## Tuesday, September 16, 2014

### The Math

I currently have two works in progress (WIPs). One is a western/fantasy mashup that is in beta reads (oh, the commas!). The other is a science fiction novel that I've just finished the first draft on and am waiting to start edits.

In the science fiction novel, my heroes (sort of anti-heroes) are space pirates and they have 10,000 kg of gold that they've extorted from two different planets.

This sounds like a lot of gold, but because gold is so dense, I calculated that it would easily fit in a one-cubic-meter of space. I've quadruple-checked that math so I'm pretty sure I'm correct.

So, as I'm waiting to do edits, I think about the novel. And I started thinking that the pirate ship has a maximum acceleration of 5 gees. So everything on board would weight 5 times more (a 200 pound man would weigh 1,000 pounds). And would the gold, which is very soft, at the bottom of that cubic meter deform under the nearly 50,000 kg of weight (the bottom layer of gold not included) it would sustain at 5 gees?

So I went to the internet. Gold has a yield stress of 205 MPa or "megapascals" or 205 million pascals. A pascal a unit of pressure like "pounds per square inch" and is defined as one newton per square meter.

The bottom layer of gold would have a surface area of one square meter so it would take 205,000,000 newtons to deform that layer of gold (I have said the gold is in 1-kilogram bars which would be about the size of two of your fingers put together and am approximating it as one solid layer for ease of math).

To convert newtons to weight you need the formula F=ma (Newton's Second Law) so algebraically (see, I use algebra after high school), m=F/a, where "m" is mass in kilograms, "F" is force in newtons, and "a" is the acceleration. So mass equals newtons divided by acceleration. The question is, how much mass would you need to deform bottom layer of gold at 5 gees. So its m=205,000,000/5, right? Wrong! Because newtons is a kgs unit (that's kilogram, meters, seconds) and mass in in kilograms so I need to convert gees to a kgs unit. One gee is 9.80665 meters per second squared (or some say meters per second per second). That means at one gee you accelerate 9.80665 meters per second for every second you accelerate. Are you lost? Don't worry about it.

So five gees is 5 x 9.80665 = 49.03325 meters per second squared.

So the mass needed to deform gold at 5 gees is: 205,000,000/49.03325 = 4.18 million kilograms (in round terms). Or about 83 times the mass there is on top of the bottom layer of gold.

I am slightly worried that using a square meter of gold rather than numerous small gold bars is throwing off my math too much. But I have trouble believing it is different by a factor of 83. Because a gold bar only a few centimeters in surface area is going to have a correspondingly less amount of mass over it.