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My train of thought here, is will PB1 Burst into sharpnel or simply split with little or no sharpnel?
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1/10 scale 1779 - 24 pounder build
- Thread starter Paul Buchel
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With a cast material, that's difficult to say.
(My data says both PB1 and SAE660 are cast bronze.)
As you know, a castings grain structure is simply a random jumble rather than the aligned linear grain flow along the length of the part.
If the cannon was made from wrought bronze I would expect it to split along its length if it failed.
A casting on the other hand could split in any direction. Whether shrapnel was produced or whether the wall would simply open up in a random direction would depend on the hardness (read brittleness) and the severity of the blast.
(My data says both PB1 and SAE660 are cast bronze.)
As you know, a castings grain structure is simply a random jumble rather than the aligned linear grain flow along the length of the part.
If the cannon was made from wrought bronze I would expect it to split along its length if it failed.
A casting on the other hand could split in any direction. Whether shrapnel was produced or whether the wall would simply open up in a random direction would depend on the hardness (read brittleness) and the severity of the blast.
OK. Just for the hell of it I ran the numbers for a .50 caliber bore using PB1 tensile and yield strength properties.
Rather than using the simpler formula for calculating the wall thickness I used Lame's equation for thick walled cylinders of brittle material with open or closed ends.
This formula will give thicker walls than the normally used formula.
Desiring to be realistic I used Lymans Blackpowder Handbook pressure for a .50 caliber roundball and a 70 grain GOEX 2Fg powder load which was 7800 psi to which I rounded up to 10,000 psi to be on the safe side..
I might also note that the 7800 psi pressure was for a 32" 1:60 twist barrel.
They say 40 grain GOEX 2Fg powder load under the patched roundball in a .50 cal pistol barrel produced a breech pressure of 7300 psi and a recoil of 376 ft/lbs of muzzle energy which would blow the cannon a considerable distance backwards when it fired.
Lame's formula is
t=D/2 X [[ the square root of [(S+p)/(S-p)]] -1)
t= wall thickness, D= bore diameter, S=material strength, p= pressure
Using the ultimate tensile strength = 52200 psi and p = 10000 psi the calculation gives an answer of .0535.
Multiplying this times a safety factor of 4 gives a minimum wall thickness of .2141.
NOTE: The 52200 psi is the tensile strength. If greater pressures or thinner walls are used the barrel may explode.
So, it looks like even some pretty poorly cast PB1 would be safe to shoot many times if the wall in the breech area is thicker than that.
We aren’t done yet though.
What about damaging the gun? For this we need to look at the Yield strength.
Yield strength represents the stress the material can withstand before becoming permanently deformed.
Up to the Yield strength, a piece of bent material will always return back to its original shape.
If the Yield strength is exceeded, the material will remain bent (discounting some spring back).
Using the 24,600 psi yield strength in the same formula, at 10,000 psi internal pressure the answer to the calculation is .1349.
Because exceeding the yield isn’t a matter of death we could use a safety factor of 2 but because we don’t want to screw up a nice cannon, I’ll use a factor of 3 which results in a wall thickness of .4047.
So, it looks like the barrel will withstand a 40 grain powder load with total safety and it will not be damaged if the barrel wall in the area of the breech is at least .410 thick.
As for the issue of elongation and the number of shots that can be safely fired there is no way of calculating that to my knowledge.
Yes, 10% is better than 8%, especially in brass or bronze which tends to work harden when it is subjected to stress.
As it gets harder, its elongation goes down (it becomes more brittle).
If it were mine, I wouldn't hesitate to shoot it.
I don't know that I'd be as comfortable after 2000 shots were fired thru it though.
Rather than using the simpler formula for calculating the wall thickness I used Lame's equation for thick walled cylinders of brittle material with open or closed ends.
This formula will give thicker walls than the normally used formula.
Desiring to be realistic I used Lymans Blackpowder Handbook pressure for a .50 caliber roundball and a 70 grain GOEX 2Fg powder load which was 7800 psi to which I rounded up to 10,000 psi to be on the safe side..
I might also note that the 7800 psi pressure was for a 32" 1:60 twist barrel.
They say 40 grain GOEX 2Fg powder load under the patched roundball in a .50 cal pistol barrel produced a breech pressure of 7300 psi and a recoil of 376 ft/lbs of muzzle energy which would blow the cannon a considerable distance backwards when it fired.
Lame's formula is
t=D/2 X [[ the square root of [(S+p)/(S-p)]] -1)
t= wall thickness, D= bore diameter, S=material strength, p= pressure
Using the ultimate tensile strength = 52200 psi and p = 10000 psi the calculation gives an answer of .0535.
Multiplying this times a safety factor of 4 gives a minimum wall thickness of .2141.
NOTE: The 52200 psi is the tensile strength. If greater pressures or thinner walls are used the barrel may explode.
So, it looks like even some pretty poorly cast PB1 would be safe to shoot many times if the wall in the breech area is thicker than that.
