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Any rocket that meets these relatively open-ended requirements can be used to gain your L1. Some people fly a minimum diameter carbon fiber 38mm rocket on a large I to over 10kft to get their cert, while others send a 6" cardboard rocket to less than 1kft on a mid-sized H. Experienced fliers will likely already have an idea of what they want out of their first HPR, but newcomers might have a harder time selecting an appropriate design. For that reason, the team has a standard design for an L1 rocket that will get around 2kft on economical 29mm H motors, perfect for fields near campus. The rocket is constructed from 3.0" cardboard LOC parts, and all of the required components can be had for under $30 per rocket. Builders of this design are free to customize the fins of the rocket to their liking, as long as it is still stable.  A boilerplate openrocket design for a good L1 rocket is located here.

Suggestions

• Keep it simple! You absolutely do not need to use more advanced techniques like dual deploy for your L1, especially as it will likely be the first rocket many people build. Resist the temptation to attempt to learn too much from one rocket. You can always build a second rocket to work on your skills while applying what you learned from the first rocket.
• Pay attention to the weather on the day of your flight. If you are at all nervous about the wind, let someone else fly first and see where their rocket lands. Team members have lost many rockets in the woods due to go fever.
• This goes for any rocket, but be sure to re-sim your rocket after it is built. Be sure to include actual, as-built measurements including CG and fin size. It is almost guaranteed that you won't build the exact rocket you originally simulated due to difficult to estimate quantities like glue mass, and you want to make sure the rocket you plan to fly is stable.
• Though there are many fin designs that will work for a nominal recovery, plan for the worst by being fairly conservative with how far aft you sweep your fins. It does help with stability, but in case of a hard landing (on a road, under a tangled parachute) you will be very happy if your fins are not the first thing to touch the ground. If you don't get your cert on the first attempt due to a very tangled parachute, you can try again the same day if your rocket doesn't need to be repaired. Having the aft end of the tube contact the ground first makes your second attempt much more likely.
• Fly the smallest motor you can safely for your cert. You can always send the rocket higher on later flights, but you really want to get it back so you can get your certification.