Sapim CX-Ray Spoke Life Calculation
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  1. #1
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    Sapim CX-Ray Spoke Failure Calculation

    Reading about CX-Ray spokes fatiguing to breakage in about 2,000 mi. in a poorly built wheel got me thinking, and then running some calculations:

    I have a Sapim catalog downloaded in 2013, showing what may be a cycles to failure of 3,500,000 cycles (equivalent to wheel revolutions) for CX-Ray spokes. If this is a correct interpretation of the data, you can understand why Sapim has since removed this info from their website. Without more info available from Sapim on the test details, let us consider that this result could describe the performance of an under-tensioned wheel.

    I measured my 700c front wheel with a 25c tire mounted to have a diameter of 26-7/8". The tire is probably somewhat under-inflated and I need to pump it up before my next ride, but I don't expect the diameter to increase much at full inflation. The circumference (diameter x pi) of this wheel is therefore, 7.04' which is also the distance the wheel will travel with one revolution. This can be expressed as 7.04 ft/rev. If this wheel were under-tensioned I calculate the CX-Ray spokes in this wheel would fail in (3,500,000 rev) x (7.04 ft/rev) / (5,280 ft/mi) = 4,664 mi, plus or minus whatever tolerance there may be in the spoke fatigue test data.

    Applications to real-life experience for wheels built with CX-Ray spokes:

    1. These wheels can last for a long time when properly built and with adequate spoke tensions. How long? I'd love to hear how long or how many miles wheels built with CX-Ray spokes are lasting in use on the road.

    2. All spokes are subject to fatigue if they are under tensioned, not just CX-Ray spokes.

    3. If the spokes lose tension they will fatigue, and with sufficient wheel revolutions in this condition, the spokes will eventually fail from fatigue, or the wheel could fail from other causes. Remember to check for even spoke tensions (pluck or tensiometer) at least annually, and maybe more frequently if you are putting high mileages on your wheels.

    I rewrote my post because it seemed better to me than just deleting the text!
    Last edited by 4slomo; 08-21-2014 at 08:42 PM. Reason: Changed my opinion, rewriting post
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  2. #2
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    Sapim CX-Ray Spoke Life Calculation

    A "load cycle" for the purpose of determining fatigue life is not equivalent to a revolution of the wheel. It is equivalent to loading the spoke until its yield point is reached.
    Normal usage does not load the spokes to their yield limit so trying to calculate mileage out of the fatigue life of the spoke is inconclusive at best.
    With bicycles in particular, you need to separate between what's merely true and what's important.

  3. #3
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    Quote Originally Posted by dcgriz View Post
    A "load cycle" for the purpose of determining fatigue life is not equivalent to a revolution of the wheel. It is equivalent to loading the spoke until its yield point is reached.
    Normal usage does not load the spokes to their yield limit so trying to calculate mileage out of the fatigue life of the spoke is inconclusive at best.
    Precisely. Much of what you are trying to do in building the wheel is ensure that it doesn't load cycle at all.

  4. #4
    wheelbuilder
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    I thought is was concluded that those Sapim numbers are made up anyway.

    Great spokes, but I ignore those numbers.

  5. #5
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    Quote Originally Posted by ergott View Post
    I thought is was concluded that those Sapim numbers are made up anyway.

    Great spokes, but I ignore those numbers.
    Yeap, and these numbers have been long removed from the Sapim website and have been replaced with an abstract chart indicating relative fatigue cycles between spokes which IMO is meaningless without the specific testing parameters.
    The OP is looking at an older Sapim document.

  6. #6
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    Quote Originally Posted by dcgriz View Post
    A "load cycle" for the purpose of determining fatigue life is not equivalent to a revolution of the wheel. It is equivalent to loading the spoke until its yield point is reached.
    Normal usage does not load the spokes to their yield limit so trying to calculate mileage out of the fatigue life of the spoke is inconclusive at best.
    Never heard of that definition, but I'm no expert. When I did fatigue tests earning an ME degree, we loaded samples into machines that put reverse stresses on the samples. The loads could be varied. The machines had counters to measure the number of cycles.
    We ran tests at various loads to failure, and then made a chart of load versus log of number of cycles to failure (S-N curve, or Wohler curve).
    I think this is still the best way to talk about understanding fatigue failure - The higher the load, the shorter the life. So looking at the S-N curve, you clearly see the life gets exponentially shorter as the load increases linearly.

    On a bike wheel, the spokes get reverse stress loads from rotation under static loads, but also dynamic events like potholes. Also reverse stress from lateral loads, like rocking a bike sprinting or climbing. These are probably the most damaging, but the last reverse stress on the drive side spokes is from applied power through the spokes from the crank/pedaling.

    In a typical case all 3 of these reversed loads are happening to the spoke, so trying to correlate a real life case to some laboratory spoke test is probably not easy.

    As usual, experience by wheel builders of what works in actual situations is likely the best info on the subject. But for various reasons, what works for say deep carbon wheels can't be translated as working the same for light shallow alu wheels, or vice versa.

  7. #7
    changingleaf
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    The fatigue life of a spoke as given by a particular test can be useful when comparing the fatigue life of other spokes given the exact same test. This will answer which spoke has a longer life, at least under the specific fatigue test, but it will not correlate to miles in a wheel.

