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"If an increase in power tends to make the nose of an airplane rise, this is the result of the line of thrust being below the center of gravity"
This statement appears in the Flight Instructor Knowledge Test question bank, but what does it mean? I can not find any references to "lines of thrust" in any source.
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There are several ways that the term 'line of thrust' is commonly used. The most common deals with twin engine airplanes. You have probably heard the term 'centerline thrust'. This refers to aircraft like the Cessna 337 Skymaster, Adam A500, or a single engine jet like an F-16 or the proposed Diamond Jet. Multi engined aircraft with centerline thrust have an advantage in an engine out scenario as there is no yawing moment due to the engine loss.
The FAA is using a much less common way of looking at things with their use of 'line of thrust' in this example. Instead of thinking about how thrust is distributed along the lateral axis, they are interested in the vertical axis.
I will use the Lake Amphibians as an extreme example. The engine is mounted above the aircraft on a long pylon. In this example the 'line of thrust' is very much above the CG. If you add power, there will be a large pitch down moment and if you remove power, the drag from a windwilling prop could theoretically cause a large pitch up moment. If you ever look at one of these airplanes, they have quite a large trim tab on the elevator.
You can see that if the airplanes line of thrust is below the CG, the situation would be reversed. Since the line of thrust and the CG are probably never going to be exactly equal, this will probably always have some effect on flight characteristics. How measurable this will be is debatable. In a conventional single, the elevator is located in the propwash and this could cause the nose of an aircraft to rise when power is applied just as easily as the line of thrust being below the CG.
Most of the information contained in FAA publications about aerodynamics is correct in a broad sense, but they tend to say the right thing the wrong way, sometimes to the extent that their statements are actually incorrect. Learn what you have to and pass the test, but I would rely more on Aerodynamics For Naval Aviators and the Illustrated Guide To Aerodynamics by Smith in the future.