Final answer:
In a straight constant-speed climb, assuming no wind or significant variation in Earth's magnetic field, the aircraft's magnetic compass should not indicate a significant change. In practice, compass errors like the Northerly turning error and ANDS can occur, affecting compass accuracy during speed changes or turns.
Step-by-step explanation:
In the scenario described, where an aircraft is making a straight constant speed climb and ignoring the effects of the Earth’s magnetic field variation or any potential errors in the compass due to its inclination, the magnetic compass should not show a significant change in its indication. As the aircraft climbs at a constant speed and assuming there is no wind pushing it laterally, the compass needle should continue to point towards the magnetic north, provided that the Earth's magnetic field lines are approximately parallel to the surface and the compass is free from local magnetic interference. Changes in the compass reading might occur if the climb were to take place at latitudes where the Earth’s magnetic field lines are not horizontal.
However, in reality, magnetic compasses in aircraft are prone to certain errors. One of them is the Northerly turning error, which occurs due to the dipping of the magnetic field lines towards the north. When flying the northern or southern heading, the compass will temporarily give incorrect readings during a turn. Moreover, whenever an aircraft changes its speed or when it banks for a turn, the magnetic compass might experience an acceleration error, known as an ANDS (Accelerate North, Decelerate South) error. This means that when accelerating, the compass will show a turn towards the north, and when decelerating, it will show a turn towards the south.