Subtle engineering humor

[drewtam]

Apparently Garrett/Honeywell has a gun nut on its staff, and he let it shine.

Buried deep in this white paper on turbo burst containment is this 3-paragraph gem about a rifle muzzle energy. To use such an esoteric example [250-gr Remington 350 Magnum, really?] must be an intentional, yet subtle attempt at spicing up some generic engineering publication.

http://www.turbobygarrett.com/turbobygarrett/sites/default/files/Garrett_White_Paper_02_Burst__Containment.pdf

Effects of Burst – An Example
For an illustration of the energy released by a turbine wheel burst, consider the speed of a bullet being fired
from a gun as it leaves the barrel. Specifically, consider a 250-grain Remington .350 Magnum bullet, which has a
muzzle velocity of 2576 ft/s. Now consider a Garrett® GT55R turbine wheel being spooled up past its safe speed
limit. The tip speed of the Inconel turbine wheel just before natural burst is roughly equal to the muzzle velocity of
the .350 Magnum bullet. In other words both of these projectiles, the .350 Magnum bullet and the tip of the
GT55R turbine wheel pre-burst, are traveling at approximately 2500 ft/s or 1700 mph (2740 kph). Given that the
tip diameter of the GT55R turbine wheel is 111.5 mm (4.39 in) and its tip speed is 2500 ft/s, the rotational speed
of the wheel is 130,500 rpm. This is well into the unsafe over-speed zone; it is 39,500 rpm past the wheel’s qualified speed limit of 91,000 rpm. By measuring the moment of inertia (I) of the GT55R turbine wheel and knowing
the rotational speed (ω), we can calculate that the kinetic energy stored by the wheel just before burst is 60,662
lb-ft (by ⁄
 
). Going back to the .350 Magnum bullet ballistics, its mass is 250 grain = 16.2 grams =
0.036 lb. Therefore the kinetic energy stored by the .350 Magnum round leaving the barrel is 3,682 lb-ft (by
 ⁄
 
).
Comparing the two ballistic projectiles, we can liken the GT55R turbine wheel pre-burst energy to the equivalent of firing (60,662) / (3,682) = 16.5 of these .350 Magnum bullets simultaneously. The actual energy that the
housing will absorb will be less however, because turbine wheels will usually break into three large pieces when
the hub bursts. Each of these pieces will travel at about 1/2 of the tip speed of the pre-burst wheel tip speed, and
has about 1/3 of the mass of the entire wheel. Therefore the kinetic energy of each piece is about 22% of the total
pre-burst wheel energy. Now consider these three pieces flying towards the turbine housing: (22% of pre-burst
energy) x (3 pieces) = 66% of the pre-burst energy must be absorbed by the housing in total, which is (60,662 lbft) x (0.66) = 40,037 lb-ft of energy.
Finally we can say that the turbine housing must absorb the equivalent of (40,037 lb-ft) / (3,682 lb-ft) = 10.8 of
these .350 Magnum bullets fired at point-blank range into the inside wall, from the center outwards (if that were
physically possible to do). If you find yourself in the position of choosing a turbine housing for a GT55R or similarsized turbocharger, it might behoove yourself to ask: “Will this housing survive being hit simultaneously by nearly
eleven .350 Magnum rounds at point blank range?” If it’s a true Garrett® turbine housing, then it was intentionally
designed and qualified to contain the wheel, and you can bet the answer is “yes.”

[Nick1911]

I read into it that a non-gunny engineer looked through a list of ballistics tables until he found something that approximately matched the tip-velocity of his turbine wheel, then followed through with the calculation for the sake of his example.  The choice of the odd caliber maybe wasn't from firearms experience, but just the line item that happened to fit what he was working with.

An interesting example of the amount of energy a turbocharger housing has to deal with.  I've cut open a T3, it was made of some impressively thick cast aluminum!

[Tallpine]

Wow, fastest N2 that I know about is only about 30K rpm