and sniggered. I think his analogy is great.

 

[S.Giles]

My understanding of the physics/maths in this thread is there's a measurable benefit from lighter wheels (as opposed to a lighter bike or rider) at the moment one accelerates from a standing start but a heavier wheelset will carry more momentum suggesting there's no difference in terms of energy expended over a ride.

I agree perception is important and I think one is more likely to clock the ease of moving off compared with the ongoing momentum as it's concentrated into a small moment. Therefore the same wheel with a more lightweight tyre for example, 'feels' like an energy saver. I agree this can make a psychological difference.

But in terms of energy expended by the rider and depending on the ride itself surely there could be a real difference. What if the ride is stop/start eg a typical traffic-bound urban commute with eg traffic lights and junctions? Any momentum from a heavier wheelset would be 'wasted' as heat generated from brake on rim would it not?

FWIW I've never upgraded wheels to save weight but have done for strength and serviceability. This gives me the confidence to ride faster being somewhat less worried about the damage likely to be caused by a pot hole for example.

I'm in broad agreement with you. My post (the one to which you replied) was somewhat absolute and I should probably have included a 'to all intents and purposes' clause in there somewhere.

There would be a measurable difference in the energy expended whilst walking if I wore a lighter pair of socks, but it's not something I tend to worry about too much. I think that cyclists are sometimes drawn into this sort of thinking by reading too many advertisements in cycling magazines and wanting to emulate those for whom 100g of weight saving is significant. Again, if it makes them happy that's fine, but I can't help wondering if there are some who would benefit from getting off this particular hook and lightening-up in a different respect!

 

[jowwy]

As above - already been done. If you don't agree with Yellow Saddle's thoughts - tell him why and come up with some better info.

no it hasnt been done above - he makes a bold statement that deep section aero wheels are no good for 99% of people on race bikes............but doesn't quantify the figures or gives a reason why

you agreed with him and then asked someone else to prove yourself and yellow saddle wrong............my response is you prove the figures right, as your the one along with yellow saddle that made the bold statement...........but its obvious you can't

 

[Citius]

no it hasnt been done above - he makes a bold statement that deep section aero wheels are no good for 99% of people on race bikes............but doesn't quantify the figures or gives a reason why

you agreed with him and then asked someone else to prove yourself and yellow saddle wrong............my response is you prove the figures right, as your the one along with yellow saddle that made the bold statement...........but its obvious you can't

Have you not read the rest of the thread? You seem to have successfully ignored a lot of posts in order to get to that assumption. The figures are there for you to disagree with. If you don't agree with them (and you clearly don't) - you're going to have to say why.

I've included below a quick summary of how arguments work:

Option A
1. someone says something and backs it up with data
2. someone else agrees
3. argument avoided

or

Option B
1. someone says something and backs it up with data
2. someone else disagrees, and explains why, using alternative data
3. argument continues until conclusion is reached

Right now, I would say you need to be referring to Option B, point 2.

 

[Yellow Saddle]

no it hasnt been done above - he makes a bold statement that deep section aero wheels are no good for 99% of people on race bikes............but doesn't quantify the figures or gives a reason why

you agreed with him and then asked someone else to prove yourself and yellow saddle wrong............my response is you prove the figures right, as your the one along with yellow saddle that made the bold statement...........but its obvious you can't

We know you are special. You are part of the 1%, don't worry.

 

[annirak]

no it hasnt been done above - he makes a bold statement that deep section aero wheels are no good for 99% of people on race bikes............but doesn't quantify the figures or gives a reason why

Easy. The cross-sectional area of the wheel is already tiny with respect to the cross-sectional area of the rider. Making the wheel more aero will make precious little difference to the overall drag, since the *rider* is not aero. A set of tri-bars will make more difference than deep-section aero wheels. They also cost less, and feel better. On the other hand, tri-bars keep you away from the brakes, so they come with certain drawbacks!

 

[jowwy]

Its seems to me that both you and citius are very special.....but still cant quantify or give a reason why aero wheels are useless for 99% of people on race bikes...

 

[Justinslow]

So I'll stick with my shimano R501's then and save my money!!!!

 

[annirak]

Good plan!

I just bought new wheels. In my defence, my previous set was damaged in a road accident. I admit to spending £26 more than I had to because I liked the look of the more expensive ones better. I don't believe for an instant that I'll notice a difference in performance!