jedi and berkeman, thank you both for your replies.
jedi: I never thought to use liquid as a medium, and am embarassed for not having done so. The simplicity of water is elegant--thank you for that. Unfortunately, other contraints (the container's use on an aircraft, in a cargo hold) prevent me from doing so for this project. I welcome any other ideas you might have.
berkeman: Thank you for your questions, as they helped me figure out certain things I had not yet considered. My answers (at present) are below:
What volume is involved? I am not certain of this figure yet but have realized in answering your other questions that the container will likely be somewhat larger than I first conceived. Design also plays into this uncertainty: if the container is approximately Dalek shaped (as I first imagined it,) its dimensions would be different than if the self-levelling sphere were placed inside a 3’x3’x3’ box of some kind.
What weights are involved? The weight of the container and base, which are variable (I am thinking of using carbon fiber for this), the weight of the liquid and dry contents of the container, and one 15 pound cat. Here I might guess that the total weight could approach 50 pounds, maximum.
What tilt angles must be tolerated? +/- 5 degrees? +/- 45 degrees? The container will be used on a commercial airliner, though I don’t know which kind of plane I will ultimately be scheduled to fly on. Consequently I would guess that the maximum tilt angle the container would have to adjust for is 25 degrees upon takeoff (using Boeing MD11 figures), and perhaps as much as 11 degrees (maximum) throughout the flight (again, based on the B-MD11). The container would also have to adjust for rotational changes (when the plane banks left/right to change course), which I believe is constant at 30 degrees maximum.
This is why I thought of using ball bearings between two spheres—the container must account for changes in pitch and roll, and at four points in the flight must do so simultaneously. (I have not committed to this idea, however, and welcome more elegant solutions!)
What frequency response is needed for this "self leveling" feature? Is it because the container ship is rolling slowly, or because the shipping 18-wheeler truck is taking mountain roads too fast? The frequency response (as I understand it—please excuse my ignorance if my apprehension is incorrect) should be constant, in that it should keep the container level throughout the climb phase of the flight, throughout all course changes (banking), and then correct to adjust for the pitch of the nose of the plane while in flight, for the entire flight.
What accuracy do you need for "level"? At least 97%. The goal of this project is to get my cat from where I am to where I am going as comfortably and cleanly as possible.
What power sources do you have available for an active leveling system (versus passive gravity-based leveling)? As this container will be stored underneath the plane, I can safely guess that levelling the container must be gravity based.
What are the consequences of the system failing? Loss of revenue for the cargo (how much revenue?)? Loss of life for the animals in the cargo? Relative to the container and its contents, system failure would include an uncomfortable, ill-tempered, and physically quite dirty cat upon arrival, as all of the liquid and dry contents of the container (cat food, water, both fresh and soiled litter) would not be where they were supposed to be inside of the container. Relative to the aircraft, I would expect that some of the liquid/dry contents of the container would end up soiling the cargo hold, which would be an embarrassing, thoughtless thing if it happened.
