Wheel Weight vs. Frame Weight, Physics for Regular Folks

Triathlon Forum
1

Hey Slowtwitch_Engineering,

I am under the impression that there is near universal agreement that the weight of one’s wheels matters more than the weight of one’s frame in bike racing. (As in, spending $X to shave Y weight in your wheels is better value than spending the same to save Y weight in your frame.) Can someone give me a more sophisticated answer than, ‘You have to push the wheels around,’?

My intuition is that even if my rims are heavier, once I get them rolling they will carry more inertia than a set of lighter wheels and hence the bike will ‘roll farther.’ I’m sure lighter wheels will feel quicker off the line, but won’t heavier wheels carry the rider farther with greater spinning inertia?

Thanks for informed answers!

2

The agreement is that weight generally does not matter in triathlon unless you are carrying it under your tri top. Aero is king baby.

3

As you point out, the static weight of the bike (wheels included) will allow it to have inertial mass as the bike moves forward (the heavier the bike, the more inertial mass), the wheels (and other spinning parts) will lend additional inertia (called rotational inertia) as they spin on their axles. Thus, a two pound wheel will have more total inertia than a two pound frame.

You want the least inertial mass (both static and rotational) that you can get. The bike with more inertia will roll farther, but it’s just giving you back the energy you had to put into it to get it up to speed. When braking for corners, the bike with more inertia will have more energy that you need to burn off using the brakes (i.e. waste) and then put back when re-accelerating the bike.

The old bike racer’s adage is that reducing a pound on your wheels is worth two on your frame. It’s a reasonable rule of thumb…though since rotational inertia depends on how far the weight is from the center of rotation, it’s really rims, tires, and tubes that matter (the hub is so close to the axis of rotation that it can be treated as static weight…and quick releases don’t spin at all).
Pedals, cranks, and derailleur pulleys are also either on such a small radius, or turning so slowly that their rotational inertia is also trivial.

Net-net:

Lighter is better

Be willing to spend 2X per gram saved for rims, tires and tubes compared to static components like frames, bars, etc.

For static weight, look for for items that save you more than 1g/$ (just my rule of thumb, no logic here). Often the best bang for the buck is on small parts like carbon bottle cages, titanium QRs, latex tubes, stems, etc.

Weight doesn’t impact performance nearly as much as aerodynamics…a big heavy disc wheel will be faster than an uber-light climbing wheel on everything except a time trial straight up an alpe.

4

Thanks - that’s very helpful.

5

You intuition is on the right track, see this link for a more complete analysis:

http://forum.slowtwitch.com/cgi-bin/gforum.cgi?post=2172133

Hey Slowtwitch_Engineering,

I am under the impression that there is near universal agreement that the weight of one’s wheels matters more than the weight of one’s frame in bike racing. (As in, spending $X to shave Y weight in your wheels is better value than spending the same to save Y weight in your frame.) Can someone give me a more sophisticated answer than, ‘You have to push the wheels around,’?

My intuition is that even if my rims are heavier, once I get them rolling they will carry more inertia than a set of lighter wheels and hence the bike will ‘roll farther.’ I’m sure lighter wheels will feel quicker off the line, but won’t heavier wheels carry the rider farther with greater spinning inertia?

Thanks for informed answers!

6

It is totally wrong though, unless the math I linked above has a flaw in it?

The old bike racer’s adage is that reducing a pound on your wheels is worth two on your frame. It’s a reasonable rule of thumb.

7

The agreement is that weight generally does not matter in triathlon unless you are carrying it under your tri top. Aero is king baby.

Are you saying that gazongas are not acceptable in tri?

8

It is totally wrong though, unless the math I linked above has a flaw in it?

The old bike racer’s adage is that reducing a pound on your wheels is worth two on your frame. It’s a reasonable rule of thumb.

Rotational mass matters if you gain benefit from rapid accelerations… hence why they’re useful in road races (and liked by roadie), or I guess very technical TT courses.

On a flat course as you say it doesn’t matter, and uphill its effectively the same as any other mass.

I suspect there might be some riders for whom higher rotational inertia is marginally better, in the same way that higher inertia indoor trainers can be easier to sustain wattage on for some.

9

You intuition is on the right track, see this link for a more complete analysis:

http://forum.slowtwitch.com/cgi-bin/gforum.cgi?post=2172133

Cool post. Lost me at “solved it numerically with a 4th order Runge-Kutta numerical differentiation”.

