The angle formed by the axle, when combined with the dish of the wheel, was designed so that it brings the lowest spoke down to bear on the ground at almost exactly 90 degrees. The history, of this combination of angled axletree arms and dished wheels is unclear, Muller, who published in 1780, had been unable to source the origin as, by then, it was already long established custom. This system had many benefits with regards to strength, prevention of wear and tear, better access to the gun. It also provided safer passage for gunners travelling on the limber ammunition boxes, with the upper section of the wheel being further from harms way of an unwary limb. Sturt, in “The Wheelwrights Shop” - late 19th century - was in no doubt whatsoever about how much strength was given to the wheel by the dish, un-dished wheels - or those with only a slight dish & not well made - were very prone to ending up well out of perpendicular - always ending op with the tyre towards the cart, like an umbrella blown inside out. This was from the lateral thrust constantly applied from the motion of a horse drawn vehicle. Of interest was that the axletree arms had to have, as well as a downwards inclination, a slight inclination, or turn forward, to the front.
From a small section of Holden’s War Dept Notes (1860s) on British field carriages:
“The Spokes are of Oak, and are dished, or inclined out-wards to enable them to withstand the lateral thrust, that they may be subjected to in passing over uneven ground, when one wheel is often much higher than the other, in which case a pressure is exerted on the Nave of the lower wheel tending to force it outwards. The dish is usually about ¼ of an inch to 1 foot in length.”
“The Axletree where it passes through the bed is rectangular in section to enable it to get a good hold of the wood. The projecting Arms are circular and tapering. The Arms are not in direct prolongation of the body of the axle-tree. They form an angle with it, turning slightly downwards to give the wheels a turn, in order to compensate for the “dish”. The turn forward is called the “lead” of the arm, - the inclination downwards is called the “hollow” of the arm, and the two together are called “the Set” of the Arm. These arrangements, besides compensating for the dish of the wheels, cause the spokes to be less liable to be rubbed in going through deep ruts. The upper parts of the wheels are also made to incline outwards. If they inclined inwards, the axletree arms and boxes would wear away where they are nearest the carriage. The greater distance between the wheels above, also leaves more room for the load, and gives greater facility of approach to the parts near the axle.”
Is there a specific carriage that you are after inclinations for? from what I have read it seems it was varied for wheel diameters etc.
Adrian.