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Postby toolonglegs » Tue Nov 27, 2007 10:16 am

artemidorus wrote:
toolonglegs wrote:Mine will get play during a ride.Even if (and I have) pulled the axle out and loctited it it still comes loose.

You mean you loctite the preload cap thread and it still loosens? How tight do you have your skewers? They are supposed to lock the cap on the axle.

I have the skewer tight but not overly as they are carbon tips on the fork.It is never a problem just annoying.But now I have a DuraAce front wheel may get ride of the SL.
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by BNA » Tue Nov 27, 2007 10:27 am

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Postby artemidorus » Tue Nov 27, 2007 10:27 am

Kid_Carbine wrote:When it comes to weight in wheels, I still ponder what it is that we are actually weighing.
Is it the mass of the whole wheel assembly complete? If so, then why leave out the skewer? [when used]
Is it the rotating mass of the wheel? If so, then why include the axle & cones?
If just bare overall weight of the finished bike is so important, then a laxative before riding would help as would leaving the bidon behind, but we never do these [well I don't] so it's really the rotating mass of the wheel that is really the important component

If we are looking for a 'lively' wheel, then surely we need to reduce the mass of the rim as this is where the greatest inertia is. [flywheel effect] This is the part that sees the greatest linear acceleration rates while the hub mass, being located so much closer to the center, will offer much less rotational inertia, gramme for gramme, so a wheel with a heavier hub & light rim would [theoretically] perform better than an identical weight wheel with light hub & heavier rim.

What I'm saying here is that it's not just the actual weight of the wheel by itself, that affects performance, but where the weight is located.

Your thoughts?

Moment of inertia of a bicycle wheel has been shown to make a vanishingly tiny difference to acceleration. It simply isn't worth worrying about. Reference below.
Only the overall weight of a wheel makes a difference, and even that is trivial for everyone except a high-cat racer. Maximum 1-2% difference between the best and worst wheels when climbing, less otherwise. Aerodynamics are a different matter, but also make only up to about 1% difference.
So, it really comes down to whatever tickles your fancy when you buy wheels.

Reference: The following was posted by "McM" on a weight weenies forum:

I can't believe that people keep arguing that rotating mass climbs slower than non-rotating mass under the same power. When you are working against gravity, mass is mass, it doesn't matter if it rotates or not. The idea that micro-accelerations due to pedal force fluctations make a difference in the overall picture is a strawman. During pedal force fluctuations, accelerations are decelerations cancel out. All that really matters is average power output vs. gravity.

Since Ras11 complained that no math has been offered, I decided to set up a model to simulate the accelerations/decelerations due to pedal fluctuations. The equations and variable values were taken from the Analytic Cycling web page.

Pedaling force: The propulsion force (from pedaling) was modeled as a sinusoidal. Since it is assumed average power is constant, the nomimal drive force will vary inversely with velocity. So, the propulsion force is modeled as:

Fp = (P/V)(1+Sine(2RT))

Fp = Propulsion force (pedaling)
P = Average power
V = Velocity
R = Pedaling revolution rate
T = Time

(Note: The angle in the sine term is double the pedal revolution rate, since there are two power strokes per revolution)

The drag forces on the rider are aerodynamic drag, rolling resistance, and gravity. These three terms together are:

Fd = (1/2)CdRhoAV^2 + MgCrrCosine(S) + MgSin(S)

Fd = drag force
Cd = Coefficient of aerodynamic drag
Rho = Density of air
A = Frontal area
M = total mass of bike and rider
Crr= Coefficient of Rolling Resistance
g = Acceleration of gravity
S = Slope of road

The total force is thus:

F = Fp - Fd

From Newton's second law, the equation of motion is:

dV/dt = F/I

I = Inertia

Because there is both rotating and non-rotating mass, total mass and total inertial will not be the same. Because mass at the periphery of the wheel as twice the inertia as non-rotating weight, the total mass and inertia of a bike are:

M = Ms + Mr
I = Ms + 2Mr

Ms = Static mass

Mr = Rotating mass

The complete equation of motion is thus:

dV/dt = {(P/V)(1+sin(2RT)) - [ (1/2)CdRhoAV^2 + (Ms+Mr)gCrrCosine(S) + (Ms+Mr)gSine(S) ] } / (Ms + 2Mr)

This equation is non-linear, so I solved it numerically with a 4th order Runge-Kutta numerical differentiation.

