how big do broad bean trees grow

do you mean the usual broadbean plants, the ones we eat? If so, they can grow to just above knee-high I would say.

Broad beans aren't trees. I had one grow to about 4ft this year but I planted it in autumn to overwinter and it was also in a slightly shady position so it got leggy.

I am thinking back many years to when we used to buy a type of bean for stock feed. For the life of me I cannot remember its name but I do remember eating them myself - they were very tasty. This same bean is the fruit of a tree which we have seen in Spain and the beans do look very much like Broad Beans.
If this should be what you are growing, Doogle, then it is a normal sized tree with a trunk etcThe name is on the tip of my tongue but just won't come. If I remember it I will edit this posting.

Catalpa is the indian bean tree, it has long bean like pods? but i dont know if you can eat them.

Yeah
I am thinking of the CAROB bean or Locust bean. Of course it tastes nice because it is the carob of chocolate substitute.
Though I doubt that this is the answer to your question, Doogle.