Right, the RN had hundreds of armed trawlers and such that would enter the fray as the battle moved to the beach. But the battle has to get to the beach for that to happen, that is, the invasion has to brush through the 80 x RN warships that attacked previously.
Yes, this provides the invasion force with another difficulty; the purpose-built warships can strip away the German escorts and do initial damage, before the auxiliaries, second-line and coastal force units can go in against the actual invasion force.
The problem with crushing the invasion "at their leisure" is that if the first wave lands intact it gets harder to crush the invasion on the beach. The British army in 1940 didn't have that many good "attack" divisions, and unit for unit, the Germans were better. If the Germans got ashore, the British might deploy reserves to contain them (a la Anzio), but to throw them back might not be possible. The barges - the weakest part of the invasion - weren't required to run supplies and more men to an established position, they were needed for the first mass of 100,000 to land. The supply after that could be done by other transports, (warships, motor boats, trawlers, tugs, anything that could make 8kt or better). The exception to that idea would be the 2nd wave, which would require a large barge transportation force. If an "Anzio" situation were to evolve, it might come to a point where the British decide to make peace, or that the Germans reverse the direction and start evacuating, or that they just bear down and decide to ride it out into 1941 in a bridgehead. None of these scenarios are good for the British, so turning the invasion back before it lands would be best I think.
You greatly overestimate the ability of the Germans to supply troops over beaches without specialised landing craft. These will be needed, as the south coast ports available (if captured, and if captured intact) did not have the capacity to unload the supplies needed for the planned landing force. As such, the barges will be needed, because they're the closest thing to a proper landing craft available. These will be easy targets for the RN. A force that is contained and cannot be supplied will soon surrender; it will not be able to expand the beachhead, the troops will run out of food and ammunition, and will not be able to prevent the British crushing them. An Anzio situation favours the British (and it will occur, because the Germans weren't landing motorised forces in the first wave), because the Germans will not be able to support the pocket beyond a few weeks in the most optimistic case. Turning back the invasion before it lands would be perfect, but even so, a landing would be easily survivable for the British.
If 80 RN warships go after the invasion convoy in daylight, let's assume the LW response is an all-out counterattack with every plane available against the RN forces attacking, at the maximum achievable sortie rate, in order to defeat that attack. Until that was achieved, no "inland interdiction", no "bombing empty ports", no "attacking RAF airfields". Everything into the Channel, all out, as many sorties as possible, or against RN warships trying to reload ammunition in port. What happens?
Well, firstly, the British Army is able to move into position to best oppose the invasion without any issues. The Luftwaffe will take heavier casualties over the Channel than it would have otherwise, and Bomber Command will have a much easier time hitting the invasion convoys. Targeting the Royal Navy will be a lot harder than hitting railway lines or airbases, since the vast majority of the Luftwaffe wasn't trained to attack ships, and often had trouble doing so. During 1940, there were a total of 68 bombing attacks that caused damage to British destroyers; of these, 11 were sunk, 21 seriously damaged and 36 slightly damaged. Of the 11 sunk, six of these were in confined waters, and five were stationary or anchored at the time of the attack. Two of the ships seriously damaged were so damaged in the Mediterranean, by Italian aircraft, while at least six more were moored; for lightly damaged ships, the total either attacked by Italians or moored was 8. As such, German attacks on British destroyers at sea sank 5 ships, seriously damaged 13, and slightly damaged 28, for a total of 46. Ignoring the uncounted attacks that did no damage at all, we can estimate the likelihood of an attacked destroyer sinking at ~10%; this is certainly an overestimate, as we only counted attacks that led to damage. Cutting this number in half seems reasonable; 5% unrecoverable losses would absolutely be survivable for the RN, and 10% would be doable - remember, heavier loss ratios were accepted at Dunkirk. I am ignoring the possibility of attacking ships attempting to reload in port, because to do so would require either occasionally 'bombing empty ports' or a level of aerial reconnaissance that is highly unlikely.
It's not yet a total war. How many warships could the British afford to lose before they decided to make peace instead? The IJN off Guadalcanal found that the number of sinkings and damage was too much to sustain. But, they were over 2,000 miles from home and had the room to stop fighting for Guadalcanal. Can the RN stop fighting in the Channel?
It becomes a total war the instant you try to invade Britain; the RN will not stop fighting in the Channel, because this is the raison d'etre of the RN.
I'm guessing that under air sea battle conditions in the most atypical air sea battle in modern history, an RN destroyer with let's say 1,000 rounds of main gun ammunition will fire about 250 or more at aircraft, 250 at the convoy escorts that are trying to shoot at them, will keep 200 in reserve that will not be used, (no captain fires off all his ammunition), and the other 300 at 6 targets in groups of about 50 rounds each, sinking, let's say 4 of them and damaging the other 2.
