Land based guns are more stable and more accurate than those on ships, in any case the 15" Langer Max had a range of 22km on ships and 47km on land but from Cap Griz Nez to Dover is about 36km so well within the maximum range.
It still requires spotting correction. The mathematical rule is that a stationary gun in perfect conditions will hit the point of aim directly once out of every 67 shots. Wind conditions at altitude, powder variations, buildup of unburnt powder in the bore, all contribute to inaccuracy at range, only partially offset by larger rounds and more powder, and increasing the farther the target is.
Langer Max had an
effective range of 22 km
on rails. The farthest it was ever known to fire was 44 km from a fixed emplacement when it bombarded Dunkerque in June 1917.
Dunkirk is actually a good example of what happens in a town under bombardment, as is Dover itself in WW2 when the Germans had much more, longer range artillery available than in WW1 on the Channel coast, and in WW2 it was directed by radar. In both cases the bombardment was by both air and gun (Dunkerque was only ranged in by German super heavy Artillery in 1917). In both cases the cities population dwindled as large numbers of people were evacuated and in both cases hundreds of civilians were killed and hundreds of buildings were damaged. But in both cases, the ports remained in operation and remained major parts of Allied logistic and naval networks. If the Germans were able to bombard Dover in 1914 ( which is unlikely, they would probably have to wait until later in the war when heavier guns were available) there seems little reason to believe that the pattern would not hold true here as well.
It was a physically slim possibility, to tactically out-march on the offensive a retreating Army is the biggest of big asks. However due to the lack of a proper Army Group command level it wasn't even identified let alone attempted. If it was attempted all manner of outcomes might have happened, it might have been largely or even partially successful, or it might have caused Lanzerac to withdraw even further or with less organisation.
Absent French cooperation it is highly unlikely to succeed at all. It would require considerably more force available to overcome the French counterattack.Besides having to be lucky enough to have that force available at the right time and place this is force that 3rd army would be required to support all the way there, eating further into their limited supplies. Meaning that, regardless of the outcome of the battle, the Germans would hit the end of their logistical tether sooner than OTL, not later.
As for logistics, they weren't so bad on 20-24 August and in any case we're only talking a tactical advance of 5-10km; a morning's march that won't snap the logistics.
Theatre level logistics had been bad since Liege. Army and Corps level logistics (limited and overstretched Motor transport companies supplementing the largely horse wagon transport from railhead to front and back) set the speed of advance and determined where the armies were during the battle of Charleroi. Just to get where they were the Germans were already using logistics strategies that increase speed but wear away your logistical network. Horses need fodder. And there is a point beyond which an army cannot be supported because their entire load would have to be fodder. Normally, about 50 km is the farthest from the rail head that an army can be supported (while being hard on your horses) while 20-30 km is much more common. The Germans were able to go further by attempting to sustain their fodder pool from the conquered area. But the time of year was wrong (August not being harvest season yet) and the year was poor. And they underestimated the requirements. So Horses were underfed on green corn that made them sick. This led to dead horses and a dwindling supply capacity.
At Charleroi, 3rd Army crossed the Meuse on the 23rd when they arrived there. The French forces guarding it had just pulled back to attack 2nd Armies flank. When they realized that 3rd Army might cut off French Retreat they returned and stopped 3rd Army’s push.
To avoid this the Germans would have had to have lunged even faster across load limited roads, taking them even further from their rail head (remembering that 5-10 km forward means 10-20 km further for your logistics section). They would then have to be well enough supplied to dig in sufficiently to resist the French counterattack. And they would have had to do this on the same day they reached the Meuse. Considering they were unsustainably burning through their logistics train just to get there it seems a tall order to push them further yet.
think 'logistics' is often use as an excuse for inaction, backed by sayings such as 'professionals study logistics'.
Well, you would have fit in well on the German staff.
Despite inadequate logistics the Germans got within sight of Paris in 1914, Moscow in 1941 and Alexandria in 1942, the logistical problem is staying there not reaching there in the first place and if tactical/operational goals are reached logistics will often sort itself out.
Absolutely none of those instances were victories and every one of them was the harbinger of disaster. It is irrelevant if you get close to the line by killing your mount, if you can then not finish. And that is what the Germans were doing. In all of those examples. Failing to finish.