Probably should post this in Science & Math instead...

Probably should post this in Science & Math instead...

Originally shared by Joshua McGee

What disqualifies a Priority Mail flat-rate envelope?

A USPS Priority Mail flat-rate envelope will ship for a fixed price, regardless of its weight, "up to 70 pounds". Neat. But hold on: seventy pounds? How much can those things hold?

I checked the Domestic Mail Manual. You are allowed to reinforce the seams and the seal with tape, but unless the envelope is slim enough to seal with its own adhesive, it is ineligible for flat-rate service. So what's the maximum volume you can fit in there?

I estimated with a stack of copy paper. The envelope will close around a 1.9cm stack. Any more than that, and it's too thick. But Priority Mail envelopes are slightly longer than a sheet of copy paper. As a rough (but generous) estimate, if you are constrained to a rectangular prism, you can maybe fit something that is 1.9cm x 22cm x 30cm into one. That's 1250cc, or 0.00125 cubic meters.

That's 0.00125 m^3 that is allowed to weigh 32kg, mind you. That means that the item you are mailing can have a density of 25,600 kilograms per cubic meter and still be permissible.

So I turned to http://www.engineeringtoolbox.com/metal-alloys-densities-d_50.html, copied the alloy density table, pasted it into Google Sheets, and sorted it.

A slab of solid aluminum has a typical density of 2712 kg/m^3. But forget that. Aluminum is light.

How about steel? 7850 kg/m^3. That's more than a factor of four.

Copper? 8940 kg/m^3. Still a factor of four.

Fine, let's pull out the big guns. I want to mail you a slab of lead in a Priority Mail envelope. That would be 14kg, or 31 pounds.

Gold? A hefty 53 pounds, but it's illegal to mail gold.

Let's scroll to the bottom. There we go: iridium! I want to mail you a 1.9cm x 22cm x 30cm slab of prone-to-shattering iridium in an unpadded cardboard-and-plastic-tape envelope. So I go out and pay the seventeen thousand dollar spot-price for a slab of iridium, stick it in a Priority Mail envelope, add some packing tape (better safe than sorry), insure it for the maximum $500 (because I'm not an idiot, obviously), and take it to the Post Office. They place it on the scale. And it would weigh ... under 62 pounds. It's mailable. I could even include a little thank-you-for-your-business note and it wouldn't take it over the seventy-pound mark.

So watch your mailboxes. It's possible that you'll be getting a seventeen thousand dollar slab of iridium in a Priority Mail envelope from me.

I mean, it's not likely. But it's definitely possible.


#science   #math   #usps  
http://eclecticquill.com/2016/06/01/what-disqualifies-a-priority-mail-flat-rate-envelope/