[GeForceFX]

Hi, I'm new here, but I wanted to share a thought experiment I've made.

I wanted to upgrade my wheels, but I just wasn't sure if I could justify spending a bunch of money. So I've set out to quantity how much real world impact to rotational kinetic energy a fancy super light race 1000g (3000 euro) wheelset would make vs just changing the tires for 100$.
A.K.A. How much easier the wheel changes speed or direction for $$$ spent on separate parts of the wheel.

TLDR:
500g (1.1 lbs) wheelset weight reduction makes less of a difference (to rotational kinetic energy) than 150g (0.3 lbs) reduction from tires at 30km/h.

Compared rotational kinetic energy at 15 & 30 KM/h (10 & 20rad/s) (≈ 932 & 18.64 mph) for a 29er wheel (approx. 740mm diam./C=~2.35m):
1) 1440g wheels + 1550g tires
2) 1000g wheels + 1550g tires
3) 1440g wheels + 1400g tires
Bonus:
4) 1440g wheels + 1250g race tires

Calculations and relevant excerpt from wiki:
30km/h:

15km/h:

Findings:

Tires make up the most (~70% in this example) of the kinetic rotational energy of the entire wheel system. And while rims do make make some measurable change - the hubs, spokes, and disc rotors amount to almost nothing.

At 30km/h:
1) 500g of wheelset weight reduction makes just 6% difference of Er from 3KG. At the cost of 3000 euros (~3,410 usd).
2) Only 150g tire weight reduction makes a 7% difference of Er from 3KG. For 100$.
3) Race tires, that drop 300g, make a whopping 14% difference Er from 3KG. For 100$.

Or in other words:
Changing tires can cost as little as ~10usd per 1% of Er savings, but on a wheelset will cost over 500$.

Turns out there is almost 1500 times more rotational kinetic energy difference between a hub and a tire. (Or 1369, to be precise, when calculated a 100g hub weight at 10mm from axis at 20rad/s, I (mom. of inertia) = 0.00001 kg*m², or 0.002 joules, versus 100g @ 370mm = 0.01369 kg*m², or 2.738 joules).

Now I'm not the smartest zergling in the control group, nor am I a physics PhD, nor have I "discovered" something new. We all know that tires have a huge effect on the bike, and that a lighter rim/tire will make the acceleration / decel. and change of direction faster due to less mass moment of inertia. But I was just shocked that a 0.5kg reduced wheel weight made less difference than shaving 150g from tires (not counting the drag).

Clarification:
This is my calculation on the power requirement (joules, or watt per second) to accelerate (and decel.) the wheel. This doesn't mean that on a flat road you will see this, it's probably going to be between wind resistance and tire friction/drag for that.

I would also like to clarify that this isn't bombproof - I'm just an idiot on the internet, and all info is just an estimate. If someone sees an issue with this please correct me.

Would like to know if any of this is what you guys find from experience? Or am I just making a fool out of myself here?

Regards

 

[D. Inoobinati]

Awesome.

You've just rendered irrelevant at least 5 different marketing departments.

 

[D. Inoobinati]

I suspect that this is roughly the same calculation made by Formula 1 teams when they decided against low profile tires: the added mass, and greater distance from the hub, of the heavier metal rims conspired to slow the wheel on acceleration.

This is my calculation on the power requirement (joules, or watt per second) to accelerate (and decel.) the wheel.

Is this linear acceleration of the entire wheel? Or the centripetal acceleration on some point of the wheel circumference?

 

[oab1]

Yes but it's not only (or maybe even at all) about energy to spin the wheels. You are still taking the whole bike uphill, at least sometimes. So even if the rim and tire weighed 1g, and the hubs 2 pounds, you'd be slower going uphill even though the inertia is reduced.

I haven't done the math, but I suspect the energy to rotate the wheels is so insignificant by comparison it's not even worth taking about rotating mass savings on a bicycle. It's enough to simplify for the sake of carrying less mass wherever.

Edit: I can't say for certain on the F1 tires comment, but I am confident that is not the case. I haven't followed the sport in awhile, but again there are way more dominant effects to consider before inertia of the wheels. Namely braking power and cooling, as well as the tire sidewall stiffness and construction with its effect on overall grip. Maybe even aerodynamics themselves, which seems to trump everything nowadays. Really hard to say with rules / regulations.

 

[Danzzz88]

Plus it's not only about reducing kinetic energy..it's also about sprung mass on suspension bikes...you could save 200g on the wheels and put that weight to use in more durable and grippy tyres with no performance hit.
But ofc price is a no brainer...tyres will always be more cost effective at reducing weight...but unfortunately you also lose plenty other positive performance attributes by installing flimsy, undamped, low grip rubber.

You could cut brake disc weight in half by fitting some Ashima rotors...you won't be stopping any time soon though and that's if they don't snap at the spider first. You could cut saddle weight to 1/4 and have piles the next day....none of these I want.

