According to the meaning, ∠ CAD = 30, ∠ CBD = 60,

∠∠CBD =∠CAD+∠ACB，

∴∠CAD=30 =∠ACB，

∴AB=BC=20 nautical miles,

In Rt△CBD, ∠ BDC = 90, ∠ DBC = 60 and sin∠DBC=CDBC.

∴sin60 =CDBC，

∴ CD =12× sin60 = 20× 32 =103 nautical mile,

So the answer is: 103.