# How many watts would be save by loosing a 1/2 pound of weight from a wheelset?

#### azdroptop

##### New Member
Just wondering? My new wheelset/tire/cog setup is 1/2 pound lighter than my old set up.(Bathroom scale weight) And I was just wondering what kind of benefit that equates to if any at all? Just curious.

#### daveryanwyoming

##### Well-Known Member
azdroptop said:
Just wondering? My new wheelset/tire/cog setup is 1/2 pound lighter than my old set up.(Bathroom scale weight) And I was just wondering what kind of benefit that equates to if any at all? Just curious.
On the flats at steady speed virtually nil. On a steep climb it depends on how much you weigh plus the weight of all your gear. Check out http://www.analyticcycling.com/ and plug numbers into their Speed Given Power calculator in the Static Forces On Rider menu. For a given power you can calculate speed on a given grade with assumptions about frontal area, air density, rolling resistance etc. You'll see a bit of difference on hills, especially steep hills but very little difference on the flats.

-Dave

#### azdroptop

##### New Member
daveryanwyoming said:
On the flats at steady speed virtually nil. On a steep climb it depends on how much you weigh plus the weight of all your gear. Check out http://www.analyticcycling.com/ and plug numbers into their Speed Given Power calculator in the Static Forces On Rider menu. For a given power you can calculate speed on a given grade with assumptions about frontal area, air density, rolling resistance etc. You'll see a bit of difference on hills, especially steep hills but very little difference on the flats.

-Dave
Hi Dave,

Thanks a lot. I'll check it out. With all the talk of ratational mass and wheels I was just curious...

#### daveryanwyoming

##### Well-Known Member
azdroptop said:
.... With all the talk of ratational mass and wheels I was just curious...
Spend some time fiddling with the calculators over there and you'll see that most of the rotational mass talk is just that...talk. It doesn't make nearly as much difference as many believe.

#### 9.8mps2

##### New Member
At a steady state you are just taking that greater mass down the road with you. On a climb you are pretty much just carrying that mass up the hill with you. The big difference is realized when accelerating ( increasing the velocity of the rotating mass). And then your brakes have a greater workload in taking that energy away when slowing. Yes, you could "coast" better, but if you are trying to pare weight for performance you are either pedaling at strongly as possible or braking.
Saving mass at the hub is much less appreciated than saving at the periphery with lighter wheels/ rubber.
Like a stock trade on comission, a heavier wheel will cost you more each time you sell or buy in brakes or muscles.
If a suspension is involved, the suspension works better with less "unsprung weight" involved - that being wheel & swingarm or fork - mass not actually carried by the suspension.

#### daveryanwyoming

##### Well-Known Member
9.8mps2 said:
At a steady state you are just taking that greater mass down the road with you. On a climb you are pretty much just carrying that mass up the hill with you. The big difference is realized when accelerating ( increasing the velocity of the rotating mass). And then your brakes have a greater workload in taking that energy away when slowing. Yes, you could "coast" better, but if you are trying to pare weight for performance you are either pedaling at strongly as possible or braking.
Saving mass at the hub is much less appreciated than saving at the periphery with lighter wheels/ rubber.
Like a stock trade on comission, a heavier wheel will cost you more each time you sell or buy in brakes or muscles.
If a suspension is involved, the suspension works better with less "unsprung weight" involved - that being wheel & swingarm or fork - mass not actually carried by the suspension.
Ya know given your handle I'd think you'd take into account a total physics model of acceleration and the work of moving uphill against gravity. Yes the larger moment of inertia of a heavier tire/rim requires additional energy to accelerate over a lighter tire/rim or weight near the hub. But you also have to consider the energy requirements of linear acceleration. From that standpoint the moment of inertia differences between "heavy" and "light" racing wheels is signifigantly less than the inertial requirements of accelerating the mass of the rider and frame. It's too easy to look at a wheel in isolation and conclude a hundred or so grams of rim weight here and there will make a huge difference in the energy required to accelerate that wheel but add the rider and the rest of the bike and it's negligible.

Check out the examples on the Wheels & Aero & Weight tab at http://www.analyticcycling.com/ the crit example of accelerating out of a corner is a great example where the aerodynamic forces are so dominant, even when accelerating, that the heavier more aero rim gains on the lighter rim even in the first 100 meters out of the corner.

As for climbing, you aren't "just carrying that mass up the hill" you're lifting that mass against the acceleration of gravity (yeah 9.8 m/s^2) which is work in the physics sense of the word. Take into account doing that at different speeds and you've defined power. IOW a large part of the power you put out at climbing speeds goes towards lifting your mass up the hill. That's why overall weight (you, your bike, your clothes, your water, your wheels...) is more important while climbing than on the flats. It still counts on the flats since it impacts rolling resistance but that tends to be small when compared to the other forces such as wind resistance you have to overcome. The half pound mentioned in the OP is a pretty small portion of the average rider plus bike plus kit so the deltas in terms of power required to maintain a given speed are also small.

