Turn off screen; let app run in the background

When using Zwift on my phone; iOS (easiest to connect with at gym) the screen stays active/on and drains the battery quickly. It would be great if the app could run in the background with the screen off (like other running apps such as Nike+, Strava, Mapmyrun). I can only get through about 5-6 miles with the screen on whereas I can get through a marathon, and even an Ultra, with the other apps and the screen off.