Borrowing the default values in the Analytic Cycling web page for "Speed given Power" page, the values used are:

P = 250 Watts, Cd = 0.5, Rho = 1.226 Kg/m^3, A = 0.5 m^2, Crr = 0.004, g = 9.806 m/s^2, S = 3% (= 1.718 deg.)


For this simulation, the pedal revolution rate was selected as 540 deg/sec. (90 rpm cadence)

To solve this equation, a 4th order Runge-Kutta numerical differentiation was set up using an Excel spread sheet. Step size was selected at 0.01 sec., and the initial Velocity was 1 m/sec. The solution was calculated for 3 cases of equal total mass, but different distributions of static and rotating mass, calculated over a 200 second period, by which time each case had reached steady state. As expected, the velocity oscillated with the pedal strokes. The average, maximum, and minimum velocities during the oscillilations during stead state were:

Case 1:
Ms = 75 kg, Mr = 0 kg (0% rotating mass)
Average Velocity: 7.457831059 m/s
Maximum Velocity: 7.481487113 m/s
Minimum Velocity: 7.434183890 m/s
Speed fluctuation: 0.047303224 m/s

Case 2:
Ms = 70 kg, Mr = 5 kg (5.33% rotating mass)
Average Velocity: 7.457834727 m/s
Maximum Velocity: 7.480016980 m/s
Minimum Velocity: 7.435662980 m/s
Speed fluctuation: 0.044354000 m/s

Case 3:
Ms = 65 kg, Mr = 10 kg (10.67% rotating mass)
Average Velocity: 7.457837584 m/s
Maximum Velocity: 7.478718985 m/s
Minimum Velocity: 7.436967847 m/s
Speed fluctuation: 0.041751139 m/s

These results agree very strongly with the solution on the Analytic Cycling web page, which predicted an average speed with constant power of 7.46 m/s (16.7 mph)

The results show that as expected, the smaller the percentage of rotating mass, the greater the magnitude of the velocity oscillations (which are quite small). But a more interesting result is in the average speed. As the amount of rotating mass decreased, the more the average velocity _decreased_, not increased (at steady stage). This result is actually not unexpected. The drag forces are not constant, but vary with velocity, especially aerodynamic drage (Because aerodynamic drag increases with the square of velocity, power losses are increase out of proportion with speeds - so, for example, aerodynamic losses at 20 mph are 4 times as much as they would be at 10 mph). Because speed fluctuates as the propulsion force oscillations, in the cases of the low rotating mass, the maximum peak speeds reached are higher than for the cases with the high rotating mass. This means that when a lower percentage of rotating mass there will be greater losses during the speed peaks. Because of the total drag losses will be greater over the long run, the greater momentary accelerations with lower rotating mass actually results in a lower average speed.

To see what happens at a steeper slope, which will have a lower speed (and presumably larger speed oscillattions), I ran the model again with a 10% (5.7 deg.) slope. Here are the results:

Case 1:
Ms = 75 kg, Mr = 0 kg (0% rotating mass)
Average Velocity: 3.217606390 m/s
Maximum Velocity: 3.272312291 m/s
Minimum Velocity: 3.162540662 m/s
Speed fluctuation: 0.109771630 m/s

Case 2:
Ms = 70 kg, Mr = 5 kg (5.33% rotating mass)
Average Velocity: 3.217613139 m/s
Maximum Velocity: 3.268918539 m/s
Minimum Velocity: 3.165997726 m/s
Speed fluctuation: 0.102920813 m/s

