Is it really necessary to physically cross (interlace) the spokes on traditional wheel lacing?

Radial patterns are lighter weight (and potentially more aerodynamic), but are, in my experience, orders of magnitude more likely to result in broken spokes and taco'd rims when spokes do break.

You also don't want to do radial spoking on rear wheels, since radial spoking will allow the hub to rotate relative to the rim while under drive tension.

I think radial spokes are generally recommended only for front wheels, because they're weaker than normally-laced wheels especially under the asymmetric torsion applied to the rear wheel.

WRT the drive forces: trailing spokes are necessary to transmit the drive force from the hub to the rim; radial spokes would make this transmission very spongy as the hub would rotate first, stretching the spokes slightly towards a tangential pattern before the force affected the rim.

You mention lateral stability as a possible, but not decisive, pro, but really I'd consider it essential, especially for accurate cornering.

As for outright strength, consider than any wheel will tend to bear most of its load through the topmost few spokes. On a radially-laced wheel, those spokes will be seated in adjacent holes, focussing all the force on the smallest possible section of flange. A tangentially-laced wheel will spread the load more evenly over the whole top half of each flange.

Perhaps more accurately, since the wheel is pre-tensioned, consider the spoke deformation under unloading. You need enough tension in each spoke that the minimal tension (at the bottom of the wheel, when the rim is slightly compressed) is still high enough to prevent the nipple unscrewing. Assuming the rim deformation is the same, a shorter spoke needs to contract by a larger fraction of its length than a longer spoke, which means more elastic deformation so higher maximum tension for the same material and cross-section.

So, a tangentially-laced spoke, at pretty much the maximum workable length, not only spreads its load more evenly over the hub flange, but requires a lower maximum tension in the first place.

As for both of your flexion concerns, I suspect the reverse is true. A true and correctly-tensioned wheel's spokes shouldn't be moving, and if anything the crossing will hold the elbow seated more firmly in the hole.

I can't speak specifically to "touching" vs "passing", as you have put it, but it would seem to be a similar rationale to tying & soldering wheels, which is supposedly done to increase stiffness, and prevent spokes from rattling in the event they break. This article (by Jobst Brandt, for better or worse) seems to dispute the stiffness claim, but I don't think it changes the rationale much.

Very interesting question.

When two spokes are touching, then they're pulling against each other. They're like two adjacent links in a chain; when the chain is under load, both the links are subject to the same amount. So this might help spread the load better; but I have no idea if this effect is actually significant, since as you said, radial wheels work just as well.

I can't comment on doing a whole wheel this way, but I have seen wheel repairs done this way while touring. It did not work, I suspect for the reason that Jobst points out. The nipples unwound after a few days (at about 100km/day with perhaps 100kg load). Doing the spokes up tighter just broke spokes and stripped nipples. The mutual tensioning effect is IMO important, and super-gluing the crossings together after the wheel was tensioned merely broke the superglue. I suspect that was because of limited contact area rather than huge strain, though. But it didn't work as a post-hoc fix. But that was not a controlled experiment.

I've read both Jobst's and Gerhard's books, and they're both worthy books. Jobst's has the advantage of being shorter. Unfortunately Sheldon's rec.bicycles.tech and the bicycle science mailing list discussions never really managed to get solid data on this, and the Journal of Human Power has not had an article that covers it either. Jobst measured the (lack of) change from tying and soldering but apparently not the change from lacing.

I'm about to relace a wheel this weekend and I'll consider lacing it as suggested. Mostly because it's a low-cost experiment for me (symmetric hub gear wheel, so easy to relace) and I'm curious. Currently it's breaking spokes at the nipple because the holes in the rim are not angled correctly, so I'll be fixing that too. But unless the pattern is a disaster it will take a few years years to find out whether it's any good (I only do 5000-6000km/year).

One-cross crosses too close to the hub to interlace. Otherwise, it's wise to interlace the last crossing, for the reason Brandt points out.

Keeping the spokes under tension is the whole challenge of wheelbuilding. It's what keeps the wheel from going out of true and, in the worst case, tacoing. Note that it's not the spoke, but the rim/nipple interface, that limits how much tension can be put on the spoke. If you don't interlace, you're giving up that last bit of insurance against untensioning a spoke.

The only argument against interlacing would be if spokes habitually broke at the place where they crossed. I personally have never seen that.

Regarding tying and soldering, I think Brandt is correct to debunk the practice. In all the tied-and-soldered wheels I've seen, the spokes easily slide against each other, so I don't see how it can improve wheel stiffness. (Brandt shows this empirically.) The only argument in its favor is that it keeps a busted spoke from flopping around, meaning you could possibly keep riding the bike with a busted spoke. (This might explain why you still see them in the cobbled classics. Although more and more teams are simply using standard carbon wheels.)

The main problem in this type of debate is that most people will just quote "accepted" wisdom without personal experience. I will say at the outset that my own experience is limited to small wheeled folding bicycles. I have built wheels for several of these over the years and I always laced them until I came across a set of wheels that had been manufactured without any spoke lacing at all; they simply crossed over at the usual lacing points. I have ridden on these for 3 years now without any of the detrimental effects mentioned above.

