A cart or wagon wheel is dished: the spokes lean outward from the hub so the wheel is a shallow cone whose hollow faces away from the vehicle, and the dish is matched to the downward slope of the axle arm so the spoke at the bottom stands vertical under load. A 5-8 degree tilt on a 50 cm spoke shifts the rim 4-7 cm sideways along the axle, and the angle must be identical in every mortise.
Part of Wheelwright Craft
Dish, gather and stagger are the three deliberate departures from a flat, symmetrical wheel; each exists to put load on the wood in the direction it resists best.
The Lower Spoke Must Stand Vertical Under Load
The vertical load on a wheel reaches the ground through whichever spoke is at the bottom. Wood in compression along the grain is strong; wood bent sideways is weak. The wheel is therefore built so that the lowest spoke is plumb when loaded, so it takes the load as pure compression along its length.
Traditional axle arms slope slightly downward toward their tips (see Axle and Bearing Design), so a wheel on one leans: its top sits further out than its bottom. A flat wheel on that arm would have a bottom spoke leaning inward. Dishing the spokes outward cancels that lean exactly.
The geometry
Let the arm slope down by an angle β and the spokes tilt outboard by a dish angle α, measured from the plane at right angles to the axle. The wheel’s lowest direction leans inward by β from the vertical; the spoke’s tilt leans it outward by α. The lower spoke is therefore off vertical by α - β, and it stands plumb when α = β. If the dish were reversed, with the hub standing outboard of the rim, the lean would be α + β, and the lower spoke would be bent rather than compressed.
Read it back as a picture: seen from outside the vehicle, the finished wheel is hollow like a shallow bowl, with the rim nearer your eye than the hub.
Dish Depth From The Mortise Angle
The parent article tilts each hub mortise outward 5-8° “from perpendicular”. With an exposed spoke length L, the rim sits sideways of the hub by L × sin α.
| Dish angle | sin α | Offset on a 50 cm spoke |
|---|---|---|
| 5° | 0.0872 | 50 × 0.0872 = 4.4 cm |
| 8° | 0.1392 | 50 × 0.1392 = 7.0 cm |
| 3° (other article) | 0.0523 | 2.6 cm |
| 6° (other article) | 0.1045 | 5.2 cm |
So a 5-8° tilt offsets the rim by about 4-7 cm. The 50 cm spoke length is an assumed round figure for a cart wheel, not a measurement. Spoked Wheels gives 3-6° for the same job, so sources differ on the angle; both agree it is small. What matters is that every mortise has the same angle, and Mortise Cutting shows how small an error ruins that.
Gather: A Slight Toe-In At The Axle Arm
In wheelwright usage, gather names a small forward convergence of the axle arms, so the wheels are marginally closer together at the front than at the back. It is a property of the axle and arm, not of the spokes. Its job is to keep a wheel on a tapered, cambered arm from working outward toward the linchpin.
Two meanings
The parent article describes gather as an angling of each spoke face toward the direction of travel. That is a different feature from the axle-arm toe-in described here, and the corpus does not source the spoke-face version. Do not set up a wheel from it; the dish and the arm’s slope are the settings that matter, and they must be set together on the same vehicle.
Stagger: Two Rows Of Mortises In The Hub
On wheels with 12 or more spokes, alternate spokes are set slightly offset along the hub, so adjacent mortises do not share the same ring of wood. Each mortise then leaves a thicker web between it and its neighbours. Hub Construction shows why that matters: on a 25 cm hub a ring of 12 unstaggered mortises takes up most of the circumference.
Common Mistakes
- Cutting dish into the spokes instead of the mortises — shimming or bending spokes after driving puts them in bending from day one.
- Dishing the wrong way round — hollow toward the vehicle puts the lower spoke α + β off vertical and bends it.
- Matching the dish to the wrong axle — a wheel built for a cambered arm and put on a straight one stands out of true.
- Treating angle sources as exact — 3-6° and 5-8° are both quoted; verify on a test wheel.
Safety
A wheel that fails under load
A wheel with a bent lower spoke or loose tenons can collapse suddenly under a loaded cart, dropping the load on whoever is beside or downhill of it. Do not load a new wheel fully until it has carried a half load over a rough route and been re-checked.
What’s Next
- Learn next: Hub Construction — where the dish angle is cut in
- Combine with: Axle Box & Bearings — the bore the arm runs in