Richard Nakka’s Experimental Rocketry Web Site
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Introduction
to Rocket Design
Appendix G
Sizing of Nylon Screws for Recovery Deployment
system
Introduction
As described in the Introduction to Rocket Design – Recovery System webpage, nylon screws are often used to secure
the separable body joint(s) of a rocket recovery system. Such joints are
applicable to both single-deploy
and dual-event deploy
recovery systems. Sizing (choosing the right diameter and quantity) of nylon
screws for both style of recovery systems will be covered in this appendix.
As used in this application, nylon screws serve two purposes. One,
to fasten a body joint to help provide a structurally secure connection between
body sections. And two, to provide sufficient containment of the pressurizing
medium, which typically is a pyrotechnic squib, but can also be cold-gas, such
as with a CO2 system. Or a mechanical system, such as spring-based.
Nylon screws are ideal in this application because they are
readily available from sellers such as Digikey, Grainger and McMaster-Carr,
come in many sizes both SAE and metric, have published strength properties, and
are inexpensive.
Strength
of Nylon Screws
Commonly available nylon screws are nearly always made from
unfilled nylon
66 (also known as nylon
6/6). There are a number of standards that these nylon products are typically fabricated
to such as ASTM D4066. By meeting an industry standard, strength properties are
guaranteed. For example, nylon 66 made for general purpose applications has a
minimum tensile strength of 70 MPa (10,150 psi). Shear strength is usually taken
as 60% tensile strength. As such shear strength would be 42 MPa (6100 psi).
In the usage of interest, nylon screws are subjected to shear loading. Specifically, single-shear,
as opposed to double-shear.
·
Single shear: Shearing occurs across a single surface.
·
Double shear: Shearing occurs across two surfaces.
Figure 1 illustrates the difference between the two loading types.
The example is for a riveted joint, but the concept is the same as for nylon
screw joints. Fastener strength is often quoted as double-shear value. For rocketry recovery system usage, the
joints are always single-shear,
so the quoted value must be divided by two.
Figure
1: Single-shear versus double-shear
Ref. https://www.quora.com/What-is-the-difference-between-single-shear-and-double-shear
Figure 2 presents both double-shear and single-shear strength of
nylon fasteners of the size of interest for our application.
Figure
2: Double-shear and single-shear strength of nylon fasteners
It is important to note that these strength values are for dry, as-molded and
at room temperature (73°F. /23°C.). Also note that the value for #10-24 screw
seems anomalous. I recommend the value shown with note [4], which is based on
expected shear strength of 6025 psi. Shear strength of nylon material is essentially
constant and as such, a straight line should fit through a plot of shear load
versus stress
area of the fastener. Figure
3 clearly illustrates the anomalous nature of the one data point, and the
corrected value.
Figure
3: Plots of screw shear strength versus stress area
(dashed line is best-fit
linear)
The strength of nylon is affected by both temperature and by
humidity. Nylon is hygroscopic and as such naturally absorbs moisture from the
air. Nylon 66 absorbs 2.5% water at equilibrium in normal atmospheric
conditions. Nylon gains strength at low temperatures (relative to room
temperature strength) and loses strength at elevated temperature. Figure 4
shows the effect of both temperature and moisture content on the tensile
strength of nylon. Figure 5 shows the ratio of
room temperature (RT) strength at various temperatures of interest to us, based
upon the curves of Figure 4.
Figure
4: Effect of temperature and moisture-content of Nylon 66
Ref. https://www.plastics.toray/technical/amilan/tec_001.html
Figure 5: Ratio of room temperature
strength of dry and wet Nylon 66 at various temperatures
Ref. https://www.plastics.toray/technical/amilan/tec_001.html
Figure 5 will be used to factor down (or factor up) the shear
strength of our nylon fasteners, depending on expected launch conditions.
Example 1 details the procedure for sizing the nylon
screw joints for my Xi rocket.
Loading
Conditions
Rocket body joints featuring nylon shear screws are subjected to
the following loading conditions:
1.
Handling loads
2.
Pressure-differential loads
3.
Momentum loading
4.
Ultimate pressure loading
Note that loading of the screws due to rocket body bending is not included in this list. The type of body
joint that is applicable to shear screw configuration is that utilizing a coupler tube. A ring coupler
should not be used, as this latter type of joint coupling relies upon the
fasteners to react bending loads. For more information on rocket body joints
and coupler types, see Body Joints section in the Introduction to Rocket Design --
Rocket Body Design Considerations.
Handling load is that which is applied to the rocket primarily due
to its mass. For example, holding the rocket upright by its upper body section
subjects the nylon fastener joints to shear due to the weight of the rocket
that is suspended by the joint. Handling load will rarely size a nylon screw
joint. Nevertheless, any form of reasonable handling load that might be
expected to occur during assembly, transport or installation on the launch pad should
be considered and assessed on a case-by-case basis.
