The Direct Indicating Compass — Page 129, Lesson 152

All right, let's get into the turning errors of the direct indicating compass. This is where the compass really shows its personality in flight, and it's a classic exam area, so I want you to understand the physics, not just memorise the outcome. First, the headline rule. Turning errors are at their maximum when you're turning through north and south. And, ignoring liquid swirl for a moment, they are zero when you're turning through east and west. So, the worst case is passing through the cardinal north or south headings, and the best case, no error at all, is passing through east or west. Now, the basic theory. It's actually the same physics we just looked at for linear acceleration errors. Remember the vertical component of the Earth's magnetic field, which we call Z? Because of that vertical component, the compass's centre of gravity, the CG, is displaced from almost directly beneath the pivot point, and it's displaced away from the nearer pole. So in the northern hemisphere, the CG sits slightly toward the south side of the pivot. Now, here's the key. When you turn, the aircraft accelerates towards the centre of the turn. So an acceleration force acts through the pivot, pointing towards the centre of the turn. But, because of inertia, there's an opposing centrifugal force acting outward through the CG. So you have these two opposing forces, one through the pivot, one through the CG. That combination of forces makes the magnet assembly tend to swing out from the turn, rotating around the pivot point. And that rotation of the magnet assembly is what we call the turning error. Now, why do we care more about turning errors than acceleration errors? Two reasons. First, they're inherently of greater magnitude, because in a turn you get a greater displacement of the magnet assembly. Second, turns happen more often, and they're likely to be more prolonged than linear accelerations. So, practically, turning errors dominate. Let's make this concrete with the example from the book. We're in the northern hemisphere, and we're turning left, from 045° to 315°, passing through 000°M, which is north. So we're turning port, anticlockwise, through north. Because of the vertical component Z, the magnet's CG is displaced from beneath the pivot, away from the north pole. Now, because of inertia, the magnet assembly gets thrown out of the turn. In this left-hand turn, that means the magnet assembly rotates anticlockwise. Now, imagine there was no turning error at all. Then the magnet would stay perfectly stationary in space, and the aircraft would rotate 90° around it. The pilot would see 90° of heading pass beneath the compass's lubber line. That's the reference line on the compass, the fixed mark you read the heading against. But here's the problem. The aircraft is turning port, and the magnet assembly is also rotating anticlockwise, in the same direction. So, although the aircraft has turned a full 90° around the compass, the magnet has been displaced and rotated in that same direction by some number of degrees, let's say 20°. So the pilot only sees 70° pass beneath the lubber line. The compass is what we call sluggish. It's not showing the full turn. And here's the rule to remember: whenever the magnet rotates anticlockwise, the compass will over-read. That's the key takeaway for this northern hemisphere left turn through north. The compass lags, it's sluggish, and it over-reads. Let me just make sure the direction of that over-reading is clear. The aircraft has actually turned 90°, but the compass only shows 70° of that turn. So the indicated heading is higher than the true heading. That's what over-reading means. The compass reads too high. So, to tie it all together: the vertical component of the Earth's field displaces the CG, inertia in the turn throws the magnet assembly out of the turn, that rotation makes the compass sluggish, and the direction of that rotation, anticlockwise in this case, tells you whether it over-reads or under-reads.