What does the term "Safety Rim" mean?

Just curious,. I’ve seen that term but never understood what it means.

It means a rim with safety humps -which has become the standard many years ago

IIRC, this reference goes back to the '50s, when Chrysler featured safety rims and most other mfrs did not. Those rims made it somewhat less likely for the tire to become detached from the rim in the event of a flat.

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Safety rims may be an advantage for people who insist on ignoring their tires and run around with very low air pressure. Even then, the safety rim should only come into play if you try to run flat with no pressure. The safety rim is designed to hold the tire bead in place on the rim in the absence of pressure. With normal pressure in a tubeless tire, a standard rim (not safety rim) will hold the tire securely. So you need not worry about this, as long as you maintain reasonable tire pressure, and don’t try to run any distance on a flat tire.

Safety rims are intended to keep a tire on the rim for a while if run with very low air pressure, so you might have a chance to drive it a little way on a nearly flat tire to get service help. There was an auto safety series show on TV some years ago demonstrating that a car might be driven up to 5 miles at 5-mph on a flat tire (if you have enough patience to stay slow). The totally flat tire will eventually come loose from the rim even with a safety rim. Having a tube inside will make no difference if it goes to zero air pressure.

No safety rim

Safety Rim
Stolen from http://mgaguru.com/mgtech/wheels/wl106.htm

Good info. I was guessing it might have to do with preventing the rim from exploding if you overfill the tire, so I was all wet on that idea. So it is to help keep the tire on the rim if it is underinflated? I can see that. But I can’t see much difference between those two photos above. Are the humps that hold the tire on the horizontal or vertical surfaces? I see a sort of indentation on the vertical surface in the lower photo, is that what you mean?

It in my best guess is the concave area on the vertical part of the rim near the horizontal part