What do you think is the minimum acrylic globe size to safely have 175w, 250w, and 400w mercury lamps in? I want to know from a perspective of heat (avoiding melting of the globe) and any potential discoloration.

Acrylic doesn't discolor. Polycarbonate does. Are you taking running the lamp base up or down? That'd make a huge difference on the thermal loading of the plastics.

Most HID fixtures that use a base down lamp in a plastic globe use a metal heat shield above the lamp.

Most HID fixtures that use a base down lamp in a plastic globe use a metal heat shield above the lamp.

Better to say are supposed to use. Then the culprit could be when that shield gone missing...

Yes, I was thinking from the manufacturer/engineering point of view. I imagine broken heat shields are not really replaced as the maintenance people oftentimes deem it unnecessary. We all know that discolouration up to and including molten globes are the result, especially in higher wattages...

Over here, 125W Mercury is run in a 400mm (~1.3ft) or 500mm (~1.6ft) Polyethylene globe, base down, with heat shield. The 400mm ones survive it barely though. The same baloons withstand a 70W HPS with or without the shield

Polyethylene have better optical performance than White colored PMMA (the pigment that gives the PMMA the White color does screw the light spectrum, while Polyethylene does not). It is a little more heat resistant than PMMA so a PMMA baloon (whether White or transparent) would have to be a little bigger for the same lamps

Polyethylene (maybe with some additive used ?) is about on par with PMMA, most of them are ok even after years, but i seen a few that didnt hold well

Polyethylene (maybe with some additive used ?) is about on par with PMMA, most of them are ok even after years, but i seen a few that didnt hold well

Are you sure it is really Polyethylene?
I have strong doubts, polyethylene normally softens below 100degC, plus heavily corrodes when exposed to UV...

Polypropylene looks and feels the same at normal temperatures even without any softener additives, but can stand way higher temperatures. That is the reason, why it is the material of choice for food boxes or so.
PMMA with some softeners may yield the same softer structure with rather high thermal robustness, plus it is quite UV resistant.

And many other base materials may look and feel the same...

The globes were described by the manufacturer (Ben Hur lighting) as Polyethylene

The material keeps its shape firmly (the shape of the thin walled globe helps there), but if pressed it will flex and bend in, and if you press from inside it will return to its original shape. Same reaction to impact. It scratches easily, more so than PMMA or Polycarbonate

Are you sure it is really Polyethylene?
I have strong doubts, polyethylene normally softens below 100degC, plus heavily corrodes when exposed to UV...

Are you sure about that? From what I have seen, polyethylene (HDPE) is known for it's excellent weather resistance.

I should have specified that I am concerned with lamps running base up with acrylic globes. I want to build a fixture but I need to know what size globe is required for each lamp type to prevent melting and damage.

Base up means base of the globe up ? If so, the globe might fare better since the hot air stream rises to the base of the lantern, which is usually more heat resistant. The base of the luminaire however might not like the combined heat of the ballast and hot air rising from the lamp. The ballast may not like the heat from the lamp either

Yes, I’m talking about the base of the globe facing upward. This is mainly because I’m planning on building a  fixture in the future. I’m not concerned about the ballast for this, but just the globe. Imagine a globe with a mercury lamp in it, and the ballast remote mounted somewhere else: that is what I want to know.