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Old 09-09-13, 09:42 PM
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Wheel build calculations

I'm planning to build a wheelset from scratch. I went through online calculators but I'm wondering if someone experienced with this can spend a few minutes to double check my results (I have to spend close to $100 on spokes of 3 different sizes and I'd rather get it right the first time).

I'm getting rims with outer diameter 633 mm, depth 50 mm, wall thickness at spoke hole 3.5 mm. This gives me the ERD of 540 mm.

Front wheel is 20T with 2 cross lacing. Hub is Novatec A291SB:

Spoke Hole Ř : 2.3mm
Slotted Aero
O.L.D.: 100mm
Spoke Circle Ř : 30mm
F.T.F. : 68.7mm
L.C.F. : 34.35mm
R.C.F. : 34.35mm

Rear wheel is 32T with 2 cross lacing. Hub is Powertap G3:

Hub center to flange 38.0mm (Non drive) 17.4mm (drive)
Flange diameter 57.0mm
Spoke hole diameter 2.5mm

I put this into two different online calculators. One gave me 266.5 front, 252.1 and 249.9 rear. The other gave me 268 front, 253.5 and 251.3 rear. I'm not sure about the source of discrepancy but I suspect that one of them forgets to subtract the radius of the spoke head.
Since these are fairly deep rims and since spokes have ~9 mm of thread on them, do I really care about getting lengths exactly right, or is it safer to round everything upwards and have a few mm of spoke protruding inside the rim?
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Old 09-09-13, 10:05 PM
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I assume you can punch numbers into a keyboard, so I'm not going to check your "math", but here's a few hints about the data itself.

Then number of holes is easy, as is the cross, but a major source of error is not to build with the same cross as calculated, ie. calculate for 3x but screw up and build 2x. Related to this is improper phasing of the flanges. The right and left flanges are 1/2 a hole apart, ie the hole in one flange lines up with the space between holes on the other. So the two nearly parallel spokes leaving the hub from opposite flanges must go to the rim in the same sequence, so (looking from the side) if the near flange spoke is slightly to the right of the far flange spoke the nar one will be 1 hole to the right in the rim. If you end up with spokes coming out hi-lo alternating in the rim, this is where you went wrong.

Flange diameter measurement is important, but not critical, with the effect on calculation varying with the number of crosses. For a typical 3x 32h wheel, 1mm error in flange diameter changes spoke length by about 1/4mm (or less).

Center to Flange distance is least critical. Here every 10mm changes the spoke length by about 1mm, so you can see that one or two millimeters error in CTF won't be a killer.

Lastly we come to ERD, where most of the errors happen. I'll spare you the gory details, but will let you know that most spoke calculators will have the end of the spokes end at a distance to the ERD you entered ±1mm or so. Errors in ERD produce calculated errors 1:2, (Radius vs. diameter) so if your entered ERD is 2mm low, the spoke will come up 1mm short of expectations.

Since you have spokes and the rim, I suggest you check the ERD yourself one of two ways.

1- measure the outside diameter of the rim at 2 or 3 places (in case it's slightly oval) & average the values. Place a nipple into any hole, and measure the drop from the outside of the rim (where you measured) to the top of the nipple. Add 1mm so the spokes end short of the top of the nipple, and double that because it's the same on then opposite side. Subtract from outer diameter to get the ERD. (this is my preferred method).

2- Thread 2 spokes into the rm on opposite sides, attach nipples and thread down to desired height. Bring spokes together at the center where they should come up short of meeting. Measure how close they come from inside of elbow to inside of elbow, and add to the 2 spoke lengths. That's the ERD. Do this twice 90° apart in case the rim is oval, and average. I'm not a fan of this method because it takes a bit of dexterity, and you have to do it twice. However, some people who build lots of wheels keep 2 310mm spokes for this purpose, because they overlap, and it's easy to measure the overlap and subtract from 620mm.

Lastly understand that there's some fudge in spoke calculating. Things like the fact that most people measure flange diameter at the centers of the holes and the spokes are measured to the inside of the bend or to the rim of the hole. There's also the lengthened path of the spokes as they bow in or out to cross over/under each other, and that spokes get longer (slightly) as tension is added. For that reason, I recommend using the same calculator every time. After a wheel or two, you'll, know if it's results are off to the long or short side, and can compensate accordingly as you round off. For instance, the calculator I use is always about 1-2mm short of where I like spokes to end up, so I always round up, adding 1 or 2 millimeters depending on the specifics.

I hope this helped and wish you luck on your first build.
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Old 09-10-13, 12:04 AM
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I'm sure I can punch in the numbers, but making sure to punch in the right numbers in the right places is half of the challenge.

