Question: How big should the Sudiball be? Answer: The Sudiball should not be smaller than mirror / optical path / tube. Practically, how much larger the ball is becomes your design choice among trade-offs. I will try to cover some of them here. Smaller diameter ball uses less material can be lighter and fits through smaller spaces. Larger shifts the balance point up (eyepiece down) and can feel smoother to slew. Other practical considerations may include - the dimensions of the stock you will be building with - how material efficient you intend to be. - will parts need to be nested/interlocked. - how you will be forming the material; clamping, tool clearance and kerf width These practical considerations will suggest a maximum sudiball diameter for a given set of material. With a disk (mirror/tube) size smaller than a Sudiball size there is a minimum height above the bottom of the ball which the disk must not (can not) be lower than. This minimum height is a function of the ratio between the ball and disk sizes Given: ball_radius = R disk_radius = r Then: The minimum height h is: h = R*(1-sin(acos(r/R)) However, I can not know your mirror/tube sizes nor guess the Sudiball size you will settle on so the best I can do is offer a chart that should help determine the "what ifs". With a standard Sudiball (3 planes tilted at 45-degrees intersecting at the center) there is the practical question of whether the mirror will sit on top of the runners or or if it could be set nested within or below the intersections of the runners. Mirror above the runners may be more straight forward to build and allow a smaller ball to disk ratio as the mirror is closer the equator where there is more room. However this may necessitate introducing counter balance. (not my favorite solution) Placing the mirror within or below the runners becomes technically more demanding unless you are fine with a sudiball several times larger than your mirror, which seems to work out okay for small mirrors but becomes daunting for large mirrors. When trying to keep the Sudiball small and the mirror as low in the ball as possible, the main consideration becomes keeping the light path unobstructed by the runners while maintaining the structural integrity of the runners. If 'd' is the diameter of the path you need clearance for, then an equilateral triangle that will clear it will have side lengths of about 1.75*d [sqrt(3)*d] which may be helpful while approximating designs but in actuality will need to account for thickness and tilt of material which we can not do much about but bevel the inside of the runners, which leaves ball diameter and width of runner (not thickness of material) As a rule of thumb with plywood I prefer the width of the runners to tend towards five or six times the thickness of the material as this allows for several finger joints each the thickness of the material. With larger ball to disk ratios, the mirror can be physically below the outside of the runners and still be within the pseudo sphere described by the runners, which is as good as it gets for balance. A Table with the fraction of the sudiball radius that a mirror *could* sit above the "bottom" for various sudiball to mirror ratios from 1:1 to 1:5 100.0% 1.0 100.0% 112.5% 0.54188 88.9% 125.0% 0.4 80.0% 137.5% 0.31365 72.7% 150.0% 0.25464 66.7% 162.5% 0.21177 61.5% 175.0% 0.17935 57.1% 187.5% 0.15409 53.3% 200.0% 0.13397 50.0% 212.5% 0.11765 47.1% 225.0% 0.10419 44.4% 237.5% 0.09296 42.1% 250.0% 0.08348 40.0% 262.5% 0.07541 38.1% 275.0% 0.06846 36.4% 287.5% 0.06244 34.8% 300.0% 0.05719 33.3% 312.5% 0.05258 32.0% 325.0% 0.04851 30.8% 337.5% 0.0449 29.6% 350.0% 0.04169 28.6% 362.5% 0.0388 27.6% 375.0% 0.03621 26.7% 387.5% 0.03387 25.8% 400.0% 0.03175 25.0% 412.5% 0.02983 24.2% 425.0% 0.02808 23.5% 437.5% 0.02647 22.9% 450.0% 0.025 22.2% 462.5% 0.02365 21.6% 475.0% 0.02241 21.1% 487.5% 0.02126 20.5% 500.0% 0.0202 20.0% The first & third columns are the same ball & mirror ratios just taken in the opposite order. The center column may be interpreted as: The mirror is guaranteed not to be lower in the Sudiball than this fraction of the Sudiball radius as you will surely want and need more clearance. It can be difficult to describe or imagine just how much more manageable a Sudiball is compared to an equivalent diameter sphere to move around or fit into a vehicle. For example a 30" Sudiball may thread through some 24" doorways easily. So please, do make a full scale cardboard mock-up, you may be pleasantly surprised by where it can be fit for transport.