Chapter 3 of AFM doesn't mention anything about prop lever setting during engine restarting for both windmilling as well as stationary propeller
2 Answers
If your engine fails in a DA-40, you've lost oil pressure, so there likely isn't enough to push the blade to the coarse position.
A DA-40 doesn't have an accumulator like a Seminole, for example. So the blade position is already a fine pitch before cranking the engine during start, and the oil pressure allows the blade to be pushed to the coarse position, not the fine position, which is also the reverse of my exemplary Seminole, which needs the oil pressure to maintain a fine pitch. The Seminole's shutdown-default is coarse for the same reason the DA-40's is fine: a lack of oil pressure.
The likely reason the emergency procedures don't specify, is the system isn't designed to allow you to feather or even coarse the propeller without the oil pressure generated by the engine, not that a DA-40 can feather at all, and you wouldn't have much oil pressure if the engine failed.
At best, the windmilling propeller would turn the oil pump, which would provide some oil pressure, which would in turn coarsen the propeller to some degree, but as soon as the propeller RPM drops further due to the resistance generated by the coarser pitch, so would oil pressure with it, and that would lead to the propeller going toward a more fine pitch again.
To maximize the chance of getting a good restart, allow the propeller to windmill by placing the propeller lever at the fine pitch, high RPM, setting.
Here is a diagram of the system hosted online. You can see that added oil pressure to the piston causes a more coarse position of the propeller.
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1$\begingroup$ Just a sidenote: it is somewhat confusing that DA40 AFM in-flight engine trouble part does have action item to check the prop lever. What the hell is that all about? To check if it is still there? I mean if it does nothing when engine is out, the why bother checking it 😃 $\endgroup$– Jpe61Commented Oct 18, 2021 at 18:39
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1$\begingroup$ Maybe it is talking about how a low prop RPM setting can increase cylinder head pressures and make the engine run in an unusual manner that can cause odd vibrations in the plane. $\endgroup$ Commented Oct 18, 2021 at 19:20
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$\begingroup$ That would make sense, common action item is to set prop on high rpm in any kind of predicament. Why the wise men at Diamond decided to tell the stressed pilot in trouble "hey man check out the prop lever" is just beyond stupid if one asks me. $\endgroup$– Jpe61Commented Oct 18, 2021 at 19:50
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1$\begingroup$ One reason to check the prop lever is to make sure you didn't accidentally pull it back and kill the engine when you meant to be leaning the mixture. These engines are so reliable (properly maintained) that accidentally killing it with the prop lever is a valid possibility (especially if the strap of your passenger's bag accidentally pulled it back- or the mixture). Checklist=bullet points reminding you to do what you learned in training. Vy, trim, find a field, head toward it, determine wind direction, plan a downwind, flow check: "fuel, fuel, fuel, spark, air, prop", radio, checklist. $\endgroup$ Commented Oct 21, 2021 at 7:40
Generally you want full coarse, to feather the prop for minimal drag. Thinking about it the other way, full fine would be showing the flat of the prop blades into the relative wind, for maximum drag.
EDIT: I stand corrected.
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5$\begingroup$ Your answer could be improved with additional supporting information. Please edit to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center. $\endgroup$– Community BotCommented Oct 18, 2021 at 13:59
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$\begingroup$ On a multiengine airplane you do want to feather the dead engine's prop to reduce drag, but on a single-engine you need the prop to keep windmilling as you troubleshoot and attempt a restart. This is the reason why, with a loss of engine oil pressure, a multiengine aircraft feathers while a single-engine does the opposite. After you have completed troubleshooting, tried everything and cannot restart, feathering may be an option if you have enough oil pressure from the windmilling prop/engine to do it. $\endgroup$ Commented Oct 21, 2021 at 7:44