  8. #8
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    Quote Originally Posted by changingleaf View Post
    The fatigue life of a spoke as given by a particular test can be useful when comparing the fatigue life of other spokes given the exact same test. This will answer which spoke has a longer life, at least under the specific fatigue test, but it will not correlate to miles in a wheel.
    I was wondering about that. There are other variables at work in a real-world build versus testing settings (hub flange height versus spoke angle, number of spokes in the wheel, spoke length - just a few I can think of). Heck, tire pressure may even impact spoke durability over long periods of time.
    Last edited by berserk87; 08-21-2014 at 12:15 PM.
    Mike

  9. #9
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    Sapim CX-Ray Spoke Life Calculation

    Quote Originally Posted by Z'mer View Post
    Never heard of that definition, but I'm no expert. When I did fatigue tests earning an ME degree, we loaded samples into machines that put reverse stresses on the samples. The loads could be varied. The machines had counters to measure the number of cycles.
    We ran tests at various loads to failure, and then made a chart of load versus log of number of cycles to failure (S-N curve, or Wohler curve).
    I think this is still the best way to talk about understanding fatigue failure - The higher the load, the shorter the life. So looking at the S-N curve, you clearly see the life gets exponentially shorter as the load increases linearly.

    On a bike wheel, the spokes get reverse stress loads from rotation under static loads, but also dynamic events like potholes. Also reverse stress from lateral loads, like rocking a bike sprinting or climbing. These are probably the most damaging, but the last reverse stress on the drive side spokes is from applied power through the spokes from the crank/pedaling.

    In a typical case all 3 of these reversed loads are happening to the spoke, so trying to correlate a real life case to some laboratory spoke test is probably not easy.

    As usual, experience by wheel builders of what works in actual situations is likely the best info on the subject. But for various reasons, what works for say deep carbon wheels can't be translated as working the same for light shallow alu wheels, or vice versa.
    Academic discussion since Sapim has not disclosed (to the best of my knowledge) the parameters of their fatigue cycle tests in quantifying the fatigue cycles they once did.

    However for discussion purposes and for whatever its worth, a wheel sees three distinctly different types of loading: radial, lateral and torsional. The extent to which spokes are affected is proportionally enhanced or diminished by the rigidity of the rim, the spoke lacing pattern, the hub offsets, the hub flange dimensions, the spoke shape, the spoke attachment to the hub (j or straight) and the number of spokes.

    The loading intensity also varies based on how the rider weight and torque are applied at the time (sitting, standing, hammering, coasting, etc), the tarmac he is riding on and possibly the size and pressure of the tires fitted on the wheels.

    Where I'm getting at is that the plethora of actions and reactions at hand make it meaningless to isolate one component of the many (i.e spoke), subject it to one force of the many (i.e radial) and attempt to quantitatively extrapolate the system (ie wheel) durability out of it.

    It's been a very long time since my strength of materials lab work but to the best of my recollection we used to begin radial loading tests by applying 2/3s of the material tensile strength and adjust from there based on the number of failures from a predetermined lot size. If I remember correctly, fatigue life of more than 1,000,000 cycles was considered "infinite". Torsional testing was done similarly.

    I agree that at the end of the day it's the wheelbuilder's experience that makes the call. When I build wheels my preference is to almost exclusively use double or triple butted spokes (like the Sapim Race or Force) for training wheels and aero spokes like the CX-Ray for racing wheels. The objectives are different for each case and like almost everything cycling related so are the trade-offs.
    With bicycles in particular, you need to separate between what's merely true and what's important.

  10. #10
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    I looked at the Sapim catalog document I downloaded on 12/31/13 and see that it was created 4/21/10, so it isn't a relatively old document, nor has it been unavailable from their website for very long. I think others have dismissed the test data because Sapim hasn't been willing to release details of the test.

    Looking on Wikipedia to "review" my materials science background, which I studied in the early 1980s, I see Fatigue Life Evaluation uses a S-N Curve (alternating stress amplitude (Sa) versus number of cycles (Nf) to failure). I suspect Nf is the data Sapim was reporting. The fatigue life concern in wheels is whether or not the spokes completely lose tension as a loaded wheel rotates through 360 degrees each cycle.

    I continue to think my analysis is correct, and that if wheel spokes experience the calculated Nf they will fail. The only thing I didn't address was that spokes usually won't consistently experience complete loss of tension, that is why adequately tensioned wheels will last longer than undertensioned wheels, and why undertensioned wheels don't last very long.



    Quote Originally Posted by dcgriz View Post
    Yeap, and these numbers have been long removed from the Sapim website and have been replaced with an abstract chart indicating relative fatigue cycles between spokes which IMO is meaningless without the specific testing parameters.
    The OP is looking at an older Sapim document.
    Last edited by 4slomo; 08-21-2014 at 07:08 PM.
    Hey everybody, ride my wheels! They ride good, real good.
    I'm a wheel builder. SRLPE Wheel Works. Send me a PM.

  11. #11
    grizzly moderator
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    Sapim CX-Ray Spoke Life Calculation

    Quote Originally Posted by 4slomo View Post
    I looked at the Sapim catalog document I downloaded on 12/31/13 and see that it was created 4/21/10, so it isn't a relatively old document, nor has it been unavailable from their website for very long. I think others have dismissed the test data because Sapim hasn't been willing to release details of the test.

    Looking on Wikipedia to "review" my materials science background, which I studied in the early 1980s, I see Fatigue Life Evaluation uses a S-N Curve (alternating stress amplitude (Sa) versus number of cycles (Nf) to failure). I suspect Nf is the data Sapim was reporting. The fatigue life concern in wheels is whether or not the spokes completely lose tension as a loaded wheel rotates through 360 degrees each cycle.

    I continue to think my analysis is correct, and that if wheel spokes experience the calculated Nf they will fail. The only thing I didn't address was that spokes usually won't consistently experience complete loss of tension, and that is why adequately tensioned wheels will last longer than undertensioned wheels.
    The Sapim data you are referring to also showed the Race fatigue cycles to around 1,500,000, if I recall correctly. So if we follow your hypothesis and your formula, the Race spokes should reliably last for about 2000 miles of use. My tires last longer than this.
    With bicycles in particular, you need to separate between what's merely true and what's important.

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