Famous Monitor's XI-inch Dahlgren Shell Guns

trice · Oct 26, 2022

67th Tigers said:
What force?

Saphroneth said:
If there are two identical round balls at different velocities, upon which the same force acts (e.g. gravity), then the faster round ball will feel the same effect in a given time but will strike the target sooner and thus have less total effect.

If the force differs according to velocity, then of course the balls will be affected in a different way. Which force are you thinking of, and how does it scale with velocity? (That second bit is important.)

All of this has already been discussed in this thread with links to examples. You have even quoted it. Please stop this nonsense and simply do the necessary work to understand and accept what you are unwilling to see.

Saphroneth · Oct 26, 2022

trice said:
All of this has already been discussed in this thread with links to examples. You have even quoted it. Please stop this nonsense and simply do the necessary work to understand and accept what you are unwilling to see.

I've quoted it, but I've also asked how it makes any kind of sense.

If you're talking about destabilization, how does a sphere destabilize? Are you claiming in fact that a sphere can be destabilized by dropping below the sound barrier?
If so, how? A non-spherical projectile is destabilized because the orientation becomes random, but a sphere is always the same no matter which way you look at it by definition.

If you're calling it nonsense that I say a sphere is a sphere no matter which way it's oriented, well, I don't know what to say, except that clearly there's something fundamentally basic that one of us is repeatedly missing; if you think it's me, point it out.

If it's not destabilization, say so and that will close off destabilization at least so I can try and work out what else it is.

Saphroneth · Oct 26, 2022

In the AR Collins linked page, which talks about projectile velocity for a smoothbore at different velocities, he discusses how the drag is greater at higher velocities (especially supersonic ones).

This is certainly the case, and I don't think either I nor 67th has ever disputed that. However, these things remain the case:

A) For a spherical projectile of a given muzzle velocity, the effect of drag is *constant* over different firings. To put it another way, if you fired ten cannonballs at 1,400 feet per second (i.e. supersonically) then drag would affect them all identically.

B) This effect drops off with lowered velocity, and it is therefore impossible for a faster projectile at the muzzle to be physically overtaken by a projectile that was slower at the muzzle.

With this in mind, I'm going to define and use a few terms. The reason for my defining them is so as to ensure that it's clear what I mean.

When a smoothbore weapon is fired, the following points can be said to exist.

1) The point at which the gun is physically pointed. This is the place that a laser pointer on the gun would make a red dot, at the moment of firing. It is constant.

2) The point at which the ball is instantaneously aimed, at the moment it leaves the barrel. This is random as it results from the last-bounce of the projectile in the barrel, which we could call "muzzle vector".
This point is randomly distributed about point (1), and for the same cannon fired at different velocities there should be no difference between the spread of (2) - or if there is, a higher velocity cannonball will have a tighter spread of (2).

3) The point at which the ball will strike the ground, considering only gravity and assuming there is no random spread of "muzzle vector". This point is constant for a given muzzle velocity, because there is no variation.

4) The point at which the ball will strike the ground, considering only gravity and "muzzle vector".

This point is randomly distributed about point (3), and for the same reasons as point (2) is randomly distributed about point (1).

5) The point at which the ball will strike the ground, considering only gravity and drag.

This point is also constant, because for a given muzzle velocity the drag profile is constant through the air. It affects a ball more strongly if the muzzle velocity is greater, but it does so in a predictable and consistent way and so point (5) is constant for a given muzzle velocity.

6) The point at which the ball will strike the ground, considering gravity, drag and "muzzle vector".

This point is randomly distributed about point (5) for the same reasons as point (4) and (2).

7) The point at which the ball will strike the ground, considering the above factors plus also wind and the Magnus effect.

These two factors (wind and the magnus effect) act over time, and consequently a higher velocity projectile (which has a shorter flight time) will have less time for them to act on it. The random distribution caused by those factors is smaller for a projectile at higher velocities.

