I was surprised at the absence of a concise illustration of magnetic dip available on the internet, so I cobbled together a short 3D animation using the excellent free software Blender. Magnetic dip is a very simple phenomenon but one which can quickly get confusing since it deals with 3-dimensional fields through space that can be difficult to visualize. The gist of it is that the Earth’s magnetic field lines are only parallel with the ground around the equator, and everywhere else the field lines actually dive downwards into the Earth by some angle, the steepest of which are found at the magnetic North and South poles. In the Philly area this angle is surprisingly steep, about 67 degrees below the horizontal — it’s actually more vertical than horizontal! This means that in areas far from the equator, tilting to the East or West will result in a compass error since the needle can align more closely with the magnetic field by deviating from the projection of the field lines onto the ground, which is what we normally think of as North. Tilt to the West in the Northern hemisphere, and the compass needle will tilt to the West as well.
It gets even more confusing when you are talking about traditional non-gyro-stabilized compasses, such as those normally found in small aircraft. The compass needle is usually weighted carefully such that it rests level with the ground under normal circumstances, but this means that when you accelerate in certain directions, that weight’s inertia keeps it lagging behind somewhat, resulting in yet more compass errors. These acceleration effects are not directly the result of magnetic dip, but they are partly the result of an incomplete attempt to deal with magnetic dip. Normally pilots are just taught to remember that this happens and vaguely what to do about it, but if you level out and stop accelerating the problem takes care of itself.
Blender allowed me to put this simple animation together in a very short time. It has a challenging learning curve, but it is a very powerful set of tools. Hopefully this animation will be useful to somebody out there other than me.