Yrurtj

The airships that I have imagined use anti-gravitational engines to allow them to hover above Earth's surface. I was thinking of having four of the engines around the vessel's hull. Could these engines be rotated at an angle to allow the ship to be propelled through the air, or would auxiliary engines be required? The speed would not have to exceed 40 knots.

Here's my take on this;

The fact that you've used the term 'anti-gravity' as opposed to a thruster of some sort means that you intend the engines to nullify the effect of gravity directly, rather than counteract it via upward thrust.

A hovercraft for example could be defined as anti-gravity because it applies a constant upward thrust by virtue of an engine pushing air down underneath it. That constant flow of air being forced under the vehicle allows the vehicle to hover, or defy gravity, in a manner that allows it to be directed over the ground by a different set of fans or thrusters. But, that's not true anti-gravity; it's more counter-gravity.

If we think of anti-gravity as that downward pointing fan that acts on gravity only, it would allow your airship to float, but you're still going to need a conventional thruster of some kind to push it through the air in the lateral direction. The reason for that is that gravity only works in this instance in a singular direction - down. This is a simplification, but functionally accurate for the purposes of a planet bound airship.

If you're using a counter-gravity system that applies conventional upward thrust, then yes you can tilt the engines a little to provide lateral thrust as well. This is how helicopters and VTOL aircraft actually work.

But, if you're actually nullifying gravity, then it's safe to say that your craft is in effect massless in relation to the Earth, but that doesn't solve the problem of lateral movement, particularly through an atmosphere. For that, you need thrusters that are more conventional, throwing something out the back in a manner that pushes you in the opposite direction. This could be a propeller, turbofan engine or anything that applies enough forward thrust to the airship to counteract wind resistance and push forward.

As Tim B II mentions, gravity-nullifying devices can't really be used for thrust. Your best bet would be a set of external thrusters.

However.

You can get a very small amount of propulsion from these devices. By reducing the power of a specific anti-gravity device, or a combination of them, you'll change the balance of the craft. So long as the others are sufficient to keep the craft aloft, you'll actually be able to tilt the craft and gain some lateral movement. This could be supplemented with things such as moving ballast around to turn the ship. It would be slow. It would be akward. But if you have no thrust capabilities, it might work.

Your best bet is to put some proper thrust-producing devices on it, and some control surfaces. But in an emergency, there's other options.