A cannon has been aimed correctly if point (5) is on top of the target, and for a given muzzle velocity and range point (5) is predictable because it does not vary. The random factors of "muzzle vector", wind and the magnus effect have a different effect on each shoot at the same muzzle velocity, but the effects of gravity and drag are constant for each shoot at the same muzzle velocity.

Since the only parts of those random factors which vary with muzzle velocity are amplified in effect at lower muzzle velocity, we should expect a higher velocity projectile to be more accurate.

trice · Oct 26, 2022

Saphroneth said:
I've quoted it, but I've also asked how it makes any kind of sense.

If you're talking about destabilization, how does a sphere destabilize? Are you claiming in fact that a sphere can be destabilized by dropping below the sound barrier?
If so, how? A non-spherical projectile is destabilized because the orientation becomes random, but a sphere is always the same no matter which way you look at it by definition.

If you're calling it nonsense that I say a sphere is a sphere no matter which way it's oriented, well, I don't know what to say, except that clearly there's something fundamentally basic that one of us is repeatedly missing; if you think it's me, point it out.

If it's not destabilization, say so and that will close off destabilization at least so I can try and work out what else it is.

Look, you already know, and to my knowledge have known for months, that a projectile that has a muzzle velocity above a certain point (roughly the speed of sound, which varies a little according to conditions) acts differently than a projectile that starts with a muzzle velocity below that point. You know this as a fact. There is no disputing this. You also know why that is. You know that the effects described are real. You seem to be trying to obsessively attribute these to "destabilization" of an elongated projectile and claim they will therefore have no affect upon a round ball.

The projectile is subject to outside force as it slows down. Once it gets below that velocity point, the characteristics of the same projectile will match. A round ball fired at a high velocity will have different flight characteristics above the speed of sound than it does below the speed of sound. Once the high velocity round ball falls below the speed of sound, it will have the same flight characteristics as an identical round ball fired at a muzzle velocity below the speed of sound. This means that in mid-flight the flight characteristics change. This is because of the force being applied to the high velocity round ball as it slows down, increasing as it approaches that velocity, and ceasing after it falls below the crucial velocity.

You know, absolutely for sure, what that force is. You know it exists. It has been included in the discussion.

So, what is it you say happens to that high velocity round ball when it decelerates toward the speed of sound? You know force is applied to it. There is a building shockwave as it slows. What happens?

BTW, there are also some differences that occur in the flight characteristics of round balls based on size. IIRR, the dividing line is somewhere near 4 inches in diameter and the differences occur below the speed of sound. As I have noted before, I am not a ballistics expert and that is simply based on memory of something I read sometime.

As I have said before, I am neither a physicist nor a ballistician. Since undergraduate days, my mathematics has only been used in application work on things like computer science, arbitrage work, metallurgy, etc. If something I have said is too imprecise for you, blame it on that. The site MISCELLANY: MISCELLANEOUS TECHNICAL ARTICLES BY Dr A R COLLINS I have mentioned a few times probably has more detailed mathematics if you want to look through them.

Saphroneth · Oct 26, 2022

trice said:
So, what is it you say happens to that high velocity round ball when it decelerates toward the speed of sound? You know force is applied to it. There is a building shockwave as it slows. What happens?

Well, it passes through the speed of sound and the drag forces on the ball change as a result. However, they do so in a consistent and predictable way, and so the same cannonball doing this several times will be affected the same way several times over - which makes the whole trajectory predictable.

The fact the forces on the ball change at different velocities does not make the ball inaccurate. Forces on the ball being different for different firings at the same muzzle velocity would be what made it inaccurate.

Saphroneth · Oct 26, 2022

trice said:
You seem to be trying to obsessively attribute these to "destabilization" of an elongated projectile and claim they will therefore have no affect upon a round ball.

For the record, I was not obsessively trying to attribute it to destabilization - I was talking about it because you mentioned it:

trice said:
Supersonic projectiles suffer from an inherent instability when the speed drops back below the sound barrier. This would apply to both small arms and cannons.

trice said:
The closer to the sound barrier the velocity is, the sooner the drop below the speed of sound, the earlier the instability occurs. The earlier it occurs, the more it is likely to affect accuracy.

trice said:
Yes. You are simply thinking wrong about the problem: all projectiles will be destabilized as they drop through the sound barrier.

trice said:
Round spheres that are supersonic also experience destabilization effects when their speed drops below the speed of sound -- which are not experienced by round spheres which are only subsonic.

