If I drop this - how fast would it be going when it hits the Ogre

It all started innocently enough—like most disasters do. And eventually ended up with a intr-connected system and weights and measures.

Picture it: a tabletop session nearly forty years ago. One of my players asked, “If I drop something from this tower, how long till it hits the (x)?” A simple question. Naturally, I did what any GM would do: I made something up on the spot and moved on.

But the question stuck with me. I knew my world, Trexlin, was about the same size as Earth. That meant gravity would be pretty similar. But I’d also decided that the air at sea level would be slightly thinner (0.93 atm instead of Earth’s 1.0)—while still having a richer oxygen content (24% O₂ instead of 21%). Why? Because I wanted high-altitude shenanigans—especially involving dragons—to be a bit more breathable.

Now, with that setup, I started crunching numbers.

• Earth’s O₂ partial pressure: 1.0 atm × 21% = 0.21 atm

• Trexlin’s O₂ partial pressure: 0.93 atm × 24% = 0.223 atm

So, even though total pressure is lower, oxygen levels are actually about 6% higher than Earth. Result: people (and fires) breathe easier and burn brighter.

That’s when I decided I needed standard units—because winging it only gets you so far (especially when spreadsheets enter the picture).

I already had a time unit in-game called the beat (roughly half a second). For distance, I created the Trant, equal to 4 feet. Then it hit me: why not define gravity using these made-up units? So, I declared that an object falls 1 Trant in 1 beat.

Time for some back-of-the-scroll physics:

We use the good ol’ formula:

d = ½ a t²

Plugging in Trexlin values:

• d = 1.2192 meters (1 Trant)

• t = 0.5 seconds (1 beat)

So:

1.2192 = ½ × a × (0.5)²

1.2192 = ½ × a × 0.25

1.2192 = 0.125a

a = 9.7536 m/s²

Boom. Trexlin gravity = 9.75 m/s². Almost Earth. Close enough for my fantasy physics.

Next, I tackled terminal velocity, because clearly I’d lost all control. After fiddling with the air density and drag math, I found that objects on Trexlin would fall about 3.7% faster than on Earth. That puts terminal velocity at:

22.55 Trants per beat (vs. Earth’s 22)

In summary:

• Oxygen’s higher.

• Fires are spicier.

• Gravity is comfortably familiar.

• And falling off a tower? Slightly deadlier.

All because one player couldn’t just let go of their curiosity.