Start another rack app from within Rails

Our Rails app depends on another (running) Sinatra rack application.
For testing purposes I would like to start this Sinatra app from
within Rails. I tried to start it in the spec_helper and in a Rake
task (with system("rackup"), but there seems to be conflicts ("shotgun
is not part of the bundle", "uninitialized constant
ActionController::Base (NameError)"). When starting it from bash
directly then everything seems to work fine.
How could I rackup the other rack app from within Rails?

Best regards,