Magnetic dip
This angle varies at different points on Earth's surface.
Positive values of inclination indicate that the magnetic field of Earth is pointing downward, into Earth, at the point of measurement, and negative values indicate that it is pointing upward.
The dip angle is in principle the angle made by the needle of a vertically held compass, though in practice ordinary compass needles may be weighted against dip or may be unable to move freely in the correct plane.
The value can be measured more reliably with a special instrument typically known as a dip circle.
Dip angle was discovered by the German engineer Georg Hartmann in 1544.
[1] A method of measuring it with a dip circle was described by Robert Norman in England in 1581.
As Earth's magnetic field lines are not parallel to the surface, the north end of a compass needle will point upward in the Southern Hemisphere (negative dip) or downward in the Northern Hemisphere (positive dip).
The range of dip is from -90 degrees (at the South Magnetic Pole) to +90 degrees (at the North Magnetic Pole).
[3] Contour lines along which the dip measured at Earth's surface is equal are referred to as isoclinic lines.
The locus of the points having zero dip is called the magnetic equator or aclinic line.
is defined locally for the magnetic field due to Earth's core, and has a positive value if the field points below the horizontal (i.e. into Earth).
[5] Outside Earth's core we consider Maxwell's equations in a vacuum,
denotes the core as the origin of these fields.
The first means we can introduce the scalar potential
, while the second means the potential satisfies the Laplace equation
Solving to leading order gives the magnetic dipole potential
is the latitude of the point on Earth's surface.
Magnetic compasses on airplanes are made so that the center of gravity is significantly lower than the pivot point.
As a result, the vertical component of the magnetic force is too weak to tilt the compass card significantly out of the horizontal plane, thus minimizing the dip angle shown in the compass.
However, this also causes the airplane's compass to give erroneous readings during banked turns (turning error) and airspeed changes (acceleration error).
[6] Magnetic dip shifts the center of gravity of the compass card, causing temporary inaccurate readings when turning north or south.
As the aircraft turns, the force that results from the magnetic dip causes the float assembly to swing in the same direction that the float turns.
This compass error is amplified with the proximity to either magnetic pole.
The effect is the opposite in the Southern Hemisphere.
[7] In the Northern Hemisphere, when accelerating on either an easterly or westerly heading, the error appears as a turn indication toward the north.
When decelerating on either of these headings, the compass indicates a turn toward the south.
Compass needles are often weighted during manufacture to compensate for magnetic dip, so that they will balance roughly horizontally.
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