This article is from the Model Rockets FAQ, by Wolfram von Kiparski with numerous contributions by others.
Above and beyond all else, high power rockets are built much stronger
than standard model rockets. This is due to the higher speeds and
acceleration achieved by these models. Some of the construction
differences are:
- High power rockets have stronger, thicker body tubes
- They have MUCH stronger engine mounts, bonded using epoxy rather
than white or yellow glue
- Engine mount rings, adapter rings, etc., are typically made from
1/8" or thicker aircraft plywood, fiberglass, or phenolic sheet, rather
than paper or balsa.
- Fins are typically made from plywood, fiberglass, phenolic, or
waferglass, not balsa; Thick balsa fins have been used on H/I powered
models, but they have to be reinforced with fiberglass/epoxy laminate.
- Fins are often mounted into slots in the body tube with Through The Wall
(TTW) mounting. Most common and recommended method is glued TTW and
directly onto the motor tube.
- Parachutes are larger and typically made from some type of fabric
(plastic chutes are not strong enough, usually)
- Heavy elastic shock cords with steel braid or Kevlar shock line
are used rather than rubber for shock cords, and these are typically
epoxied to the motor mount or a bulkhead
- Positive motor retension systems (clips, bolts, etc.) are important,
as HPR reload casings start to get pretty expensive
 
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