Cover the light mechanism is to slightly

The Frisbee itself is stable and can be cast well. Light effect is very good. Both I and the dog can see the disk even at large distances.
My Problem:
The small lamp (diameter as the CR 2016 battery) is located in the middle and is fixed by a clip-on mounting on the inside of Frisbee. Unfortunately, this is my feeling on too quickly. In my view, a far cry from "pet safe Battery Cover". If the cover or going on the dog withdraws falls out the light. As you can imagine you're looking for a long time after this small light source (the good luminosity by means of light transmission in the material reaches Frisbee).