Richard Nakka’s Experimental Rocketry Web Site
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Introduction
to Rocket Design
Appendix H
Recovery Deployment system using Non-fixed
Bulkhead
Introduction
As mentioned in the Introduction to Rocket Design – Recovery System webpage, a rocket Recovery Deployment system
utilizing a Non-fixed Bulkhead has been used with great
success for my newest generation of EX rockets (such as DS, Zeta, Xi). In this
appendix, the details of such a system used for the Xi rocket are described.
Overview
Figure 1 illustrates an exploded view and a cutaway view of the parachute
deployment system for the Xi rocket. Figure 2 illustrates the as-packed
configuration with the Non-fixed Bulkhead (NFB) slid into position, butting
against the (fixed in place) Ring Bulkhead. The pyro for main deployment is
installed in the cavity between the AvBay and the NFB.
Operation of the system is straightforward. The main pyro is
triggered by the Flight Computer at an altitude typically 500-900 feet AGL.
Combustion of the pyro charge pressurizes the cavity contained by the Forward
Body tube, the Avbay bulkhead and the NFB. The resulting force acting on the NFB
is reacted by the fixed Ring Bulkhead. When the pressure reaches a critical
level, the resulting force acting on the AvBay bulkhead causes the nylon screws
in the Main Joint to fail in shear. This forcibly ejects the AvBay. The
resulting momentum of the AvBay pulls the tether taut and withdraws the NFB. In
turn, the Main Tether connecting the NFB to the parachute and eyebolt on the
Nosecone base is pulled out. The parachute, attached to the Kwik-link, is
withdrawn from the chute bay and enters the airstream.
Figure
1: Parachute deployment system for the Xi rocket
Figure
2: Cutaway view of as-packed configuration
Design
Details
Non-fixed Bulkhead
A NFB is similar in functionality to a piston with one key difference. A piston transfers
force from an expanding gas to generate motion. The NFB likewise transfers the
force from the expanding deployment charge gas, however, motion is initially arrested
by the fixed Ring Bulkhead. Motion only occurs once the pressurizing gas has
been vented and subsequently is pulled by the attached tether connecting it to
the AvBay.
Design criteria are closeness of fit within the body tube and
structural strength to withstand the pressure loading from the deployment
charge. For the Xi rocket, which has a diameter of 3.0 inches (76mm) the NFB is
made of a diameter 0.005 inch (0.13mm) smaller than the inside of the rocket
body to give a free-sliding fit. The outer surface of the of the NFB skirt is
rubbed with paraffin to reduce friction and to provide thermal protection.
Thermal protection of the exposed face of the NFB is not required, due to the
very brief exposure to the hot combustion gases.
Structurally, the NFB must withstand the pressure due to
combustion of the deployment charge. The axial component of the applied
pressure force is reacted (R) by the Ring
Bulkhead around the outside forward edge. This is illustrated in Figure 3. The
skirt must be sufficiently strong to resist the hoop loading due to the radial
force component of pressure.
Figure
3: Free-body diagram of pressure loading of NFB
The original NFB for the Xi rocket was machined from Delrin polymer. A subsequent version was machined from aluminum alloy. The newst version is 3D printed using PLA filament. A finite-element analysis of the PLA NFB design indicated a safety margin
of 1.5 based on worst-case loading. Proof-load
testing confirmed the robustness,
withstanding an applied load of over 400 lbf conservatively applied over a 0.79
inch (20mm) circular region at the centre of the NFB.
For one of my newer rockets (Arrow) I had a NFB made using Stereolithography (SLA)
photopolymer resin based 3D printing. Although it was similar in overall
appearance (except having a smoother surface) to the filament printed PLA NFB,
it shattered on its first usage (I should have proof-load tested it..!).
Figure 5: Proof-load testing of 3D
printed filament PLA NFB.
Forged eyebolts are attached to both sides of the NFB using an
threaded aluminum coupler to connect the two. The eyebolts are forged 304
stainless steel of grade 4.8 (400 MPa or 58 ksi tensile strength). Thread is M4´0.7.
Figure
4: M4 stainless steel forged eyebolt (bought from Amazon)
Ring Bulkhead
The Ring Bulkhead (RB) serves to react the axial load applied by
the NFB when the deployment charge fires. The RB is made from a short length of
body tube, with a piece removed to effectively reduce the diameter to match the
ID of the body tube.
