Black powder Cannon Ballistics in the Age of Sail

hal · 10-14-2018, 06:59 PM

Hello Folks,
If given the information that a given cannon weighs x, and its carriage weighs Y, and its given recoil is given in tons - can you, given the following, determine the damage that is inflicted by the cannon ball itself (ie velocity and mass etc) as well as the recoil of the cannon and carriage in the event that someone fails to get out of the way of the recoil?

For example, this is from a book I own...

"Long 12-Pounder
Length: 9’ 0”
Caliber: 23.361
Weight of Gun: 3584 lbs
Weight of Gun: 32 cwt, 0 qtrs, 0 lbs
Weight of Carriage: 6 cwt, 1 qtrs, 17 lbs
Weight of piece and carriage: 38 cwt, 1 qtrs, 17 lbs
Total weight of piece and carriage: 4301 lbs
Proportional weight to shot of gun: 298.6
Weight of shot: 12 lbs
Shot diameter: 4.40 inches
Bore Diameter: 4.64 inches
Powder charge standard weight: 4 lbs
Range maximum at 6 degrees: 1320 yds
Range point blank (Gun level): 375 yds
No of gun’s crew, single side: 10
No of gun’s crew, both sides: 5
Total force exerted upon breeching ropes and tackle upon firing: 10 tons
"

If the force exerted backwards is the same as forwards, then the cannon ball that weighs 12 lbs - is going to be accelerated with 10 tons of force, and the carriage weighing 4301 lbs. I figure that it should be possible, but am having a brain fart at the moment. At least this way, if we have say, the speed of the carriage going backwards, we can maybe treat it as Collision damage etc.

Help? I'm hoping that with more specific information, using Doug's formula for damage based upon ballistics, we might have a better approximation for the damage inflicted by a 12 lbr cannon during the age of sail (as this is one of the guns from the HMS VICTORY.)

Ulzgoroth · 10-14-2018, 08:32 PM

"Total force exerted" sounds like one degree away from word salad. It could conceivably be defined in a way that is useful and relevant, but without such a definition presented I can't even tell you what it's purporting to measure.

There's no possible way that you can get what you need out of force alone, no matter what force is being measured.

However, "Range maximum at 6 degrees" could be what you need. Combine it with the point blank range, to back out the effects of the carriage height. You should be able to back out muzzle velocity from that. At least if you can ignore air resistance.

mlangsdorf · 10-14-2018, 08:54 PM

You can estimate the air resistance if you try. It's a mostly spherical cannon shot, you can approximate the drag force as 1/2 * rho * A * C * v^2. rho is air density (~1.29 kg/m^3), C is roughly 0.5, A is the cross- sectional area of the shot, and velocity is the instant velocity at any point in time.

Set up a spreadsheet to do a linear approximation of acceleration, velocity, and distance over time and play with the numbers a bit. There's going to be a bunch of errors, but you can probably get the velocity to within +/- 15%.

Gigermann · 10-14-2018, 09:03 PM

Just thinking that through: for the recoil, can probably take the mass-based HP/ST for the gun, and the distance it moves back during recoil (without being restrained), and figure collision damage from there…

scc · 10-15-2018, 12:58 AM

Quote:

Originally Posted by Ulzgoroth

"Total force exerted" sounds like one degree away from word salad. It could conceivably be defined in a way that is useful and relevant, but without such a definition presented I can't even tell you what it's purporting to measure.

No, it makes sense as a unit of measure, but it doesn't make any sense to report it because you'd actually want the peak moment of force, not the total load over a period of time.

Ulzgoroth · 10-15-2018, 01:37 AM

Quote:

Originally Posted by scc

No, it makes sense as a unit of measure, but it doesn't make any sense to report it because you'd actually want the peak moment of force, not the total load over a period of time.

If you integrated force over time, you wouldn't get tons as a unit. You could average it over time, but I don't know why you would do that, or call that "total".

But yes, peak force would make more sense as a thing to report.

hal · 10-15-2018, 06:49 AM

So it can't be done then?

Addenda:

I did a search on the use of "tons" as a unit of force, and found that 10 tons converts to poundals as 65616.7979002625 second^2 (short ton). A poundal is a unit of force equal to that required to give a mass of one pound an acceleration of one foot per second per second. So if we're talking about an 18 lb mass, dividing by 18 gives us 3645.377 feet per second per second.

If the time interval is 1 second, would that not mean that the initial velocity of an 18 lb ball from the cannon would be about 3645.377 feet per second?

If so, that same force applied to an object weighing 4301 lbs would have a movement of 15.26 feet per second per second backwards, or 15.26 feet for 1 second. So, maybe a collision of 5 yards per second initially for the 2.1 ton object? I'm guessing at this since it has been so long since I've done physics...

copeab · 10-15-2018, 07:58 AM

Quote:

Originally Posted by hal

So it can't be done then?

Kinetic damage can be estimated with VE2. Recoil impact damage is probably fatal, given the medical technology of the period.
Addenda:

Quote:

If the time interval is 1 second, would that not mean that the initial velocity of an 18 lb ball from the cannon would be about 3645.377 feet per second?

