How this calculator works
The flange reaches the hole entrance at t = x = 0 in the hole frame. Before any stress signal reaches the tip, that tip keeps its incoming velocity. The earliest possible signal travels at c from the entrance; real elastic signals are slower. If the tip reaches the bug before this earliest signal, contact cannot be prevented by flange impact. If no contact occurs before it, later contact remains unspecified because the material and stopping history have not been modelled. The event labelled unhalted tip is a kinematic continuation if stopping has already begun. The rivet frame is its original inertial rest frame, not an accelerating frame attached after impact. Both frames agree on event coincidences.
Formula
Incoming length l = a/gamma; earliest stop time after flange impact t_signal = l/(c-v). Tip reach = l+v t_signal = a sqrt((1+beta)/(1-beta)). Critical beta = ((L/a)²-1)/((L/a)²+1), clipped to zero if L <= a. Lorentz event transformation: t_prime = gamma(t-vx/c²).
Worked example
At 0.6c, a 1 m rivet has incoming length 0.8 m. Its tip can reach 2 m from the entrance before the earliest stop signal catches it. A bug at 1.9 m is contacted before that signal; at 2.1 m there is no contact before it arrives.
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Frequently asked questions
Does a short contracted rivet guarantee the bug survives?
No. A stop command cannot reach the tip instantly. The tip keeps moving until a causal stress signal arrives.
Does no contact before the signal mean survival?
No. Later motion depends on stress propagation, deformation and stopping details that this tool leaves unspecified.
Why do the two frames give the same contact conclusion?
A contact event is a spacetime coincidence. Lorentz transformations change its coordinates, not whether the two objects meet.