As long as I've been cycling folks have been touting the advantages of light rims and tires based on moment of inertia, but it really isn't as important as many cyclists think, not unless you're just rolling wheels downhill by themselves and leaving the bikes at home.

#### wiredued

##### New Member
The last time I calculated my 1/2 hour climb I think 10 lbs extra used 24 watts aprox. but rotating mass is the worst kind for climbing.

#### 9.8mps2

##### New Member
Quite right Dave. The handle is no accident, my name is Michael Patrick Simmons , and I am also no stranger to physics. What I was trying to do was teach, and give it in terms so that someone may easily glean the big picture w/o any mathematical masturbation.( since with the data provided neither you nor I can precisely quantify what benefit is gained .)
If azdroptop comprehends your model better than mine - OK - I have failed.

#### daveryanwyoming

##### Well-Known Member
9.8mps2 said:
Quite right Dave. The handle is no accident, my name is Michael Patrick Simmons , and I am also no stranger to physics. What I was trying to do was teach, and give it in terms so that someone may easily glean the big picture w/o any mathematical masturbation.( since with the data provided neither you nor I can precisely quantify what benefit is gained .)
If azdroptop comprehends your model better than mine - OK - I have failed.
Fair enough. I'm not knocking your model for moment of inertia, just the isolation of one fairly minor component of the entire system. I can't count the number of times I've heard a cyclist explain the evils of rotating weight without a thought to the bigger picture. I'm sure it sells a lot of light tires and rims

#### 9.8mps2

##### New Member
I'm hip - and for a while I was sucked into the ultra and lunar light tubes until I put some proper conti tubes on and my mass to time changing blownout tube coefficient improved dramatically ! And it is frequently the 15 stone cats like me-with 10% body fat ( 10% over ideal) that go that route. The aftermarket guys love us folks that will spend a few hundred to save 40 grams...letsee by all means don't consider losing 40 gm of WEIGHT !

#### sidewind

##### New Member
wiredued said:
The last time I calculated my 1/2 hour climb I think 10 lbs extra used 24 watts aprox. but rotating mass is the worst kind for climbing.
In climbing doesn't matter wether mass is rotating or not. Acceleration was the case when one rotational kg counts as two stationary kgs.

#### rmur17

##### New Member
azdroptop said:
Just wondering? My new wheelset/tire/cog setup is 1/2 pound lighter than my old set up.(Bathroom scale weight) And I was just wondering what kind of benefit that equates to if any at all? Just curious.
Say you climb around 5 m/s (18 kph) on a steepish hill, dropping 1/2 lb will save you: ~ 11 x hill gradient (%)

IOW, not a whole lot. Savings are directly proportional to speed so you can scale up or down as you see fit from the 18 kph basline.

edit: yes I've simplified the sine(arctan(gradient)) bit ... for these masses it's doesn't matter much.

#### NM87710

##### New Member
Not a whole lot is relative if you've ever lost a TT(they're not all flat) by a 1 or 2 seconds. Not saying one should or shouldn't ride light equipment - just depends how much you're willing to do to achieve your goals.

#### 531Aussie

##### Well-Known Member
azdroptop said:
just wondering

on climbs, according to the Kreuzotter calculator, any drop in weight as a percentage of the weight of bike and rider combined is pretty much commensurate with the same percentage speed increase.

http://www.kreuzotter.de/english/espeed.htm

so, (obviously) if a 90kg rider has a 10kg bike and he drops 1kg off his ****, his speed should increase by about 1%. This might sound like nothing, but 1% off a 30min climb is 18 seconds. Eighteen seconds is nice amount of time to win by

#### daveryanwyoming

##### Well-Known Member
rmur17 said:
Say you climb around 5 m/s (18 kph) on a steepish hill, dropping 1/2 lb will save you: ~ 11 x hill gradient (%)

IOW, not a whole lot. Savings are directly proportional to speed so you can scale up or down as you see fit from the 18 kph basline.

edit: yes I've simplified the sine(arctan(gradient)) bit ... for these masses it's doesn't matter much.
And even these are optimistic in terms of power savings since they don't take into account the other forces we have to overcome and most of us can't hold 18 kph on a 15% grade.

