main calculator | triplet lacing calculator

Triplet lacing (AKA 2:1 lacing)

Rim Dimensions

Enter values manually, or add rims
to your bench
to select them here.

Hub Dimensions

Enter values manually, or add hubs
to your bench
to select them here.

Build Parameters

ERD Center-flange distance # Spokes
Drilling offsetA positive value will move left nipples to the left or right nipples to the right. (Negative values do the opposite.)
Flange pitch circle dia
Cross patternIndependent left & right values. Decimal cross values are handled just like Damon Rinard's spocalc.xls, but are not currently supported by the rendering engine.
Spoke hole diameter
Hub offsetA positive value will move the entire hub to the right of center.
 - ICE trike = 6mm
 - Pugsley = 17.5mm
 - Moonlander = 28mm
Rim FlipAuto will flip your rim to the strongest orientation. (only affects asymmetrical rims)
Left Right
Spoke length
Tension distribution
NOTE: left tension will be roughly twice what this currently computes!
Spoke head clearance
NOTE: left side math needs to be verified!
Bracing angle
Wrap angle (at rim)
Total angle at rim
Effective tangential PCD
Flange exit angle
Theta angle
wheel dish rendering spoke lacing rendering (left flange) spoke lacing rendering (right flange)

This is a lacing pattern where there are two right spokes for every left spoke. The stated goal is to increase tension on the left side spokes (by having half as many as usual). What this actually does to wheel strength and durability is left as an exercise for the user. It is possible to use "normal" rims and hubs (drilled in multiples of 4) to achieve this lacing, but only with a few speific combinations that fit the 2:1 criteria.


Hub  Rim
48     36
44*    33*
40     30*
36     27*
32     24
28     21*
24     18*
(*denotes nonstandard drilling)

Typically, the right side spokes are laced with a cross patternand the left side spokes are laced radially. There is nothing to stop you from crossing the left side spokes, and symmetrical patterns should easily result, but you'll need to be careful to select the correct left flange holes.

Unlike with a common lacing pattern, there are effectively positive and negative cross patterns. There seems to be no mathematically-based way of assigning positive or negative to each of these (as best as I can figure), so I have arbitrarily assigned them. Locate a pair of neighboring right side spokes on the rim (neighboring meaning there is not a left spoke between them) and follow them to the hub flange. If they cross one another, this is a negative cross pattern. If they do not cross one another, this is a positive cross pattern.

Manufacturers commonly associated with triplet-laced wheels are Campagnolo and Fulcrum, but Roval and even Shimano have dabbled in this realm.

For example, Campy triplet-laced rear wheels use what I am calling a negative cross pattern, while Fulcrum wheels use a positive cross pattern. To determine, find a pair of drive side spokes that are adjacent neighbors at the rim (even if there is a notable space between them). If they cross on the way to the hub, they are laced with a negative cross pattern, and if they do not cross they are laced with a positive cross pattern. To calculate for a negative three-cross lacing pattern, literally enter -3 for the right side cross pattern.

The author of this post about triplet lacing refers to these two patterns as "type 1" and "type 2". The ASCII art used to visually differentiate the two is not 100% foolproof, as both lacing patterns have drive side crossing in front of each radial spoke, just at different elevations off the hub.

A zero-cross drive side lacing will not be perfectly radial. The mismatch in drillings means there is not a hub flange hole directly between the axle and the rim hole. The correct clocking of rim and hub is with the left (non-drive) rim and hub holes aligned with the axle to allow the left spokes to be exactly radial. Between every two left spokes are two rim holes and three hub flange holes, so they cannot all lay on radial lines like on a conventional wheel.

Sheldon Brown's site has an excellent breakdown of how the basic spoke length formula works. Normally the theta value is determined with a simple formula taking into account drilling and cross pattern, but this assumes you are building a conventionally-laced wheel. Instead, we are going to be using the theta values shown above (derived in CAD, but a formula would not be very difficult). These theta values work for equally spaced rim and hub holes (conventional parts).

figure showing theta angle caused by cross pattern

Wrap angle (theta) is the angle between a line from the axle to the rim hole and a second line from the axle to the hub hole. For a conventional lacing pattern, this can be calculated as 360 * [cross pattern] / ([number of spokes] / 2). Life gets a little harder when we mismatch the hole count of the rim and hub, because the hub flange holes no longer all lie on radial lines between the axle and rim holes. For this lacing system, all of the left spokes are on radial lines, and all of the right spokes must necessarily be slightly off a radial line even if laced zero cross.

hub wrap angles (theta) for 32/24 combo right side spokes:
+4x  93.75° (bad idea; way more than tangential for any part combo)
+3x  71.25°
+2x  48.75°
+1x  26.25°
0x   3.75°
-1x  -18.75°
-2x  -41.25°
-3x  -63.75°
-4x  -86.25° (probably almost exactly tangential depending on ERD and PCD. Watch spoke head clearance though!)
each distinct type of 32/24 spokes repeat every 45 degrees (360 / 24 holes * 3rd rim hole)

hub wrap angles (theta) for 48/36 combo right side spokes:
+4x  62.5°
+3x  47.5°
+2x  32.5°
+1x  17.5°
0x   2.5°
-1x  -12.5°
-2x  -27.5°
-3x  -42.5°
-4x  -57.5°
each distinct type of 48/36 spokes repeat every 30 degrees (360 / 36 * 3rd rim hole) 

The zero-cross angle is calculated as ((360/rim)-(360/hub)). Each cross more or less is adding or subtracting (cross*(360/(hub/2))) from this base value.

You might be wondering: Why is this referred to as 2:1 lacing when all of these ratios are actually 4:3? There are two drive side spokes for each one non-drive spoke (2:1) but only half of the left hub flange holes are populated. A 32h hub laced to a 24h rim with this method will use all 16 right flange holes, but only 8 left flange holes (and 8 are left empty). 16:8 = 2:1.