How heat accelerates spring build up

[Finman]

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How heat accelerates brood rearing.

If we measure the brood area of 10 cm radius, 10 cm x 10 cm x pii 3,14 = 314 cm2

Then if heat add the radius to 15 cm, the area will be 15 cm x 15 cm x pii 3,14 = 707 cm2

So the brood area in one frame is 2,25 bigger.

But the whole brood area is a ball. Lets look the rise of volume of brood area.

4/3*3,14 * pii3 10x10x10 = 4 200

Add 50% more to radius

4/3*3,14 * pii3 15x15x15 = 14 100

The bigger radius has 3,4 fold volume compared to smaller radius.

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[wightbees]

I now know why i should of went to school

 

[rae]

That's just the start of it - the bigger ball is much more efficient as well.

A 10 cm diameter ball has a volume of (4/3) x Pi x 5^3 = 523 cm cubed. It has a surface area of 4 x Pi x 5^2 = 314 cm squared.

If you think of the volume of the sphere as the number of bees - this is equivalent to the amount of "work" a hive can do. The surface area of the sphere is the area over which the ball of bees loses heat.

Scale up the ball to 15CM diameter:

Volume = 1766 cm cubed (more than 3x the volume)
Surface Area = 706 cm squared (~double the surface area)

So the big ball loses twice as much heat, but contains 3x as many bees - so each bee will be more "efficient" than in the small ball.

 

[wilderness]

That's just the start of it - the bigger ball is much more efficient as well.

A 10 cm diameter ball has a volume of (4/3) x Pi x 5^3 = 523 cm cubed. It has a surface area of 4 x Pi x 5^2 = 314 cm squared.

If you think of the volume of the sphere as the number of bees - this is equivalent to the amount of "work" a hive can do. The surface area of the sphere is the area over which the ball of bees loses heat.

Scale up the ball to 15CM diameter:

Volume = 1766 cm cubed (more than 3x the volume)
Surface Area = 706 cm squared (~double the surface area)

So the big ball loses twice as much heat, but contains 3x as many bees - so each bee will be more "efficient" than in the small ball.

so how did those little bees work all that out?

 

[oliver90owner]

Circumference = Pi*D

Area = Pi*D*D/4

Volume = Pi*D*D*D/6

Surface area = Pi*D*D

Where Pi is approx 22/7 and D is the diameter.

I know, I know, at school one always uses radii. But do you know anyone who actually measures a radius (r)? No! It is always the diameter (D) which is actually measured!

Seems just toooo much to understand that D*D/4 is r*r?

Regards, RAB

 

[Finman]

So the big ball loses twice as much heat, but contains 3x as many bees - so each bee will be more "efficient" than in the small ball.

Yes, that is a good calculation. I did not noticed that.

Loosing heat means to consuming food 2 units instead of 3 unists. It means too making 2/3 work.

 

[Hebeegeebee]

Economies of scale.

 

[Finman]

But do you know anyone who actually measures a radius (r)? No! It is always the diameter (D) which is actually measured!

Devide diameter with 2 and you get radius

What happens actually. No one even measure the diameter because it is not needed in beekeeping. We measure them with occupied frames. But many are eager to split weak hives in spring. What you get then?

Weak colonies are not balls. They look bigger than they are. Bees rise up and try to be as high as possible because heat rises up.