Otdfbt

My team is designing a glider and I am unsure about whether or not to include a vertical stabiliser. The task the glider must complete is to achieve the largest possible displacement in a straight line.

Our glider will not be able to automatically adjust the vertical stabiliser's position so it would stay upright and inline with the glider's fuselage for the duration of the flight. Since our glider does not require any changes in it's yaw angle (because it is flying in a straight line), I don't think there is a need for it.

Should we include a vertical stabiliser or not?

The stabilizer is meant to keep the nose pointing into the wind.

Any asymmetry in he wings/fuselage will create a tendency to yaw, you will need to compensate for that. The easiest is a fixed vertical stabilizer at the rear.

The underlying function of a VTP (not rudder) is mitigating the lateral-directional eigenmodes of the aircraft (Dutch roll, spiral divergence and roll subsidience). Unless you can guarantee a perfect launch and no crosswind, you will need some kind of yaw damping.

For a conventionally-shaped aircraft, Dutch Roll will likely be the worst offender, as roll subsidience is convergent and spiral divergence is slow.

A vertical tailplane is just one solution, however. Other things that can contribute to yaw control are positive wing sweep and active control via spoilerons or differential engine thrust. The latter is commonly employed in flying wings, but since your airfoil is not a reflex one, I take it you are going the conventional route.

It's unlikely that your project will succeed without a vertical fin. Are you aware that there are countless radio-controlled model airplanes and gliders that feature a fixed vertical fin but no rudder? The fin is much more than just a thing to attach the rudder to. The rudder itself is not very necessary if the aspect ratio of the wing is not too high. (High-aspect-ratio designs tend to suffer from severe "adverse yaw".)

But, the birds seem to be able to pull it off, so you never know. The distribution of the "twist" or washout in the wing seems to be a key factor for them.

The literal answer to the question in the title is definitely "no". Many successful gliders have been flown without vertical fins. and they can do much more than just fly in a straight line. But they don't typically look like a "normal" glider with the fin chopped off.

Coming from a very different background here - I am a keen archer.

It is normal practice (as with aircraft) to have fins (fletches) on the back of the arrow to keep it straight, but it is also a normal part of "tuning" to remove those fletches from an arrow or two, and shoot them 'bareshaft'.

The point of this test is that they are less forgiving, but because all arrows have a heavy point, the centre of mass is forward of the geometric centre, which means that the whole of the shaft acts as a stabiliser, and given good conditions, the arrow will still fly straight (and this IS largely aerodynamic flight, quite different from the ballistic flight of a bullet).

Going back to what I was saying earlier, it would be difficult to predict how much disturbance it could survive, but a simple, long straight fuselage, with no stabilising fins at all, IS going to fly fairly straight unless/until tubulance goes above a critical threshold. To be fair, this is also true of a glider with 'normal' fins, its just that the critical amount of turbulance is much higher.

One question that doesn't seem to have been mentioned is 'what is the penalty for failure?' - In a manned vehicle, failing to fly straight is considered 'a bad thing' but if your model is allowed multiple flights, then a few failures may be worthwhile if the trade-off is reduced drag.

Some swept-wing designs have no vertical surfaces e.g. "Horten" or "flying wing" or "Alsomitra".
NASA's Albion Bowers presented recent advances in "Why Birds Don't Have Vertical Tails" and "On the Minimum Inducted Drag of Wings".

Designing an optimal washout for a swept-wing is an advanced subject.
The simplest design is a conventional glider with a straight wing and a vertical stabilizer on the tail.
Find some easy-to-build gliders by searching: free-flight glider plans

A longer tail and more dihedral will make the glider fly straighter.

It may not be whether you need one or not, it will probably be getting the right size.

Theoretically, one can design without one like a delta wing dihedralled paper airplane.
The sides of the fuselage aft of CG act as a vertical stabilizer (make them flat).

However, in practice, for free flight (uncontrolled), it is almost impossible to get the wing drag to perfectly match for long efficient high aspect ratio wings, so on go the fin(s), but where?

Many gliders have wings longer than the fuselage. A fin can go at each wing tip, or conventionally on top of the fuselage. The wing tip fins will have a longer torque arm,
there for can be smaller. But the conventional tail placement has a drag saving trick up its
sleeve, putting the vertical stabilizer on top. This uses the drag of the T tail for down force rather than deflecting the elevator. And, of course, you can combine the Hstab and V stab
and make a "Vee" tail.

So design for a vertical fin, and test in in various sizes. If it works without one great! If not
put it (them) on there. That is exactly what the Air Force did when they converted the propeller driven B35 flying wing to that jet powered B49.

In reference to radio control models, there have been many that don't have a vertical fin of any kind. The Klingberg Wing (from the 1980s/1990s) is a fine example; it's a pure wing R/C sailplane. There have also been human-carrying sailplanes built along similar lines (generally, a Horten derived layout) that flew well without any sort of vertical surface.

If the glider is built for free flight (i.e. uncontrolled), it will generally need some kind of vertical in order to maintain spiral stability, but this is largely because free flight models are generally set up to fly in circles, both so they can catch thermal lift, and so they don't just fly away as soon as they're launched. In your case, however, where you want the glider to fly a maximum straight line distance, a setup similar to a Klingberg wing (swept wing, longitudinally stabilized by tip twist) is likely to be one of the most efficient possible.