From this question I've learned that after a propeller change the plane should go through a test flight. Why is this?
3 Answers
The purpose of the test flight is for the safety of passengers. For most maintenance, in a not-for-hire aircraft, a private pilot can perform the test flight and determine the aircraft is airworthy, but they must do it without passengers.
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1$\begingroup$ It should go without saying that replacing the propeller may have "appreciably changed [the aircraft's] flight characteristics or substantially affected its operation in flight" $\endgroup$– voretaq7Commented Nov 13, 2015 at 18:31
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1$\begingroup$ @voretaq7 I'm not so sure that "goes without saying". Today's manufacturing techniques are very good at exactly replicating items to very tight tolerances. It's reasonable to expect a routinely manufactured item like a plane propeller to be exactly like the previously used one (and therefore a safe item to swap at will). $\endgroup$– SnakeDocCommented Nov 13, 2015 at 19:23
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3$\begingroup$ If you replace breaks on a car the car breaks differently then it has been for the last few months. Why should a new prop be identical to the one your replacing. If that were true you wouldn't need to replace it. If it's not identical then "something" changed. $\endgroup$– coteyrCommented Nov 13, 2015 at 19:32
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4$\begingroup$ @SnakeDoc It doesn't matter how perfectly you replicate something, it still needs to be physically installed on the aircraft - an error-prone process. Installing new flight control surfaces doesn't intuitively mean different flight characteristics to a non-aviator either (and for that matter some aviators might think it's no big deal - they're identical to the old ones, right?). Any mechanic will tell you it can seriously change flight characteristics though - especially if there's a problem in the reassembly. $\endgroup$– voretaq7Commented Nov 13, 2015 at 23:23
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1$\begingroup$ @voretaq7 That's a great clarification and explanation. It should be added to this answer if possible, as it fully answers the "Why" in the OP's question. $\endgroup$– SnakeDocCommented Nov 13, 2015 at 23:56
Often when people talk about propellers, they think of them as a solid piece of material attached to the crankshaft of an engine. This is true for small planes, but absolutely untrue for larger aircraft.
On small aircraft, you might do a test flight to insure that the propeller functions properly in all flight modes. Mostly you'd be looking to insure that replacing the prop actually fixed the problem your were having. Defects in a fixed prop might make it vibrate due to not being properly balanced, which will show up on runup, or it might have an internal flaw that will only be apparent at particular flight modes, like ascending, descending or level flight and turns.
On larger aircraft, propellers are more sophisticated.
A reciprocating engine tends to develop maximum power in the 2200 to 2500 RPM range, so the engines are set to run in this range and the actual thrust is modified by changing the angle of attack of the propeller blades. This is usually accomplished by either an electric motor or a hydraulic piston. The motor or piston is in the hub and geared to the blades.
This makes the overall propeller system much more complex, and requires exercising it before certifying it flight ready even more important.
Adjustable propeller blades can be turned to a negative angle to allow engine braking on landing, and backing up on the ground. It can also be 'feathered' if there is an engine failure, so that the engine will not continue to turn over if it is shut down in flight.
Additional notes:
There are other adjustable propeller systems that use air pressure or mechanical gearing.
Gas turbine engines have an even narrower maximum power range, and require even more complex propeller systems. They turn at around 10,000 RPM and use a gearbox to turn the props in the 2200 rpm range.
During my time in the Air Force, I changed propellers on C-124s, C-130s, C-133s, and a few other propeller driven aircraft. None of these changes required an actual flight verification, but did require a runup with a checklist for specific verification. Of course the pilots and flight engineer would be aware that the prop had been changed.
It is so that the props are tested to see if they have any defects or not as well as to make adjustments based on their behaviour.
A test flight must be done anytime after maintenance, preventive maintenance, rebuilding, or alteration
<-- This is not strictly true: It's certainly good practice, but not a regulatory requirement (at least under FAA regulations - Greg cited the relevant FAR below). $\endgroup$