"HIGH-PWR" Loads, Waters method
Steven R Faber +1 708 979 3147
Here is an update on the Waters method calculations.
To review, the Waters method measures the "pressure ring" diameter
just behind the case head to tell when the pressure of a load becomes
excessive. The theory was that when this diameter stops growing or reaches
a .5 mil increase over moderate loads, that it signals that the pressure
is getting too high.
Last time we calculated the inside diameter expansion due to
50,000 psi on the inner chamber wall. Now I'll add some more pressure
points and calculate the amount of spring-back of the case.
The case will expand from its original dimensions (sized) until it
reaches the chamber wall. The brass will stretch according to its
modulus of 16e6 psi until the yield stress is reached, after which the
pressure it supports will stay relatively constant with further elongation.
I found a chart of yield stress vs. hardness for cartridge brass in the
book "Sniper Loads". I also measured the hardness of the mid section of
some 30-06 and .223 cases with a Rockwell N-T tester and found they were
at 160-165 brinnell. This corresponded to a yield stress of 58K psi. (at .5%
elongation).
The case stretch at the yield point would then be 58000/16e6 = .36%.
The thin wall vessel pressure formula then predicts a 30-06 case would hold
5,400 psi given a .021 in wall thickness.
The .308 case at .464 in diameter would stretch 1.67 mils.
Given that there is at least this much clearance for the case to stretch
I claim that the pressure at the chamber wall will be lowered by an amount
similar to what was calculated for the 30-06 (even when it is at the yield
point and touching the wall, Gary ).
Then when the pressure is released it should spring back by 1.67 mils.
Here are some chamber ID expansion distances vs. pressure at the chamber wall
using a .47 in estimate for the diameter near the case head.
50,000 psi 1.25 mil
60,000 1.50
65,000 1.62
68,000 1.70
69,000 1.72
70,000 1.74
75,000 1.87
This shows about a .25 mil increase per 10,000 psi.
The point where the expansion equals the spring-back of the brass is
at 68,000 psi or so. At this point or beyond the case would be stuck
and the bolt lift would be hard. I don't know how much bolt lift resistance
one would get as you approach the zero clearance point due to dirty chamber
effects, but you might notice a sticky bolt before that point.
A quick look at Daniel's tests show that he experienced signs of bolt
sticking around 63,000 psi with heavier bolt lift at higher pressures.
In summary, the results are consistent with Water's observations of a
.5 mil increase if you go from say 45,000 psi to 65,000 psi.
The increase should also stop when you reach the 68,000 psi point.
(For chambers of these dimensions).
The sticky bolt lift probably makes a better high pressure indicator, since
it seems to be noticable somewhat gradually before the stuck case point,
where this is probably not the case with the Water's method.
It would also be inconclusive to judge what pressure you are at by some
absolute amount of pressure ring expansion, since it would be relative to
the starting pressure, which you probably don't know.
Steve Faber
david.fu...@nt.com
Steve Faber writes:
#Here is an update on the Waters method calculations.
#To review, the Waters method measures the "pressure ring" diameter
#just behind the case head to tell when the pressure of a load becomes
#excessive. The theory was that when this diameter stops growing or reaches
#a .5 mil increase over moderate loads, that it signals that the pressure
#is getting too high.
........
#Then when the pressure is released it should spring back by 1.67 mils.
#
#Here are some chamber ID expansion distances vs. pressure at the chamber wall
#using a .47 in estimate for the diameter near the case head.
#
#50,000 psi 1.25 mil
#60,000 1.50
#65,000 1.62
#68,000 1.70
#69,000 1.72
#70,000 1.74
#75,000 1.87
........
#This shows about a .25 mil increase per 10,000 psi.
Steve, it's been a while since I read Waters' method; my recollection
of his method was to take a box of new factory ammo, and pull the bullets
and dump the powder on (say) 15 out of the 20 rounds. This gives 5 rounds
loaded to factory standards, and 15 hopefully identical brass cases (i.e.,
same lot, neither group has been work hardened, same primers, etc). The case
head diameter of the factory rounds, after firing, is measured. Then the
virgin primed cases are used for the handload under consideration, and miked.
I believe the source of the 0.5 mil is that this is half a division on a
0.001" mike; it seems that an implicit assumption is being made that this
is the greatest degree of precision you can get out of a common 1" by 0.001"
micrometer (without a vernier scale). In fact, it isn't really difficult to
read to a tenth of a division, i.e., 0.1 mil, without the use of a vernier.
I interpret this to mean "within the precision of commonly available
micrometers, and an assumed level of operator skill, do not exceed case head
expansion generated by a factory load". I think he also makes the caveat
that this is to be done only if other traditional pressure signs do not
appear - i.e., if the bolt on your handload is sticky, but the factory
load does not produced such a stickiness, even if the micrometer tells
you all is well, pay heed to this pressure sign and reject the handload
as being too hot.
Anyhow, 0.5mil works out to about 20,000 psi, which is a rather large
margin in excess of typical high pressure cartridges (such as .308 Win),
which develop a nominal pressure in the 50,000 psi neighborhood. And
it would be disastrous in a low pressure gun/cartridge combination.
An additional 20,000 psi in a .308 Win would give many other "pressure
signs," such as flattened/extruded/cratered primers, brass flow into
ejector, stiff bolt lift or case extraction, etc. Therefore you would
not see the 0.5 mil increase in a .308, before you run into other pressure
problems.
