Figuring Out Package Growth

[Papakeith]

While I was basking in my bee's apparent successes, I started doing some basic calculations on the potential growth of these new packages. 

10 frames of drawn comb and supplies and add a package of bees.
Queen laying ~1k per day and estimating ~3k cells per frame available for laying.  Then I took 10 frames (OK call it 8 just to round down) and you have a possible 24000 cells for brood which should take the queen 24 days to lay in all cells in a perfect world. 
Anything she laid since being released needs 21 days to emerge and another 18 or so to begin foraging.  So her first brood to start gathering won't do so until sometime in early June.  From that point the hive population and foraging power should grow exponentially until mid August where historically we are in a dearth and the queen stops or dramatically slows egg laying for a bit.

Taking the numbers above as gospel I applied the same numbers to the split that I made a few weeks ago.
For this split I need to figure out When to add the second deep(also drawn comb). 
Yeah, I could just look at them and see what is what; but I 'm having fun with this exercise.

split on 4/19  approx 2 frames of bees and brood (all stages) and added a mated queen.  For simplicity I'll say 2k capped brood, 2k larvae and 2k eggs.
Took 1 week for her to be let out (time constraints on my part and bees that were not interested I guess.)  In any event she was out on the 26th 
so, I'm saying 24k cells available total, but starting with 6k already laid and in various stages of growth which leaves her initially with 16,000 cells to lay in which should take her two weeks give or take. 
Capped brood should have been out on the 2nd week or may 3 with all of the other brood that came over with the split following.  At some point there will be a break ,1 week or so, in the brood cycle accounting for the new queen setting up shop.
Not counting any foragers that came over with the split, new foragers should be coming on line right around the 24th of may with more following

All of this is based on having enough bees to cover whatever brood is laid.

I guess the real question is ; How many bees does it take to cover a frame of brood? because that number will probably do more to dictate the growth rate than most any other factor.

[LazyBkpr]

From what I have read, it takes one bee to cover two to three cells.
   Doing the math is a little difficult, because ALL of those cells will not be available. they will have honey around the outside (or nectar) and pollen in a ring just inside the honey, with the circular brood inside the pollen, so you can figure a third less cells for her to lay in..   That is in the center frames of the brood chamber..  typically I see smaller brood areas as I move outward from the center, with more honey around the edges, but about the same amount of pollen around the brood area...     To make this worse.. sometimes the bees dont follow convention..  I have seen seven frames packed wall to wall with brood..  I have also seen three frames with a soccer ball size brood chamber while the bees fill the rest of the frames with nectar and pollen...
   If you want those ladies to do something a specific way, you have to stick your nose in the hive and DEMAND they do exactly the opposite of what you want...      Hey, it works with my wife!

[Papakeith]

  If you want those ladies to do something a specific way, you have to stick your nose in the hive and DEMAND they do exactly the opposite of what you want...      Hey, it works with my wife!

 

[riverbee]

after all the math there pk.....
"I guess the real question is ; How many bees does it take to cover a frame of brood? because that number will probably do more to dictate the growth rate than most any other factor."

i don't really count bees, i count frames of bees, and as long as bees and then some are covering the frames will tell you in part how well your queens/packages are doing and coming along.  i have read estimations of how many bees are on a frame of brood.  dave cushman has a good web page on this with pictures and estimation:

Estimation of Bees on a Frame

gee, i really thought shinjack had it bad.......
hello, my name is papakeith and i DO HAVE a bee problem.........

[Papakeith]

No problem here, just some idle thoughts put to paper.

[Papakeith]

nice visual link River... Thanks

[riverbee]

hey you are welcome pk, it is a good visual.
when some of you guys get all mathematical, makes my head spin......but then i am not a math person.......

[Papakeith]

  just a scary peek inside my thought processes.  I tend to (over) analyze stuff to death. . . then I end up doing what "feels" right.

[blueblood]

I think I am leaking brain fluid after all that math....

[Zweefer]

it takes fluid?!?!?  there's my problem.  I don't think I've ever topped off... 