10

The cliff notes is that everyone more or less agreed that at constant velocity (which a time trial mostly is) wheel weight wouldn’t matter any more than frame weight

BUT, some wondered if the pulses of acceleration as you pedal, which involved a tiny acceleration then deceleration, would cause heavy wheels to be more of a penalty than a heavy frame

he did the math and found “no, its actually LESS of a penalty, but not enough less to worry about”

You intuition is on the right track, see this link for a more complete analysis:

http://forum.slowtwitch.com/cgi-bin/gforum.cgi?post=2172133

Cool post. Lost me at “solved it numerically with a 4th order Runge-Kutta numerical differentiation”.

11

Rotational mass matters if you gain benefit from rapid accelerations… hence why they’re useful in road races (and liked by roadie), or I guess very technical TT courses.

On a flat course as you say it doesn’t matter, and uphill its effectively the same as any other mass.

I suspect there might be some riders for whom higher rotational inertia is marginally better, in the same way that higher inertia indoor trainers can be easier to sustain wattage on for some.

Correct. Plus, even in the examples listed you have to take the difference in weight into account as well, meaning that: is there really a difference in spin up on wheels that are less than 500 grams difference it weight each, when most of that difference is hubs and spokes?

So, light wheels probably are not worth that much in road races either.

12

It is totally wrong though, unless the math I linked above has a flaw in it?

The old bike racer’s adage is that reducing a pound on your wheels is worth two on your frame. It’s a reasonable rule of thumb.

Nothing wrong with the math on that link, it’s just that it covers steady state riding and is attempting to prove that micro-accelerations that happen during the pedal stroke aren’t significant (I fully agree, the bike+rider have too much inertia for this to matter).

There are lots of cases (even in a TT) where accelerations are necessary: corners, passes, etc. As a % of total time they are minimal, but the extra wattage needed for these comes at an exponential metabolic cost, so there is some value here.

Since the question was not "does weight matter, " but rather “does shaving rotating mass matter more than shaving static mass” what we need to look at is the total inertial mass and store kinetic energy of a rotating component compared to a static one…let’s look at a carbon rim

Assumptions:

Mass: 400g

Distance from center of rotation: 300mm (I’m treating this as a point mass just to make the math easier, it’s a reasonable approximation)

So, the wheel’s rotational moment of inertia is 400g*.3m^2= 36gm^2

Now let’s say the bike is moving at 30kph (8.333m/s), and correspondingly the wheel is spinning at 3.79rps (assuming the OD is 700mm)

The momentum from the static weight of the rim will be: P= Iv = 400g*8.333m/s = 3.333gm/s

The total kinetic energy for the rim will be:

1/2I(v/r)^2 + (1/2m v^2)

Rotational component: 0.5I(v/r)^2 = 0.536(8.333/.35) = 10,204

Static component: 0.5mv^2 = 0.54008.333^2 = 13,888

You can see these are roughly the same…thus the 2:1 rule of thumb.

13

It is totally wrong though, unless the math I linked above has a flaw in it?

The old bike racer’s adage is that reducing a pound on your wheels is worth two on your frame. It’s a reasonable rule of thumb.

Nothing wrong with the math on that link, it’s just that it covers steady state riding and is attempting to prove that micro-accelerations that happen during the pedal stroke aren’t significant (I fully agree, the bike+rider have too much inertia for this to matter).

There are lots of cases (even in a TT) where accelerations are necessary: corners, passes, etc. As a % of total time they are minimal, but the extra wattage needed for these comes at an exponential metabolic cost, so there is some value here.

Since the question was not "does weight matter, " but rather “does shaving rotating mass matter more than shaving static mass” what we need to look at is the total inertial mass and store kinetic energy of a rotating component compared to a static one…let’s look at a carbon rim

Assumptions:

Mass: 400g

Distance from center of rotation: 300mm (I’m treating this as a point mass just to make the math easier, it’s a reasonable approximation)

So, the wheel’s rotational moment of inertia is 400g*.3m^2= 36gm^2

Now let’s say the bike is moving at 30kph (8.333m/s), and correspondingly the wheel is spinning at 3.79rps (assuming the OD is 700mm)

The momentum from the static weight of the rim will be: P= Iv = 400g*8.333m/s = 3.333gm/s

The total kinetic energy for the rim will be:

1/2I(v/r)^2 + (1/2m v^2)

Rotational component: 0.5I(v/r)^2 = 0.536(8.333/.35) = 10,204

Static component: 0.5mv^2 = 0.54008.333^2 = 13,888

You can see these are roughly the same…thus the 2:1 rule of thumb.

Can you put that in terms of the % of total kinetic energy of a bike+rider? Thanks :wink:

edit: Oh…and then take a look at the change in the total when you cut your assumed rim weight in half (which is a highly unlikely occurance).

