I'm just intrigued to know why the vertical tail of a majority of aircraft is tapered? Is it due to aerodynamics, structural design or due to some instrumentation or multiple other reasons?
The vertical tail and the horizontal tail are wings, and follow the same construction rules. The span-wise lift distribution is much better if the wing is tapered: more lift at the root, less at the tip.
- The wing can be built lighter, root area is larger, torsion stiffness is higher.
- Vortex induced drag is lower.
As a reference, from Torenbeek: pages 232 & 233
It is observed that nowadays there are basically three forms of straight wings: the tapered wing, the untapered (rectangular) wing and the wing with a prismatic inner portion and a tapered outboard portion.
About taper for wings (and for tail surfaces):
Tapered wings have been adopted for the majority of aircraft since they offer an efficient solution on account of their low induced drag, high maximum lift, low structural weight...(and) acceptable stalling characteristics can be obtained, provided the wing is not too sharply tapered.
Untapered wings are inferior and cheap:
The untapered wing is attractive from the point of view of manufacture, since only one airfoil contour is involved; this simplifies jigging as there are no compound curvatures. It is aerodynamically inferior to the tapered wing, but may nevertheless be the logical choice for inexpensive private aircraft, where the utilization factor is low and initial cost and cheapness of components are important.
There are obvioius aerodynamic and structural advantages for taper (and sweep), but also remember that a signficant factor in a vertical tail's shape is what comes down to... styling. The fin and rudder form maybe a third of the airplane's shape in profile and the "look" that defines it. Designers aren't machines; they are humans with a sense of aesthetics like anybody else, and there is a bit of art to it, and one of the great things about aviation is artistic forms flow naturally from efficient shapes, like teardrops and tapered and swept surfaces. Any designer will consider the look as part of the overall shape of the tail to some degree or another.
Now, the Pilatus Porter uses a constant chord vertical tail and it works perfectly fine and is cheaper and simpler to build and in most light low speed airplanes that is a more important factor than the aerodynamic ones. But it looks incredibly ugly, and who the hell wants to build something ugly unless you've decided to make that part of your brand, or you don't care about the look at all, or the plane was designed by a committee with no sense of aesthetics.
Since the 50s, on GA aircraft, sweep became associated with "modern" and high performance, since on high performance aircraft that was actually true.
Between 1950 and 1966, Cessna's tails went from:
and it made not the slightest difference in the airplanes' handling or performance. It was strictly for looks. From a manufacturing and aerodynamic perspective, they should have stuck with the middle square tapered one used from the mid 50s to the early 60s, but in the mid 60s swept tails were all the rage in GA.
A little quandary here (again thanks for John's artwork) for the designer:
Earliest tail Pros - very strong with desirable Prandtl style trailing edge and swept forward edge, low aspect ratio and high stall AOA. No accident this was the tail of the Bf 109. Cons - not as effective at generating lift as a straight wing (ASE readers should be seeing this trend), lots of area for cross wind "weather vaning". The fillet seen in the P 51 would also improve high AOA lift.
Squarish tail Pros - again, very strong, low aspect ratio, high stall AOA. Reliable and easy to make. Cons - not as effective in lifting, there for needs to be bigger (drag, weather vaning).
Swept wing tail Pros - Stylish, better spanwise load distribution (thanks Peter), more efficient at generating lift (same lift for smaller size). Less weather vaning. Cons - will stall at a lower AOA, and because of its greater length, is not nearly as strong. This is why airline pilots cannot rudder aggressively, particularly at high speeds. It will break.
So, aerodynamicly, the tapered tail gets a plus for looks and lifting efficiency, but a minus for strength and high AOA performance. The first two, particularly the earliest one, may be a better pick, particularly for aerobatics.