Multiple times, including specifying that it happened to round spheres.

trice · Oct 26, 2022

Saphroneth said:
For the record, I was not obsessively trying to attribute it to destabilization - I was talking about it because you mentioned it:

Multiple times, including specifying that it happened to round spheres.

The effect happens. If "destabilization" is the wrong word for it -- as you and @67th Tigers seem to think -- so be it.

But again: you know force is applied to the round ball. You know when. You know how. You have link to a discussion of it. What do you say is the effect of the force applied to the round ball?

Saphroneth · Oct 26, 2022

trice said:
But again: you know force is applied to the round ball. You know when. You know how. You have link to a discussion of it. What do you say is the effect of the force applied to the round ball?

It slows down, in a consistent and predictable way that does not change between firings of the same cannon with the same orientation.

What this means is that, if you point a cannonball upwards at 5 degrees and fire it at 1,400 fps, such that it drops to 800 fps by the time it strikes the target, it will undergo a consistent velocity profile. The only things preventing it from following exactly the same trajectory every time are the Magnus effect, the random last bounce out of the barell, and the wind.

67th Tigers · Oct 26, 2022

Indeed, because apart from the Magnus effect, which is somewhat intertwined with the last bounce (since the spin is likely to be along that axis), nothing apart from a crosswind really deflects the ball.

Cannon balls have Reynolds numbers above 10^5, and so aren't in oscillating flow.

1-s2.0-S2214914715000835-dt163-fig-0006.jpg

When the Reynolds number drops to 1,000, then unsteady oscillating flow starts, which can disturb the ball.

For an 11" ball in the transonic regime, the Reynolds number is ca. 1*10^7. The ball is so large that it never enters the unsteady oscillating region at all.

trice · Oct 26, 2022

Saphroneth said:
It slows down, in a consistent and predictable way that does not change between firings of the same cannon with the same orientation.

What this means is that, if you point a cannonball upwards at 5 degrees and fire it at 1,400 fps, such that it drops to 800 fps by the time it strikes the target, it will undergo a consistent velocity profile. The only things preventing it from following exactly the same trajectory every time are the Magnus effect, the random last bounce out of the barell, and the wind.

I think you are obscuring data here to make sure your claim sounds good to you.

You know that the same gun firing the same ball with the same orientation will not produce the same results at different muzzle velocities. Your statement conveniently ignores what you know to be the cause of the difference. You have had this pointed out to you many times, so you obviously know it is true.

You know that the ballistic effects of that muzzle velocity difference are not consistent from one shot to another in the point being discussed.

The flight of the two shots will not have the same ballistic trajectory.

Use a formula that will work accurately for the low-velocity firing and it will not work accurately for the high-velocity firing.

Use a formula that will work accurately for the high-velocity firing and it will not work accurately for the low-velocity firing.

Dahlgren noticed that accuracy decreased at higher velocities, but could not explain it. It was one of the reasons he favored smaller powder charges. He could see the inaccuracy in his test results, but he could not gather the data to determine why it was there. Not surprising, since no one had the tools needed or the knowledge of fluid dynamics involved that would have led to an accurate solution. No one actually seems to speak of a "sound barrier" until about the time of World War II

Once again: What do you say is the effect of the force applied to the round ball?

Saphroneth · Oct 26, 2022

trice said:
The flight of the two shots will not have the same ballistic trajectory.

Use a formula that will work accurately for the low-velocity firing and it will not work accurately for the high-velocity firing.

Use a formula that will work accurately for the high-velocity firing and it will not work accurately for the low-velocity firing.

I think there is a fundamental misunderstanding here of what I am claiming, in terms of what "accuracy" means. I've never claimed that you can use the same formula for high and low velocity firing - but that you can use a formula, or an empirical rule, for high velocity firing.

