Richard Nakka’s Experimental Rocketry Web Site
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Introduction
to Rocket Design
Appendix H –
Example 1
Design of the Xi rocket NFB Tether
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.
The AvBay is connected to the NFB with a 29 inch tether made of
2.5mm Marlow Excel Dyneema A SK78 12-strand rope
with knotted loops at each end (in fact, a pair of tethers are employed, with
one being slightly longer, serving as a failsafe feature). The displacement
versus load was measured with the results shown in the plot below.
A best-fit linear curve is fitted through the points. The slope of
this curve is the spring constant.
k = 405 lbf/inch or 4860 lbf/ft.
The AvBay has a loaded weight of 1.21 lbm. The NFB with attached
tether has a weight of 0.119 lbm. Therefore:
m1 = 1.21/32.18 = 0.0376 slugs
m2 = 0.119/32.18 = 0.0037 slugs
The AvBay is joined to
the forward rocket body with six #6-32 nylon screws. These screws have a
maximum shear strength of 67.6 lbf (see Appendix G – Example 1). Therefore:
Fm = 6 (67.6) = 406 lbf
The distance over which this force acts (dimension e in Figure
2) is:
e = 2.5 inch = 0.208 ft.
The
velocity of the AvBay following separation is given by
Plugging
in the values
Once
the tether is taut, the velocity of the combined AvBay and NFB is given by
Plugging
in the values
The
displacement of the stretched tether is given by
Plugging
in the values
= 0.056
ft.
Tether
maximum static tension is therefore
T = 4860 (0.056) = 271 lbf
Applying a design factor of 3
T design = 3 ´ 271 = 813 lbf
The 2.5mm Marlow Dyneema
rope has a rated breaking strength of 1250 lbf. As there are knotted loops at each end, the
strength is de-rated by 20%:
Tult
= 1250 (1 – 0.20) = 1000 lbf
The
resulting Safety Factor is therefore:
S.F. = 1000/271 = 3.7
One
final note. The spring constant of the rope was measured at room temperature
(20°C.).
The most severe loading condition is at -25C. The spring constant may be
different at that temperature and could increase the maximum tension load to
some extent.
The
Xi tether is shown below. For enthanced thermal protection, the tether is
rubbed with a light coating of silicone RTV.
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Last updated November
15, 2024
Originally posted November
15, 2024