Hi ravenx,
I fly an aircraft which has a VPP, but not a CSU (Europa with a Rotax 914 engine). I have also flown Piper Arrows which have a CSU.
Here's how I understand it - I know someone will correct me if I'm wrong
I suspect my understanding is at least over-simplified, even if it's not wrong, but it works for me.
First of all, propellor blades are aerofoils, just like a wing. They're shaped a little differently, and have a different purpose in the grand scheme of things, but they work exactly the same way.
We know that angle of attack is a crucial factor in finding the performance of an aerofoil. Angle of attack is defined as the angle between the aerofoil chord-line and the relative airflow.
Obvious point coming up here: if you twist your propellor blades round, you change the angle of attack. Increased angle of attack is known as coarse, decreased is known as fine.
Less obvious point: if you change your airspeed, you'll change the angle of attack of the blades. Imagine a prop blade striking a stationary parcel of air. The angle at which it will hit it will be the angle between the aircraft's lateral axis and the blade's chord line (I'm sure there's a name for that, but I don't know what it is!) Now, imagine that the air isn't stationary, that it's moving towards the blade (or that the blade is moving towards it). The angle of attack decreases. This is very hard to visualise - I had to use fingers and hands in some very strange poses before I could visualise it! (It also follows that increasing the speed of the prop increases the angle of attack.) If the angle of attack decreases, the lift which the blade produces (and therefore the thrust which the propellor produces overall) decreases. Therefore, a prop with too fine a pitch won't work well at high airspeeds.
One solution is to use coarser blades. However, if you make the blade too coarse, it will stall. It will also slow the engine down because it will meet more resistance from the air - piston engines produce more power at high speeds, and in fact running a piston engine at low speed and high power can damage the engine (try driving off in 5th gear going up a steep hill, and see what nasty noises your car engine makes!) Plus, the propellor turns slower, and lift is a factor of speed, so the prop will produce less horizontal lift (i.e. thrust). I'm led to believe that the effect on the engine power is small compared to the effect on the angle of attack and speed of the blade, but I don't know any numbers. So a coarse prop, although it works well at low speeds, won't work so well at high speeds. These props are known as "climb props" because they help you climb faster, versus "cruise props" which are finer and help you cruise faster at the expense of climb performance.
The next step is a variable pitch prop, such as the one I have. Some VPPs have a "climb" setting and a "cruise" setting, which are roughly analagous to the two different types of fixed-pitch prop, except that you can switch between them in flight. I have a continuously-variable prop, i.e. I can set any pitch between two limits. There is one optimal pitch for each engine speed/airspeed combination. But, in practice, I can't continuously change the pitch. And the effect of the engine speed is minimal compared to the effect of airspeed. So I tend to use ultra-fine for taxiing, fine for take-off and in preparation for go-around, slightly coarser for cruise-climb, and almost full-coarse for cruising.
Imagine I'm flying along at cruise power, in the cruise, with a cruise setting on my prop. Then I pull up. Immediately, my airspeed drops, and I need to reset my prop. A CSU attempts to get around this by fining the prop automatically for you. By attempting to maintain a constant engine speed, the CSU is forces to fine the propellor in response to the decreased airspeed. This results in the angle of attack remaining almost, but not quite, constant, and avoids slowing the prop down - close enough that the pilot of a CSU-equipped aircraft won't necessarilly need to reset the propellor controls in response to a moderate change in pitch. (It also avoids loosing engine power due to reduced engine speed, but this is negligable anyway.)
Of course, there are engine management and fuel consumption issues to worry about, apart from pure performance, so it's actually more complex than this once you start looking into it (and that's where I give up!)
I hope that's pretty close to accurate (and if it's not, well, we'll both have learnt something when someone corrects me!), and that it helps answer the question!
FFF
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