I'm trying to find a story I read maybe fifteen or twenty years ago. The story itself might be much older, of course: it had a 1950's - 60's 'golden age of hard SF' feel to it.
As I remember it, the plot involved an effort to find out if the universe is closed in 4D by having two ultra-fast ships complete a flight around the entire universe. One of the ships was shaped like a ring so that the other, needle-shaped ship could fly through its central hole.
The idea was that the ring-shaped ship would take off, and after a while the needle-shaped ship would accelerate on a course exactly through the hole in the ring-ship, overtaking it; then the roles would reverse and the ring-ship would accelerate on a course to overtake the needle-ship passing through its hole - and so on. I think this alternating aim-accelerate-overtake process was very fast, the drive being inertia-less hyperdrives or what have you: the crew aboard never noticed the acceleration.
The story follows the crew of only one of the two ships: they could not maintain contact during the flight supposedly because of the choppy flight pattern. They even never saw the other ship during the mission, because they passed one another way too fast for that.
I suppose that the idea was that this would plot a straight course through space (though it would of course be subject to 4D curvature nonetheless). The only other thing I remember is that at a certain point in the story the ship's gyroscope (or whatever they had) revealed their course had begun to curve anyhow.
A detail that I think comes from this story is that when they are really far out on their mission, there are no galaxies or stars in sight anywhere near and the only thing visible is a kind of faraway glow of the assembled galaxies of familiar space. However, I might be conflating it with "The Ethics of Madness" by Larry Niven, where two people in relativistic ramscoop ships fly off, ever closer to light speed and thus eventually covering a huge distance in their subjective time as well.
I also seem to remember that the crew noticed something else; something strange and a bit spooky when they were very far away. But what that something was keeps eluding me, and it might also come from the memory of yet another story, like the Star Trek TNG 'The Traveller' episode, which featured a similar journey to the other side of the universe.
That's what comes from reading too many short SF stories, it seems ;)
Does this sound familiar to anyone? Thanks!
- edited to add more remembered details