Case 3:
Ms = 65 kg, Mr = 10 kg (10.67% rotating mass)
Average Velocity: 3.217618914 m/s
Maximum Velocity: 3.265921742 m/s
Minimum Velocity: 3.169047012 m/s
Speed fluctuation: 0.096874730 m/s

This data follows the same pattern as above. The speed oscillations (micro-accelerations) are greater with the lower rotating mass, but the average speed is also slightly lower with lower rotating mass. So next time you want to claim that lower rotating mass allows faster accelerations, remember too that the greater speed fluctuations (due to greater accelerations) will also results in greater energy losses due to drag forces.

But, in reality, the differences in speed fluctions and average speeds are really very small between all these cases. For all practical purposes, when climbing, it is only total mass that matters, not how it is distributed.

I'd be happy to send the Excel spreadsheet to anyone that is interested.
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Postby toolonglegs » Tue Nov 27, 2007 10:40 am

:shock: :shock: :shock:
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Postby sogood » Tue Nov 27, 2007 10:42 am

There are many mathematically proven facts in cycling. As much as the small difference they showed, the only issue that I question is how relevant are those small differences when it comes to racing?

For regular non-competitive cyclists riding into the sunset, those data indeed proved that people were worrying over nothing. But for racing cyclists who need the snap to catch an attacker's rear wheel, when you are already working at 99.99% capacity, I wondered if those tiny variations can become a more relevant issue?
Last edited by sogood on Tue Nov 27, 2007 10:48 am, edited 1 time in total.
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Postby sogood » Tue Nov 27, 2007 10:46 am

toolonglegs wrote::shock: :shock: :shock:

Relax. It's all just high school level math. :wink:
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Postby mikesbytes » Tue Nov 27, 2007 10:59 am

So in plain english, if a 82kg 46year old with extra wide (poor aerodynamic) shoulders is riding at 40kph, how much difference is 100gms of rim (each) going to make?
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Postby mikesbytes » Tue Nov 27, 2007 11:01 am

Richard I appologise for making fun of your posts in the past.
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Postby artemidorus » Tue Nov 27, 2007 11:04 am

sogood wrote:The facts of the matter are, 1) Apple is no longer more expensive when compared with name brands.

But who would buy a name brand? OK, silly question, I know many do. But, in fact, as well as it costing up to twice as much as a homebuilt, most of the components of a name brand are much inferior to those that I would use, with mine costing half the price.
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Postby Kid_Carbine » Tue Nov 27, 2007 11:06 am

I tend to go with Sogood here. The maths are undeniable but when it comes to that sprint at the finish, would the rider with the heavier rim/tyre combination [ALL other things being equal] be at a disadvantage or not.
Laymans logic [hey, it's the best I can do] suggests that the lighter rim/tyre rider would probably have something up his metaphoric sleeve. [But the maths tell us he would be too tired to use it]

sogood wrote:As can be seen, computer allegiance can be a religion too, just like bikes.

The facts of the matter are, 1) Apple is no longer more expensive when compared with name brands. 2) Enjoy virus threats on PCs.

As for pricing, well I have never purchased a new computer in my life, of either type, so I offer up no argument there.
In my family, we build & upgrade our own computers, so the costs are way down. This way we get the spec's we want at pricing we can afford & it's so easy, all I really need is a Phillips screwdriver.

Virus? Well, so far so good, our constantly updated AV programs have kept us free from problems, so that's not an issue at the moment, thank goodness.
Last edited by Kid_Carbine on Tue Nov 27, 2007 11:10 am, edited 1 time in total.
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Postby artemidorus » Tue Nov 27, 2007 11:07 am

mikesbytes wrote:So in plain english, if a 82kg 46year old with extra wide (poor aerodynamic) shoulders is riding at 40kph, how much difference is 100gms of rim (each) going to make?