We aren’t done yet though.
What about damaging the gun? For this we need to look at the Yield strength.
Yield strength represents the stress the material can withstand before becoming permanently deformed.
Up to the Yield strength, a piece of bent material will always return back to its original shape.
If the Yield strength is exceeded, the material will remain bent (discounting some spring back).
Using the 24,600 psi yield strength in the same formula, at 10,000 psi internal pressure the answer to the calculation is .1349.
Because exceeding the yield isn’t a matter of death we could use a safety factor of 2 but because we don’t want to screw up a nice cannon, I’ll use a factor of 3 which results in a wall thickness of .4047.
So, it looks like the barrel will withstand a 40 grain powder load with total safety and it will not be damaged if the barrel wall in the area of the breech is at least .410 thick.
As for the issue of elongation and the number of shots that can be safely fired there is no way of calculating that to my knowledge.
Yes, 10% is better than 8%, especially in brass or bronze which tends to work harden when it is subjected to stress.
As it gets harder, its elongation goes down (it becomes more brittle).
If it were mine, I wouldn't hesitate to shoot it.
I don't know that I'd be as comfortable after 2000 shots were fired thru it though.
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Zonie,
The only thing I would disagree with is worrying about elongation and work hardening. Unless the material yields there is neither elongation nor work hardening. If the material is operating within its elastic limits, it will not cold work. By the same token, the material would have to yield to elongate. Using your numbers,as long as the wall is greater than the 0.4xx thickness (and that is calculated using a generous safety factor of 3) there will be no yield, work hardening, or elongation during any conceivable number of firing cycles.
The only thing I would disagree with is worrying about elongation and work hardening. Unless the material yields there is neither elongation nor work hardening. If the material is operating within its elastic limits, it will not cold work. By the same token, the material would have to yield to elongate. Using your numbers,as long as the wall is greater than the 0.4xx thickness (and that is calculated using a generous safety factor of 3) there will be no yield, work hardening, or elongation during any conceivable number of firing cycles.
Paul Buchel
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Zonie and Dave.
Thanks for the effort again. Zonie, I don't get the t=D/2 ?? Here are the the exact measurements of my cannon, if you have the time, I would appreciate it if you could give me the ratio factor to the actual limits of my PB1 barrel with a starting load.
OD of breech 1,77 inch (45mm)
Length of cannon to the base ring 11 inch.
Length of actual barrel 10.4 inch.
Actual barrel caliber .46.
Load 25gr ffg ?? BP.
Ball .44, 127gr.
I wish to apologize to Claypipe, I was sarcastic in a comment I made to him. You are no fool and I respect your knowledge and input, and yes, as a range officer, safety comes first. If you accept my apology, It would be nice to talk to you again.
Regards all
Paul.
Thanks for the effort again. Zonie, I don't get the t=D/2 ?? Here are the the exact measurements of my cannon, if you have the time, I would appreciate it if you could give me the ratio factor to the actual limits of my PB1 barrel with a starting load.
OD of breech 1,77 inch (45mm)
Length of cannon to the base ring 11 inch.
Length of actual barrel 10.4 inch.
Actual barrel caliber .46.
Load 25gr ffg ?? BP.
Ball .44, 127gr.
I wish to apologize to Claypipe, I was sarcastic in a comment I made to him. You are no fool and I respect your knowledge and input, and yes, as a range officer, safety comes first. If you accept my apology, It would be nice to talk to you again.
Regards all
Paul.
You don't get the
t=D/2 X [[ the square root of [(S+p)/(S-p)]] -1) ??
You really don't need it but if I was to tell you what to do it would be,
Add the material strength to the pressure,retaining the results.
Subtract the pressure from the material strength and divide this answer into the first answer.
Take the results of this and calculate the square root.
Subtract one from the answer.
Multiply this answer times one half of the bore diameter.
The result is the calculated barrel wall but it would be dangerous to use that value. There are too many variables in life for this to be safe.
Multiply the answer times the safety factor to get a usable answer.
For things that won't be life threatening multiplying the answer by a safety factor of 2 is commonly done.
For things that are life threatening if they fail or are involved with explosive forces a safety factor of 4 is recommended.
When I calculated the failure strength of your cannon I used a safety factor of 4.
The powder and ball load you mentioned (25 grains) will produce a velocity of about 1000 ft/sec. The energy produced will be similar to a .38 Special.
25 grains of powder with a .440 diameter ball will be totally safe to shoot.
I think Claypipe can read your post but don't expect him to answer.
Noting his posts are now shown as being posted by "Anonymous" tells me he is no longer a member of the Forum.
I have no idea why.
I'm sure his leaving the forum did not have anything to do with this topic so don't blame yourself.
t=D/2 X [[ the square root of [(S+p)/(S-p)]] -1) ??
You really don't need it but if I was to tell you what to do it would be,
Add the material strength to the pressure,retaining the results.
Subtract the pressure from the material strength and divide this answer into the first answer.
