How long did it take to get news of the sighting of the Spanish Armada from Land’s End to London?

The question is not based on reality.

In the 16th century beacons were lit in a sequence to identify where along the coast there was a suspected enemy landing. Beacons in near-coast valleys had three baskets, coastal hilltops two, and inland hilltops one. When two valley baskets were lit, the fore hills lit one; when three were lit the forehills lit two and inland hills lit.

This was about summoning troops to the localities of threats.

There was no advantage in sending a signal to London or York or wherever, unless there was a means of backing this up with detailed instructions on horse-back. Otherwise what are people fifty, a hundred, three hundred miles away to decide based simply on seeing a light?

During the threat of Napoleonic invasion 1803-1806 they lit sequences of bonfires to relay information inland such as to London, but again backed by riders.

This is based on research I carried out for a book "Hilltop Bonfires: marking royal events" but you can equally look up White's papers on the subject in the 1930s.

The Armada beacons were designed to be seen over shorter distances to mark an area of immediate threat. London already knew to expect the Armada ships, and our seamen followed them up the channel and engaged them. Near land beacons were lit where a landing was feared.

But there is not a question to be answered because in the 16th century the exercise described would have been pointless.

FWIW: From years of cooking on open fires in the bush, it is not an instant to go from candle to conflaguration. Under exceptionally dark nights, you can see the flare of a match from a long distance. At night it may be sufficient to have a dark lantern, and open the shutter of it. I would normally think of making a pilot fire (candle or lamp) into a easily visible at 15 miles fire to take several minutes.

In day it is somewhat easier, as a fire kept burning can be turned into a column of smoke very quickly by dumping green vegetation, wet grass or straw on it.

The Armada is far more likely to be seen in daylight. No sensible captain wants to be close to a not very well known shore in darkness, so if at all possible they would have been well out at sea -- you would want to be further from shore than your maximum likely error dead reckoning. I would hazard a guess of at 10-15 miles off shore. At this distance, you can see land murkily from the deck, more clearly from the masthead.

So the night transmission problem would only occur if the the fleet was spotted late in the day, near or after sunset. (Right after sunset, the ship's rigging would be silhouetted against a bright sky. if anywhere vaguely toward sunset from the observer. )

Using heights would be essential. At 15 miles, there is about a 200 foot drop in the horizon. You would need to around 100 feet above sea level to even see the rigging tops. A sight path that goes near the ocean surface is badly distorted by changes in temperature and air density.

(When I was canoeing in Canada's north, from eyes 3 feet above water level I could distinguish trees as being individual trees up to about 3 miles. At 6-8 miles headlands became silhouettes. And around 10-12 miles you'd get mirage effects, and only the tallest land forms would stand out. Now, nearly all my visual path was in the disturbed layer, but it illustrates the problem.)

In either night or day transmission, you need a visibly large contrasting signal to be absolutely clear and unambiguous.

When the Canadian Geological Survey was laying out the primary set of triangles or mapping Canada, their maximum fetch was about 20 miles. They had portable towers that they would erect on hill tops, then use a lantern on top at night. This allowed a very accurate angular bearing to the next tower.

Lets suppose an average leap of 10 miles. The message cycle works something like this.

• "John, is that the Butterpot beacon?" "Hmm. My eyes aren't quite as good as yours. Yes, I think it is. Ok. Let's do it!

• They build up the fire, adding 3 armloads of dry brush to it. A bucket of water is dumped on the pile of spruce boughs, then it's added to the fire. In 3 minutes they are producing a thick column of smoke.

Add to this: Some fraction of the time, the watcher is paying more attention to Cecil's stories about the new wench at the local pub than watching, or is taking a piss. So lets suppose on the average it takes 5 minutes for a station to repeat the signal.

This is 12 stations an hour. With an average spacing of 10 miles this would be a net speed of 120 miles an hour.