On the flat, none. Up a steep hill, 0.2% difference.
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Postby artemidorus » Tue Nov 27, 2007 11:10 am

Kid_Carbine wrote:I tend to go with Sogood here. The maths are undeniable but when it comes to that sprint at the finish, would the rider with the heavier rim/tyre combination [ALL other things being equal] be at a disadvantage or not.

If the rider with the heavy wheels has shallow rims, then you are correct. If the rider with the heavy wheels has deep rims, and the rider with light wheels does not, then the heavy wheel rider will win, all other things being equal. Aero is more important than light, even in a sprint. Again, this is well established - go to analytic cycling.
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Postby toolonglegs » Tue Nov 27, 2007 11:17 am

sogood wrote:
toolonglegs wrote::shock: :shock: :shock:

Relax. It's all just high school level math. :wink:


No wonder I flunked it!
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Postby toolonglegs » Tue Nov 27, 2007 11:24 am

Sorry about the Mac/PC debate :lol: ...i have never owned a PC,never been to computer store to get a repair and never had a comuter crash...not bad for 12 years...wheres the wood to touch.But then my polar (R.I.P) dosent have a mac program..neither does the compu trainer.
But then my 3.0GHz 8-core Intel Xeon-based Mac Pro will crunch thru huge photo files faster than anything else...even faster than i crunch thru wheels :lol:
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Postby Kid_Carbine » Tue Nov 27, 2007 11:25 am

toolonglegs wrote:
sogood wrote:
toolonglegs wrote::shock: :shock: :shock:

Relax. It's all just high school level math. :wink:


No wonder I flunked it!

You & me both.
When we get down to as little as 0.2% difference in performance between component specs I begin to wonder if the thrust from a bloody good fart would make the difference in the final few yards.
OK, I'm getting silly here & in reality I will never have the fitness to be competitive, nor the money to afford the ultra components, but I must confess this has been a particularly educational thread, even if I will never actually benefit from the final conclusions.

Thanks to all.
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Postby toolonglegs » Tue Nov 27, 2007 11:27 am

Kid_Carbine wrote:
toolonglegs wrote:
sogood wrote:
toolonglegs wrote::shock: :shock: :shock:

Relax. It's all just high school level math. :wink:


No wonder I flunked it!

You & me both.
When we get down to as little as 0.2% difference in performance between component specs I begin to wonder if the thrust from a bloody good fart would make the difference in the final few yards.
OK, I'm getting silly here & in reality I will never have the fitness to be competitive, nor the money to afford the ultra components, but I must confess this has been a particularly educational thread, even if I will never actually benefit from the final conclusions.

Thanks to all.


Yes 0.2 isnt much,especially when you are about as aero as a bus :lol:
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Postby artemidorus » Tue Nov 27, 2007 11:27 am

sogood wrote:2) Enjoy virus threats on PCs.

Never had one in 14 years! I'll keep waiting.
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Postby sogood » Tue Nov 27, 2007 11:35 am

mikesbytes wrote:So in plain english, if a 82kg 46year old with extra wide (poor aerodynamic) shoulders is riding at 40kph, how much difference is 100gms of rim (each) going to make?

Ummm... Where should we stick that age variable in the equation? I am sure it'll significantly affect the calculation. :wink:
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Postby sogood » Tue Nov 27, 2007 11:46 am

Kid_Carbine wrote:I tend to go with Sogood here. The maths are undeniable but when it comes to that sprint at the finish, would the rider with the heavier rim/tyre combination [ALL other things being equal] be at a disadvantage or not.

I should qualify to say that I do not know if the weight difference (rim or combined bike) would have a significant effect as I don't know just how much of a difference would affect one's ability to catch another wheel. However, I can feel a difference in terms of "liveliness" b/n my Bianchi and Ridley, a difference in wheel weight as well as overall weight (1-1.5kg). But the difference could also be in the stiffness of the frame.
Virus? Well, so far so good, our constantly updated AV programs have kept us free from problems, so that's not an issue at the moment, thank goodness.