Pressure-differential loading results from the difference in
pressure inside the sealed cavity that houses the ejection charge relative to
the outside (ambient) air pressure. On the ground, the pressure levels are the
same. However, as the rocket climbs through the atmosphere, the ambient
pressure drops, thereby generating this pressure differential (the cavity is
assumed sealed, and the air pressure within remains at ground level pressure).
Momentum loading is solely applicable to dual-event recovery.
Momentum, which is the product of mass and velocity of the separating body sections,
is a consequence of the recovery system apogee-event. This generates loading of
the second (main-event) joint.
Ultimate loading is the load applied to the screws as a result of
the activation of the pressurizing medium, either a pyrotechnic squib or
cold-gas cartridge. A variation of ultimate loading could be the release of a
mechanical device, such as a compressed spring, applicable to a mechanical
recovery system.
Pressure-differential, momentum and ultimate loading are detailed
in the sections that follow.
Pressure-differential loading
The bay(s) that contain the deployment charge and (parachute, if
applicable) are, while on the ground,
filled with air that is at the same pressure as the the surrounding ambient air.
After liftoff, the ambient air pressure decays as the rocket ascends through
the atmosphere, as shown in Figure 6. As the bay is sealed*, necessitated to ensure
expected pressure develops within the bay when the deployment charge goes off,
the pressure within remains at ground air pressure level as the rocket ascends.
This results in a pressure difference between the bay (PB) and the
outside enviroment (PA). This difference in pressure is the net pressure. This is illustrated in Figure 6.
PNET = PB – PA
The net pressure generates a force acting on all walls of the
enclosure, in this case, the body tube, the fixed bulkhead and the AvBay aft
closure. This means that the nylon screws attaching the AvBay to the body tube
are loaded in shear as the screws resist the force developed by the pressure
acting on the AvBay endcap (the AvBay pressure is the same level as the
surrounding ambient air, owing to its static ports). The shear force acting on each screw is:
where N = number of
screws in the joint
Di =
inside diameter of the body tube
* usually not a perfect
seal, as the AvBay-to-body joint has some degree of clearance. However, for
sake of analysis, the seal is assumed perfect.
Figure 6: Standard atmospheric pressure
decay with altitude
Ref. https://en.wikipedia.org/wiki/Atmospheric_pressure
Figure
7: Concept of pressure-differential loading
Pressure-differential loading typically sizes the
nylon screw joint for single-deploy and sizes the apogee-event joint for the
dual-event deploy system.
Momentum loading
Loading of a nylon screw joint due to momentum of the separating
rocket sections is applicable solely to the dual-event deploy system. This
loading condition occurs at the time of the apogee-event, when the deployment
device fires, the Apogee Joint separates, and the rocket sections fly apart. The
tether connecting the two sections fully extends and becomes taut. This is
illustrated schematically in Figure 8. The joint connecting the AvBay to the
forward section (Main Joint) must remain intact, else the parachute will be
deployed prematurely (at apogee, not at all a good thing).
Figure
8: Concept of momentum loading of nylon screw Main Joint
The tension force (T) developed in
the tether is reacted by the mass of the forward section (mf)
multiplied by its abrupt change in velocity (T
= mf ´ a), as shown in
the free-body diagram of Figure 8.
Figure
9: Free-body diagram of rocket forward section
If the acceleration (actually, deceleration, as the tension in the
tether causes the velocity of the forward section to decrease) is known, it is
straightforward to calculate the tension force and use this to size the nylon
screw joint. As the AvBay is still attached to the forward section, the peak
axial acceleration can be taken from the flight computer accelerometer output
at the moment of apogee-event. Unfortunately, this won’t be of help when
designing the joint. However, this data can be later used to verify the design.
In order to estimate the tension load that develops in the tether,
and as such to be able to size the nylon screws in the Main Joint, a
conservation of energy approach is taken. The work done by the deployment charge while separating
the two sections is equated to the elastic
potential energy stored in the stretched tether and the kinetic
energy of the rocket. Work
done is considered as the force required to separate the sections (i.e. shear
the Apogee Joint nylon screws) multiplied by the distance over which this force
acts (d in Figure 9). The potential energy of
the stretched tether is the integral of the tension load (T)
with respect to its displacement (DL), represented by the area under the T-DL curve. A simplifying assumption is that the applied force is
constant (i.e. deployment pressure remains constant once nylon screws shear and
separation occurs). The kinetic energy of the rocket is due to the net velocity
of the rocket, due to the deployment event, at the moment that the tether is
stretched taut. The effects of aerodynamic drag on slowing down the velocity of
the separating rocket sections is conservatively neglected. If we make the
assumption that the two separating sections have equal mass, then the net velocity of the rocket (due to the
work performed by the deployment charge) will be zero, a consequence of conservation of momentum, and the
kinetic energy term is dropped. Note that this is a conservative assumptions
with regard to sizing the Main Joint.