[LazyBkpr]

it takes fluid?!?!?  there's my problem.  I don't think I've ever topped off... 

 Yeah, same here, I was wondering what that grinding sound was......  and the smoke.....

[iddee]

Mine must be draining, too. My socks are wet.

[riverbee]

...........

[Papakeith]

Well almost 24 hours later and after adding fluid. I remembered what started my thought process.  I have drawn comb deeps for all of the packages and splits I've started so far.  I was aiming to figure out when would be appropriate to throw the second deep on.  I figured it would be a bit quicker than with a package on foundation because they didn't have to draw out the comb before the queen started laying.  But then I got thinking about bees necessary to cover/feed the brood.  Then there is having extra space that might give rise to homes for SHB. So that got me trying to calculate the growth of bees .  On the way to that I confirmed that I prefer smooth over crunchy peanut butter.

[LazyBkpr]

WOW!!!  I have not done that yet, it should be one of my priorities. One of those things that bothers you in the middle of the night until you get it figured out... Crunchy or creamy....     

   I try to start my splits/packages etc...  with 4 drawn frames in their box, (mediums) and two drawn frames centered in the box above them.   Room for the queen, room for some stores, and expansion room. They usually rapidly grow and build comb from there. I have started them with mostly drawn comb, but found that expansion was not exceeded by growth in the 2 over 4 set up.
   I figured wax moth would have their way with the extra comb, so tossed all of it into the last split. I noticed very little difference in the size of that colony compared to those that started with the 2x4.   My thoughts are that as the queen lays, and the first of the brood emerges the bees are capable of keeping up with demand.
   We dont have much problem with hive beetles, (yet) but wax moth are of great concern, so it is conceivable that the wax moth could inhabit a far corner while the bees build..  Just how I do it, by guess or by golly as long as it works!

[riverbee]

pk, you have an advantage with the drawn comb, so in general,  i would add the 2nd deep when the 1st deep is 60 - 70 % full of bees and brood, so if you are using 10 frames, when you see 6 to 8 frames packed full of bees and brood, and before the queen runs out of laying space. this will also vary with each individual package and queen, as to how quickly they build up.   i don't have problems with wax moth or shb, so you want to add the 2nd deep when there are enough bees to move up and protect the 2nd deep.

ps i like both, crunchy and smooth pb.....

[Papakeith]

Excellent!
Sounds like I should be looking right at the 3-4 week mark then.  'cause the population can't increase before the first brood start emerging.

[apisbees]

Yes the brood laying area is defined by the population of bees in the hive. I don't count individual bees, but frames of bees. that being said it takes 2000 bees to cover a frame. a 2 lb package covers 4 frames a 3lb covers 6 frames.
As you have said above, the queen lays only where they have a bee population to cover the brood. actually she will lay in less space than the bees will cover as the like to have the cluster surround the brood and the cluster to also be covering some of the honey stores. So a hive will have 2 frames less brood than the what the bee population is covering.
Now the calculation for growth, there are 25 cells per square inch of comb, a bee is 1/4" wide by 1/2" long so it takes 8 bees to cover the one square inch of comb. So that equates A 3 to 1 expansion rate, but then we need to subtract the mortality rate of the old bees. 3 weeks to develop from egg to emerging, 3 weeks as house bees, and another 3 weeks as a forager. this means that as one cycle of brood is developing 1/2 the bees in the hive are dying. Or another way to see it is as a frame of brood emerges 1/3 of the bees go to replace the bees that are\have died so in the growth of the colony 1 good solid frame of brood will produce bees that will cover an additional 2 frames. Count your frames as you do your inspections to calculate the expansion in bee population. All the brood in the hive will emerge with in the next 21 days  but it can be broken down even finer. Capped brood will emerge over the next 12 days and the eggs and open brood the following 9 days. So the growth rate and expansion room of a colony can be calculated in advance so we can have an idea of when more space will need to be added for the expanding bee population. 

[Papakeith]

glad to see I'm not the only one that "maths" this out