I was wondering how the efficiency of a fixed-pitch propeller changes during different stages of flight and why it does so. I suppose when we are talking about propeller efficiency we are actually talking about propeller slip. So my follow up question is what causes propeller slip to change, what conditions make a propeller lose efficiency. I am aware that it has to do with Pitch, but I can't figure out why efficiency changes throughout the flight. THANKS
The reason that efficiency is reduced during phases of flight that are flown at high airspeeds is because the angle of attack between the propeller and relative wind is reduced. If an aircraft is stationary on the ground, its propeller is taking a larger "bite" of air because there is no relative wind. When there is more air moving past the prop, it takes a smaller "bite" of air, therefore producing less thrust and being less efficient. The advantage of a constant speed prop is that you can change the pitch of the prop depending on your airspeed, so it maintains a constant angle of attack, and is more efficient in every phase of flight. I'm not totally sure that's what you are asking, but that's what I got :)
Pitch is essentially how much the propeller would move forward in a complete rotation if it was by itself. You can now rotate the propeller at any rate (read RPM) you can achieve. So if you pitch is 10 cm, and your RPM is 1000, then in 1 minute it would 10000 cm in 1 minute ,ie 100 metres, giving a velocity of 1.66 m/s. If the propeller could move at that speed there would be zero slip, but it in reality it is attached to a shaft and has certain "loading". While moving through air, it experiences drag as well as generates thrust, and since it has a body attached to it, that also experiences drag and cumulatively a significant drag. So the actual distance travelled is may be 60 m, giving a speed of 1 m/s. (40m is the slip here). The drag is a closely related to velocity (for entire aircraft) and rpm of propeller (for the prop). Now the propeller pitch being fixed, and the velocity changing through out the flight, the velocity would be changing in the entire flight regime and consequently drag and therefore slip.
Hence you can imagine, there would be velocity for which the slip is the least. This would be the design speed, where efficiency is maximum (the peak). To either side of this speed efficiency would be lower.