Figure
10: Definition of distance (d) over
which work is performed
W = F d work done by deployment charge to separate rocket
PE = ½ DL T elastic potential energy of stretched tether
where
F = force to shear nylon screws in Apogee Joint
(lbf or N.)
d = distance over which pressure due to
deployment charge acts (inches or metres)
DL = max. elongation (change in length) of the tether due to momentum
of separating rocket (inches or metres)
T = Tension force developed in tether at max.
elongation (lbf or N.)
Note that the expression for PE assumes a
linear relationship between load (T) and
displacement (d ) as is typical for springs. Equating work
done to elastic potential energy:
F d = ½ DL T Equation 1
In order to determine how much the tether increases in length when
stretched, it is necessary to know the elastic properties of the tether.
Manufacturers of quality rope provide this information, either in the form of a
graph or table that presents elongation as a function of load, or in terms of
axial stiffness (EA) value. Examples of the former
for two nylon ropes are given in Figure 11.
Figure
11: Rope elastic properties, typical
Owing to the nature of rope construction which consists of bundled
fibres or strands, elongation with respect to applied load tends to be non-linear. However, to simplify the method, we’ll assume a
linear relationship Besides, if the load% is kept reasonably low, say less than
20%, the linear approximation is not far off. I have measured the stiffness of
a number of ropes which verified this.
It is convenient to use an axial stiffness
(EA) value to describe the rope
property. Elongation as a function of load data can be converted to axial
stiffness, details on accomplishing this are provided in Addendum 1 at the end
of this web page.
Axial stiffness (EA) is the
slope of a load (T) versus strain
(e) plot for a given rope
as shown in Figure 12. Note that units of EA are force
(lbf or N.).
Figure
12: Axial stiffness definition
EA = T/e Equation 2
and strain is defined as change in length (DL) over non-stretched length (L).
e = DL /L Equation 3
From equations 1, 2 and 3, tension in the tether can be
determined:
Now that we know how to calculate the tension load in the tether,
the Main Joint can be designed to withstand this loading without failing. A
suitable design
factor is needed to mitigate
the assumptions and simplifications of the analysis method. As the method is
fairly conservative, a design factor in the range of 1.5 to 2 is appropriate.
It is helpful, from a design perspective, to take a closer look at
equation 4. Tension load is greater when:
1.
Apogee joint is stronger (F)
2.
Distance over which the deployment charge acts is longer i.e. length of the joint coupler (d)
3.
Tether is made of stiffer material (EA). Materials such a polypropylene, polyester and
kevlar are more stiff than nylon
Tension load is lower when:
1.
Tether is longer (L)
We want our Main Joint to be no stronger than necessary, in order
to minimize the output of the main deployment charge. In summary, to reduce the
needed strength of the Main Joint, the Apogee Joint should not be made stronger
than necessary, the coupler length should be kept short (or vents should be
incorporated, see Example 1) and a less stiff tether material such as nylon
should be chosen. If these are not feasible, the offsetting solution is to
simply use a longer tether.
If axial stiffness or elongation as a function of load data (as per Fig.11) is not
available for the tether material being considered, it is relatively
straightforward to conduct testing to measure the stiffness. This is described
in Addendum 2 of this webpage. Two final notes regarding tethers and the
applicability of the above method.
1.
The axial stiffness of a rope given by the manufacturers
specifications, or determined by measurement, is that for static loading. Clearly, the nature of the loading of a rocket tether
during the apogee separation event is a dynamic
event. The response to a rope to dynamic loading may differ from the response
to static loading.
2.
As a bonus, Equation 4 allows us to size the apogee tether. A
suitable design factor should be used, such as 2 or greater. Redundant tethers
should be employed, bearing in mind this may
increase the effective stiffness of the tether proportionally (this can be
mitigated by having the redundant tethers of slightly different length).
Ultimate loading
When the deployment
charge fires, either at apogee or to deploy the main chute, the resulting
pressure generates sufficient force acting upon the AvBay bulkhead to fracture
(shear) the nylon screws in the affected joint. This is the ultimate loading
condition. The force required to fracture the nylon screws in the joint 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.)
The size (diameter) of the screws chosen for a particular joint is
pretty much up to the designer. Quantity-wise, I prefer to use no fewer than 3
screws at any joint. A smaller diameter screw is preferable to ensure good
thread engagement to help ensure a clean shear (and therefore predictable
shearing load).