But say you were loading for a .30-40 Krag, which is safe for pressures
in the neighborhood of 40,000 psi. The Krag rifle has a single locking
lug, and is supposedly (I've never done the calculation) a weak link in
the system. It would be possible to develop (say) 55,000 psi without
exceeding the 0.5 mil case head expansion. This pressure would not
cause excessive pressure signs in the primer, nor would it extrude brass
into the ejector (causing stiff bolt lift). Only if the action were
sufficiently flexible to cause this pressure level to produce a stretched
case (and therefore stiff bolt lift), would the reloader have some warning
signs. In this case, Waters' method may lead you to unknowingly assume
that .308-class pressure levels are safe in your Krag. If you were to
make the measurement more carefully, say to 0.1 mil, you would be able
to estimate that your load doest not exceed factory spec by more than
roughly 4000 psi. You could even underload by 0.1 mil worth of case
head expansion, so that the 0.1mil precision of your measurement would
ensure that you don't exceed factory pressure. This of course assumes
that factory ammo is generating a "safe" pressure level _in your rifle_.
Other things to consider: The pressure required to produce 0.5 mil
of case head expansion would be:
greater that 20,000 psi in any case with a smaller head diameter
less than 20,000 psi in any case with a larger head diameter
greater than 20,000 psi for a thicker chamber
less than 20,000 psi for a thinner chamber (e.g., Featherweight)
This is all relative to a 1.25" O.D. chamber, and a "standard" (0.474")
case head.
#The point where the expansion equals the spring-back of the brass is
#at 68,000 psi or so. At this point or beyond the case would be stuck
#and the bolt lift would be hard. I don't know how much bolt lift resistance
Bolt lift may become hard before this point. Brass flowing into the
extractor, for instance, will cause a stiff bolt lift. But when the
pressure finally reaches a level such that the chamber spings back more
than the brass, there will start to be sticky _extraction_ problems. This
may manifest itself as stiff bolt lift, because most bolt actions have
some camming action to assist extraction.
#one would get as you approach the zero clearance point due to dirty chamber
#effects, but you might notice a sticky bolt before that point.
#A quick look at Daniel's tests show that he experienced signs of bolt
#sticking around 63,000 psi with heavier bolt lift at higher pressures.
This is correct.
#The sticky bolt lift probably makes a better high pressure indicator, since
#it seems to be noticable somewhat gradually before the stuck case point,
#where this is probably not the case with the Water's method.
This certainly is the case on my Model 70 (.308 cal). The pressure reading
instrumentation indicates that maximum safe pressure correlates very
well with onset of a sticky bolt. This is primarily due to brass flow
into the ejector area of the bolt face, I have observed.
In the case of a bolt face that did not have an ejector, or perhaps an
action with a smaller diameter ejector, this pressure sign would be
absent. It would be interesting to ask Toby Bradshaw about pressure
signs in a benchrest action (which uses no ejector). Is there any
stickiness in bolt lift, or difficulty in extraction, or does everything
remain easy to operate up until the point of blowing primers?
I know that in my .223 bolt gun, I'll blow a Federal primer before any
bolt-lift stickiness is observed.
Bottom line: Is Waters' method sound? I don't think so, if you are
willing to tolerate a 0.5 mil growth beyond that produced by factory
loads. This is a 20,000 psi overpressure, for .308-class case head
diameters, and relatively large chamber o.d. (1.25"). If the measurement
is made with a greater degree of precision (0.1 mil), then the method
looks like it should be OK. Some additional calculation should
be done for larger diameter cases (magnums, and .45-70), and for thinner
walled barrels.
- Daniel
Steven R Faber +1 708 979 3147
#(.. written by Daniel Chisholm)
#
#Steve, it's been a while since I read Waters' method; my recollection
#of his method was to take a box of new factory ammo, and pull the bullets
..
Thanks for clarifying the Water's method. I just caught the tail end
of some of the posts on it.
#
#
#>The point where the expansion equals the spring-back of the brass is
#>at 68,000 psi or so. At this point or beyond the case would be stuck
#>and the bolt lift would be hard. I don't know how much bolt lift resistance
#
#Bolt lift may become hard before this point. Brass flowing into the
#extractor, for instance, will cause a stiff bolt lift. But when the
#pressure finally reaches a level such that the chamber spings back more
#than the brass, there will start to be sticky _extraction_ problems. This
#may manifest itself as stiff bolt lift, because most bolt actions have
#some camming action to assist extraction.
Good point, so the brass will start flowing at its yield point of around
58K psi causing stiff bolt lift due to that.
...
#
#In the case of a bolt face that did not have an ejector, or perhaps an
#action with a smaller diameter ejector, this pressure sign would be
#absent. It would be interesting to ask Toby Bradshaw about pressure
#signs in a benchrest action (which uses no ejector). Is there any
#stickiness in bolt lift, or difficulty in extraction, or does everything
#remain easy to operate up until the point of blowing primers?
#I know that in my .223 bolt gun, I'll blow a Federal primer before any
#bolt-lift stickiness is observed.
#
I noticed the flow into the ejector hole of an AR-15 occured above
45K or so on our scale. It seems our pressure estimates are low on
our .223 guns, also considering the pressure where your primer blew.
I wonder if the chrome plating on the chamber affects this? :)
The chambers are relatively thicker on these guns, so the stuck case
point will be quite high - I'll have to calculate that.
I finally did some pretty hot loads in the AR - up to 550 microstrain
that caused a fair amount of flow into the ejector hole. One even
jammed probably due to the difficult bolt twist similar to what you
related above.
Steve