## Sunday, November 27, 2016

### CRS-7, when buoyancy blew up a rocket

Not necessarily recent new; on June 28 2015 a rocket (Crs-7) built by SpaceX failed during launch losing \$110 million between the company and NASA.  More recently another rocket Amos-6 blew up rather spectacularly before launching destroying a \$200 million satellite.  The company hasn't officially announced the cause for the more recent explosion as they continue to investigate.  Given the amount of money involved in these launches, understanding what failed and fixing the issue is obviously incredibly important.  And in the case of the 2015 launch the issue boils down to buoyancy and a weak metal strut.

At right is a general layout of the upper stage of a Falcon 9 rocket.  The area to focus on here is the LOX or liquid oxygen tank.  Oxygen, fuel and heat make fire and the LOX is where a rocket stores its oxygen to fire the engine.

Embedded in the LOX tank are smaller helium tanks which pressurize the main tank during flight.  Well the helium tanks are suspended at the bottom of the LOX tank (to keep them cold) and held in place by 2 metal struts.  The liquid oxygen will be exerting a buoyant force on the smaller helium tank, and since helium is significantly less dense it will want to rise.  The struts can normally take a combined 20,000lbs being rated at 10,000lbs of force per strut, however SpaceX announced one strut was faulty and could only handle 2,000.

So we effectively just have a buoyancy problem with very messy units.

The helium tank is closer to a cylinder and has dimensions of:

r=0.3m
h=1.5m
v=.424m3.

LOX has a density of 1141kg/m3.

So using our basic equation for the force of buoyancy to be 4,741N or 1,065lbs of force...but the we know that the strut failed at around 2,000lbs.

However the strut here failed during flight when the rocket was accelerating, so we can't just use 1g here.  Luckily we know the rocket was accelerating at 3.2gs when the strut failed.  So we have to multiply the force of gravity by 3.2 and plug this back into our equation.

FB =0.424*1141*(9.8*3.2)=15,171N.
15,171N=3410lbs.

Divided among 2 struts and we get 1705lbs of force on each strut.  Add in some factors like how the liquid would have been compressible and we get closer to the released value.  When the strut broke the Helium tank accelerated to the top of the tank and released its helium gas into the still full LOX tank.  The massive increase in pressure ruptured the sides of the tank causing the entire rocket to disintegrate.

Following this discovery SpaceX began testing the struts themselves, finding many of them to fail well below their advertised strength.  It hasn't been released if the more recent explosion was caused by a similar problem but it is unlikely since our first equation shows the struts would have to have failed at only about 500lbs of force since the rocket hadn't taken off yet so gravity was still 1g.