I don't actually have the rims or the spokes yet. I'm in process of ordering the rims, it should be a week or two before I get them, and I want to order spokes at the same time so I don't have to wait another week for those. Manufacturer reports 540 mm ERD, same as my calculations above. I don't know if the rims can really be off spec by so much that I won't be able to use spokes I order now based on my calculations.

Other points are helpful, or will come helpful once I come to the point of assembly.
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Old 09-10-13, 12:51 AM
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Originally Posted by hamster
I'm sure I can punch in the numbers, but making sure to punch in the right numbers in the right places is half of the challenge.

I don't actually have the rims or the spokes yet. I'm in process of ordering the rims, it should be a week or two before I get them, and I want to order spokes at the same time so I don't have to wait another week for those. Manufacturer reports 540 mm ERD, same as my calculations above. I don't know if the rims can really be off spec by so much that I won't be able to use spokes I order now based on my calculations.

Other points are helpful, or will come helpful once I come to the point of assembly.
.......based on my own personal experience, which is relatively good, though
probably not in the same league with Francis, I would urge you to not do this.

I know it sounds cruel, but the rims really can vary from batch to batch, and
the maker's data can be either in error or out of date. It happens. It has happened to me.

While it may not make your spokes unusable, it can make them less utilitarian, either
in the too long or too short direction. With a box section rim, too long is not the PIA
it once was, but too short can be a major failure factor if the spokes don't thread
all the way to the head of your nipples. The big problem with too long is if you end up
so far out of the nipples that part of the spoke at the nipple insertion is no longer
threaded..............thus fewer threads are in the nipples holding things together.

My own two rules are:

1. Always have your rims and hubs to measure before you order spokes.

2. Always do your own measurements of rim ERD and hub flanges

Mr. Bunny was a bear about this, and rightly so. He's been absent of late.
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Old 09-10-13, 01:18 AM
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Originally Posted by hamster
.. I'm in process of ordering the rims,... and I want to order spokes at the same time...
Understandable, yet risky.

Originally Posted by hamster
...I don't know if the rims can really be off spec by so much that I won't be able to use spokes I order now based on my calculations.
It's not as much being off spec that's the problem, but rather WHAT the spec actually says, and how to interpret it - or possibly how it's interpreted by the spoke calculator.

IME, ERD to a rim manufacturer tends to refer to the outside face of the inner wall of the rim, where the inside face of the spoke nipple flange will end up, while the ERD you feed into spoke calculators tends to refer to where you want the end of the spoke to end up.

So manufacturer's ERD tends to ignore the flange thickness of the nipple, and if you use it you'll typically end up with your spokes 2 mm short of ideal nipple engagement.

Note that I say tends to, I don't build enough wheels or carry good enough notes, or have a good enough memory to cover all the possible permutations.

One sneaky little trap I've encountered once was when a manufacturer decided to update an old and popular rim version.
Maybe the extrusion tool got worn out and had to be replaced, I don't know.
Either way, it led to the same model rim being available in two different ERDs for a while.
And naturally, the old ERD was a lot easier found on the net than the new one.
I'll leave you to figure out the rest to the sound of the cursing and cussing of your choice.
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Old 09-10-13, 01:29 AM
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I'm not really hoping for a change, but wouldn't it be nice if rim manufacturer's used a reference like Nipple Seat Diameter, and spoke calculators used Spoke End Diameter? Or something along those lines.
Im' not gonna fight for the actual phrases, but the current situation where ERD can be used for both describing where the nipple sits and where the spoke ends is certainly setting the stage for misunderstandings and confusion.
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Old 09-10-13, 08:23 AM
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Originally Posted by dabac
I'm not really hoping for a change, but wouldn't it be nice if rim manufacturer's used a reference like Nipple Seat Diameter, and spoke calculators used Spoke End Diameter? Or something along those lines.
Im' not gonna fight for the actual phrases, but the current situation where ERD can be used for both describing where the nipple sits and where the spoke ends is certainly setting the stage for misunderstandings and confusion.
I've long argued that ERD isn't a true spec that anyone can publish because it depends on an assumption. It's like the Nwlywed game. The manufacturer has to guess what nipples the wheelbuilder is using and where the spokes should end. The wheelbuilder has to guess what the manufacturer thinks he's he plans on using. It's circular and leads to error.

The diameter at the nipple seat is a real spec, which can be measured and confirmed, and which doesn't rely on any assumptions.

If the actual dimensions are used, the builder can either add the compensator for spoke height in the head of the nipple to the calculated result, or double it and add it to get the ERD. Either is fine, avoids guesswork and assumptions, and puts the decisions back in the hands of the builder where it belongs.
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Old 09-10-13, 08:48 AM
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My rules include those above (have hub and rim first) as well as rounding up on anything beyond .2 (253.3 becomes 254, etc). Also keep in mind other sources of error can include being sent spokes that are off by a mm or 2. It's best to aim for the most perfect length possible. Allowing slop might conspire all errors in the same direction and put you out of range.

