Bay window dripping rain on sill

[carolinejkaye]

I have a 5 unit projecting bay window on the upper floor (front bedroom) of my house. My problem is causing me sleepless nights, it is, when it rains the noise of dripping rain onto the sill below is unbelievably loud and probably not great for the window itself.
The roof of the bay window is lead and runs along, over and back under the edge of the bay window roof. The rain then runs over and under the lead and drips constantly onto the sill below as it protrudes out more than the roof. The lead does not meet the window surround, its about an inch away. How can I cure the problem.
Is there any special guttering I can fix easily to my bay window roof without it looking out of place. I want to try and avoid replacing all the led. It'll be expensive. Help I need sleep!

Thanks
Caroline :cry: