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The Wikipedia tripod page mentions that most tripods are braced around a center post.

However, in in this slightly amusing cheapo tripod test video, I noticed the Gitzo tripod isn't braced around a center post whereas every single one of the cheapo tripods is braced around a center post. Thus, based on the very low sample size:

  • Cheap tripod = braced around center post
  • Expensive tripod = not braced around center post

I recently bought a cheapo ($50) tripod that is not braced around a fixed center post. When looking at the video, the amount of wobble in my tripod is much, much closer to the amount of wobble in Gitzo than to the amount of wobble in the extremely cheap tripods in the video. I don't have a Gitzo so I can't do a fully scientific comparison, but the wobble in my tripod seems extremely low, and after purchasing it, I was positively surprised by the very low wobble, because I knew the tripod was cheap and lightweight.

When thinking about the bracing around the center post, it may not be entirely free. My tripod even doesn't have a fixed center post! To have the fixed center post, you would need more material, thereby having more weight. The same weight could be used to make the legs more sturdy and the joints higher-quality.

So: is there any benefit in having a tripod braced around a center post? What is the purpose that some tripods are braced around a center post? Is it low wobble, or higher weight rating (my tripod has only 2 kg rating, with 1.5 kg ideal load, with the tripod itself being 0.9 kg and the weight I'm planning to use at most 1.0 kg)?

I can at least name one benefit of NOT having a tripod braced around a fixed center post: the "stick" that holds the camera can in some tripods be turned downwards, so that you can have the camera very close to ground level. My tripod doesn't have this feature, but the Gitzo does.

Certainly, given the evidence in the video, adding a center post to a poor tripod doesn't automatically make it a good tripod.

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...And if you go even more expensive, you'll often find these braces again. They are not inherently a sign of being cheap or bad.

This is simple, really. The brace makes a triangle when the leg is unfolded. Triangle is naturally rigid; it is the lightest way to make a rigid structure. So normally, having braces will make the tripod lighter, not heavier, if it's designed with them in mind properly (and other things being equal).

Why not make them, then? Well, there are other design considerations.

  • A structure that is nominally rigid and strong in its proper triangular shape will be very, very thin and lightweight. Like, paper thin. But as soon as it loses its shape - say, a slight bend or dent - it may easily collapse. We need to ensure that the shape stays intact - either by putting a whole web of struts, or by making each leg rigid enough by itself.

    In addition, we need to ensure sideways stability (out of the plane of the triangle). We can either make yet more braces - between the legs - to create a tetrahedron, or again, just make the legs and hinges stronger. Or alternatively, we can make a smaller triangle by splitting each leg in two: many video tripods have it like that, like the one I linked above.

    In the end, if we make each leg and hinge strong enough to satisfy all other structural and manufacturing requirements, we may no longer need the bottom brace. This is particularly true for structures made of lightweight materials, such as carbon fibre: each element can be bigger and thicker (hence more rigid for the same strength) but still light. Nevertheless, adding more struts will only make the structure yet more rigid.

    Note that any tripod will form a tetrahedron when put on the ground, provided that its feed don't slip. The brace you are talking about will then provide additional stability to each leg, holding its shape.

  • Additional braces make kinematics more complicated, clumsy, prone to jams, etc. This is particularly important for portable applications.

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By "braced around a fixed center post" I think you mean the strut braces at the bottom of the center post?

This is traditionally a feature of tripods used for video cameras and also sometimes large format view cameras, or studio work.

A non-cheap tripod for still photography does not have these because they are usually not required (IMO) and add weight, bulk and complexity of set up which is not what you want when you are out of the studio, i.e. carrying it around on location (again the exception being large heavy cameras that need the added rigidity).

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I would guess that the center post is used in cheap tripods because they are made of cheap, weaker materials and thus need the extra stability.

More expensive ones use better materials, often carbon fiber to make them both strong and light weight. The lack of the center post allows the tripod to spread the legs out more and thus be much more adaptable (in addition to the points you already mentioned).

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