If you do put it on the roof of your vehicle have a strap run from front to back as well as from side to side.
How to tie a mattress to roof racks.
First wrap the mattress in a bag new mattresses generally come in one or you can buy one at a hardware store and use packing tape to close the bag and secure any loose plastic.
Then place the rope across the mattress length wise then secure both ends starting with the front then the back to the front and back bumpers respectively.
Roll down all windows.
Tie the rope that you placed the mattress on in place.
This will stress any knot no matter how securely tied.
Secure the front end of the mattress and then the other end of the mattress.
Put a piece of rope on the roof of the car that goes from back bumper to front bumper.
Use strong rope or straps and make sure the mattress is tied down lengthwise and widthwise keeping the fastenings well centered.
Use a tie down that wraps around the item and the rails.
What types of tie downs work best.
Mattresses are large bulky and can pick up resistance from the wind.
The mattress had lifted up in the front and ripped the roof racks right off.
I came across a guy on the highway that only had a strap going across.
Once tightly packed in the mattress bag haul the mattress onto your roof and center it in the middle.
Pull the rope tight so there is no extra slack.
After the mattress is secure in the plastic place the mattress on the roof.
Put the mattress on top of the car and rope so that it goes length wise with the length of the car see pics above.
Drive on surface streets if possible to avoid heavy air pushing up on the mattress at the front of the car.
Ratcheting straps are much less likely to fail when moving a bulky item like a mattress.
If you do secure your mattress to a roof rack or safely in the bed of a truck strap it down with ratcheting straps.
Tie one end of the rope on a handle on the rear inside roof of the car.
With the third option crossbars with side rails you can secure an item to the side rails and run tie downs from front to back securing them to the crossbars.