An RN destroyer captain will fire no main gun rounds at aircraft, because his main guns do not elevate sufficiently to target dive-bombers or level bombers, being intended for use against torpedo bombers instead; the Germans had a lot of the former, but very few of the latter. This nearly doubles the number of rounds available. Secondly, RN captains proved willing to fire off the vast majority of their ammunition; against the
Espero convoy, Tovey's cruisers fired close to 5000 6-in rounds, leaving just 800 in the entire Mediterranean theatre; this suggests that, if these were all aboard Tovey's cruisers, they would have an average of ~20 rounds per gun. Scaling this to a destroyer, it would suggest that just 100 rounds would be retained. Finally, RN accuracy was enough that they would score hits on more than 6 targets with 300 rounds; doubling this would be more reasonable, especially on small barges. Taking all this into account, we would expect 26 targets to be sunk/damaged, not to mention damage done by torpedoes, AA guns, ramming, or the confusion caused by the arrival of the destroyers.
553,099 tons in 5 months is 110,000 tons per month. If the RN in the Channel in 1940 scored at the Tunisia rate - 110,000 tons per month - against a Sealion campaign, would you say that would be enough, nor not nearly enough, to stop the invasion?
The rate doesn't tell you much; 110,000 tons/month is nothing if a billion tons of shipping is being used, dangerous if a million, and if 110,000 tons is being used, it's catastrophic. What you have to look at is the percentage of ships sunk, and that was 20-50%; this would be an unsustainable rate of loss for a Sealion campaign.
Bone and Malta were about 6 hours steaming from the major Axis ports. How much closer did they need to be?
They needed to be two-three hours away, such that the raiding force could get in, fight, and get out, under cover of darkness. They also needed to not be on the other side of a massive minefield, laid over the course of several months.
Ajax had radar fire control in that battle, hence the big difference in performance.
No, she didn't. She had the Type 279 radar, an air-search radar which in theory had the capability to range on surface targets. In practice, it had a poor range against destroyer-sized targets - experiments suggested that two miles was all that could be expected- and commanders typically preferred to keep it on air-search mode to give warning of any incoming aircraft. In any case, the radar was disabled by the second hit on
Ajax, which occurred before she opened fire. The entire engagement was carried out without the use of radar.
Yes, from the ammunition expenditure profile I sketched up response, I think to win the battle and repulse the invasion, I think it's pretty clear the RN would need to do exactly that, plus use air and RN aux. forces. That it did not have the ammunition aboard the RN 80 warships otherwise to repel Sealion in one go.
Yes, the RN will need to keep coming back until the Germans stop; this is not surprising, and should not be. The point is that the RN, for as long as the Germans choose to keep up an invasion attempt, can cause unsustainable losses to it.
Two things. First, when the captain of Jarvis Bay turned and challenged the Scheer, do you think he was under the illusion he could "effectively engage" a pocket battleship? What do you think he was doing? Second, if an RN destroyer group encounters a dozen enemy motor boats sailing ahead of the convoy, do you think they might attack them, or just wave and sail on by?
In answer to your first, he was buying time for the convoy to scatter. This is fine for a convoy of merchant ships, which have no pressing need to arrive together, in a consistent order, or at a particular time and place. The complete opposite is true for amphibious shipping. If you try to scatter an amphibious convoy, you end up with troops penny-packeted all over the place, follow-up units landed before the assault troops, supplies landed far from the units that need them, and all sorts of confusion. This is not conducive to success. Also, the merchant ships of HX 84 were quite a bit faster than the amphibious convoys planned for Sealion, meaning that scattering was much more effective for them. In answer to your second, they will fight, they will win in short order, and then they will be able to attack the convoy they were escorting, because it cannot scatter. If it does scatter, then job done; the Army will get a lot of practice mopping up scattered platoons of German soldiers.
Samar is just an example of an air sea battle where the overwhelming surface superiority didn't pan out due to the grinding effects of constant - even if largely ineffective - air attacks. You list a bunch of reasons why you think this example won't play in an air sea battle in 1940. But we don't really know, do we?
Samar is also an example of a commander having a limited amount of time to fight because of an overwhelming enemy force that could arrive over the horizon at any time. The possible arrival of Halsey, or of Kinkaid's battleships, weighed on Kurita's mind just as much as the constant air attacks. The Kriegsmarine had no such overwhelming force available; the RN could remain in the Channel for as long as it chose. The situation is a lot closer to Crete than it is Samar, hence why I use it as an example.
I was picturing it that if an RN destroyer went right in close against 40 ships that these might have more than one submarine deck gun. Am I wrong on that?
My point was that all the submarines the RN fought on the surface, put together, scored two hits, neither of which did any significant damage. We could expect similar effects from a convoy of barges of the same size (though likely worse, because naval gunnery is a hard skill to teach, especially in a limited time).