 

[D. Inoobinati]

Wired magazine, and an actual physics professor, wrote as much in this article: We Can Prove Why Extra Mass on Bike Wheels Is Your Worst Enemy:

There's a saying that adding mass to the wheel of a bike has twice the impact compared to adding the same mass to the frame. Why would that be true?

So yes, adding mass to the wheel is worse than adding mass to the frame---but only when accelerating. Still, every little bit helps.

From my own experience, I've had to put thorn-proof tubes in my commuter bike tires, which turned it molasses slow on the uphills. As slow as I was, however, it was much faster than fixing flats every 1/2 mile. But yeah, increasing tire weight, slows you down!

 

[GeForceFX]

Discard, had a website in the post to a calculator.

 

[GeForceFX]

Is this linear acceleration of the entire wheel? Or the centripetal acceleration on some point of the wheel circumference?

I wanted to keep this as basic as possible, so I did the raw calc using omnicalculator; no drivetrain drag, etc included.

Plus it's not only about reducing kinetic energy..it's also about sprung mass on suspension bikes...you could save 200g on the wheels and put that weight to use in more durable and grippy tyres with no performance hit.
But ofc price is a no brainer...tyres will always be more cost effective at reducing weight...but unfortunately you also lose plenty other positive performance attributes by installing flimsy, undamped, low grip rubber.

You could cut brake disc weight in half by fitting some Ashima rotors...you won't be stopping any time soon though and that's if they don't snap at the spider first. You could cut saddle weight to 1/4 and have piles the next day....none of these I want.

Actually this already has the lightest ashima rotors possible - the listed 160g weight is for two rotors. I even forgot to add the rotor price. So this looks even worse for the 'wheels' upgrade as they got a mega light rotor upgrade for free. If you either add the rotor price, or remove the rotor weight saved then the result would be even better for the tires.

I agree about the unsprung mass, I guess I don't really think about that much because I'm riding mostly flat XC trails. If you were riding real MTB stuff on actual mountains or where suspension performance is key, then I'm sure that makes a big difference to the suspension performance.

Regarding tires - the 150g weight reduction across two tires is not that much really, sometimes manufacturers even have a paper and real weight difference for a single tire as big as 100g. The tire weight on MTBs is around 2kg, I'd say there's healthy space to drop 75g per tire.
Now compare this to your saddle example, even if you cut nearly all saddle weight of a standard 250g saddle, even with a "no padding" carbon saddle of 50g, the weight loss of 200g for a rider+bike system weight of what, 100kg? will make a difference of 0.2% for going uphill, now compare that same 200g weight loss from tires - this would make a huge ~10% drop on the kinetic energy of the entire wheel+tire system.

Yes but it's not only (or maybe even at all) about energy to spin the wheels. You are still taking the whole bike uphill, at least sometimes. So even if the rim and tire weighed 1g, and the hubs 2 pounds, you'd be slower going uphill even though the inertia is reduced.

I haven't done the math, but I suspect the energy to rotate the wheels is so insignificant by comparison it's not even worth taking about rotating mass savings on a bicycle. It's enough to simplify for the sake of carrying less mass wherever.

Edit: I can't say for certain on the F1 tires comment, but I am confident that is not the case. I haven't followed the sport in awhile, but again there are way more dominant effects to consider before inertia of the wheels. Namely braking power and cooling, as well as the tire sidewall stiffness and construction with its effect on overall grip. Maybe even aerodynamics themselves, which seems to trump everything nowadays. Really hard to say with rules / regulations.

Actually I have to disagree. The rotational mass does make a huge difference, but only if it's far from the rotational axis (as can be seen in the mass of inertia formula I = m * r², the radius is squared, so any distance added from the rotational axis is exponential). It's all about the rim and tire weight, not about the hubs, spokes, or rotors. The thing is though, shaving weight, from the already smaller part of the moment mass of inertia - the rim, is much harder than from a tire. Because tire makes up about 70% of the kinetic/MMoI of the entire tire+wheel system - there's much more margin for weight reduction.

I can attest to this when I changed from allu rims + dhr to carbon rims + dissector. The change was night and day, and literally transformed my bike just from that - the acceleration and change of direction difference was immense - the bike felt zippier, and from a slow roll out of corner, or stop going uphill the required torque was soooo much less to start the wheel going, and these stats kinda back it up.

I was looking mostly at the rotation kinetic/mass moment of inertia - This has most effect whenever you want to either brake, accelerate , start rolling from a stop, or change direction. So for example on my twisty local trails, where it's kinda narrow and you constantly have to brake/accel and thread between the small tight corners or change direction in narrow paths between the trees - this is where you'd see the most difference.

If you look at going up hill - this only applies on technical (where you have to momentarily stop and start, or change lines), and steep terrain from where, for example, you go from a corner (slowing down/braking) and then have to accelerate into a hill - this would make the first 2-3 pedal strikes much easier requiring less torque*, the rest (once the wheel is in motion) of course will not matter as much.
But to gain any significant advantage for going consistent speed uphill would be hard anyway, as the biggest mass of the system is the rider, so unless you wanna go on a diet - there's not much more I can say about that.

