When does personal property become real property by the manner of affixation to the ground?

I.e. a hanger assessed as personal property that was transported to the aitrport but attached by cemenet and anchor bolts such that the structure is essentially permanent - can this affixation make the hanger become real property as opposed to remaining personal property

Generally, one a structure is attached to real property by some durable means, it is considered a real property fixture.

There are several factors, which vary by state, as well as some rule adopted by most states in Article IX of the Uniform Commercial Code.

But the primary factors are the intent of the person affixing the structure, how much the structure was custom-made for that place or installation, and how much damage would be done to the underlying property if the structure was removed.

In the example above, the intent is a big element, as well as how much the cement and anchor bolts were custom fit to the hangar. If the hangar is a standard off-the-shelf structure that could be purchased anywhere, that makes it less likely to be considered a fixture than if it (or the cement attachments) were specifically designed for that hangar. Finally, if the hangar could be removed simply by loosening a few bolts/nuts, that would also tend to make it less of a fixture, compared to more permanent attachment.

An attorney could do a more detailed analysis, applying the actual laws and case precedents that are in effect for the target state.

What?

Anthing that is affixed to a building or the ground in such a way that its removal will physically harm the ground or the building is probably considered to have become real property or fixtures (which are a type of real property).

The laws that determine this are state laws, so find out what the law is in your state.

when it can not be removed without doing damage or irreperalble harm.

In Texas any structure/fixture that is permanently attached to the ground is considered Real Property. Even a MOBILE home can be considered Real Property if you remove the wheels and/or axles thereby making it permanent.
Contact a Real Estate Attorney or the governing Real Estate Commission in your state to be sure of their guidelines/definitions for Real Property.

Generally never