Here are some general ideas with regard to prop size/pitch. I hope somebody will correct me if I have made any mistakes here.

Larger prop:

- Makes more thrust than smaller prop. This effect is non-linear because lift scales proportional to area, not length. Larger props make much more thrust than smaller props.
- Draws more power at the same kv rating.
- Is more efficient to generate a fixed amount of thrust. In other words, a big prop on a low-kv motor making some amount of thrust will draw fewer amps than a small prop on a high-kv motor making the same amount of thrust.
- For a motor of a fixed kv rating, a larger prop will have a lower rpm than a smaller prop. This is because the motor is loaded down by the prop, causing it to run slower. Larger props load the motor more.

Higher pitch prop:

- Makes a plane go faster. The airplane's nominal speed in flight (known as
*pitch speed*) equals the prop pitch (inches) times motor rpm, converted to km/h or mph as you like. So let's say you have a 10x4.7 prop spinning at 8,000 rpm. 4.7" * 8000 = 37,600 inches per minute = 35.6 mph. A plane's actual speed in the air will not be exactly the same as its pitch speed, but pitch speed is a good way of starting to think about a plane's capability for speed.
- Draws more power at the same kv rating.
- Because larger props spin slower, all else being equal, larger props result in a lower pitch speed. This means that you can make a plane fly faster (but with less thrust) by putting a smaller, prop of equal or higher pitch on it. To a point, anyway. At a certain point, the prop is small enough that the motor is not loaded down at all, and it is already spinning close to its kv rating. At that point, a smaller prop won't make it spin any faster.
- Typical motor loading is about 75% or higher of kv rating. A prop that loads a motor past about 75% of kv rating is likely to draw too much current and overheat the motor. This means you have about a 25% window at most to increase or decrease pitch speed by adjusting prop size. You could make a plane that goes 45 mph, go 50 or even 55 mph by switching props, but you're not going to make it go 70 mph under any circumstances without switching to a different motor.

Higher voltage (3S vs. 4S vs. 6S etc...)

- Makes a motor spin faster, assuming a fixed kv rating. kv is rpms per volt, so as volts go up, rpms go up.
- Generates more thrust (because spinning faster) and higher pitch speed (because spinning faster).
- Is more efficient to generate the same amount of thrust compared to lower voltage.
- Amperage is lower to generate the same watts (power) compared to lower voltage.
**EDIT: Assuming the same prop size and only voltage changes,** Real-life amperage goes up compared to lower-voltage system, because power consumption goes up. In other words, you may be generating 1 kg of thrust at 10 amps on 3S, and generating 1.4 kg of thrust at 12 amps on 4S. Your efficiency is better, but your absolute current draw still goes up. (Those numbers completely made up to illustrate the point.)

Taking all this into account, we can see that there is a balance relationship between prop size, pitch, kv rating, and voltage. For example, let's say that you have a 10x4.5 prop on a 980 kv motor, on 3S, pulling 10 amps, to make 1 kg of thrust, at a pitch speed of 35 mph. Let's say that you want to go faster, and you don't need as much thrust, because your plane only weighs 600 grams, so 1 kg of thrust is more than you need. Maybe you go down to an 8x6 prop or a 7x7 prop. This increases your pitch speed while decreasing your thrust, keeping your current draw about the same. Your plane goes faster, doesn't accelerate as hard, can't go vertical up any more, and your flight time stays about the same.

Take the same example. Let's say you are thinking about switching to 4S. Going to 4S while keeping everything else the same will significantly increase both thrust and speed, but it will also increase current draw, and maybe the motor isn't rated to take that much current. So you drop your prop down from 10x4.5 to 9x5. The smaller prop puts the overall current draw back down to where the motor can handle it. The smaller prop, combined with higher voltage, results in higher rpm, and so higher pitch speed. Because the prop is spinning faster, thrust remains about the same, or even goes up, even though the prop is smaller. Net result is a plane that accelerates better and flies faster, with similar flight times to what you had before.