You say the earth is round? Prove it
I have utter and absolute trust that the Earth is a sphere. And yet I have never had any personal experience that would convince me of this. I have accepted it as a matter of faith. As someone said, "Common sense is what tells us that the world is flat." For all I know from personal experience, the world might be shaped like a frisbee, which is round and has a curved surface, but is not a sphere. Perhaps Magellan, in circumnavigating the Earth, sailed in a circle around the North Pole in the middle of the frisbee to get back to his starting point. Taking the word of the astronauts is like taking the word of somebody about his religious experiences — interesting but not convincing.
My unfounded albeit profound faith that the world is a sphere is matched only by my faith that you can come up with some proof I can personally experience to prove that our planet is indeed an orb.
I know you mean this question to seem delightfully impertinent, Allan, but you're about 30 years too late. There are, after all, innumerable photographs of the earth taken from space which reveal it to be spherical. Assuming you are not about to join the Flat Earth Society in proclaiming these a fake, I gather your complaint is that looking at a photo doesn't qualify as "personal experience." Big deal. I've never personally experienced Disney World, either. Most of what we know about anything depends on taking somebody else's word for it.
That said, there are a few home-demonstration-type indications — not proofs — that the earth is a ball. We'll start with ones you've already thought of:
(1) Departing boats gradually sink below the horizon, as do buildings on the shore from the viewpoint of the sailors. Admittedly this only proves the earth is round right where you are — the frisbee hypothesis.
(2) "The sphericity of the earth is proved by the evidence of … lunar eclipses," Aristotle says. "For whereas in the monthly phases of the moon the segments are of all sorts — straight, gibbous [convex], crescent — in eclipses the dividing line is always rounded. Consequently, if the eclipse is due to the interposition of the earth, the rounded line results from its spherical shape" Of course a frisbee, properly angled, would make a round shadow too. But if the frisbee rotated while the eclipse was in progress, the curvature of its shadow would change. The earth's does not.
(3) The constellations shift relative to the horizon as you move north and south around the globe, something that could only happen if you were standing on a sphere. (You may have to draw a few diagrams to convince yourself of this.) Given sufficient world travel combined with careful observation on your part, the frisbee hypothesis becomes well-nigh insupportable. I suppose this doesn't qualify as a home experiment, but I never said science would be easy.