What I consider "accuracy" to mean is that you can point a gun, based on information you can know in advance (i.e. before putting the spark to the powder charge) and that the shot will hit close to your point of aim. The trajectory of a high velocity ball can be known in advance to at least the same extent that the different trajectory of a low velocity ball can be known in advance.

I do not dispute that a high velocity ball will follow a different trajectory to a low velocity ball. What I am arguing is that a high velocity ball will follow the same trajectory, or a very similar one, to another high velocity ball.

The reason that's what I think accuracy means is that a low velocity ball has to be aimed according to range and elevation tables anyway (e.g. 1.5 degrees elevation = 800 yards, that kind of thing), and those tables differ depending on muzzle velocity anyway.

trice said:
Dahlgren noticed that accuracy decreased at higher velocities, but could not explain it.

Would you be so kind as to provide a citation to this effect?

Saphroneth · Oct 26, 2022

trice said:
Once again: What do you say is the effect of the force applied to the round ball?

The ball slows down, and it does so in a way that is consistent if fired more than once at the same powder charge (i.e. initial velocity). That makes the trajectory consistent, and a consistent trajectory can be used to aim with.

Certainly it has a greater deviation from how the projectile would travel under gravity alone than a low velocity round ball does.

Saphroneth · Oct 26, 2022

I've converted the equations from the linked site into my programming language of preference, and here are four trajectories.

All four are for 11 inch iron cannonballs at 5 degrees elevation.

Blue = 1400 fps, no drag.
Green = 1400 fps, drag.
Orange = 1000 fps, no drag.
Red = 1000 fps, drag.

All four were run until the cannonball returned to the ground, having been fired on a flat plain. The velocity, drag and position were recalculated 1000 times per second.

@trice, would it be correct to say that the difference between green/blue being greater than the difference between orange/red is what you refer to as inaccuracy here? I'm not trying to put words in your mouth but I hoped a visual aid might clarify things.

Saphroneth · Oct 27, 2022

Per further tweaking with my code, here's a range table for the Dahlgren 11" firing at 1400 feet per second. Elevation is in degrees, range in metres.

Run	elevation (deg)	range (m)	time_of_flight (s)	impact_velocity (m/s)
1	0.25	156	0.38	401
2	0.50	300	0.75	380
3	0.75	433	1.11	361
4	1.00	558	1.46	346
5	1.25	676	1.81	332
6	1.50	787	2.15	320
7	1.75	893	2.48	310
8	2.00	993	2.82	301
9	2.25	1089	3.14	293
10	2.50	1181	3.46	285
11	2.75	1270	3.77	279
12	3.00	1355	4.09	273
13	3.25	1438	4.39	268
14	3.50	1518	4.70	263
15	3.75	1595	5.00	259
16	4.00	1670	5.29	255
17	4.25	1743	5.58	251
18	4.50	1815	5.87	248
19	4.75	1884	6.16	245
20	5.00	1952	6.44	242

This obviously took a lot of calculations by computer, which isn't feasible in the 1850s, but empirically determining these values (or the true equivalents) is feasible simply by firing the gun a lot of times. Fire on a flat surface 15-20 times at a given elevation, recording the points of impact of each cannonball, and you have the range value for this table at least.

Interestingly, at this muzzle velocity the projectile remains supersonic until the range corresponding to about 1 degree elevation, which on a flat surface is about 600 metres. It retains a higher velocity than 1,000 fps for almost two seconds, corresponding to a range of 900-1000 metres.

This can be defined as the range over which a 1400 fps Dahlgren has greater penetration power than is possible for a 1,000 fps dahlgren at point blank range. This is the scale of the sacrifice made by going to 1,000 fps instead of 1,400.

trice · Oct 27, 2022

My use of the word "inaccuracy" is this: the shot will be less likely to hit where the gunner believes it will.

Saphroneth · Oct 27, 2022

trice said:
My use of the word "inaccuracy" is this: the shot will be less likely to hit where the gunner believes it will.