Take the results of this and calculate the square root.
Subtract one from the answer.
Multiply this answer times one half of the bore diameter.
The result is the calculated barrel wall but it would be dangerous to use that value. There are too many variables in life for this to be safe.
Multiply the answer times the safety factor to get a usable answer.
For things that won't be life threatening multiplying the answer by a safety factor of 2 is commonly done.
For things that are life threatening if they fail or are involved with explosive forces a safety factor of 4 is recommended.
When I calculated the failure strength of your cannon I used a safety factor of 4.
The powder and ball load you mentioned (25 grains) will produce a velocity of about 1000 ft/sec. The energy produced will be similar to a .38 Special.
25 grains of powder with a .440 diameter ball will be totally safe to shoot.
I think Claypipe can read your post but don't expect him to answer.
Noting his posts are now shown as being posted by "Anonymous" tells me he is no longer a member of the Forum.
I have no idea why.
I'm sure his leaving the forum did not have anything to do with this topic so don't blame yourself.
Paul Buchel
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Many thanks Zonie and Dave for your time. I am getting there, the powder pan is finished. I am so pleased that it will not be an ornament or a door stop. :thumbsup:
Paul.
Paul.
Claypipe left? :shocked2: That's a bummer. I'll miss the ol' rascal. 
Paul, I gotta admit that Zonie and Dave made some good points, and I can't argue with Zonie's math on this one. Looks like you've indeed got yourself a shootable cannon. I'm glad it worked out and that my doubts were proven wrong. Like I said, it'd be a real shame to relegate a beauty like that to being a doorstop. Let us know how it goes when you get a chance to touch her off. :hatsoff:
Paul, I gotta admit that Zonie and Dave made some good points, and I can't argue with Zonie's math on this one. Looks like you've indeed got yourself a shootable cannon. I'm glad it worked out and that my doubts were proven wrong. Like I said, it'd be a real shame to relegate a beauty like that to being a doorstop. Let us know how it goes when you get a chance to touch her off. :hatsoff:
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Claypipe sent me an email saying he was leaving the forum. I hope it was not because of this discussion. I have learned a lot I never knew by exchanging ideas on this and other forums. Often times I was corrected in a mistaken belief by others who had a more complete knowledge of a particular topic. Sometimes I even argued my incorrect opinion for a while before I understood the explanation that I was being offered. I have always been very thankful that someone would take the time to explain things to me. I hope this exchange about Velocity's cannon didn't upset Claypipe so much he bailed out on the forum. The intent was to correct a mistake and help out a fellow who spent a hell of a lot of time making a beautiful cannon model. It was certainly not my intent to alienate anyone. I will send back an email to find out what's up with him.
Claypipe was here for a long time. I'd be surprised if a single lively debate would be enough to chase him off. Then again, you never know. Whether he left due to this thread or whether it was totally coincidental, it was his choice. Even if he did leave due to this thread, there's no need to feel like you're at fault. If the discussion was ticking him off, he could have just bowed out of the thread without leaving the forum. I have a suspicion there was more to it than just this thread, but only he knows for sure at this point.
Claypipe, I'll miss your input, and I wish you well. I hope we'll see you here again at some point. Best of luck, amigo. :v
Claypipe, I'll miss your input, and I wish you well. I hope we'll see you here again at some point. Best of luck, amigo. :v
Paul Buchel
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Musketeer Von Blunderbuss said:Claypipe left? :shocked2: That's a bummer. I'll miss the ol' rascal.
Paul, I gotta admit that Zonie and Dave made some good points, and I can't argue with Zonie's math on this one. Looks like you've indeed got yourself a shootable cannon. I'm glad it worked out and that my doubts were proven wrong. Like I said, it'd be a real shame to relegate a beauty like that to being a doorstop. Let us know how it goes when you get a chance to touch her off. :hatsoff:
And Musketeer, you are indeed a gentleman for accepting the facts. I will keep posting my progression, and I will video my first shot.
All the best, Paul
Paul Buchel
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The barrel is finished, a little sanding and buffing before mounting. Here are pics of the flash pan.
Regards.
Regards.
Paul Buchel
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Wes/Tex said:
Many thanks Wes/Tex, the wood work is complete, Making rings, threading brazing rods, the little bits and pieces are the worst.
:thumbsup:
Paul Buchel
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The fit is good, the conversion from inches to mm has been the worst as I get fractions that become a little guess work.
Treestalker
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What kind of wood on your carriage? Mahogany? Wenge? Sure looks nice. Beautiful tube. :bow: Tree.
Paul Buchel
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treestalker said:
Thanks Tree, it's Oak, Walnut would have been good, but you can't buy little bits and pieces here.... :thumbsup:
:rotf:Velocity said:
I hate fractions. :cursing: One of the downsides of us sticking to the old Imperial system. Metric is definitely a lot easier to work with.
I love the coppery hue of that PB1 bronze. Really beautiful. :bow:
