Yes the Cape Wheel is free to ride on your birthday.
To ride the Cape Wheel free on your birthday you need to be signed up for the birthday club for the Cape Wheel and then you get a free ride voucher to redeem on your birthday.
Just redeem the free ride voucher on your birthday and you'll be able to ride the Cape Wheel free of charge on your birthday.
You usually have to be signed up for the birthday club before your birthday though but you might be able to sign up for the birthday club on your birthday or a few days before your birthday and then ride the Cape Wheel free on your birthday.
I rode the Cape Wheel free on my birthday and it was great.
I've also rode the Cape Wheel before as well.