Actually, We Are Rocket Scientists, A.W.A.R.S.
Flying a rocket isn't too hard. Flying a rocket higher takes some effort. Flying a rocket higher than anyone else at a competition takes science.
There are several sciences involved and each study will help you acheive better rocketry results.
A good rocket maximizes thrust, minimizes weight, minimizes air resistance, and is stable.
Thrust is measured over time. The duration of the thrust is just as important as the strength. Thrust is typically controlled by varying the nozzle diameter. Some launch pads allow different diameter nozzles. The open throat soda bottle is not optimum. A better size nozzle would be about 1/2 that. Launch a rocket and note that the entire thrust is complete about 5 feet above the launch pad. Length the thrust and you will see more of the energy converted into motion. Most of the rocket flight is simple ballistic, non-powered, in other words coasting until gravity and air resistance turn it around to come back down.
Minimize weight by using lightweight materials. A heavy nosecone doesn't help with wieght but may help with stability. Find ways to attach fins with minimum amount of material but provides good strength. Use a hollow nosecone that helps with air resistance but doesn't add much weight. Use less glue. Some people join soda bottles but the lightest joints minimize material and glue.
Minimize air resitance by reducing changes in air flow. The best air flow is a long straight rocket with a taper in the nose and the tail. Some rockets have an air fairing that closes over the nozzle after launch to reduce turbulance at the catch lip. Certainly a good nosecone can make a big difference. One of the most populare shapes is a plastic Easter egg shell half. Shape the leading edge of thick fins and taper the trailing edge. Ensure all transitions are smooth. You can gain a little more altitude by smooth air flow even if you add a little more weight. Avoid objects that stick out of the air fairing. Some parachute releases are designed so that something sticks out in the air flow. Try redesigning the release mechanism to be completely enclosed in the fairing.
A stable rocket flies higher simply by not expending energy in directions other than the straightest path to apogee. A long rocket is more stable than a short rocket. Ensure the center of pressure is behind the center of gravity. That isn't so simple for a water rocket. The water is below the center of the rocket. However, the water is expelled quickly so the rocket stability is mostly goverend by an empty rocket. So ensure stability for an empty rocket. Keep the rocket construction straight, centered over the nozzle and the nozzle center pointing to the center of the nosecone. You can insert a length of PVC pipe in the nozzle to see which way it is pointed. Nozzle alignment is important just like nosecone alignment and fin alignment. Fins must be mounted rigid and straight. Spending energy with a spin will reduce apogee. A common way to lengthen a soda bottle is to place an empty soda bottle on top, bottom to bottom, with a mid-section of another bottle adding a fairing to cover the transition. The FTC, flourescent light tube cover, rockets are long, slender and very stable.
The safest way to start with water rocketry is to use ready made pressure vessels: soda bottles. Also known as pop bottles and carbonated beverage bottles. They are made of PETE plastic which is light, durable, and designed to hold at least 100 psi.
The pressure vessel can be enlarged. Soda bottles can be chained together, spliced, and carefully assembled with glue joints. Tape alone will not hold pressure. Anyone intending to create a new pressure vessel by such methods must study ways to glue plastic, and how to lap joints for pressure holding strength. Pressure containment science must be learned. Until you learn the science, ensure safety by hydrostatic pressure testing the rocket before launching.
Flourescent light tube covers, FTC, are made of polycarbonate and can hold 100 psi. But they don't come with soda bottle ends. We sell molded soda bottle ends to fit FTC ends. Or you can make your own. Soda bottles shrink to a mold real easy, just make sure you don't over heat them or they become brittle.
Other methods of pressure containment are: metal cans, fiber glass or carbon fiber wrapped soda bottles.
Avoid water bottles that are thin and not designed to hold pressure. Avoid heavy PVC pipe because they weigh too much.
The optimum shape for a water rocket is a semi-spherical nose cone, a long body that tapers back to the nozzle. That shape is difficult to make. The parts of the rocket that come in contact with the air flow are the nosecone, body, fins and nozzle. Optimize airflow across all of them and you will have a good apogee.
The nosecone must be mounted rigid. There will be a lot air air pushing on it. The transition from nosecone to rocket body must be smooth. If the nosecone is to come off to release the parachute, then try to mount the release system totally enclosed with nothing outside the rocket disturbing air flow.
The body needs to be smooth. Adding tape to hold things together introduces small edges in the airflow. Try making joints that don't have to be taped on the outside of the body. Painting the rocket adds very little to the air stream. But putting tape to decorate may slow the rocket a whole lot.
Use fins that are smooth and mount them in a manner that minimized anything from altering airflow. Fins must be mounted rigidly to be effective. You might be surprised by how little the fin can be on a long rocket.
The nozzle is the most difficult to cover. There are ways to extend the body fairing at least a little to push the airstream collapse just pass the nozzle. See what you can come up with that will work with your launch pad.