After some exploratory testing, it is clear to me that the route to repeatable and comparable testing of tripods runs through the damped torsional harmonic oscillator model. If you are curious on the details the wikipedia article on the subject is thorough. However, I do not intend to make differential equations a prerequisite for understanding the testing done on this site.
Naturally, one might ask why we are going to use a rotational model for tripod stability, and the answer is simple. Rotation is the type of motion that will affect the final sharpness in images. An image gets blurred by the camera pointing in slightly different directions, not by the camera translating slightly in any direction. The exception to this is of course macro photography, where shifts in the camera position can have a large impact on sharpness. Rotational motion can be described in terms of pitch, yaw, and roll and we will look for those rotations about the tripod’s apex. The center of the coordinate grid below will sit right at the mounting screw on the top of the tripod’s platform.
Tripods are typically weakest in the yaw type rotation. This only requires the whole tripod assembly to twist. Pitch and roll type motions are much stiffer as they would require one or more of the legs to compress or splay out along the ground, a motion to which the tripod is much more resistant.
This framework will allow us to better understand some aspects of tripod stability. A center column for example, will typically not have a huge affect on the yaw motion. However, moving the camera up will increase its effective moment of inertia (the rotational equivalent of mass), and thus cause the pitch and roll motions to be much more pronounced. More on this later.
We will also have some extensive discussions on manufacturer weight ratings. There is no standard for this, and for good reason. Most tripods can support a massive amount of weight before physically collapsing. Manufacturers are trying to hint at the amount of weight the tripod can be practically used with. The actual figure of merit should be the amount of rotational inertia that the tripod can effectively support. The tripod may be able to support a lead brick at its apex with no issue, but a camera attached to a 600mm lens with severe difficulty. The large amount of mass at a significant radius from the apex increases the rotational inertia and causes problems.
The actual testing process will involve measuring the characteristic torsion spring constant k, better known as the stiffness of the tripod, and angular damping constant C. A tripod with higher stiffness will keep camera movements smaller when subject to forces such as wind, a human hand or even the internal moving mechanisms of the camera itself. More damping will make the resulting vibrations from such forces die out faster. More of both factors is better. The procedure for these measurements will be explained, developed and explored in the coming weeks.