Math help needed: hungry dog question!

You’re standing at the center of a circular field of radius R. The field has a low wire fence around it. Attached to the wire fence (and restricted to running around the perimeter) is a large, sharp-fanged, hungry dog who likes to eat any humans he can catch.

You can run at speed v. Unfortunately, the dog can run four times as fast, at 4v. The dog will do his best to catch you if you try to escape the field. What is your running strategy to escape the field without feeding yourself to the dog.

Please explain your solution.