That is a very high velocity for a black powder weapon. The 88mm gun on the Tiger I had a lower velocity than that.

Here is a page with javascript code for calculating velocity. You should be able to use the formula in a spreadsheet with a little work:

https://www.arc.id.au/CannonBallistics.html

Anaraxes · 10-15-2018, 08:10 AM

"Total" could merely be a synonym for "peak" or "net". They might have used the word "total" because in practice you'd add up the forces on all of the set of those "breeching ropes and tackle", no one of which bears all the force for a single convenient measuring point

Much like "pound" is the spelling of a unit of both mass and force*, "ton" is probably a unit of force here, the force exerted by 1 ton of mass in 1G.

If you know the recoil force, you also know the force applied to the cannon ball - equal and opposite. F = ma (gun) = ma (shot). The acceleration of the gun can be taken from F=ma directly. That gives you the acceleration of the shot. (The book conveniently gives you the ratio m_gun) / m_shot.)

I'm willing to assume the gun designers were doing a good job of optimizing their powder charges (even if by trial and error), and that acceleration is applied to the 12-lb shot for the entire length of the barrel (given as 9 feet). That gives you the muzzle velocity and KE for the round. So here's where you do the sanity check to make sure that's a reasonable muzzle velocity for such a cannon, and thus that the numbers in the book and assumptions above are sensible.

That should give you enough for the Doug Cole spreadsheet, or at least calibration versus some standard cannon(s) if that spreadsheet only fits well for the small arms.

--
* The standard abbreviations distinguish pounds-mass from pounds-force, lbm and lbf. An "lb" could be either; you just have to know the context. 1 lbf = 1 lbm * g (32.17 ft/s^2)

People that can't stand having the same spelling for the units of force and mass take one of two paths. You have to take out the factor of 'g' (32 ft/s^2) that connects the two somehow, so you either declare a "pound" to be a unit only of mass and wind up with a "poundal" as the unit of force (which accelerates one lbm to one ft/s in one second, just as a Newton is a kg * m / s^2, so 1/gth of a lbf). Or, you declare a "pound" to be the unit of force, and then invent the "slug" as the unit of mass to match (the mass that's accelerated by 1 ft/s^2 when you apply 1 lbf to it, or around 32 lbm).

Fred Brackin · 10-15-2018, 10:19 AM

Quote:

Originally Posted by hal

Hello Folks,

If the force exerted backwards is the same as forwards, then the cannon ball that weighs 12 lbs - is going to be accelerated with 10 tons of force,)

Momentum of the gun and carriage backwards will be equal to the combined momentum of the cannonball, powder gasses and associated things like waddiing.

You'd need separate masses and velocities for all items going forward out of the mouth of the gun and if you have mass and velocity of the cannonball you need nothing else.

If you were dealing with an electromagnetic gun with nothing but a projectile going forward you'd be golden. Unless it was the kind that uses a discarding sabot. :(

Really, you want mass and velocity of the projectile alone and if you're trying for true precision you need that mass in a dependable unit. Are thouse "lbs" avoirdupois (US customary) or maybe Troy or Apothecaries? If you can get mass in grains I think all grains in the above systems are equal.

10-14-2018, 06:59 PM	#1
hal Join Date: Aug 2004 Location: Buffalo, New York	Black powder Cannon Ballistics in the Age of Sail Hello Folks, If given the information that a given cannon weighs x, and its carriage weighs Y, and its given recoil is given in tons - can you, given the following, determine the damage that is inflicted by the cannon ball itself (ie velocity and mass etc) as well as the recoil of the cannon and carriage in the event that someone fails to get out of the way of the recoil? For example, this is from a book I own... "Long 12-Pounder Length: 9’ 0” Caliber: 23.361 Weight of Gun: 3584 lbs Weight of Gun: 32 cwt, 0 qtrs, 0 lbs Weight of Carriage: 6 cwt, 1 qtrs, 17 lbs Weight of piece and carriage: 38 cwt, 1 qtrs, 17 lbs Total weight of piece and carriage: 4301 lbs Proportional weight to shot of gun: 298.6 Weight of shot: 12 lbs Shot diameter: 4.40 inches Bore Diameter: 4.64 inches Powder charge standard weight: 4 lbs Range maximum at 6 degrees: 1320 yds Range point blank (Gun level): 375 yds No of gun’s crew, single side: 10 No of gun’s crew, both sides: 5 Total force exerted upon breeching ropes and tackle upon firing: 10 tons " If the force exerted backwards is the same as forwards, then the cannon ball that weighs 12 lbs - is going to be accelerated with 10 tons of force, and the carriage weighing 4301 lbs. I figure that it should be possible, but am having a brain fart at the moment. At least this way, if we have say, the speed of the carriage going backwards, we can maybe treat it as Collision damage etc. Help? I'm hoping that with more specific information, using Doug's formula for damage based upon ballistics, we might have a better approximation for the damage inflicted by a 12 lbr cannon during the age of sail (as this is one of the guns from the HMS VICTORY.)