On my Mac OS X 10.4/10.5 machines, I don't even need to run any AV or 3rd party firewall program in the background to sap my CPU cycles. Unix has firewall built-in and virus threat just isn't there. The only AV program I have on the same Mac is Norton AV, running within Windows XP that I occasionally runs through VMware virtualization environment.
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Postby MichaelB » Tue Nov 27, 2007 11:47 am

Kid_Carbine wrote: When we get down to as little as 0.2% difference in performance between component specs I begin to wonder if the thrust from a bloody good fart would make the difference in the final few yards.


Depends if you are directly behind the farter (i.e. you are the fartee) or not.

Depends also on the consistency, type & length of fart
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Postby sogood » Tue Nov 27, 2007 11:57 am

artemidorus wrote:On the flat, none. Up a steep hill, 0.2% difference.

Bear in mind that those are all primarily static state calculations. Weight is only important when there's acceleration involved (basic F=ma) eg. Gravity (9.8m/s^2), hence the difference in climbing up hills. So for a racing rider needing to suddenly jump and catch an attacking opponent on the hill, the acceleration and forces required would be more significantly affected by the weight parameter. So I have just that tiny residue doubt over this matter. But as I said, this is irrelevant for those non-competitive riders.

To date, I have not seen anyone include this parameter in their calculations. I guess the recalc isn't too hard given the change in speed and the time it takes for the transition can be estimated for the chase rider, hence acceleration. But I am too damned lazy to go through with it. In any case, I need some justification, even if it's just a lingering one, for the existence of that second bike. Don't anyone blow it for me! :wink:
Last edited by sogood on Tue Nov 27, 2007 12:20 pm, edited 2 times in total.
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Postby sogood » Tue Nov 27, 2007 11:59 am

artemidorus wrote:
sogood wrote:2) Enjoy virus threats on PCs.

Never had one in 14 years! I'll keep waiting.

Don't forget to keep that AV proggie running in the background and keep it updated every few days. :wink:
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Postby sogood » Tue Nov 27, 2007 12:02 pm

Kid_Carbine wrote:When we get down to as little as 0.2% difference in performance between component specs I begin to wonder if the thrust from a bloody good fart would make the difference in the final few yards.

Doesn't work, as one, they are pointed in the wrong direction, and two, that lycra and pad was designed to dissipate the jetstream laterally, similar to how a recoil-less gun works. :P
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Postby artemidorus » Tue Nov 27, 2007 12:18 pm

sogood wrote: So I have just that tiny residue doubt over this matter.

What are you doubting?
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Postby sogood » Tue Nov 27, 2007 12:22 pm

artemidorus wrote:
sogood wrote: So I have just that tiny residue doubt over this matter.

What are you doubting?

Exactly what I outlined earlier. The amount of extra force/energy required for a chase rider to make that jump (ie. Extra acceleration on top of static gravity pull) to catch an opponent. When a rider is working near capacity, that extra difference may just mean the difference b/n able or unable to attach to the opponent's rear wheel.
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Postby artemidorus » Tue Nov 27, 2007 12:31 pm

sogood wrote:
artemidorus wrote:
sogood wrote: So I have just that tiny residue doubt over this matter.

What are you doubting?

Exactly what I outlined earlier. The amount of extra force/energy required for a chase rider to make that jump (ie. Extra acceleration on top of static gravity pull) to catch an opponent. When a rider is working near capacity, that extra difference may just mean the difference b/n able or unable to attach to the opponent's rear wheel.

Noone said that 0.2% wasn't significant at an elite level, or even if you're sprinting uphill against your mate. It's not only going to increase the steady state workload uphill, but it is going to increase the wattage required for a given acceleration, slightly. Nothing to doubt.
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