One way the fast speed of the Cray-1's CPU was achieved was by keeping the wire lengths short. How did the C-shape of the Cray-1 help here? Were the speed-dependent portions on the inside edge where the wire lengths are shortest, and if so what were these speed-dependent portions?
In part the design was made for show effect. Reduction in wire length had only a minor influence, especially as it's only present in one dimension.
Cray 1 at the Deutsches Museum in Munich (Image taken from Wikipedia)
Mainframe circuit boards are connected via a hand wired backplane. In theory, arranging them in a circular fashion may save about 20% (*1) in horizontal wire length, but none in vertical (*2). In reality, and since Cray did put the boards horizontal, while not using the inner room for wiring, there were ZERO savings compared to a traditional setup.
(Taken from the CHM's Cray-1 Logic Column cutaway page)
Even more importantly, in backplane design it's not about making all connections as short as possible, but making them of defined length. Even more importantly, for wire groups where equal length is mandatory (*2). Looking at the above picture, we see that the wires aren't straight. The same can already be seen in its predecessors and successors (all the way to the 960) at CDC.
The design decision was much influenced by public reaction to a mock-up of the CDC 8600 with a quite similar design. In this multiprocessor setup, each CPU was meant to be one wedge-shaped unit allowing easy removal as a whole block before being opened (*3). While the machine was never finished, the positive reaction to the unconventional design might have stuck and transferred to the Cray-1, despite no longer being a CPU cluster.
Bottom line: It could have been built in a straight fashion; rolling it up was a great way to make it stand out - nerds do have aesthetics :).
Another, much more relevant, effect of this setup is cooling. This was in fact the main reason, even before compactness, why this setup was originally considered for the CDC 8600.
*1 - For a maximum value, the inner diameter as well as the medium can be used - this will give some upper limit. The outer diameter is about 1.45 m, while the inner is ca. 0.75 m. Thus the inner circumference is 2.35 m, while the median is ~3.45. So the upper limit of shortening in horizontal direction is about ~32%. In reality this would come to less than 20% - except it had zero effect on the real Cray :)
*2 - Maximum speed is only possible if all bits of a word arrive at the same time. The very same can be seen with modern PC mainboards, usually between CPU and RAM.
*3 - Design goal for the 8600 was extreme compact miniaturization, moving away from classic mainframe design. That's one of the reasons why it didn't work out.
The inside edge of the C contained the Cray's backplane, where the various segments of the machine were electrically connected. Minimising the length of this would have reduced electrical interference and signal propagation times.
The Cray-1 also needed a lot of cooling due to the type of electronics used to implement it; the extra space between the segments created by splaying them out provided enough room to insert the piping and heatsinks.
A very large portion of the Cray 1's logic was designed for exactly 6 logic gates and 4.5 feet of wire between registers. That was more easily done by shortening all the wire paths to be on the inside of the cylindrical arrangement. The greater outer circumference allowed more room for the power bars and thermal management necessary to supply and remove 0.15 megawatts of power.