Bicycle Mechanics - Predicted life of heavy duty spokes.

Wheelsmith fatigue tested 76 spokes 68 of them broke at the elbow and 8 of them broke at the threads. They also came up with a formula that relates stress to life the math will be at the bottom. If wheelsmith's test applies to the real world an if I did the math right then a 2.0mm spoke will last 2.01 times as long as a 1.8mm spoke and a 2.34mm spoke will last 2.84 times as long as a 2.0mm spoke. How much longer will a spoke longer will a single butted spoke last compared to a plain spoke? The problem is wheelsmith combined the two types of breaks into one formula but it looks like a 2.34mm/2.0mm spoke is effectively as strong as a 2.34mm plain spoke. Here is the formula Log(stress)=-.3xLog(cycles)+4.12 all logs base 10 the stress is in megapascals. For a given stress the formula gives the number of cycles where half of the spokes fail. The Log of the stress forms a normal distribution with a standard deviation of .072 and the Log of the cycles forms a normal distribution with a standard deviation of .24

Don't mean diddly. You can pretty much throw that formula out of the window so far as real life use is concerned because you can't normalize the quality of the wheel assembly. Arguably, that's the most significant factor.

The thing is, a spoked wheel should not permit enough spoke flex to achieve a fatigue issue. Ultimate strength can be a concern to a truely hardcore hucker, but to calculate how many cycles a spoke can withstand excludes too many variables. Spoke tension, force applied, inconsistent spike loads, etc.
I am all for engineering data however, so don't let me quash the fun.

As others have said, there are to many variable and unknowns to fully predict how durable a spoke would be. I think that if some one were to try to fully calculate this, it would have a wide margin of error, and simply wouldn't apply to some situations. A road wheel would probably be the easiest to figure out, as there is possibly the lowest number of variables on that style of riding/wheel. A mountain bike prediction, throw everything out the window. There is simply no way to add into the calculation (at least practically) things like maintenance, rider style etc., and give these a number. An experienced wheel builder may be able to guess to the durability, that probably won’t involve math.

I think the formula could be reasonably used to compare one spoke to another assuming a given riding style. It's interesting they got two somewhat equivalent break points which suggests a near optimum design. I'm not sure I know anyone who actually counts wheel revolutions, except indirectly by mileage so the numbers them selves are somewhat academic ;)

Could do it like landing gear. That is if you did jumps a lot ;)
cycles(landings)

There should not be any failure difference between butted and unbutted as long as the J-hook and threaded end are the same dia. A butted spoke might even last longer because they are a little stretchy and remove some of thefatigue from the other more prevalent failure points. I have never seen a spoke fail at the butt.
Spoke quality is so high I never consider failure rates(Excepting straight 15g spokes, they breal to often for my taste) when picking them. My concern is ride and total wheel durability(OK, maybe weight :) )

Charles, are you bored? Why in the world would you fuss over such drible? I ride DT Competition double butted spokes that have over 30,000 miles on them...do you think I care about how much more life I would have gotten had I opted for thicker spokes? NO!!

Charles, are you bored? Why in the world would you fuss over such drible? I ride DT Competition double butted spokes that have over 30,000 miles on them...do you think I care about how much more life I would have gotten had I opted for thicker spokes? NO!!He's trying to trump 53-11 in the minutiae dept.

Look at the economics a 2.34/1.8/2.0 spoke weighs less than a 2.0 spoke and at 25 cents more will pay for itself in spoke replacement costs. Good spokes have rolled threads this makes the threads larger than the shaft this means the spoke holes have to be drilled too large. A double or triple butted spoke fits better in the spoke hole and should result in less stress to the flange. A perfect spoke would have an equal chance of breaking at the elbow or the threads. If any one is using these spokes let me know where they are breaking. Wheelsmith makes a 2.34/2.0 called a DH or a downhill. DT makes a 2.34/1.8/2.0 called the alpine and a 2.0/1.7/1.8 called super comp. The formula came from www.duke.edu/~hpgavin/papers/HPGavin-Wheel-Paper.pdf or if that doesn't work look for it on damonrinard.com

Still doesn't mean much. A properly-built wheel, for the job at hand, will last for tens of thousands of miles and more. A butted spoke will last longer than a straight-gauge spoke.

Jobst Brandt, who has ridden well over 200,000 miles, and wrote arguably the definitive book on Wheel building, uses the same spokes when his rims wear out! Spoke breakage is not a problem, again, with properly built wheels.

I agree, I have reused a ton of spokes through the years and to date I have only had 2 broken(not even a wheel I owned or made).

People are breaking spokes they are tandems tourists and working bikes. Say you have a 40 spoke wheel and you break your first spoke at 4000 miles then your next break will be due at 4762 miles and your third at 5333 miles and your forth at 5820 miles. Now I tried to answer a specific question what happens if you build the same wheel but with stronger spokes. In the above example if you go from 2.0mm spokes to 2.34/2.0mm spokes then your first break will be due at after 10000 miles. This is what people are reporting stronger spokes seem to be indestructible. My first thought was a plain guage spoke was near opimum but it looks like all the breaks at the threads were at the highest cycles. It looks like a spoke needs to 1.48 times stronger at the elbow to get equal breaks at the elbow and the threads.

Spoke breakage like this can be completely eliminated if the wheel is properly stress releived, and built with adequate spoke tension-assuming good quality spokes, and a properly designed hub flange. If the cyclical stress is low enough, the spoke will last indefinately.

Agreed. As I said before, if it is tensioned propperly fatigue life will not arise.