Assume two black holes in the most common size range, spiraling into each other until they merge. The event releases significant amounts of energy via gravitational waves, which warp the space-time.
If the distortion is powerful enough, it would get noticed in daily life, or perhaps even detected by the proprioceptors in the human body.
How close, as an order of magnitude estimate, would you have to be to the merger to perceive it like that, without any instrument?
Best Answer
The gravitational distortion at a distance $r$ from gravitational waves due to a radiating system of mass $M$ with typical speeds of $v$ is roughly \begin{equation} h\approx \frac{GM}{c^2} \times \frac{1}{r} \times \left(\frac{v}{c}\right)^2 \end{equation} see e.g. http://www.tapir.caltech.edu/~teviet/Waves/gwave.html for an explanation.
So let's say that roughly at the merger speeds are close to the speed of light, so that \begin{equation} h\approx r_{sch}/ r \end{equation}
the average black hole is roughly $~20$ miles, so to get a ~$1$% distortion in lengths observable by human senses, $r\approx 2,000$ miles.
If a merger of two black holes is happening at this distance, gravitational waves would be our least concern.
This also illustrates how feeble gravitational waves are!