The parachute should be deployed after the rocket has reached maximum altitude (apogee), but before striking the ground. The ideal time is not necessarily exactly at apogee, however, as the rocket can drift considerably during descent on the parachute (and there is less drift in regular flight). So, a balance of timing is reached between these two competing desires.
It is also desirable to not deploy the parachute at a high air speed, as this increases the loads (and could result in the breaking the lines attaching the parachute to the rocket). And the parachute should not be deployed before the rocket has reached maximum altitude.
The water rocket flight time and altitude profile may be estimated from online calculator such as Dean's Benchtop: Sim Water Rocket. For a 200 gm total empty weight and a typical “propellant” load (100 psig initial air pressure, 50% water fill), a 2 liter water rocket may reach a height of 77 m in 3.47 s. If the parachute is not deployed, it will reach the ground at 8.05 s total flight time, impacting at 26.5 m/s. So, why not just use, say, 6 s after launch as the parachute deploy time? This is roughly half way between predicted apogee and touchdown (without the parachute deployed).
The simulation assumes that the rocket goes straight up. With no wind and a stable rocket design this is a fair assumption. However, with wind (or a not so stable rocket, due perhaps to some mishap during launch), the rocket does not go straight up. This can reduce the maximum altitude attained and the flight time before touch down (a euphemism for impact, if the parachute does not deploy) to less than 6 second.
Also, different simulators use different assumptions (particularly about drag), and predict different apogees and flight durations.
One web site Water Rocket Safety Rules recommends “a recovery system which limits their descent rate at time of touchdown at ground level to a maximum velocity of 10 meters/second (33 feet/second).” This was used as a guideline for picking the logic for the parachute deployment 1 s after apogee. The rocket can accelerate downward at at most 9.81 m/s^2 (gravitational acceleration, neglecting drag), and in 1 s it reaches a maximum fall rate of -9.81 m/s (just under the 10 m/s maximum touch down velocity limit). This also keeps the air speed a time of parachute deployment to a low value, reducing the loads on the parachute strings.If the rocket had a sub-normal launch and only reached 4.9 m height, it would impact at at most the 9.81 m/s speed (neglecting any lateral speed). If it reached a higher apogee, there would be time for the parachute to deploy and decelerate the rocket.
Unfortunately, this criteria does not limit the drift very much while descending on the parachute. The rocket descends only 4.9 m from apogee in 1 s. I suppose a more complex logic could calculate the maximum height above ground (apogee) attained, and deploy the parachute at some distance above ground (perhaps 20 m, verifying that apogee was great than this), but I have not implemented that yet.
Why include the 6 s launch time criteria at all? For a nominal flight, the rocket would reach the 1 s past apogee criteria before the time since launch criteria. However, the ability to sense launch is viewed as more reliable (and may be augmented in the future by an accelerometer), so this is provided as a back-up if sensing apogee is not accurate. Some parachute deployment devices use time since launch as the criteria (such as
The time since apogee is a fixed value, if the goal is to stay under the 10 m/s fall rate. The time since launch criteria would ideally be variable, to account for different expected performance (due to initial pressure, water load, weight, etc.). This value can be changed by reloading the program (although that might be challenging to do at the launch site).
While this logic is intended to deploy the parachute at an altitude that will effectively limit the ground impact velocity, there is no guarantee that it will actually deploy effectively. So, launch only in areas large enough so that uncontrolled impacts will not be hazardous, and have all persons in the area aware that a launch may occur.