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View Full Version : Datu's Mata Gun: A comprehensive performance analysis.

Red Shirt
Nov 12th, 2013, 07:51 PM
I'll put this here, since some of it could be spoilerish...

With Datu's success with his pneumatic gun some of the discussions taking place around it, I wanted to do an analysis of its potential performance and compare it to the weapons that they have (had) or may have reasonable access to. For the purposes of this analysis, I'll be ignoring details like wind resistance, round fragmentation and wound channeling. Instead, I'll be looking at raw numbers and pure impact power. So, let me take of my foil hat and put on my math hat for a minute and we'll dive in.

Now, the formula for determining the power of an impact is: E = 1/2 m v^2. This means half of the the mass (in kilograms) of the projectile multiplied by the square of the velocity (in meters per second) equals the force of the impact expressed in Joules (1=1 Newton/Meters). A simple conversion then give us Foot/Pounds. From the Wiki: It is the energy transferred on applying a force of one pound-force (lbf) through a displacement of one foot.

So, with that in hand and some heavy wiki (and other sites) digging, I pulled out all of the figures I would need. Riley's bow was a little trickier and needed a little more digging... I learned that the average draw of a Women's Olympic competition bow is 38 pounds and the recommended weight of an arrow for hunting is 6-8 grain per pound of draw. Thus, I arrived at the figure of a 304 grain weight (0.02 Kg) arrow. With these figures in hand, I "programed" a spreadsheet and these are the numbers that popped out:

2779

Note that I highlighted the .308. It hasn't been mentioned if they have a weapon chambered for that round... though CJ might have a SWAT sniper rifle the uses it. I included it for completeness's sake.

This gives us a basis for comparison. I then set about working on the numbers for the Mata Gun. I was able to locate a resource that gave the foot/weight of re-bar which is believed to be an appropriate analog to the ammunition that is being used. Assuming that Datu might have used 1/2 (0.668 lb/ft), I calculated the weight of 6, 12, 18 and 24 inch long bolts at both 300 ft/sec and 400 ft/sec:

2780

Note the green highlighted entry, a 12 inch rod at 400 ft/sec. That seems to be the optimum combination... it will out perform (single shot) everything they are known to have except for the .50 cal and Glenn's Winchester. Pretty damn good for something that probably started out as scrap. Range notwithstanding, Datu is on to something here and CJ should back it.

Here's a full table that might be easier to look at:

2781

Here are my references:

Formula & Conversions:
http://www.engineeringtoolbox.com/impact-force-d_1780.html
http://www.convertunits.com/
https://en.wikipedia.org/wiki/Foot-pound_%28energy%29

Ammo:
https://en.wikipedia.org/wiki/5.56_mm_NATO
https://en.wikipedia.org/wiki/7.62x51mm_NATO
https://en.wikipedia.org/wiki/.50_BMG
https://en.wikipedia.org/wiki/9_mm_NATO
https://en.wikipedia.org/wiki/.45_ACP
https://en.wikipedia.org/wiki/.50_Action_Express
https://en.wikipedia.org/wiki/30-30_Winchester

Archery:
http://www.olympic.org/archery-equipment-and-history
http://www.huntingnet.com/staticpages/staticpage_detail.aspx?id=15

Re-bar:
http://www.engineeringtoolbox.com/rebar-rods-weight-d_1709.html

FunkyDung
Nov 12th, 2013, 08:35 PM
1. AWESOME breakdown
2. Joules = Newtons * meters, not Newtons/meter

Red Shirt
Nov 12th, 2013, 08:48 PM
1. AWESOME breakdown
2. Joules = Newtons * meters, not Newtons/meter

I just double checked (https://en.wikipedia.org/wiki/Joule) and it should be expressed Newton-meter or N-m. At least in this application insofar as I can tell.
I also goofed the foot-pound. It is also hyphenated when spelled out, or ft·lb.

FunkyDung
Nov 12th, 2013, 08:56 PM
I just double checked (https://en.wikipedia.org/wiki/Joule) and it should be expressed Newton-meter or N-m. At least in this application insofar as I can tell.
I also goofed the foot-pound. It is also hyphenated when spelled out, or ft·lb.

Well, I was more worried about the correct unit derivation than proper expression. I just wanted to bust your balls for dividing Newtons by meters instead of multiplying. :P

Storm
Nov 13th, 2013, 12:55 AM
Even though I can't see the pictures I still gave you a like :D
I'm sure you've done a niiice job. Hehe.

Kc
Nov 13th, 2013, 11:47 AM
Way better than my math! ;)