What would happen if a plane (for the sake of the question let's say that the plane is an Airbus A380) lose its Vertical Stabilizer?
The plane will probably crash.
The vertical stabilizer provides stability in yaw to conventional aircraft. Aircraft such as the B-2 manage to provide stability through computer control, and aircraft such as the Northrop flying wings are designed to fly without one. But if an aircraft designed to be stable using a vertical stabilizer loses that surface, it will be very difficult for pilots to stabilize manually with the remaining systems. While roll and differential thrust will both affect yaw, they will both be slower to react than a rudder, especially in a large aircraft like an A380. This can also damage the hydraulic systems, making it more difficult to control the remaining surfaces.
If experienced test pilots are at the controls (as in the B-52 incident below), or if the failure is anticipated and trained for, it's possible that the aircraft would be controllable enough to land safely. However, as the incidents below show, this kind of failure does not happen often, and can easily exceed the crew's ability to control the plane.
Examples where this has happened:
Japan Airlines Flight 123 lost most of its vertical stabilizer when the rear pressure bulkhead failed. Despite also losing hydraulic systems, the pilots managed to keep the plane in the air for a while, but ended up crashing into a mountain.
American Airlines Flight 587 lost its vertical stabilizer when the pilot's rudder inputs over-stressed the structure. It crashed shortly after.
In 1964, a B-52 lost most of its vertical stabilizer due to extreme turbulence. The pilots were able to extend air brakes on the wing tips to provide some stability. The Air Force sent up a chase plane to help guide the pilots, and provided engineering guidance from the ground. The crew were able to bring the plane back for a safe landing (see a video). There were at least three other instances where the vertical stabilizer failed on B-52's, all ending with the loss of the plane. This particular flight was conducted with test pilots to intentionally fly through turbulence, recording data to help understand the failures on the other aircraft. However, the flight encountered unexpectedly severe turbulence, leading to the separation of the vertical stabilizer.
As always, it depends. There are several things which provide directional stability:
They have to work against the destabilizing parts:
If the vertical is the only stabilizing part, losing it means to crash shortly after. Airplanes need to face forward to create sufficient lift. Momentary exceptions don't count: WW I fighter airplanes had very small vertical tails, and consequently low directional stability. Several German pilots of WW I perfected a technique where sudden rudder input would push the airplane beyond the stable regime of yaw angles, and the airplane would make a quick, full rotation around its vertical axis. This would scare the pilots of pursuing airplanes, because now the machine guns of their adversary would point at them. But there was no real possibility to aim, and the rotation speed was so high that very few shots would actually go in the direction of the pursuing aircraft.
The size of the vertical tail of multi-engined aircraft is driven by the need to counteract the yawing moment due to a failed engine. If all engines are running, the vertical tail needs only to be 1/3 as big. If low dutch roll stability is tolerated, it could be cut back even more. Therefore, if the other parts can contribute enough stability, a partial loss of the vertical surface can be survived. With a swept wing, the key is to fly in a flight regime where it helps the most, that is at low speed. In the case of the B-52H 61-023, which had this happen to it on January 10, 1964, additional help was provided by lowering the rear landing gear which contributed a small fin effect and by shifting the center of gravity forward by pumping fuel.
Also, if any more of the stabilizer had broken off, longitudinal stability would have been lost. Those guys were both lucky, and very skilled pilots.
61-023 was repaired and flew for more than 40 years after this incident. It was retired in 2008.
There are several planes that are designed to fly without vertical stabilizers (like the B-2 bomber, for example). But they have very clever split flaps that make up for the lack of stability/control usually provided by a horizontal stabilizer/rudder setup. Basically a split flap will open up and create more drag on the wing the aileron is placed on, pulling that side of the aircraft back. Thus those aircraft use that system for horizontal stability.
If a plane is not designed to work without the verticle stabilizer, it would have problems if it lost it. On craft with horizontal stabilizers, in general, if the plane gets a little bit sideways the airflow will push against the stabilizer and thus move the plane back in line. If you lost that system, you'd have the find another way to compensate for yaw instability.
It is theoretically possible that you could use differential thrust between the engines to keep the plane in line. Granted, the response would be very sluggish and difficult to control (especially on a big jet like the A380), but it's possible that it could be done given the right plane (one with quickly responding engines) and the right conditions (smooth air, basically).
Probably not. One sad example is American Airlines Flight 587. If the plane loses just a small part of of the fin, it might be ok, but if it loses the fin completely two major things happen:
Aggravating to the above is the fact that most likely the pilots wouldn't be aware of what actually happened and it would be very difficult for them to take proper action.
I am pretty sure a plane that has fly by wire will not crash. Fly by wire controls the stability of a plane by adjusting the control surfaces. When the flaps are out it will balance both sides to prevent yaw. I see no reason why the failure of the vertical stabilizer cannot be compensated by controlling the flaps. A pilot couldn't do that. A computer yes.
Edit: I am not so sure anymore. Loosing the whole vertical stabilizer is much worse than loosing just the rudder. But I would say there still is hope.
Sure it will (aerodynamically speaking). As previously mentioned, it pretty much requires a digital flight control system though (aka 'fly by wire').
Lockheed Martin X-44 Manta is pretty much the F-22 without vertical flight control surfaces.
It can perform an emergency landing if there is no further damage at tail section such as elevators. On JAL 123 crash, vertical stabilizer was missing but that was not the reason why they crashed. JAL crash occurred because of failure on elevator controls.
Flight 587 was undergoing violent yaw rotations before the vertical stab snapped. Once it was lost, nothing stopped the plane's rotation and it just continued to yaw until entering a spin. If the vertical stabilizer had simply come off while the plane was in normal flight, then who knows if it would have survived to land, but it probably would not have instantly spun out of control.
Other instances where planes crashed after losing the vertical stab are the XB-70, where it lost both its vertical stabs after a collision, and DHL Flight 611, also lost its vertical stab due to a collision. Flight 611 survived longer than the aircraft it struck, but broke up soon after due to stresses put on the plane from the violent yawing and dive. It should be noted that a modern airliner would lose its crucial hydraulics if the fin detaches, rendering all control surfaces unusable.
It is not hard to design a swept-wing aircraft to fly fine without a vertical tail. For example a "Zagi" flying wing like thiswill still fly ok if the vertical tip fins are removed, though adverse yaw will be more pronounced, and the CG must be further forward than the aftmost CG that can be tolerated if a vertical tail or tip fins are present, or else the aircraft will yaw out of control and then "tumble" violently. Similarly, most hang gliders don't have vertical tails. However, if an airliner as per the original question could fly fine without a vertical tail, the vertical tail wouldn't be there. The design has been been optimized for the tailed configuration and the complete removal of the entire vertical tail would probably have disastrous consequences. Loss of a just a portion of the vertical tail could be tolerated as long as adverse conditions, such as failure of one or more engines, were avoided. As far as the famous B-52 example goes, note that this aircraft has quite a lot of flat-sided fuselage area aft of the CG.