I don't think you mentioned the rims so I can't sanity check it against the databases (or personal measurements) I use.

Does 540 sound like too small of a an ERD for a 633 wheel to anybody else?

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Old 09-10-13, 09:23 AM
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Are you ordering spokes and hub from the same source? If so why not at least try a phone call directly to the supplier? Even if ordering the rims separately they may have received feedback from others who have built on the rims they supply. It amazes me that people often forget that keyboard and mouse is not the only means of communication
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Old 09-10-13, 09:32 AM
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Originally Posted by dbg
Does 540 sound like too small of a an ERD for a 633 wheel to anybody else?
.......I didn't pay much attention, but with a stated depth of 50 mm, I think it's some kinda deep V.
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Old 09-10-13, 09:38 AM
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To the OP.

You're going to live with the wheels for a long time (hopefully), so what's a week. Published ERDs are fairly unreliable, so it's worth the wait to get the rims first, make your own measurements, and buy the right spokes.

One other note, there's some variation us usable thread lengths on spokes and nipples, so you're usually best off buying the same brand (unless you know thread lengths) so the combination will give you the most latitude in thread engagement. Most same brand spokes and nipples allow the spoke to thread about 2mm beyond the top of the nipple.
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Old 09-10-13, 10:13 AM
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Originally Posted by FBinNY
............the calculator I use is always about 1-2mm short of where I like spokes to end up, so I always round up, adding 1 or 2 millimeters depending on the specifics..........
FB- Which calculator do you use?
I use Spocalc and see similar results. I usually round up about 0.7-1.5mm
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Old 09-10-13, 10:26 AM
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The rounding that always makes me wonder is when I get a value like 281.5 and the seller only sells spokes in odd numbers. Trying to figure out whether to round up by 1.5 or down by 0.5. On a rim with some depth, trying to get perfect isn't essential, but I like getting as close as possible, which is why it takes me a long time to do just about anything.
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Old 09-10-13, 10:40 AM
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Originally Posted by Bill Kapaun
FB- Which calculator do you use?
I use Spocalc and see similar results. I usually round up about 0.7-1.5mm
I don't use an online calculator. I have a formula loaded into a scientific calculator. However, I've had good consistent results with spokecalc.

The key isn't which you use, it's using the same one each time, so you're used to how high or low the results are.

Originally Posted by himespau
The rounding that always makes me wonder is when I get a value like 281.5 and the seller only sells spokes in odd numbers. Trying to figure out whether to round up by 1.5 or down by 0.5. On a rim with some depth, trying to get perfect isn't essential, but I like getting as close as possible, which is why it takes me a long time to do just about anything.
If you always use the same calculator and measure everything yourself, you know exactly where a spoke of the calculated length would end. That and your judgement will always tell you which way to round.
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Old 09-10-13, 12:20 PM
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Originally Posted by FBinNY
If you always use the same calculator and measure everything yourself, you know exactly where a spoke of the calculated length would end. That and your judgement will always tell you which way to round.
True. Only built a few wheels, been a few years since my last one and the last several times, I think I used 3-4 different ones and took the most common value (I think that's the mode in math terms). Should have written down somewhere which one I used for my last wheelset because it came out just right (of course those spokes I came out to all being even or odd or whatever my source at the time was selling them as).
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Old 09-10-13, 01:52 PM
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Originally Posted by dabac
IME, ERD to a rim manufacturer tends to refer to the outside face of the inner wall of the rim, where the inside face of the spoke nipple flange will end up, while the ERD you feed into spoke calculators tends to refer to where you want the end of the spoke to end up.

So manufacturer's ERD tends to ignore the flange thickness of the nipple, and if you use it you'll typically end up with your spokes 2 mm short of ideal nipple engagement.
So what you're saying is that I want my spokes to extend all the way to the end of the nipple flange, which is 2 mm past the inner wall of the rim?
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Old 09-10-13, 02:39 PM
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Originally Posted by hamster
So what you're saying is that I want my spokes to extend all the way to the end of the nipple flange, which is 2 mm past the inner wall of the rim?
That is what I strive for when calculating spoke lengths. I have built wheels with spokes that were kind of short, like 2mm short of reaching the end of the nipple just before the screwdriver flat on the non-drive spokes. The wheel built up fine but has broken a couple nipples on the person riding it (friend who understood that the non-drive side spokes were a hair too short). Its because the nipples are designed to have the spoke extend all the way through it to provide full support.
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Old 09-10-13, 02:57 PM
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Originally Posted by hamster
So what you're saying is that I want my spokes to extend all the way to the end of the nipple flange, which is 2 mm past the inner wall of the rim?
Remember, that as currently used ERD, refers to the circle formed by the end of the spokes, not the diameter of the rim in any sense of the word.