Okay. So if the gunner has a range table which takes the different drag at different velocities into account?

For example, if I am a gunner and I have a range table of the sort shown above, and the target is 500 metres away, and I elevate to fire at 0.9 degrees elevation, surely that is the correct elevation and the round is, thus, accurate?

trice · Oct 27, 2022

Saphroneth said:
Okay. So if the gunner has a range table which takes the different drag at different velocities into account?

For example, if I am a gunner and I have a range table of the sort shown above, and the target is 500 metres away, and I elevate to fire at 0.9 degrees elevation, surely that is the correct elevation and the round is, thus, accurate?

How would the gunner get such a table?

Put yourself in the late 1850s. Dahlgren is one of the world's greatest authorities on gunnery (some would say the best of them). Dahlgren does not know what is going on. He believes that at some point muzzle velocity becomes too high. He thinks that it then begins to degrade accuracy and has some results that lend credence to that idea. Dahlgren has enough data to know something is happening that he cannot explain exactly, but he does not know what it is.

At the same time, Dahlgren also believes that high muzzle velocity (and the higher powder charges that go with it) shorten the life of the gun and lead to explosive failures of the gun when fired. He himself almost died during a test firing from such a failure (the gunner did). Dahlgren is looking for long service life -- which also means guns that the gun-crew will trust not to kill them.

Along with this, Dahlgren has to deal with real-world practical limitations. Before the Civil War, Dahlgren cannot even get permission to test guns to see if they can penetrate ironclad targets. He has budgetary constraints. He has functional limitations in his testing facility. He has superiors who are firmly wedded to the past and resist everything he proposes.

I would say that an attempt to investigate what was happening might easily involve a very long and repetitive series of test firings that would be tracked and recorded. It would have been dangerous to some degree to attempt it. It would have been expensive and probably been considered wasteful. Most likely, Dahlgren would need a new firing range in order to undertake it (he actually did get a new one when he undertook extensive testing for the needs of the Civil War). Since he cannot even get permission to do test-firings on armor penetration, I would think he has no chance of getting permission to conduct expensive tests for a condition he cannot even define very well.

Beyond that, the entire question of high-muzzle-velocity accuracy issues would probably be no higher than third on the list of concerns for gun-testing, quite possibly lower than that.

Possibly such an effort might produce a range chart such as you describe. It would probably have been useful if it existed. Since there might well be more than one cause-and-effect interacting, the results might not be anywhere near as clear-cut as you think.

Belfoured · Oct 27, 2022

trice said:
How would the gunner get such a table?

Put yourself in the late 1850s. Dahlgren is one of the world's greatest authorities on gunnery (some would say the best of them). Dahlgren does not know what is going on. He believes that at some point muzzle velocity becomes too high. He thinks that it then begins to degrade accuracy and has some results that lend credence to that idea. Dahlgren has enough data to know something is happening that he cannot explain exactly, but he does not know what it is.

At the same time, Dahlgren also believes that high muzzle velocity (and the higher powder charges that go with it) shorten the life of the gun and lead to explosive failures of the gun when fired. He himself almost died during a test firing from such a failure (the gunner did). Dahlgren is looking for long service life -- which also means guns that the gun-crew will trust not to kill them.

Along with this, Dahlgren has to deal with real-world practical limitations. Before the Civil War, Dahlgren cannot even get permission to test guns to see if they can penetrate ironclad targets. He has budgetary constraints. He has functional limitations in his testing facility. He has superiors who are firmly wedded to the past and resist everything he proposes.

I would say that an attempt to investigate what was happening might easily involve a very long and repetitive series of test firings that would be tracked and recorded. It would have been dangerous to some degree to attempt it. It would have been expensive and probably been considered wasteful. Most likely, Dahlgren would need a new firing range in order to undertake it (he actually did get a new one when he undertook extensive testing for the needs of the Civil War). Since he cannot even get permission to do test-firings on armor penetration, I would think he has no chance of getting permission to conduct expensive tests for a condition he cannot even define very well.

