Moving large objects such as mattresses is often a struggle, but proper equipment and handling simplifies the task. Tying a mattress to an SUV allows you to save money on a rental truck, and gets the mattress to its intended destination. Your mattress must be securely fastened to the SUV to avoid wind-caused accidents. SUVs are not known as aerodynamic vehicles, and mattresses might fly away if caught by a strong gust.
Place moving blankets on top of the SUV so the box springs do not scratch or damage the paint and finish.
Wrap the mattress in the tarp to ensure that it remains dry during transport. Place the box-spring mattress on top of the SUV. Place the softer mattress on top of the box spring.
Place the 2-by-4 lumber -- evenly spaced -- on top of the mattress to help weigh it down. Open the windows of the SUV, and tie the mattress down using ratchet straps; place the straps through the windows of the vehicle. Use rope -- with a tight cinching-knot such as a trucker's knot -- if you do not have ratchet straps.
Tighten the ratchet straps or rope as much as possible. Align the straps evenly over the mattress. Secure the pieces of wood underneath the straps.