Years ago (before Jobst Brandt wrote the book) wheel builders used to refer to the rim diameter meaning the diameter where the nipples sat. I don't remember if we ever used the phrase effective rim diameter since most of us didn't speak bureautocratese, but in any case JB defined it as the circle at the ends of the spokes.

That means that as used by most Americans the ERD is bigger than the nipple seat diameter by the amount of engagement in the head of the nipple (doubled). Unfortunately, many Europeans have been doing this a long time (Before JB) and never read the book, so to them the ERD is measured at the rim, which is what leads to the confusion. I measure the same way and call it the rim diameter as I always did, but when speaking to post JB builders call it the nipple seat diameter so as not to add to the confusion.

Figuring typical 3mm engagement in the head, the ERD in 5-6mm greater than the RD (or NSD).

The key in all this is to remember that most calculators will bring spokes out to whatever ERD value you enter (or very close) so if, like me) you measure rims, you have to either add 5-6mm before calculating, or add 3mm to the result.
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Old 09-10-13, 10:13 PM
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Originally Posted by dbg
My rules include those above (have hub and rim first) as well as rounding up on anything beyond .2 (253.3 becomes 254, etc). Also keep in mind other sources of error can include being sent spokes that are off by a mm or 2. It's best to aim for the most perfect length possible. Allowing slop might conspire all errors in the same direction and put you out of range.

I don't think you mentioned the rims so I can't sanity check it against the databases (or personal measurements) I use.

Does 540 sound like too small of a an ERD for a 633 wheel to anybody else?
I'll probably get flamed for this, but I'm getting Chinese rims from light-bicycle.com.

This is the profile drawing I got from them:



They said that the wall thickness of the spoke hole is around 3.5 mm.
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Old 09-11-13, 04:27 AM
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So this is probably a stupid question to tack on, but I know that if I use nipple washers I add twice the thickness of those washers to the ERD (or measure it with them in place if I already have them in hand, which I don't), but what about using spoke washers? Do they effectively shorten the spoke and need to be accounted for? Am going to be reusing some older hubs this time (every other time have used new) and thought that reinforcing the holes with spoke washers might not be a bad idea. Do I just add whatever their thickness is to the length of the spokes that I calculate to get the true length I need?
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Old 09-11-13, 04:28 AM
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Originally Posted by hamster
So what you're saying is that I want my spokes to extend all the way to the end of the nipple flange, which is 2 mm past the inner wall of the rim?
Something like that, but there's some variation due to the nipple profile. And a bit of personal preference here.
Some shoot for flush with the bottom of the screwdriver slot, some shoot for flush with the nipple head top surface.
Only time you shoot for below the nipple head is when using something like DT 16 mm nipples and DT spokes, where thread interference won't allow you to get full protrusion.

Then there's a bit of a balancing act. The nipples and spokes I use allows for about 2 mm overshoot, and I try to manage that reserve wisely. For my commuter and my MTBs, roundness isn't a huge factor, but I sure like to be able to keep the tension up even if the rim would happen to take a beating, so I like to keep some of that margin. Then you have to consider what lengths the spokes are available in, and how much you expect them to stretch. For a 1.5 mm spoke , it can be enough to be important.
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Old 09-11-13, 04:39 AM
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Originally Posted by himespau
So this is probably a stupid question to tack on, but I know that if I use nipple washers I add twice the thickness of those washers to the ERD (or measure it with them in place if I already have them in hand, which I don't), but what about using spoke washers? Do they effectively shorten the spoke and need to be accounted for? Am going to be reusing some older hubs this time (every other time have used new) and thought that reinforcing the holes with spoke washers might not be a bad idea. Do I just add whatever their thickness is to the length of the spokes that I calculate to get the true length I need?
I've never heard of anyone compensating for spoke washers, and I don't think it's required. They're only affecting the spoke where it's basically perpendicular to the hub flange, so should have a really tiny influence on the effective length of the spoke.
Nipple washers is even rarer to see than spoke washers. I've used them on occasion, when it's been the only choice to be able to finish a build with what was available right then, and to extend the life of a beater bike when one of the spokes had pulled through. Never heard of them being used in a planned build.

If you intend to use them, simply measuring their thickness won't tell the whole story, as their "functional" thickness would depend on how the fit to the nipples are. Unless the hole is a perfect fit, the nipple will sink into the hole just a tad.
At a guess, I'd say that adding double the thickness to the ERD would work, unless all other error sources decide to gang up on you.
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