Water rocket flight stability

Of course you want your rockets to go straight up in the air. This stability is governed by two design factors.
First the center of gravity of the rocket CG) and second the center of pressure (CP).
CG is the point of the rocket where all the weight seems to be concentrated. The rocket stays perfectly in balance if it is put on a needle in this point.

The CP is the point where all the external force trough air-flow seem to focus.
In general you want the CP to be at least one rocket body diameter below the CG for just adequate stability, a larger distance makes the rocket more stable.
While the CP stays on the same spot during flight because its only determined by the external shape of the rocket, the CG varies rapidly during thrust-phase. As the air-pressure expels the water and the rocket accelerates, the CG shifts up the rocket rapidly (becomes more stable). On the right you see the commonly used annotation, CG is the black and white checkerd type symbol, the CP is the symbol with the crosshairs. The design in the picture has, as what is considered for stability the minimum, one body diameter spacing between CG and CP. Rockets that have less spacing between CP and CG are much more susceptible for cross winds and can lose their stability very quickly as soon as the angle of attack of the air is a only bit out of line with the longest axis of the rocket.

To overcome stability problems during the first part of the thrust phase it is wise to use a launchrod or launchtube. A launchtube can also be a very effectif piston like driver, that can aid in reaching higher speeds (and heights).

How to determine the best shape and size for your rocket?. For this you can use the Barrowman equations. James S Barrowman wrote in 1966 working for the NARAM his findings on the practical calculation of the aerodynamic characteristics of slender finned vehicles. It is a relative simple algebraic method to find the center of pressure (CP) of a rocket flying at sub sonic speeds under small angles of attack (longest size of rocket in line with vector of speed).
Here you find Barrowmans report on calculation of the CP
A handy program for doing these calculations, I find, is VCP from Gary A. Crowell sr. VCP is freeware.
VCP can be downloaded here