Scaling

[Gobae]

Generally speaking are there any issues with scaling down a recipe? I've got a 2 gal brie recipe that I'd like to make using a 1 gal milk because I really don't have the room to work with 2 gal at a time. If I do this should the mold size also be scaled down also?

Thanks!

[OzzieCheese]

It should be a linear relationship.. half the milk = half the molds

-- Mal

[Gregore]

Ageing is where you might run into problems if it is a harder cheese that needs longer ageing, as it could dry out more  than one would like .

Younger  moister cheeses tend to not be aged very long anyways

[awakephd]

With many cheeses, form factor is an important issue -- meaning that you are looking for a cheese that has a certain ratio of height to diameter. This is particularly important with a mold-ripened cheese like a brie -- get the cheese too tall, and it won't ripen evenly.

As Mal says, if your 2 gallon make is intended for multiple molds -- let's say 4 molds -- then cut the number of molds in half, e.g. 2 molds. That would be likely if you were doing a camembert recipe. But if your 2 gallon brie recipe is intended for just one mold, you will need to reduce the size of the mold proportionately. Do not simply reduce the diameter by half. To keep exactly the same proportions, the math gets a bit complicated, and if you're interested in the gory details, I have put them below -- as best I understand them! But here's a quick example: If you are going from a 6" diameter mold for 2 gallons, you'd need about a 4.75" diameter mold for 1 gallon.

Here's the math -- be warned that I am not entirely sure about some of this:

area of the surface of the curd = pi * radius ^ 2
volume of curd = height x area
desired proportion of the cheese = diameter / height (I think -- or would it be area / height??)

So the generic formula for the volume of a cheese where there is a desired proportion of diameter to height is as follows:

volume = v
diameter = d
height = h
p = desired proportion = diameter / height, so p = d / h
h = d / p                                              <--- solve for h

v = h * pi * (d/2)^2                            <--- volume of a cylinder
v = (d/p) * pi * (d/2)^2                      <--- substitute for the height using the formula above
v = pi * (d^3)/(4p)                             <--- simplify; this is the generic formula for the volume of a cheese where p = diameter / height

To calculate the change in diameter when changing volume by a target amount:

Let the initial volume be v1, with a diameter d1; using the generic formula above, v1 = pi * (d1^3)/(4p)
Let the target volume be v2, with a diameter d2; using the generic formula above, v2 = pi * (d2^3)/(4p)
Let the change in volume be c, so that v2 = c * v1

v2 = c * v1                                                       <--- desired change in volume
pi * (d2^3)/(4p) = c * pi * (d1^3)/(4p)         <--- substitute for v2 and v1 using the generic formula generated above
(d2^3) = c * (d1^3)                                       <--- simplify by crossing out pi and (4p) on both sides
d2 = cube-root(c) * d1                                    <--- take the cube root of both sides

So, at last, here is the general formula:

Target diameter = cube-root(change in volume) * initial diameter

Testing with our example above, starting with an initial diameter of 6", desiring to reduce the volume by 1/2:

target diameter = cube-root(1/2) * 6 = 4.76

Simple, right? 

After all that, let me say that I never actually go through any of this calculation when I am adjusting the size of a recipe; instead I use the TLAR method ... That Looks About Right. After all, I only have a certain set of molds, so I'm looking for one that is approximately right, not one that is exactly right. And if the cheese doesn't come out right, I make appropriate adjustments the next time I make it!