14

but 95% of the time the triathlete is at steady state.
the 2:1 rule of thumb probably only applies during the act of accelerating (if even then, since any energy you use to accelerate and pass, will result in a longer sustained higher speed once you stop putting in the extra power )

the only time the lighter wheels would offer more advantage than a lighter frame would be corners where you have to brake, and then accelerate out of of.

You can see these are roughly the same…thus the 2:1 rule of thumb.

15

but 95% of the time the triathlete is at steady state.
the 2:1 rule of thumb probably only applies during the act of accelerating (if even then, since any energy you use to accelerate and pass, will result in a longer sustained higher speed once you stop putting in the extra power )

the only time the lighter wheels would offer more advantage than a lighter frame would be corners where you have to brake, and then accelerate out of of.

You can see these are roughly the same…thus the 2:1 rule of thumb.

…and how much does the system mass matter at steady state? Not very much, since it only impacts rolling resistance and bearing load friction. Again, the issue was the RELATIVE value of paring rotating weight vs. static weight, not trying to debunk the cult of weight weeniness.

16

It is totally wrong though, unless the math I linked above has a flaw in it?

The old bike racer’s adage is that reducing a pound on your wheels is worth two on your frame. It’s a reasonable rule of thumb.

Nothing wrong with the math on that link, it’s just that it covers steady state riding and is attempting to prove that micro-accelerations that happen during the pedal stroke aren’t significant (I fully agree, the bike+rider have too much inertia for this to matter).

There are lots of cases (even in a TT) where accelerations are necessary: corners, passes, etc. As a % of total time they are minimal, but the extra wattage needed for these comes at an exponential metabolic cost, so there is some value here.

Since the question was not "does weight matter, " but rather “does shaving rotating mass matter more than shaving static mass” what we need to look at is the total inertial mass and store kinetic energy of a rotating component compared to a static one…let’s look at a carbon rim

Assumptions:

Mass: 400g

Distance from center of rotation: 300mm (I’m treating this as a point mass just to make the math easier, it’s a reasonable approximation)

So, the wheel’s rotational moment of inertia is 400g*.3m^2= 36gm^2

Now let’s say the bike is moving at 30kph (8.333m/s), and correspondingly the wheel is spinning at 3.79rps (assuming the OD is 700mm)

The momentum from the static weight of the rim will be: P= Iv = 400g*8.333m/s = 3.333gm/s

The total kinetic energy for the rim will be:

1/2I(v/r)^2 + (1/2m v^2)

Rotational component: 0.5I(v/r)^2 = 0.536(8.333/.35) = 10,204

Static component: 0.5mv^2 = 0.54008.333^2 = 13,888

You can see these are roughly the same…thus the 2:1 rule of thumb.

Can you put that in terms of the % of total kinetic energy of a bike+rider? Thanks :wink:

edit: Oh…and then take a look at the change in the total when you cut your assumed rim weight in half (which is a highly unlikely occurance).

Ever ask a question you knew the answer to ;). Yeah, it’s small; I’m not trying to make a case that shaving weight (rotating or not) makes large gains in performance, just looking at the relative value of removing rotating vs. non-rotating grams. The rotational KE is only 1-2% of the total.

17

yes, I get that

and I am suggesting that even the relative difference
is the same (except maybe at the turnaround, if it exists)

…and how much does the system mass matter at steady state? Not very much, since it only impacts rolling resistance and bearing load friction. Again, the issue was the RELATIVE value of paring rotating weight vs. static weight, not trying to debunk the cult of weight weeniness.

18

Ever ask a question you knew the answer to ;). Yeah, it’s small; I’m not trying to make a case that shaving weight (rotating or not) makes large gains in performance, just looking at the relative value of removing rotating vs. non-rotating grams. The rotational KE is only 1-2% of the total.

Right…but when it’s stated that way, it sounds like removing wheel weight should be an over-riding concern in terms of overall performance…when it’s actually an exceedingly small factor, even for road races and crits.

If I had a dollar for every time someone asked me about why I run Jet90s in crits since “…those heavier rims are harder to spin up in a sprint”, while they totally ignore the aerodynamics of the situation…I’d be…well…I’d have a couple more dollars at least :wink:

19

man up and start rocking the 1080s

Right…but when it’s stated that way, it sounds like removing wheel weight should be an over-riding concern in terms of overall performance…when it’s actually an exceedingly small factor, even for road races and crits.

If I had a dollar for every time someone asked me about why I run Jet90s in crits since “…those heavier rims are harder to spin up in a sprint”, while they totally ignore the aerodynamics of the situation…I’d be…well…I’d have a couple more dollars at least :wink:

20

man up and start rocking the 1080s

I would if I could…afford them, that is :wink:
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