Taking the Stone Wall

I think not. The goal of both operations was to move past the wall One did not and another did. In military speak one failed and one succeeded. Numbers are meaningless to that.Success can only be determined by pre-operational intent of the commanders involved.
The numbers are meaningless? Hmmmm...I think the numbers are what determined the failure and success to begin with. To say the numbers, aka the details, are meaningless...one might as well just say the North won the war and we can all move on to some other web site.
 
E. Porter Alexander's artillery at Marye's Heights was well-placed to sweep the field with canister, and had a lot to do with the repulse. Hunt's artillery at Pickett's charge returned the favor a few months later.
The problem is you are going to take a short range aimed volley. There is a good chance that it would stop your charge.

You might be able to take the wall, with high casualties. But now you stop to catch your breath, and get organized and you are swept with canister.

And hopefully, your supports will come up. And if they do, they might just jumble up with your guys and do more harm than good like the Mule Shoe.

A problem with positions like this is the defenders can respond more easily. Frequently, they can counter attack and expel the attackers. For something like the to work, the attackers need to have a series of things break their way.
 
Could the Stone Wall have been taken by the AOP? Reading O'Reilly's book on Fredericksburg and came across this:
Nelson Miles brigade piled across Hanover Street and into the backyards of George Rowe and Thomas Proctor houses. A garden with a tight board fence delineated the property. The fence hid the enemy from our sight recalled a soldier of the 61st NY, but the distance to their nearest line of rifle pits was short. Miles estimated that the stone wall stood about forty yards beyond the wooden fence. Miles convinced himself he could capture the stone wall at the foot of Marye's Heights. 'We were then within 40 yards of the enemy and it only needed a spirited charge with the bayonet to close in.'

He needed Caldwell's and Zook's to support him however but both balked at the idea that there was no support.

'I only regret I did not make the attempt alone to carry the hill, had there been any support I should not have hesitated to give him the order' wrote Caldwell.
Very interesting discussion point! I am certainly one who leans on the "not possible" side of the coin...but...the fact that Caldwell is the one writing makes me suspicious! My experience with Caldwell is that falls way short of the mark quite often....hiding behind a haystack at Antietam while his brigade wad sorely needed..... sending his division in piecemeal at Gettysburg while they got cut to pieces. To me....jusy my humble opinion....Caldwell was just writing that to cover his own tush.
 
Taking the wall was only part of the problem. If you did take it, then you have Marye's Heights above you. It was a forlorn hope.
 
In Fighting for the Confederacy, Gen. E. Porter Alexander described how he set up the artillery positions on Marye's Heights. "Very soon after my arrival I was directed to assist Gen. Lee's engineer officers in locating & constructing some pits for artillery at various points along the range of hills overlooking the town & valley of the river. The idea was that the enemy was likely to shell the town at any time, & our pits were to be located so as to fire upon their batteries, if they did. But, in selecting the positions, I persuaded the engineers always to advance the guns to the brows of the hills so as to be able to sweep the approaches to the hills if it became necessary, and this brought about an incident with Gen. Lee, which, in the end, I enjoyed immensely.

One day when the pits were nearly finished, I was with a party working upon one on Marye's Hill, when Captain Sam Johnston, Gen. Lee's engineer in charge of the whole business, came up to tell me Gen. Lee was inspecting the line near by, & was blaming him for not locating the pits further back on the hill. He said, "you made me put them here. Now you come along and help me take the cussin."

So I rode with him & when I came up Gen. Lee said "Ah, Gen. Alexander, just see what a mistake Captain Johnston has made here in the location of his gun pits, putting them forward at the brow of the hill!" I said "Gen., I told him to put the pits there, where they could see all this canister and short range ground this side of the town. Back on the hill they can see nothing on this side of the river." "But", he says, "you have lost some feet of command you might have had back there." I answered that that was a refinement which would cut no figure in comparison with the increased view, but he rather sat on me & had the last word, though I knew I was right & did not give it up.

Well, when the battle came on, Burnside's most powerful effort was made at that exact point, & the guns there never fired a shot at their distant view, but thousands of rounds into infantry swarming over the canister & short range ground, & contributed greatly to the enemy's bloody repulse. And a few evenings afterward, visiting Gen. Lee's camp, I took the opportunity, when the general was near enough to hear, to say loudly to Johnston, "Sam, it was a mighty good thing those guns about Marye's were located on the brows of the hills when the Yankees charged them!" I was half afraid the general might think me impertinent, though I could not resist the temptation to have one little dig at him. But he took it in silence & never let on he was listening to us. I was however frequently put on location jobs afterward, &, thence to the close of the war, I never got but one more scolding (Oct. 7, 1864) which I will tell of when I get to it."​
 
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Okay, so looking at the Stone Wall (and Marye's Heights as a whole) as a tactical problem, using contemporary tools.

The first thing to note is that the frontage from the river (around Dr. Taylor's) to the unfinished railroad and Hazel Run is about 2.5 miles - that is, it's about 13,000 feet. This means that very roughly speaking a two-deep line is 13,000 men.

As things kick off, Anderson (7,600 CS PFD), McLaws (8,000) and Ransom (3,900) are in that sector, though McLaws and Ransom are concentrated at Marye's Heights itself. That means that the Heights are extremely dense - I believe there's a quote about a quintuple line at the wall.

Any attack that might succeed needs mass. Attacks need momentum and density if they're going to continue through the beaten zone to reach close quarters; if the Union troops can reach close quarters then they're likely to succeed, the problem is getting there (and of course mass exposes more men to Confederate fire, though the historical piecemeal attacks did that anyway). Honestly a better approach is going to be to cannonade the works along the rest of Marye's Heights, but let's say for now that destroying the works isn't an option and that all the artillery is doing is counter-battery; fortunately the Union has over 300 guns so they should be able to conduct effective counter-battery.


The first obstacle is the ditch canal. On the Confederate left the main canal is close to the Confederate main line of resistance; further south around Marye's Heights, though, the ditch canal is several hundred yards (400 yards or so at closest approach) from the Confederate main line of resistance, and so the canal is an obstacle that isn't covered by the full power of the Confederate defences. It can be passed and the Union units form up on the far side of it.

Taking for now that the Union main attack will be with about 40,000 effectives, while another division or so is facing Anderson to the north, the frontage from the Washington Monument to the Hazel Run is just over a mile (and so a two-deep line would consume about 7,000 effectives).

The Napoleonic-French doctrinally correct approach here would be to push forwards a thick line of skirmishers to engage the wall at all points (and take control of farmhouses near the wall), while brigade columns (probably consisting of columns of double companies at half or quarter distance) pushed forwards to strike the Confederate defences; these columns would be good targets for musketry, but they'd also have the momentum and speed to push through the beaten zone relatively quickly and in effect each one needs to be beaten individually (but at the same time) for the Confederates to succeed. One of these columns should follow the unfinished RR and come up on the southern side of the Heights themselves, then turn north and cut in behind the Confederate position.



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Notional structure with 12 brigade columns advancing (4 divisions) behind the cover of 2 divisions of skirmishers. Since the columns are comparatively dense they have momentum and, importantly, they can follow the easier terrain.

This wouldn't necessarily work. The position is strong. But this is how it would be done if you were trying to do it properly (i.e. in accordance with principles of mass using tactical methods which already existed at the time).
 
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