In the comments on my running by default post, one of the more common responses was that people often have backpacks and a bouncing backpack is somewhere between "annoying" and "painful, risking bruising".

There was some discussion on how to set up your backpack to reduce bouncing. Tips:

• Some backpacks have straps you can buckle across your front, or you can get add-on ones. Wear them super snug.

• Put your water bottle inside where it's more central and less likely to fall out.

• Figure out if there are things you don't need to be transporting so you can have a lighter pack.

• Use a fancy backpack with good padding and a rigid back.

• Hold the shoulder straps as you run to absorb jostling.

These all seem like fine ideas, but I don't do any of them. My backpack is relatively low-end ($27) and non-rigid, without any sternum or waist straps. I keep my water bottle in the outside pocket, I have many little things in it that I could probably carry fewer of, and I don't hold the shoulder straps. And yet I probably do the majority of my running with a backpack on: I'm commuting and I have things I need to bring with me. Even when I was trying to run fast and repeatedly beat my personal best times I had my pack.

What works for me instead is that I've learned to run with a gait that doesn't bounce my backpack. I take a lot (~190 bpm) of short strides which means I have less time to fall between steps, and I generally stay pretty level. I think this is probably also beneficial from a perspective of minimizing the impact forces on your joints (ex: a paper I skimmed). Whether my backpack is heavy or light, it mostly stays put on my back.

It's still less pleasant to run with the extra weight of a backpack since it's more work, but if I think of it as intentional exercise (a bit like a weighted vest you already have with you!) I don't mind it too much.