My prefix has won the fights  
My infix marks the start of flights   
My suffix you can almost solve  
My whole makes friendly rubber revolve

What am I?

**Hint 1:**

>! Reverse my infix and you have a music instrument

**Hint 2:**

>! You could say my prefix was chosen

**Hint 3:**

>! The opposite of my prefix once continued fighting for too long

**Hint 4:**

>! My suffix is almost beyond understanding