Richard Nakka’s Experimental Rocketry Web Site
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Introduction
to Rocket Design
Appendix E –
Example 1
Sizing Deployment Charges for Xi rocket
The Xi is a 3.0 inch (76mm) diameter rocket that is
used for test flights of new EX motors as well as for development testing of
innovative features such as smoke tracking, cameras, recovery techniques and
avionics. The rocket features dual-deploy recovery system with free-fall
descent following apogee separation with parachute deployment nearer the ground.
Both the apogee deployment charge and the main (chute) deployment
charge are Crimson Powder. The apogee charge will be sized first.
The cavity between the fixed bulkhead and the AvBay that holds the
apogee deployment charge and the tethers (no drogue chute is employed) has the
following dimensions:
D = 2.93 in.
L = 7.0 in.
Giving an empty volume
of:
V = ¼ π (2.93)2
7.0 = 47.2 in3
(neglect the volume
occupied by the tethers and smoke canister)
The AvBay joint is
fastened with three #4-40 nylon screws.
We wish to be conservative and use the highest
expected strength of the screws, which is at the lowest
expected launch temperature, -25°C (-13°F) .
FAJ_max
= Ffail = 3 (1.38) 25 = 103.5
lbf (Ref.)
The pressure required to
be developed to fail the joint is given by:
The mass of deployment
charge requires is given by:
Since pressure and
volume are both in US units, we’ll use the following values for R and T , applicable
to Crimson Powder:
R = 429 lbf-in/lbm-°R
Tv = 3105° Rankine
This gives the mass of Crimson Powder, converted from lbm
to grams, as:
To account for factors
such as reduced pressure due to heat loss to the cold cavity and friction in
the joint, as well as considering the flight-critical nature of the
apogee separation event, a charge mass of 1 gram of Crimson Powder is
employed.
The parachute deployment charge is determined next. The cavity
between the non-fixed bulkhead and the AvBay that holds the main deployment
charge and the tethers has the following
dimensions:
D = 2.93 in.
L = 4.0 in.
Giving an empty volume
of:
V = ¼ π (2.93)2
7.0 = 27 in3
(neglect the volume
occupied by the tethers)
The AvBay joint is
fastened with six #6-32 nylon screws.
We wish to be conservative and use the highest
expected strength of the screws, which is at the lowest
expected launch temperature, -25°C (-13°F) .
FAJ_max
= Ffail = 6 (1.38) 49 = 406 lbf (Ref.)
The pressure required to
be developed to fail the joint is given by:
Mass of Crimson Powder required, converted to
grams:
To account for factors
such as reduced pressure due to heat loss to the cold cavity and friction in
the joint a charge mass of 1.5 grams of Crimson Powder is employed.
Last updated December
5, 2024
Originally posted December
5, 2024