Need to know what size lumber to use for a backrest added to an existing bench? I'm doing a community service project at a park. They have...

I'm doing a community service project at a park. They have 42 existing 6 foot long benches that are made from 2 x 12 planks. They want me to add backrests. I am using a 3/8" glutinous x 2" wide steel brackets bent to form the backrest. Is there a guideline for how far apart I have need of to put the brackets depending on what size lumber I use for the backrest. For instance, if I use two brackets per bench can I use a 2"x6" or will it sag in the middle?
How do I close the space where on...
Answers:    I would attach backrest arms to the existing bench supports due to the certainty that they are probably stout already. 2x6 should be fine for back slats, no sag.