This error is thrown when a process in your web dyno accepts a connection, but then closes the socket without writing anything to it.
2010-10-06T21:51:37-07:00 heroku[router]: at=error code=H13 desc="Connection closed without response" method=GET path="/" host=myapp.herokuapp.com fwd=17.17.17.17 dyno=web.1 connect=3030ms service=9767ms status=503 bytes=0
One example where this might happen is when a Unicorn web server is configured with a timeout shorter than 30s and a request has not been processed by a worker before the timeout happens. In this case, Unicorn closes the connection before any data is written, resulting in an H13.