The physics of X01 vs GX cassette weight

[D(C)]

I was trying to decide whether it's worth paying double what a SRAM GX cassette costs for an X01 cassette.

SRAM X01 XG 1195 weight - 263 g
SRAM GX XG 1150 weight - 393 g

Difference: 130 g

The extra weight adds overall weight and unsprung weight, but the concern most people generally cite is rotational weight. So I thought I would see how extra rotational cassette weight compares to weight in tires.

Based on a quick calculation, it seems the extra torque needed to accelerate a cassette 130 g heavier is about equal to the torque needed to accelerate a tire only 2 g heavier.

So I might as well buy the cheaper cassette and put in a couple drops less of Stans.

Can another nerd with too much time on their hands weigh in?
_________________________

Calculation:

Torque = (moment of inertia)*(angular acceleration): so comparing moments of inertia will determine the amount of torque needed for a given wheel acceleration.

Moment of inertia = (mass)*(radius^2)

Radius of cassette centre of mass ~ 1.5 inches
Radius of 27.5 tire centre of mass ~ 12.5 inches

So comparing moments of inertia, (12.5^2)/(1.5^2) = 70

Basically, weight in tires has 70 times the effect on torque needed than the cassette. Based on this, 130 g increase in cassette weight is equivalent to just under 2 g added to a tire.

[shirk]

It appears I need to start a winter night Fiver series to keep you busy, obviously you have too much time on your hands.

[D(C)]

It appears I need to start a winter night Fiver series to keep you busy, obviously you have too much time on your hands.

These are the things that keep me up at night!

But I won't say no to more racing.

[toast2266]

So based on those same calculations, in terms of acceleration, an 800g tire on a 29" wheel is equivalent to a 720g tire on a 27.5" wheel and a 645g tire on a 26" wheel. That's surprisingly significant. That's also assuming center of mass for each tire size is at 29, 27.5, and 26, respectively (I suspect if I actually measured, 29 and 26 would be close, 27.5 would be a bit off).

(I'm just running more numbers because its interesting. Sorry, too far out of high school physics to confirm that your calculations are correct, but they seem to produce plausible results.)

[davep]

You only included rotational energy in your calc. Need to add non-rotational kinetic energy (otherwise you would calculate that non-rotating mass, like your frame, requires 0 energy to accelerate).

Total energy required to accelerate an incremental mass connected to your wheel scales like:

energy ~ (1 + (r/R)^2)*m

r: radius of the mass in question from axis of rotation
R: radius of the wheel
m: mass

R ~ 13.75" for your example.
r ~ 1.5" for the cassette; r ~ 12.5 for a tire.

for the cassette: (1+(1.5/13.75)^2) = 1.012 so the cassette takes 1.2% more energy to accelerate than non-rotating mass on your bike.
for the tire: (1+(12.5/13.75)^2) = 1.83 so the tire takes 83% more energy to accelerate than non-rotating mass on your bike.

130g in cassette weight is worth 132g of frame/fork/saddle/etc weight; or worth 72g of tire weight

[jamesp]

so take a piss or a big shit before riding & it all evens out?

[davep]

pooping before a ride is always worthwhile.

[D(C)]

You only included rotational energy in your calc. Need to add non-rotational kinetic energy (otherwise you would calculate that non-rotating mass, like your frame, requires 0 energy to accelerate).

Total energy required to accelerate an incremental mass connected to your wheel scales like:

energy ~ (1 + (r/R)^2)*m

r: radius of the mass in question from axis of rotation
R: radius of the wheel
m: mass

R ~ 13.75" for your example.
r ~ 1.5" for the cassette; r ~ 12.5 for a tire.

for the cassette: (1+(1.5/13.75)^2) = 1.012 so the cassette takes 1.2% more energy to accelerate than non-rotating mass on your bike.
for the tire: (1+(12.5/13.75)^2) = 1.83 so the tire takes 83% more energy to accelerate than non-rotating mass on your bike.

130g in cassette weight is worth 132g of frame/fork/saddle/etc weight; or worth 72g of tire weight

Thanks; this makes sense. I was surprised by how dramatic the effect I calculated was. Considering energy as a whole is more useful.

[Sutter]

Where is Supu with the old skool "No Nerds!!!!!!!" shit when you need him??

I used to ask DaveP in the car on the way home from the mountain to explain what he studied for his pHD program. I would then try and repeat it to him at a later date. Never even got past a sentence or two without him just being like "nope."

[~mikey b]

Where is Supu with the old skool "No Nerds!!!!!!!" shit when you need him?? ."

He got scared when I came looking for him at Kirkwood after talking shit a couple years ago. Scurried off with his tiny tail between his short little legs.

[jm2e]

Suddenly we're at MTBR again.
Though it's comforting to know we've got some pretty smart fellers here at TGR,
it's also enough to simply say, you're retarded if you pay the extra money for the XO1 cassette.

[panchosdad]

So based on those same calculations, in terms of acceleration, an 800g tire on a 29" wheel is equivalent to a 720g tire on a 27.5" wheel and a 645g tire on a 26" wheel. That's surprisingly significant. That's also assuming center of mass for each tire size is at 29, 27.5, and 26, respectively (I suspect if I actually measured, 29 and 26 would be close, 27.5 would be a bit off).

(I'm just running more numbers because its interesting. Sorry, too far out of high school physics to confirm that your calculations are correct, but they seem to produce plausible results.)

That seems counter to what I would have guessed. I would have thought that the bigger radius tire would with a lighter tire would require the same torque as a heavier tire on a smaller wheel. What am I missing?

[Canada1]

Initiation versus centrifical force working to your benefit once in motion.

[smmokan]

it's also enough to simply say, you're retarded if you pay the extra money for the XO1 cassette.

Especially at retail prices.

[Sutter]

pooping before a ride is always worthwhile.

This is more in line with what I've come to expect from this place over the years.

[Anospa]

Tried the mid-ride poop a few times this year, does wonders!

[Dantheman]

pooping before a ride is always worthwhile.

Dropping a deuce at 5:30 am before leaving for a mid-summer dawn patrol ride is always a good omen.

[detrusor]

Do you bag and carry your mid ride poop? If so that negates the savings (but feels so good)

[joetron]

But what about the XDomezzz vs the Full Pinzzz?

[jono]

That seems counter to what I would have guessed. I would have thought that the bigger radius tire would with a lighter tire would require the same torque as a heavier tire on a smaller wheel. What am I missing?

Toast's work. Results not correct, but kinda moot--see davep's post for better math.

[toast2266]

That seems counter to what I would have guessed. I would have thought that the bigger radius tire would with a lighter tire would require the same torque as a heavier tire on a smaller wheel. What am I missing?

Yeah, I wrote it backwards, but per davep's post, the math is wrong anyways.

[DasBlunt]

Dropping a deuce at 5:30 am before leaving for a mid-summer dawn patrol ride is always a good omen.

great post and this thread is awesome.

Not being a math guy i know I can drop mega weight with the 11x1 full carbon cranks and that sweet cassette. The way that one piece of the cassette is forged separate= pretty bad ass and stiff. I hate grinding gears going up under load and the stiffer and lighter the better.

[pureantigravity]

I have some Carbon Brake Rotors that you need.
+ Less rotational inertia.
+ Also get faster entry into corners.
+ Better heat management
+ doubles as rad bbq hotplate for bacon.
Tgr sprockets will swoon.
Nasa materials and quality.
Excellent resale value.

Shimano is taking the lead again though as far as the drivetrain is concerned.