Addendum 1 – Axial Stiffness (EA)
The following is an excerpt from ProteusDS Manual (ProteusDS
v2.45) June 4th, 2018
Addendum 2 – Measuring Rope Stiffness
I have devised a relatively simple setup for measuring stiffness
of ropes. The setup has worked well and allowed strain versus load to be determined for several ropes which
I have used (or potentially will use) for recovery system tethers. The various
components of the apparatus are shown in Figure 13.
Figure
13: Rope stiffness measuring apparatus
Apparatus
A
description of the various components is as follows
1.
Spine – This forms the structural backbone of the device. The important
aspect of the spine is stiffness such that no significant axial deflection
occurs when the rope is under full tension (up to 350 lbf for this setup). I
used a 5.5 ft piece of 1-1/4² steel EMT which I found in my stock of metal tubes. Any
suitably stiff member can be used, even a length of wooden stud (2´4).
2.
Scale – My setup used my 150 kg (330 lbf) digital crane scale.
3.
Turnbuckle – I used my tie-rod style turnbuckle which I had bought for another project. This
unit has M10´1.5 threaded rods. Each full rotation of the
turnbuckle body results in a length change of 3mm.
4.
Angles - Two angle sections, bolted to the spine, serve as anchor
points for the scale and the rope. A forged eyebolt was attached to each angle
for connecting the scale hook and rope.
5. Rope – the rope being tested had loop style
knots made at each end. Two knots shown below work well. Note:
knots reduce the breaking strength of rope by as
much as 60%, depending on the type of knot. My own testing indicated the knots
illustrated below reduce the breaking strength by 10-20%.
Procedure
The Turnbuckle is first expanded to its maximum length then hooked
to the Scale. A length of specimen rope is prepared by tying knots at each end,
making the effective length of the rope just long enough to fit between Turnbuckle
end and Angle Eyebolt.
The Turnbuckle body is then rotated such that the rope has all
slack removed. The scale is turned on and zeroed. The first step is to
pre-stretch the rope to tighten the knots and set the rope fibres. This is done
by tightening the rope, by turning the Turnbuckle body, until the target
maximum load is achieved (20-30% of ultimate strength). The Turnbuckle is then
loosened until the rope is nearly slack. The rope effective length is then
measured (mid-loop to mid-loop).
The scale is then zeroed. The rope is then tightened in the same
manner as was done for pre-stretching, except load readings are taken every one
or two rotations of the Turnbuckle. Briefly stop rotating the body and note the
reading. The load will tend to drop off after stopping the rotation of the turnbuckle
body, so it is important to note the maximum load right after each stop.
The rope length is re-measured to verify it is the same (or nearly
so) as prior to performing the load measurement. If not, the procedure is
repeated.
Displacement per each rotation is equal to twice
the pitch of the turnbuckle screw. The load versus displacement can then be
plotted. Strain is calculated as displacement divided by the rope effective
length. Fitting a linear curve through the results gives the value of axial
stiffness EA as the slope.
Caution: Wear eye protection.
Photos
1. Scale and turnbuckle
2. Rope connection to Angle
3. All components
4. Ropes that were tested
Example 1:
I have used this particular rope for my earlier Xi rocket flights
for both apogee and main tethers. This rope has a non-structural sheathe over
the structural fibres for protection.The dashed line is a linear trendline with
the equation of the line shown. The slope is equal to the axial stiffness, EA = 2868 lbf.
Example 2:
This rope is paracord. Paracord has a non-structural sheathe over the
structural fibres for protection. Appears to be nylon but may be mixed fibres. I
use a pair tethers of this particular rope to connect the AvBay to the aft
section of the Xi rocket (apogee-joint), as well as for the main-joint. The
dashed line is a linear trendline with the equation of the line shown. The
slope is equal to the axial stiffness, EA = 5839
lbf.
Example 3:
This rope is Dyneema, which
is comprised of UHMWPE strands. Much stiffer and stronger than nylon
(rated breaking load 1250 lbf), I use this rope to connect the Non-fixed
Bulkhead to the AvBay. The dashed line is a linear trendline with the equation
of the line shown. The slope is equal to the axial stiffness, EA = 17806 lbf.
Example 4:
This rope is Spectra, which
is also comprised of UHMWPE fibres. This rope has a non-structural sheathe
over the strands for protection. Much stiffer and stronger than nylon (rated
breaking load 1050 lbf). The dashed line is a linear trendline with the
equation of the line shown. The slope is equal to the axial stiffness, EA = 18905 lbf.
Example 1 – Sizing the Nylon
Screw Joints for Xi Rocket
Last updated November
5, 2024
Originally posted October
30, 2024