10-14-2018, 08:32 PM	#2
Ulzgoroth Join Date: Jul 2008	Re: Black powder Cannon Ballistics in the Age of Sail "Total force exerted" sounds like one degree away from word salad. It could conceivably be defined in a way that is useful and relevant, but without such a definition presented I can't even tell you what it's purporting to measure. There's no possible way that you can get what you need out of force alone, no matter what force is being measured. However, "Range maximum at 6 degrees" could be what you need. Combine it with the point blank range, to back out the effects of the carriage height. You should be able to back out muzzle velocity from that. At least if you can ignore air resistance. __________________ I don't know any 3e, so there is no chance that I am talking about 3e rules by accident.

10-14-2018, 08:54 PM	#3
mlangsdorf Join Date: Aug 2004 Location: Austin, TX	Re: Black powder Cannon Ballistics in the Age of Sail You can estimate the air resistance if you try. It's a mostly spherical cannon shot, you can approximate the drag force as 1/2 * rho * A * C * v^2. rho is air density (~1.29 kg/m^3), C is roughly 0.5, A is the cross- sectional area of the shot, and velocity is the instant velocity at any point in time. Set up a spreadsheet to do a linear approximation of acceleration, velocity, and distance over time and play with the numbers a bit. There's going to be a bunch of errors, but you can probably get the velocity to within +/- 15%. __________________ Read my GURPS blog: http://noschoolgrognard.blogspot.com

10-14-2018, 09:03 PM	#4
Gigermann Join Date: Jul 2009 Location: Oklahoma City	Re: Black powder Cannon Ballistics in the Age of Sail Just thinking that through: for the recoil, can probably take the mass-based HP/ST for the gun, and the distance it moves back during recoil (without being restrained), and figure collision damage from there… __________________ The Art of D. Raymond Lunceford, The Daniverse: Core Group Annex The Daniverse Game Blog

10-15-2018, 06:49 AM	#7
hal Join Date: Aug 2004 Location: Buffalo, New York	Re: Black powder Cannon Ballistics in the Age of Sail So it can't be done then? Addenda: I did a search on the use of "tons" as a unit of force, and found that 10 tons converts to poundals as 65616.7979002625 second^2 (short ton). A poundal is a unit of force equal to that required to give a mass of one pound an acceleration of one foot per second per second. So if we're talking about an 18 lb mass, dividing by 18 gives us 3645.377 feet per second per second. If the time interval is 1 second, would that not mean that the initial velocity of an 18 lb ball from the cannon would be about 3645.377 feet per second? If so, that same force applied to an object weighing 4301 lbs would have a movement of 15.26 feet per second per second backwards, or 15.26 feet for 1 second. So, maybe a collision of 5 yards per second initially for the 2.1 ton object? I'm guessing at this since it has been so long since I've done physics... Last edited by hal; 10-15-2018 at 07:36 AM. Reason: addenda...

10-15-2018, 08:10 AM	#9
Anaraxes Join Date: Sep 2007	Re: Black powder Cannon Ballistics in the Age of Sail "Total" could merely be a synonym for "peak" or "net". They might have used the word "total" because in practice you'd add up the forces on all of the set of those "breeching ropes and tackle", no one of which bears all the force for a single convenient measuring point Much like "pound" is the spelling of a unit of both mass and force, "ton" is probably a unit of force here, the force exerted by 1 ton of mass in 1G. If you know the recoil force, you also know the force applied to the cannon ball - equal and opposite. F = ma (gun) = ma (shot). The acceleration of the gun can be taken from F=ma directly. That gives you the acceleration of the shot. (The book conveniently gives you the ratio m_gun) / m_shot.) I'm willing to assume the gun designers were doing a good job of optimizing their powder charges (even if by trial and error), and that acceleration is applied to the 12-lb shot for the entire length of the barrel (given as 9 feet). That gives you the muzzle velocity and KE for the round. So here's where you do the sanity check to make sure that's a reasonable muzzle velocity for such a cannon, and thus that the numbers in the book and assumptions above are sensible. That should give you enough for the Doug Cole spreadsheet, or at least calibration versus some standard cannon(s) if that spreadsheet only fits well for the small arms. -- The standard abbreviations distinguish pounds-mass from pounds-force, lbm and lbf. An "lb" could be either; you just have to know the context. 1 lbf = 1 lbm * g (32.17 ft/s^2) People that can't stand having the same spelling for the units of force and mass take one of two paths. You have to take out the factor of 'g' (32 ft/s^2) that connects the two somehow, so you either declare a "pound" to be a unit only of mass and wind up with a "poundal" as the unit of force (which accelerates one lbm to one ft/s in one second, just as a Newton is a kg * m / s^2, so 1/gth of a lbf). Or, you declare a "pound" to be the unit of force, and then invent the "slug" as the unit of mass to match (the mass that's accelerated by 1 ft/s^2 when you apply 1 lbf to it, or around 32 lbm).