Should I use concrete for a 2" square metal fence post?

Question

I recently moved into a new home in upstate New York which has a fence around the backyard. The fence is made out of some kind of metal and the fence posts are about 2" square. One of the fence posts had risen a few inches since it was first installed due to frost heave. It had been set in a concrete footing and the whole footing had risen. I have dug out and removed the concrete (by my estimates it had gone down 33±3") and now have a roughly 40" deep hole approximately 9" in diameter. The fence post itself only goes about 20" into the ground.

I haven't been able to find a solid answer on the frost line up here, but my plan was to dig down to around 42", place an 8" cardboard tube form, and fill it with four 50lb bags of quickrete and set the post in the footing.

My concerns are:

1) is this enough? I never want to have to dig out this concrete footing again, so if I'm going to use concrete, I want to make sure this is the right way to go. I'm using a clamshell post hole digger and at 40" deep it's getting harder to go any further.

2) is this overkill? Given it's only a 2" post going ~20" into the ground, would I be better off just setting it in gravel or crushed rock or something and tamping some dirt on top? Even if it heaves out of the ground again, it would be much easier to dig down and fix than if I had to dig out the 42" concrete footing.

Here are a couple pictures of the fence and post:

Answer 1

Eight months later, here is my answer and update:

I called the my town's building division and determined the frost line for my region is 48". It wasn't possible for me to dig below 48", so I dug to the frost line and instead of using cement, I filled the hole with pea gravel (roughly three 0.5 cu ft bags), tamped it down with a 2x4, and topped with some of the soil I had removed when digging. My thought is the pea gravel will allow draingage, while still providing enough support for my narrow fence post. This might not work for larger posts.

So far, the fence post has been very sturdy and having gone through one winter, has not risen. I will report back if I find any issues with my solution, but so far, I'm satisfied with it.

Answer 2

Since your 2" post is short you do need to set it in a deeper hole with cement. I don't use the card board tubes unless above ground just fill the hole with concrete it will hold better. 36" sounds deep enough to me but I have only lived as far east as Ohio where I did have a long fence that did not have any problems in the few years I lived there.