With a CYA of 40, it will be necessary to bring your FC up to around 20 to combat black algae. The algaecide will not help you.I meant how high do I need to bring the FC to kill the ALGAE.
Here is an important thing.....Read "How to Shock Your Pool up in Pool School. You will find that it is a process not a one time dosage. If you are serious about getting rid of black algae, you will have to MAINTAIN your FC at the least around 20ppm. This requires constant testing and additions of liquid chlorine to bring FC back up to 20 each time it lowers.
Secondly, you will need to brush the spots with a stainless steel brush daily until the spots are gone. Last, you will need to maintain your FC up around 6-10ppm for at least a few weeks after the black algae is gone and I would suggest keeping it there all summer
Black algae is VERY troublesome, but if you want to get rid of it, you won't be able to do it without a serious, daily program.