the same type of question has been asked about a beeyard located by a water body. the bees will find a source. they dont go by a beekeepers map.
True, the bees will find a source. There is then the added problem of distance traveled for that source. part of what I see in the progressive bloom issue. It is one thing for bees to be able to forage in every direction. they will locate far more forage on any given day if they are completely surrounded by it. if all the forage is in one direction then the same acreage is further away. they will still forage it.
I make no claim to accuracy as to these numbers but they where chosen based upon past things I have read.
1. Bees will forage as far as 7 miles from the hive in any direction. that is approx 196 square miles by simply square calculation. 14 X 14 = 196
2. the vast majority of forging will be done within 3 miles of the hive or again by simple square calculation is 36 square miles. 6 X 6 = 36
3. it is estimated that anything over 5 miles in a net wash as far as return or benefit to the colony. as much energy is being uses as calories in food stuff is being gathered.
4. now lets assume that any colony will find that minimum 9 square miles to forage. In the case of unlimited direction that forage will be 3 miles away in every direction. but ins the case of limited direction either by progressive bloom or a body of water. all of that 36 square miles lies to the south. In that case half of it lies within three miles where the majority of foraging will accour. another two miles fall beyond three miles but within 5 miles. The last mile falls beyond the 5 mile mark and is a net loss to the colony.
The rough net result will be a band of available forage 6 miles wide and 3 miles deep form the hive for a forage area of 18 square miles. potential range of 30 square miles and 6 square miles they will forage but will actually reduce the overall increase to the colony.
This 18 square miles is in comparison to the 36 square miles a hive would have if forage was in every direction for three miles.
The actual forage range fora circle with a radius of 3 miles is about 28 square miles. if half of that circle lies only to the south it makes a forage range of 14 square miles.
Now in reality the situation would be even worse in the case of a progressive bloom. because as the bloom was moving up from the south for example. there will be days that all of it lays beyond that 5 mile mark. days that it lies partially within that 5 mile mark and days that it completely surrounds the hive. unlike the flat land bloom that surrounds the hive in every direction every day.
I then see that there could be one day of negative benefit foraging. one day of partially beneficial foraging of which is cancelled by the one day of loosing. and one day of beneficial foraging for three days of bloom. the flat land hive has 3 full days of beneficial foraging. As the bloom moves north you will have the same effect in reverse. for two days of beneficial forage out of 6.