Beyond that, the entire question of high-muzzle-velocity accuracy issues would probably be no higher than third on the list of concerns for gun-testing, quite possibly lower than that.

Possibly such an effort might produce a range chart such as you describe. It would probably have been useful if it existed. Since there might well be more than one cause-and-effect interacting, the results might not be anywhere near as clear-cut as you think.

Regarding a table of fire that accurately accounts for "different drag at different velocities", I am uncertain where a U.S. gunner would get such a table at the time of the Civil War. The authoritative treatise on ordnance was Benton and IIRC he had one relatively short chapter on exterior ballistics. Gibbon's Artillerist's Manual doesn't delve into this subject in detail. The math in this area became much more a matter of interest for Ordnance and the Army later in the 19th century and into the 20th.

Saphroneth · Oct 27, 2022

trice said:
How would the gunner get such a table?

By the designer firing the gun at different elevations (several times each) to determine the location at which it lands.

It's not like you need to do it at all that many different elevations. This is the plot of distance versus elevation for the 1,400 fps muzzle velocity, calculated with motion at 1,000 times per second:

It's not quite a straight line, but if you interpolate between full degrees you're almost exactly correct except at close range:

elevation (deg)	range (m)	time_of_flight (s)	impact_velocity (m/s)	interpolated range	Error in interpolation
0.25	156	0.38	401	139.5	16.5
0.5	300	0.75	380	216.5	83.5
0.75	433	1.11	361	418.5	14.5
1	558	1.46	346	558	0
1.25	676	1.81	332	666.75	9.25
1.5	787	2.15	320	775.5	11.5
1.75	893	2.48	310	884.25	8.75
2	993	2.82	301	993	0
2.25	1089	3.14	293	1083.5	5.5
2.5	1181	3.46	285	1174	7
2.75	1270	3.77	279	1264.5	5.5
3	1355	4.09	273	1355	0
3.25	1438	4.39	268	1433.75	4.25
3.5	1518	4.7	263	1512.5	5.5
3.75	1595	5	259	1591.25	3.75
4	1670	5.29	255	1670	0
4.25	1743	5.58	251	1740.5	2.5
4.5	1815	5.87	248	1811	4
4.75	1884	6.16	245	1881.5	2.5
5	1952	6.44	242	1952	0

So to get an almost complete range table out to 2,000 m (which is easily enough for naval combat) you'd need to do experiments of firing at 0.5, 1, 2, 3, 4, 5 degrees; at that point, simple interpolation gets you within 12 metres of the true value for all elevations less than 5 degrees. It could probably be done during the proof firing to test that the gun could take that powder load, since all it requires is extra book-keeping for shots you're firing anyway.

William P. Buckner's tables (which are official 1865 US Navy tables for range) actually start based on ranges found from experiment anyway, they just use a different formula for interpolation instead of simple linear interpolation. But simple linear interpolation is close enough here.

This is a lot closer than you'd get by assuming a parabolic trajectory, even for a muzzle velocity of 1,000 fps. At 1,000 fps and 2 degrees elevation, no-drag gives you an expected range of 661 metres; the true value with drag is 591 metres.

There is no way to get an accurate range table without actual experiment anyway - the air drag even of a subsonic projectile is simply large enough that you have to do experimentation to get starting values, and you interpolate from there in some way.

Saphroneth · Oct 27, 2022

Belfoured said:
Regarding a table of fire that accurately accounts for "different drag at different velocities", I am uncertain where a U.S. gunner would get such a table at the time of the Civil War. The authoritative treatise on ordnance was Benton and IIRC he had one relatively short chapter on exterior ballistics. Gibbon's Artillerist's Manual doesn't delve into this subject in detail.

As noted, Buckner's table from 1865 explicitly uses an interpolation formula based on drag and values found by experiment. All that is necessary to give a starting point is values found by experiment, and you can interpolate between the two values after that.

There's error-compounding calculations you can do to work out how uncertain each individual value found by experiment would be, depending on the gun's deviation at given ranges.

Famous Monitor's XI-inch Dahlgren Shell Guns

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