The Ring Bulkhead is firmly attached to the body tube by a radial
pattern of reinforced-epoxy slug rivets. Matching
holes are drilled through the RB and body tube, as shown in Figure 5.
Figure
5: Attaching Ring Bulkhead to rocket body tube
For my Xi rocket, the slug rivets are made from J-B Weld, which is a steel reinforced epoxy adhesive (fun fact: J-B Weld was invented in 1969. I started
using it a few years after that for my rocketry work and it has remained a favourite
mis-labeled rocketry product). Slug rivets are flush to the surface on both sides. The number
and size of slug rivets is chosen to withstand the loading applied to the RB by
the NFB. The total ultimate load (Fult)
that N slug rivets can carry in shear is
given by:
where Ds = slug diameter (in or mm)
USS = shear strength of slug material (lbf/in2 or
MPa)
J-B Weld has a published tensile strength of 5020 lbf/in2.
Taking shear strength to be 60% of tensile strength, gives:
USS =3000 lbf/in2
For example, my Xi rocket has N=9 slug rivets
of 5/16 in. (7.9mm) diameter. This gives:
The applied load acting on the RB is equal to the total shear
strength of the nylon screws of the Main Joint. Xi uses six #6-32 nylon screws
for this joint, each screw having a maximum strength, in shear, of 67.6
lbf (see Example
1, Appendix G). Using a Design factor
of 2, the maximum factored applied load is
Pmax = 2 ´ 6 (67.6) = 811 lbf.
As such the factor of safety = 2071/811 = 2.5 which is
better than 2. This extra factor accounts for unavoidable imperfections in the
slugs (it’s hard to avoid getting tiny air bubbles in the adhesive).
Parachute Bay
The Parachute Bay incorporates Vents, as shown in Figure 1, just
aft of the Nosecone. The purpose is to allow air to enter the bay as the NFB is
pulled out. This is to avoid the formation of a partial vacuum, which would result
in a force acting on the NFB opposite to the direction of motion. The Xi rocket
has ten vents of 9/32” (7.1mm) diameter.
NFB Tether
The NFB Tether experiences tension loading resulting from the
momentum of the AvBay is it forceably separates from the rocket body, pulling
out the NFB in turn. The tension load can be estimated using principle of
conservation of both momentum and energy. The tether is idealized as a spring
connecting two bodies of mass, the AvBay (m1)
and the NFB (m2) moving in the
positive x-direction (taken as aft, or to the left) with velocities u1 and u2
as shown in Figure 6.
Figure 6: Model of AvBay connected by
tether to NFB
Initially, the spring (tether) is slack and the NFB is stationary
(u2 = 0). The AvBay is ejected
with an initial velocity, u1.
The AvBay velocity can be calculated by equating work done by the deployment
charge to kinetic energy of the AvBay. Work done is considered as the force (Fm) required to separate the sections (i.e. shear
the Main Joint nylon screws) multiplied by the distance over which this force
acts (dimension e in Figure 2):
Solving for initial velocity of AvBay:
From conservation of momentum:
m1
u1 + m2
u2 = (m1 +
m2) v
where v = velocity of
combined AvBay and NFB once the tether is stretched taut and both items are
moving at same velocity.
Setting u2 =
0 and solving for v:
From conservation of energy:
½ m1
u12 + ½ m2 u22 =
½ (m1 + m2)
v2 + ½ k x2
The term on the right represents potential energy stored in the stretched
tether, where k = spring constant of the tether
(force per unit length) and x =
displacement of the stretched tether. Setting u2
= 0, this leads to the following expression for tether displacement x:
Knowing the displacement and spring constant, the tension load in
the tether (T) is calculated as such:
T = k x
One important note. This assumes a static loading condition. However, as
the tether is initially slack, when it is pulled taut, it is subjected to a
dynamic or shock loading condition. This increases the maximum tension over the
static value. The most expedient way to handle this is with the design factor. A
recommended design factor of 3 or higher should be used for the tether design.
Units must be consistent in the equations above (US or MKS):
mass: slug or kg
force: lbf or N.
length: ft. or metres
Example 1 - Sizing the NFB
tether for Xi Rocket
Last updated November
15, 2024
Originally posted November
14, 2024