Richard Nakka’s Experimental Rocketry Web Site
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Introduction
to Rocket Design
Appendix G –
Example 1
Design of the Xi rocket nylon screw joints
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 and parachute deployment typically at an
altitude of 600-900 feet (180 - 275m.). Maximum design altitude is 7500 feet
(2300m.). Typical dry mass is 6.5 lbm (3.0 kg).
Nylon screws are employed for both the Apogee Joint and the Main
Joint, at each end of the AvBay.
The Apogee Joint design is considered
first. As the rocket is relatively lightweight, handling load is not considered
to be critical for this joint. Pressure differential load is calculated:
Ref. https://www.engineeringtoolbox.com/standard-atmosphere-d_604.html
Launch site elevation is approximately 500 feet ASL and maximum
expected altitude is 7500 + 500 = 8000 feet ASL. Using linear interpolation,
the pressures are as follows:
PB = (500 – 0)/(5000 – 0) (12.228 – 14.696) + 14.696 = 14.45
lb/in2
PA = (8000 – 5000)/(10,000 – 5000) (10.108 – 12.228) +
12.228 = 10.96 lb/in2
The net pressure is
PNET = 14.45 – 10.96 = 3.49 lb/in2
The mid-body airframe housing the deployment charge is aluminum of
3.0 inch outside diameter with a wall thickness of 0.035 inch. This gives an
inside diameter of 2.93 in. The cross-sectional area of the deployment charge
bay is therefore:
A = ¼ π (2.93)2 = 6.74 in2
The force acting on the Apogee Joint screws due to the net
pressure is therefore:
FAJ = 3.49 (6.74) = 23.5 lbf
Nylon screw factored strength is given by:
PULT = NSJ f ENV PSS
where
NSJ = number of screws in the joint
f ENV = Environmental knock-down factor
PSS = basic shear strength of the screw (lbf or N.)
Launch temperature range for the Xi rocket is -25°C to 30°C (-13°F to 86°F). Humidity levels range from dry in winter and
mild in summer. For the Apogee Joint, we wish to be conservative and use the lowest expected strength of the screw, which is at the
highest expected temperature, 30°C. As far as humidity effect on the screw
strength, mild humidity will be taken as half-way between dry and
wet. As such the following environmental factor will be used for the
Apogee Joint design:
f ENV = ½ (0.92 + 0.56) = 0.74
Giving the following shear strengths for candidate screws:
#4-40: PSS = 0.74 (25) = 18.5 lbf
#6-32: PSS = 0.74 (49) = 36.3 lbf
We’ll use a design factor of 2 for the Apogee Joint. Therefore,
the screw joints must be capable of handling an applied load of 2 ´ 23.5 = 47 lbf.
This boils down to a choice of two #6-32 screws (2 ´ 36.3 = 72.6 lbf) or three #4-40
screws (3 ´ 18.5 = 55.5 lbf). The latter is the
better choice as this will impart less momentum to the separating rocket
sections when the apogee deployment charge fires which is beneficial for the
design of the Main Joint. As well, I prefer to never use less than three screws
in a joint.
FAJ_min
= 55.5 lbf
The Main Joint design is considered next.
Handling load is not considered to be critical for this joint. The primary
criterion for design is that the joint remain intact when the apogee event
occurs. Loading of this joint is the result of momentum of the separating
rocket sections which generates a tension load in the tether connecting the two
separating rocket sections.
Equation 4 is used to calculate tension load in the tether
connecting the aft section of the rocket to the AvBay.
where
F = force to shear nylon screws in Apogee Joint.
For designing the Main Joint, it is not obvious which of the
temperature/humidity extremes is the more critical. As such, both conditions
are considered, the highest temperature (when the nylon screws have lowest
strength) and the lowest temperature (when the nylon screws have the highest
strength).
First consider at the highest
temperature extreme (30°C.) As determined, the Apogee Joint will utilize
three #4-40 screws.
FAJ_min = 55.5 lbf
As we want to design the joint to withstand the maximum tether
tension (T),
F = FAJ min
d =2.83 in. see figure above
The aft section of the rocket is connected to the AvBay with a pair of 1/8² Everbilt
paracord of length L = 108 in. (9
ft.). The ropes are of different
length such that only one is considered effective (the longer tether acts as a failsafe member). This particular rope has an axial
stiffness EA = 5839 lbf. This gives a tension load
of:
Applying a design factor of 2 to the tension load:
T = 2 (130) = 260 lbf
At 30°C half-damp, f ENV = 0.74, giving the following shear strengths
for candidate screws:
#6-32: PSS = 0.74 (49) = 36.3 lbf
#8-32: Pss = 0.74 (82) = 60.7 lbf
Requiring the following number of
candidate screws for the Main Joint:
#6-32: N = 260/36.3 = 8 screws
#8-32: N = 260/60.7 = 5 screws
Next consider the lowest
temperature condition (-25°C, dry.) with fENV = 1.38. As
determined, the Apogee Joint will utilize three #4-40 screws.
FAJ_max = 3 (1.38) 25 = 103.5 lbf
As we want to design the joint to withstand the maximum tether
tension (T),
F = FAJ max
This gives a tether tension load of:
Applying a design factor of 2 to the tension load:
T = 2 (178) = 356 lbf
At -25°C (dry), shear strengths for candidate screws
are:
#6-32: PSS = 1.38 (49) = 67.6 lbf
#8-32: Pss = 1.38 (82) = 113 lbf
Requiring the following number of candidate
screws for the Main Joint:
#6-32: N = 356/67.6 = 6 screws
#8-32: N = 356/113 = 4 screws
The higher
temperature condition is therefore critical for the Main Joint design. We will
need eight #6-32 nylon screws or five #8-32 nylon screws to ensure the joint remains intact
when the apogee deployment occurs.
Design Modification
There are two simple ways to reduce the
number of screws required for a joint. The tether can be made longer (to reduce
tension load) or by adding vent holes. Due
to space limitation, making the pair of tethers for the Xi rocket longer is not
an option. As such, vent holes are added. These are holes drilled in the
airframe that allow venting of the deployment charge. This effectively reduces
dimension d, the distance over which pressure due to deployment charge acts.
For the Xi rocket, ten 9/32” holes were
added to provide venting. This reduces the distance to d
= 1.85 in.
Applying a design factor of 2 to the tension load:
T = 2 (155) = 211 lbf
Requiring the following number of
candidate screws for the Main Joint:
#6-32: N = 211/36.3 = 6 screws
#8-32: N = 211/60.7 = 4 screws
For better thread engagement, the smaller
screw is a prefered choice.
The photo below shows the implemented
configuration. Three #4-40 screws for the Apogee Joint, six #6-32 screws for
the Main Joint, and ten 9/32” holes for venting the apogee deployment charge.
Last updated November
5, 2024
Originally posted November
5, 2024