Assuming a 156 pound rider with 20 pounds of bike and kit (80 kg) as a baseline and taking the analyticcycling defaults for frontal area, sea level air density, rolling resistance, etc. and assuming the rider can hold somewhere near 250 watts on a climb you'd get the following savings by dropping half a pound(0.23 kg).
• 5% grade, ~12 mph you save 0.6 watts for 0.5 pounds (matches nicely with your slope model rmur!)
• 10% grade, ~6.8 mph saves you 0.7 watts
• 15% grade, ~4.6 mph saves you 0.7 watts
Dang rmur, your much simpler slope only model is pretty darn accurate and saves punching a bunch of numbers into the online calculators.

NM87710 said:
Not a whole lot is relative if you've ever lost a TT(they're not all flat) by a 1 or 2 seconds. Not saying one should or shouldn't ride light equipment - just depends how much you're willing to do to achieve your goals.
Yeah, true enough if you're trying to get that last bit of TT performance that half pound may be noticeable but if you consider that same 250 Watt/ 80kg rider in a 5 mile TT up a 7% steady grade you'd get:
• @ 250 watts, 9.27 mph, 32 minutes, 21.7 seconds to climb 5 miles for 80kg
• @250 W, 9.29 mph, 32 minutes, 17.05 seconds at 79.77 kg
So sure 'nuff it could easily make the winning difference in a competitive field. If you're finishing within seconds on a long hill climb but just a bit out of the money every ounce of savings is worthwhile. But how many cyclists out there who are finishing minutes back and have five or ten extra pounds of body weight to lose are buying wheels 100 grams lighter or titanium skewers in the hopes of getting that win

#### rmur17

##### New Member
daveryanwyoming said:
Dang rmur, your much simpler slope only model is pretty darn accurate and saves punching a bunch of numbers into the online calculators.
I specialize in simple things .

As you mention the speed is likely >5 m/s on the 5% grade and < 5 m/s on the 15% grade. So to simplify even further, I'd say we're talking saving roughly 1W across the board which is really precious little.

#### Alex Simmons

##### Active Member
daveryanwyoming said:
Yeah, true enough if you're trying to get that last bit of TT performance that half pound may be noticeable but if you consider that same 250 Watt/ 80kg rider in a 5 mile TT up a 7% steady grade you'd get...
Somehow I don't think 3.1W/kg is gunna threaten a podium spot

#### [email protected]

##### New Member
Slightly off topic, but if you're interested in saving power, I heard somewhere that if you maintain your same power output, you "save" 1.3% power for each kilogram of body weight lost. So if roughly 2.21 pounds is one kilo, its .294% for a 1/2 pound. I'm not sure if this applies to the bike and wheels somehow, although you are not likely to have a wheelset which is a few kg's lighter than another. Just thought you'd be intersted to know... And I agree gravity plays a role, and weigth counts majorly when climbing!

#### daveryanwyoming

##### Well-Known Member
Slightly off topic, but if you're interested in saving power, I heard somewhere that if you maintain your same power output, you "save" 1.3% power for each kilogram of body weight lost. ....... I'm not sure if this applies to the bike and wheels somehow, although you are not likely to have a wheelset which is a few kg's lighter than another.....
Actually, that's entirely on topic as this entire thread has been about power savings as you drop weight. Given a steady power output it doesn't matter whether it's your weight or component weight or weight in your water bottles, but most of us have a lot more spare body weight to drop whereas the bikes are already pretty lean.

Your estimates make way too many assumptions. IOW on a moderate climb a 100 kilo rider won't save 1.3% by dropping a kilo but a 40 kilo rider might save more than 1.3% by dropping the same weight. It also depends on terrain and other factors like how aerodynamic the rider is. If you're talking about a steep hill climb at low speeds then weight will be real important (but still as a percentage of total weight so the 100 kg rider will need to drop more weight than the 40 kilo rider) if you're talking about a dead flat TT, then weight is negligible compared to aerodynamics.

#### dhk2

##### Well-Known Member
An easy way to figure the power on steep climbs is just to multiply weight by the vertical rate of climb. If you work in SI units (newtons and meters/sec), the product (n-m/sec) is watts.

EG, if climbing speed on a 10% grade is 3 m/sec (~6.8 mph), the vertical rate is 0.3 m/sec. 0.5 lbs converts to 2.23 newtons in SI units. Multiplying 0.3 x 2.23 yields 0.67 watts savings....quick and easy.

For an 80 kg (784 nt) rider and bike, total power at the road is 235 watts. Adding a 5% factor for drivetrain and tire losses bumps this up to 247 watts output needed. In this case the 0.67 watt savings would be 0.3% of total.

Agree with the previous posts that this kind of savings is important to racers looking for a few seconds on a big climb, but not worth a lot to us club riders.

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