Why are holding patterns in an oval shape? Why not circular or more square-like?
I don't have any definitive information on why the oval shape was chosen. However, it seems to me to be the most practical shape given the navigational equipment available when holding patterns first became necessary. VOR, DME, and GPS technology did not exist. Holding patterns were flown, often by single pilots hand flying, with reference to an ADF needle, maybe with a little marker beacon help.
I don't know if a square-like pattern was considered, but if it was I think it would have been rejected for at least the following;
- a rectangular pattern would involve 4 turns, better to keep it simple with only 2 turns.
- flying any kind of a leg perpendicular to the holding radial would mean getting farther away from the radial than necessary with no advantage to be gained, and it might involve more terrain clearance problems.
Flying a circular pattern makes it more difficult to keep track of where you are in your head (no glass cockpits, indeed no HSIs even, not even rotating ADF cards at first), than an oval. Worse, though, is what could occur in some wind conditions. For example, let's say you're supposed to hold north of a fix on the 360 radial (inbound course 180). Further, lets say there's a significant north wind. You're approaching the fix on a course of 180. You cross the fix and then fly a circle with respect to the air you're in. In a no-wind condition, you'll come back to the fix. However, with a north wind, you'll come back to the course south of the fix, and will have thus violated where you were supposed to hold.
With today's navigational technology, we can of course easily fly any kind of shape we want, but the disadvantages previously mentioned would still apply.
An IFR holding pattern is along some bearing (typically, a VOR radial).
By flying a racetrack pattern, the plane is flying inbound on the radial for a period of time (straight line), making a standard turn (semi-circle), flying outbound on the same heading, slightly offset from the radial (straight line again), and making another standard turn to come inbound again.
On each pass, the pilot has time to verify his heading and alignment on the radial, and correct as needed.
If instead he were flying a circle, he'd never be established on any fixed heading for more than a moment. His heading would always be turning, which is a chance to get disoriented, uncertain, and off course.
A constant circle would also be less comfortable for passengers. With a standard hold, they get a couple minutes of straight flight before a gentle turn.
Imagine trying to turn a perfect circle, at night, in clouds, in stormy, turbulent weather. Without GPS, you could never be sure you were in the right spot. (aviation techniques were created long before the days of GPS)
According to various sources I've seen, the original purpose of the 'racetrack' holding pattern was to eliminate cumulative precessional error in gyroscopic intruments such as simple attitude indicators. Basically, the straight legs of the track allow the gyros to settle down again after a turn, and (just as importantly) allow the pilot to check that the instruments have settled down again, before starting the next 180° turn.
As was well explained in this answer to another question, in a good gyro there should not actually be any cumulative error in continuous turns because, at each point in a 360° turn, the error introduced by the gyro's 'erecting mechanism' should be precisely cancelled 180° later. But, in early instruments there certainly were cumulative errors (eg. due to frictional forces on the gimbal), and the racetrack pattern was a simple answer to that problem.
Wind correction in a "parallel" course racetrack pattern is much less complicated than in a circular pattern. This is the number one reason.
Square patterns would require steep turns, inconsistent with the concept of a standard rate turn in instrument flight.
It's not about comfort, it is about navigation and maintaining the aircraft reliably in a specified region.