*Regarding torque - I'm mostly referring to very steep stuff where you're already on 50T so you can't reduce the drive ratio any further.

 

[mikesee]

You lost me at 30km/h.

 

[GeForceFX]

You lost me at 30km/h.

Haha, that's why I included the mph and lbs conversions on some spot, thought most of the readers may be from US.

 

[mikesee]

Haha, that's why I included the mph and lbs conversions on some spot, thought most of the readers may be from US.

I didn't have a problem with the conversion. I got stuck on the fact that that's a lot of speed for any trail I get to ride in a given year. Not entirely sure I got going that fast at all in '21.

Cut that in half and it'd be closer to what most people I know see for the first few hours of an average ride. And then things slow down from there...

 

[GeForceFX]

I didn't have a problem with the conversion. I got stuck on the fact that that's a lot of speed for any trail I get to ride in a given year. Not entirely sure I got going that fast at all in '21.

Cut that in half and it'd be closer to what most people I know see for the first few hours of an average ride. And then things slow down from there...

Yeah you're right, unless you ride XC 30 might be too much. Although for beefier setups the MMoI will be higher... anyyway:

Done a quick calc for 15km/h(9.32057mph), but because all of the forces are smaller, but with the same exponential - it ends up with pretty much the same result, slightly in favor of the wheels (for less than 1%) at 10rad/s (15kmh), just the "noticeable" part to a human will be less, as the forces are smaller (since the angular momentum for speed is squared).

Have in mind that these are pretty light wheels and tires (comparing 1440g and 1000g wheelsets, which are pushing even XC weights, and 1250g, 1400g, 1550g weights for both tires, we're talking about racing ralph, kenda booster pro, rekon race, rekon, and similar level of tires here), so if you run heavy trail / enduro and such the wheel weight will make moving mass bigger, which will make the forces bigger even at slower speeds.

Corrected rotor weights, as I accidentally included a "free rotor upgrade" for the wheels on the first go, only accounts for 0.24% deviation.

 

[Jack Watts]

Actually I have to disagree. The rotational mass does make a huge difference, but only if it's far from the rotational axis (as can be seen in the mass of inertia formula I = m * r², the radius is squared, so any distance added from the rotational axis is exponential). It's all about the rim and tire weight, not about the hubs, spokes, or rotors. The thing is though, shaving weight, from the already smaller part of the moment mass of inertia - the rim, is much harder than from a tire. Because tire makes up about 70% of the kinetic/MMoI of the entire tire+wheel system - there's much more margin for weight reduction.

You're dramatically overstating the contribution of rotational mass. It makes a difference. It does not make a huge difference.

Kraig Willett wrote this article 20 years ago...and physics haven't fundamentally changed: - “An Ounce off the Wheels is Worth a Pound off the Frame”: Is Rotational Weight Crucial?

bottom line, while it won't be a massive difference, the lighter wheels and heavier tires will be faster in all uphill conditions. System weight will trump MOE. Sorry to burst your bubble.

 

[Thoreau]

i shaved weight in the wheels, cassette, etc. mainly to counteract the tire weight. Light tires dont last long here, and i went for the net result of saving where I could while not dealing with flats or rim strikes.

id be in hog heaven if i could also go with lighter tires, but the rocks here override those dreams.

sure as hell loved the s-works captain tires, tubeless, on my 26in hardtail til the night when a sidewall slash sent me flying into additional jagged rocks. =)

 

[Reaperactual]

My brain switched off after I read the title. 😲

My formula for choosing wheels is:-

(bp⁴bq+d/s-w,🤷‍♂️=😃)

Best price for best quality + durability/strength - weight, not bothered = happy.

 

[D. Inoobinati]

Sorry to burst your bubble.

The OP made an excellent case against spending stupid money on super light wheels. In the context of his thesis, rotational weight IS a big deal.

Additionally, the article you referenced was written less than 2 years ago, not 20 years ago.

 

[ocnLogan]

I’ll admit to skimming this, as it is more dense than my “finally done working and putting kids to bed and finally have time to myself” brain wants to digest.

But I lol’d at “I’m not the smartest zergling in the control group”. So props for that.

Now if you’d said Dragoon, I might have been more worried….

 

[eri]

Difference between bicycle and f1 cars, bikes don’t accelerate then dissipate that same kinetic energy to make rotors red hot. In cars with continuous accel/decal that reduced inertia saves energy, on a bike the extra ke you put into a heavy wheel will dissipate by carrying you up the hill. For bike climbing it’s total mass that matters and inertia is along for the ride.

it’s ok to spend money on light wheels and tires as long as the $/g is sensible.

 

[uzurpator]

Whether it is inconsequential vs 86% of inconsequential it remains inconsequential.

 

[GeForceFX]

Disregard, quoted a link.