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The dynamic amplification factor for a dynamic system with one degree of freedom can be approximated as the ratio of the peak, suddenly applied loads to the inertial force the system has to resist that shock.
CDAF = Fspike / m g
Where:
CDAF = Damage Amplification Factor
Fspike = Suddenly Applied Peak Load/Impulse
m = Structure Mass
g = Acceleration Due to Gravity
For dynamic strain, the dynamic amplification factor is multiplied by the peak static load to determine how much greater the peak dynamic load could be. Structural computations made solely using static models must include a margin at least equal to the amplification factor or the structure will eventually fail under peak load.
Note that the dynamic amplification factor is not a safety margin. It is a measure of required strength for normal operation of a dynamic system. It represents expected loads. However, since the simplified equation given here is NOT a thorough treatment of the dynamic amplification factor for anything but a simple cable, it is often difficult to apply. Thus, it has become popular for engineers in some disciplines to include this factor in their "safety margin" for systems which are too complicated to model accurately but whose dynamic amplification factor is empirically known to be a low value.
The dynamic amplification factor for my virtual beanstalk prototype varies between 1.4 and 3 during ascent, depending on how much cable is deployed and expected wind forces. It is quite low at full extension, allowing some relaxation of the tether specs (i.e., tapering of the tether) during the very last few kilometers of its length. However, the tether must have a "safety margin" beyond the static case of at least six if it is expected to survive deployment in the worst case scenario.
This is simply not possible – the tether would have to be able to withstand a peak load of 180 tons. In theory, we have no business launching into worst case conditions anyway. But upper level winds cannot be predicted with 100% accuracy, even using balloon soundings. In practice, this will force us to treat the platform much more delicately during launch than a static analysis suggests. We will have to compensate by increasing our requirements for favorable conditions, which will shrink our launch windows and increase the waiting time between them.
The prototype will be most vulnerable during ascent and descent, when the structural dynamics are the most prevalent.