Simple way of making your backpack mountable on your bike rack, without losing any backpack functionality.
What you need:
*webbing, or fabric that you really trust. Webbing is everywhere, though. You could even trim a little off of a strap off your bag. I pulled mine off of a suitcase i found in the trash
*bungee cord that isn't too long.
*bicycle with rack
*needle and high quality thread or floss
Step 1: Cut and sew on webbing
First off, you have to cut up some of that webbing, into 3 pieces. They don't have to be very big, really. The opening in mine is bigger than it has to be. All the top two openings have to do is allow you to pull the hook of the bungee ends through. The bottom one needs to be big enough to have 2 widths of your bungee cord through.
Make sure you sew the top two far enough apart so that it's appropriate with your rack. Racks will have cross pieces of metal, and where those intersect with the side piece is where you'll be attaching the bungee hooks. Make sure that the distance between the top and bottom webbings is slightly shorter than the distance between the top of your rack and the hook at the bottom
The other thing to keep in mind is, depending on the size of your bag, you will need to offset the bottom webbing to one side or the other to prevent your heel from kicking the bag. In my bag in the picture, the bottom webbing is actually still a little to close to the center, and I need to move it maybe an inch to the right, so that when i mount it on the left side of my bike I'm not kicking it.
Sew it good and strong and make sure you use a high quality synthetic thread. Cotton threads will rot in the rain. Floss would work well, as well. I use upholstery thread, which is very strong. You can steal it at any big box fabric store, or buy it from your local fabric store.
Things that would improve the straps that differ from the picture:
*sewing over more surface area, specifically with an X in a box style. you know what i mean. A box with an X in it.
*(i will probably be doing this one) riveting into a piece of thin metal or wood or something on the inside of the bag. This will also give the bag more of a frame, if you're worried about the bag getting into your wheels.