I think a 2 cross is stronger than a 0 cross but it doesn't always look as cool especially on a low spoke count wheel. 0 Cross is for the front only. Sometimes maybe you only have shorter spokes around. Radial will not be as forgiving of a bad build. Here is my latest compromise on the rear wheel as I am trying to evolve the Holy Grail of wheels. 16 spokes 2 cross on the drive side. 8 spokes 0 cross on the non drive side(nds). All 24 spokes have the same tension on the meter. If there is any future truing to be done, only the 8 nds spokes will be adjusted.

The Shimano XTR M988 Trail Wheelset is built with the spokes crossing but not interlaced, they just pass over without contact and after a fair bit of riding (and not gentle) they seem adept in corners and rigid as any other wheelset I have ridden. Possibly down to the rim technology though? I am now in the process of builing a wheelset using the same technique but using lightweight components for my XC bike. Hopefully I'll get the same results from this project....

It only ever seems like an additional stress point when they are interlaced although the derrailleur clearance is a decent point.

Vintage English bicycle wheels (1950-1960) sometimes had a 3-cross NOT-interlace pattern from the manufacturer (I own one). Interlacing did not become "standard practice" (accepted without question) until the mid-1960s. Interlacing is now "always" done, perhaps because there is little disadvantage while providing the advantage of additional lateral stiffness.

Some data points:

Almost all the factory-built fancy wheels I see on group rides are now laced 'passing' rather than 'crossing'. Seems to be standard practice across Campagnolo, Fulcrum, Shimano, Zipp, Mavic, etc. This may be because they like to use bladed spokes and perhaps there is an incompatibility there. But it may also be that it is as strong and removes a warranty-claimable failure mode.

I did a google image search for 'broken spoke' which finds a lot of spokes broken at the elbow (as you would expect) and very few broken elsewhere. However the few which have broken elsewhere (and not as the result of a crash) look to have broken at the 'crossing' point. This makes sense because it should be the most-fatigued point in a double-butted spoke laced 'crossing'.

I tried building a set of wheels 'passing' not 'crossing' and here are my observations:

It was easier to lace the spokes.

Tensioning and truing was more difficult because the tension of the inside spokes needs to be significantly less than the tension of the outside spokes to exert the same lateral pull.

I had to cross the spokes on the rear drive-side: a short test revealed the rear mech was clipping the outside spoke otherwise. That was on an 11-speed hub with 10-speed drivetrain and the 1.8mm spacer behind the cassette, so on a true 11-speed system or with a 10-speed hub it might be possible to rip the mech off entirely.

With disc brakes you might need to cross the spokes on the caliper-side to clear the caliper.

With normal hubs and J-bend spokes I recommend that you interlace all sides of both wheels because the benefits of even spoke tension for all spokes on the same side of the same wheel far exceeds the minor benefits of not interlacing the sides you don't need to interlace.

Looking at my wife's DT Swiss wheels they are laced crossing with the inside and outside spokes leaving the hub from almost the same plane, so they are close to achieving the benefits of both systems.

It is heavily advisable to physically cross the spokes.

Consider for example DT Swiss Alpine III spoke (2.34mm - 1.8mm - 2.0mm).

On my 36-spoke wheels (laced cross 3), the spoke crossing of the 300mm spokes is 90mm away from hub and 210mm away from rim.

Normally the spoke centerline goes 0.9mm to left due to the crossing and 0.9mm + 1.5mm (half of flange) + 1.17mm (half of spoke elbow area thickness) to right. We can calculate from Pythagorean theorem that the crossing adds 0.0727057325297 mm to spoke length.

Now consider what if one spoke goes completely slack. It needs a certain amount of flex at the rim to do this. Normally 0.64641 mm is enough to make spoke originally tensioned to 1200 N to go slack (the stiffness of these spokes is 1.8564 kilonetwons per milimetre).

Now if the spoke goes slack, the other spoke becomes completely straight, thus increasing the length the slack spoke has to cover. The crossing midline is now (1.5+1.17)*210/300 mm = 1.869 mm to the left at the non-slack spoke. The other spoke midline is now 1.8+1.869 mm = 3.669 mm to the left. We can calculate from Pythagorean theorem that the slack spoke now needs to be 0.2550111614167 mm longer than 300 mm (it used to be it needed to be 0.0727057325297 mm longer than 300 mm). Thus the spoke extra elasticity is 0.1823054288870 mm per 1200 Newtons.

Note that the elasticity used to be 0.64641 mm per 1200 Newtons but now is 0.1823054288870 mm per 1200 Newtons more! This gives 28.2% more strength for the wheel for radial loading.

The effect of the physical spoke crossings is to make spokes more elastic than they used to be. This extra elasticity contributes to radial wheel strength.

A 36 spoke wheel where the spokes are not physically crossed is equal to a 28 spoke wheel where the spokes are physically crossed.

A 28 spoke wheel is marginal and cannot withstand large loads.

I've laced my wheels without a physical crossing for years, for the simple reason that I use sound to judge spoke tension. With a musical ear, it's quite easy to build a wheel with very even spoke tension, but it requires that every spoke can vibrate on its own. You can't tune spokes when they touch. Building a wheel with even spoke tension and interlacing requires a tool to measure the spoke tension.

That said, I arrived at some quite robust wheels. This was certainly helped by the fact that the tuning method delivers very even tension among the spokes.

So, it's not really necessary to interlace spokes. You can do it, and, as the accepted answer states, your wheel may be more robust with interlaced spokes, but you can definitely build rideable wheels without interlacing.