Start Sinatra app in the background with stdout and stderr redirected (append) to a file
Under bash, try:
nohup ruby app.rb >> /log/file 2>&1 &
screen -L -dmS somename ruby app.rb
This will start a screen process with the name of 'somename', with all output from the program being logged to screenlog.0 in the current working directory.
If you ever want to get back the application's console for some reason, you can do screen -r somename
.