In this photo of a coach (hi-res, 5.7MB) in the Coach Museum in Belém, Portugal, the wheels are cambered out at an impressive angle. This was very consistent across dozens of coaches in the museum.
Is there an engineering reason for this?
I think if the coach was occupied, the weight might flex the axles enough to make the wheels stand upright.
I don’t think that’s it. If those wheels are on a common axle, then a half-turn of the wheels would reverse the direction of the camber, and weight on the axle in that state would make the sag even worse. And if they’re not on a common axle, then weight will make any camber, positive or negative, even more extreme.
My suspicion is that it facilitates steering in some way, similar to the bevel on a train’s wheels. But I’m not sure how it would work.
It may be a safety/reliability issue. With the axle canted down like that it would take stress off the wheel nut, and if the nut were to fail I think the wheel would be less likely to fall off.
positive camber lowers steering effort at low speeds. it’s why certain types of farm tractors have closely-spaced front wheels with seriously positive camber. Especially when they’re slogging through dirt.
It almost looks like that’s just the coach’s suspension–it looks like there’s a solid bar with a bracket in the middle. The wheels are mounted on the ends and can spin there freely (i.e., the bar isn’t an axle, just a mount for the wheel bearings). It starts in a curved down state to give the wheels room to flex upward with bumps and extra weight.
Well, maybe. Hard to see, but it seems plausible.
According to wheelwrights at Colonial Williamsburg, the camber and the design of the wheels allow the wooden spokes at the bottom of the wheel to be perpendicular to the edge of the wheel and the ground when bearing the weight of the coach or wagon, This is the spoke’s strongest orientation and requires it to bear primarily compressive forces from each end (axle and tire). Other orientations my bend the spoke, leading to a failure. You can see the same design on Conestoga wagons and other wheeled carts where the wooden wheels are slightly dished.
It may be a trick of perspective, but the wheels also look dished - the hub is not in the plane of the rim. It looks like it might be the case that the dish of the wheel combined with the camber of the wheel put the individual spokes vertical when they are, uh, vertical…directly under the hub.
If the wheels weren’t dished, and the camber was still there, the spokes would be getting a big torque on them as they passed directly below the axle.
So… the dished wheel is needed to accommodate the camber, and vice versa. Perhaps the question should be why the wheels had to be dished, which then necessitated the camber?
I agree with Robot Arm that this setup would tend to keep the wheel on the axle rather than letting it go flying off if something happened to the wheel nut.
Aha! Check this book about carriage buildingout! It seems to confirm that the camber is used to get a ‘plumb spoke’ because of the dish of the wheels.
So why does the wheel have to be dished? Perhaps there is a balance of forces in a dished wheel that make it more stable than if it was planar, in the same way that a paper cone is less floppy than a sheet of paper.
ETA: gah! ninja’d by ZonexandScout
I infer that “dished” means that the spokes lie on the surface of a cone, rather than being coplanar with the wheel hub. Is that correct? If so, why is that?
Correct. Good reference here explaining some of the issues, although only one page is available for free. One of the advantages of a dished and cambered wheel is that all of the crud picked up by the tread doesn’t get dropped onto the hub, reducing axle/bearing wear as compared to a vertical cylindrical wheel. I’m having trouble parsing the other advantages listed there, i.e. cylindrical wheels requiring a greater distance between them, and the problems with the jolting motion due to being horse-drawn. 
Wikipedia mentions another issue, in that a dished wheel copes better with the expansion contraction of wooden spokes due to moisture; a planar wheel whose spokes grew would overstress the rim, and/or result in spontaneous large changes in dish to accommodate the lengthened spokes (sort of like linear railroad rails severely buckling to accommodate thermal expansion), whereas a well-dished wheel won’t experience much change in dish when the spokes grow a little bit.
All of this is in addition to what earlier posts have explained about dished wheels handling lateral loads better.
I think that when properly done, this prestresses the wheel in a predictable way, and keeps it from assuming a less desired shape (ie a taco or something wavy).
Those old spoked wheels worked under compression rather than tension like a modern wire-spoked bike wheel. The metal tire was hammered on red-hot and shrank, which compressed the rim and spokes and seated the spokes hard in the hub. Wedges would have been driven in to the mortise between hub and spoke to keep the spoke pitched out at the correct angle to have the proper dish to the wheel.
References:
The Dish of Wheels
Popular Mechanics 1905
Yes, dished wheels handle the expansion and contraction of the wood more easily. If the (iron) tire, wheel, spokes, and hub are in a straight line, expansion of the spokes may damage the wheel. There’s no “give.” In a dished wheel, the spokes can expand and they simply push the hub slightly farther away from the wheel and it becomes a bit more concave. This has little impact on the operation of the wheel. Remember, these are wooden spokes and they are exposed to rain, run through streams and rivers, and allowed to dry in the sun.
Wood doesn’t expand very much along the grain line due to changes in moisture level, though; it expands much more across the grain. Wood can expand by about 8% tangent to the growth rings, 4% radially, but only 0.01% longitudinally. So a wet spoke will be fatter than a dry one, but not longer. So the hub may go out of round and the felloes may swell, but the spokes won’t get longer.
It sounds like the advantages of having dished wheels is the fundamental thing, and the answer to the OPs question is mainly, “because the wheels are dished”.
This website says that dished wheels are less likely to fail when turning at speed.
It makes sense, at least for the outside wheel. The force of the carriage pushing against the outside wheels would tend to “undish” the wheel, tightening it up.
That would seem to have a negative effect on the inside wheel though.
But because the center of gravity of the carriage is well above the ground, the wheel on the outside of the turn has more weight on it.