March 19 and 23, 2002 Meeting Notes
Phil Eaton (Tuesday)
Neil Milburn (Tuesday)
Joseph LaGrave (Saturday)
We learned a valuable lesson. Build and test is great and all, but sometimes, it really pays to
do all the calculations before you break something
The actual failure mechanism last Saturday was that one
blade pulled itself off of the hub, shearing the epoxy and retaining
bolts. The huge imbalance then caused
the other blade to break the hub bar.
This was initially seen as very unfortunate, because the hub
was originally built with longer bars to be inserted into the blades, but
during test assembly it got stuck in the blades and we had to cut some length
off. If we had the original length, there
would have been enough bond area to hold the blades on.
However, after working through all the calculations, I found
that all sorts of things were going to break before we got to our design
RPM. The engine mounting bolts would
have failed, the plumbing would have exploded, and the hub bar itself would
have failed in tension.
Force = m v^2/r
4 meter diameter rotor
675 rpm, (138 m/s) the speed that our hub failed at last
1100 rpm, (226 m/s) our design target at 0.7 mach
1600 rpm, (327 m/s) around mach 1, which we expect to be
self limited below at sea level due to compressibility drag increases
If we can have it theoretically survive at 1600 rpm, that
will be an acceptable margin of safety at 1100 rpm.
Things divide out so that you can calculate the force of an
evenly mass distributed rotor by assigning the full mass at the midpoint. Each rotor blade (with the tip engine) has a mass of about 8 kg, which we will
calculate at the 1 meter radius point and speed.
675 rpm: 38,088 N = 8550 pounds
1100 rpm: 102,151 N = 22,932 pounds
1600 rpm: 213,858 N = 48,009 pounds
The original hub bar was made of 6061-T6 aluminum, 3/4"
in diameter. 6061 has a yield strength
of 40ksi, so it would start stretching at 17,671 pounds, and break at 45 ksi
stress, or 19,880 pounds, unless the yielding caused an attachment failure
first. So, a blade would have yanked
itself off around 1000 rpm, even if the bonds had been strong enough..
We are building the new hub bar out of 7068 Aluminum, which
has a 99 ksi yield strength, for 43,560 pounds of strength. We could use stronger steels, but the
fabrication would be more difficult, and the bonding might not be as good. We can accept this strength level.
The metal filled epoxy we used has a 2,700 psi shear
strength, so it will need 16.2 square inches of bond area, or 6.9 of bonded
bar length to equal the strength of the bar itself. We will have this much bonded area, plus more bar length that we
will put bolts through. Bolt holes will
weaken the bar, but the bond area near the hub will be bolt free, and the extra
bolted bar length farther out from the center is strictly extra backup. Four high strength 8000 pound double shear #10
bolts will roughly match the reduced bar strength in that section.
Tip Engine retention
Each tip engine assembly weighs 1.25 kg, and is 2 meters
from the hub.
675 rpm: 11,902 N = 2,671 pounds
1100 rpm: 31,922 N = 7,166 pounds
1600 rpm: 66,830 N = 15,002 pounds
This force needs to be held by the engine to blade bar, the
bond between that and the blade, and the bolts that secure the engines to the
The bar is the same thickness as the hub bar, so there is no
The epoxy would need 2.65 square inches of bond area for the
1100 rpm load, which is only 1.1 inches of bonded bar, which is also not a
problem. Heat soak back into the epoxy
will probably weaken it some, but we do have silca insulation between the
engine and the mount. Because the bar
has a lot of margin on this end, we can use 1/4" bolts for backup
retention. A single AN-74 (1/4-24) bolt
in double shear can support 7,360 pounds
The engine bolts are another story. We have 4 #8 socket head cap screws
retaining the engines, in 18-8 stainless with 100ksi tensile strength. Tensile stress area from http://www.engineersedge.com/fastener_thread_stress_area.htm
gives 0.014 square inches per bolt, for a total of only 5,600 pounds, and there
will be some de-rating for increased temperature operation. The engines would have flung off at around
We can get 180ksi bolts, but that alone isnt enough margin
for our operating rpm.
The engines can certainly be lightened a fair amount,
especially because the right angle nozzle is made out of square bar stock. Going to better materials and thinner walls could
also save a lot of mass. Saving mass
here would probably be a good idea, because the tip engines also account for almost
a third of the stress on the hub bar.
The high strength bolts could be used just to hold the cat
pack to the square chamber, which they would be strong enough for. We could then use larger and stronger bolts
to hold the chamber to the blades.
We could redesign the engine for eight bolts, but one bolt
would have to be skipped for the right angle nozzle exit. This would be sufficient strength, but to
get eight bolts through the chamber would require going to larger bar stock,
which would add more mass.
We could build the chamber and blade bar as an integral
unit. This would need to be insulated to minimize the heat transfer to the
We are probably going to take a combination approach for
now: use stronger cap screws, lighten the nozzle block, and add two more
1/4" bolts between the bar flange and the chamber, in addition to the
bolts going through the cat pack, chamber, and bar flange.
Calculating peroxide feed pressure is sort of the opposite
of hub retention, you calculate the mass of the peroxide in the feed line,
calculate speed and force at the midpoint, and divide by cross sectional area:
pascals = density (kg/m^3) * tip velocity (m/s) ^ 2 * 0.5
psi = pascals / 6895
Peroxide is 1.4 g/cm^3, or 1400 kg/m^3
675 rpm: = 1933 psi
1100 rpm: = 5185 psi
1600 rpm: = 10,855 psi
Line losses probably reduced that somewhat, but the tubing
we had in there was only rated for 2324 psi, so it likely would have burst by
1100 rpm. I have ordered a lot of 0.065
wall stainless steel tubing, which is rated for 8000 psi, and that is likely
The next thing to explode will be the engine catalyst
chamber. The 0.2" thick brass walls would be taking 10,000 psi of
hoop stress at a 4000 psi chamber pressure. Annealed (which we certainly
are, after a run) 360 brass has a yield strength of 44,000 psi at room
temperature, but at peroxide engine temperatures it will have lost well over
three quarters of its strength. On the other hand, going that fast in the
air will be providing a significant amount of cooling, so we might still live
for a while. We are getting some 316 stainless chambers for future work.
New Work This Week
We finally did a big organization on our shop space,
clearing up a huge amount of space. We
still need more shelves and tables, but things are much more organized.
We got some good work done configuring things on the
trailer. We can now just push the trailer
ten feet out the door and test fire smaller engines off the side. When we go to the 100 acres for big engine
tests, we can just park the trailer by the vertical test stand, and fill
without unloading anything. I was
rather surprised at how well things went as far as preparation on our first outing
last week, but there were a number of good ideas that came up to improve things.
Our big silver screen order came in, so we now have 50
square feet of 36 mesh silver screens.
A denser mesh might have been nice, because it took 70 silver screens
(alternated with 70 stainless screens) to get clear exhaust and smooth running.
After we got the new pack working we tried to light the
biprop with it, and we had no luck at all.
We tried everything, including:
Changed peroxide and kerosene jets a dozen times.
Added more silver screens, bring the total to 80, in case it
wasnt fully decomposing even though it was clear and smooth.
Tried turning off the cooling water, theorizing that the
kerosene might be condensing on the cooler walls
Checked peroxide concentration, because this is a new drum
Tried ethane in a number of ranges
We didnt get a bit of flame. Right before we left, we tried just venting some ethane over a
torch flame to make sure it was actually flammable
We found that our solenoid trigger button has gotten very flaky,
only occasionally opening the valve. We
dont think this is the extent of our problems, but it certainly didnt help.