January 25, 2014 - 8:23am
How do I scale up from a 9in springform to a 10 inch?
I have a tart recipe that fits beautifully in a 9 inch springform pan but I want to make a larger tart in a 10 inch pan.
Is there a formula for doing this? Add so much percentage for every inch? Is it a volume calculation? Scale everything up by 10%?
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if the area of a circle is pi x radius squared then
9" pan is = 3.14 x 4.5 squared = 63.585
10" pan is = 3.15 x 5 squared = 78.5
Then I divide the 63.585 by 78.5 = .81 or 81%
So it looks like an increase of 19% would be the increased area of the larger circle.
What kinda tart is it?
Happy Baking
Josh
Going down from a diameter of 10 to one with 9 would be a decrease of 19% I agree.
But going up from 9 to 10 would be an increase of 23,5%. (19% / .81 = 23,45...%)
Your calculation is wrong. If you increase 63.585 by 19 % you'd get 63.585 * 1.19 = 75.66. You need to divide the other way around, 78.5 / 63.585 = 1.235 (approx), which tells you that you would need to increase the amount by roughly 23.5%.
And anyways one must account for the edge of the tart. Let us differentiate the dough that is used in a tart into two parts:
D (dough) = B (base) + E (edge), s.t. 0 < E < B < D
We assume uniform thickness of dough. We have already calculated that the base portion needs to be increased by 23.5 %. Suppose the edge is of height H, in inches, in that case the edges will need, for the 9 inch tart, 9pi*H sq. in. and for the 10 inch tart, 10pi*H sq. in. of dough, which yields a ratio of 10 / 9 = 1.(1), so there is only an 11% increase needed for the edge.
Now comes the difficult part: without knowing what part of the dough goes into the edge of the tart and what part is the base, it is impossible to conceive of how much to increase the dough. Let us make a reasonable assumption, suppose that:
B = 0.8D, E = 0.2D. In such a case, the new amount of dough will be 0.8 * 1.235 + 0.2 * 1.(1) = 1.21 (approx) times larger than the last one.
So I recommend a 21% increase.
10^2 / 9^2 = 1,234567... (what a cool number!)
This would be an increase of about 23,5%.
I did consider that the increase would be more for the filling than the crust but that would just take some tinkering I suppose. Anyhow thanks for addressing the backwards math. I actually thought of it in bakers percentage and just called the 78.5 the (100%) and divided the 63.585 by it to determine its percentage. Which was 81. Hence my 19% outcome. Wrong math. But it was certainly close enough to Work.
Josh
I assumed a uniform increase as I would want the same proportions throughout. It doesn't fill a springform- it is about 1-2inches tall.
This is a very nice Jam Tart that has a cookie-dough-like base and cover and a thin jam filling. I make it with all kinds of fillings. The last was sliced mango and peach preserves. Delicious! Enjoy the recipe-as you can see I haven't fully converted to weights, yet but am in the process.
Easy Jam Tart
Adapted from Ready for Dessert 9 in springform 375F preheated oven Bake 25-30 minutes Make ahead
Excellent! Not too sweet-not quite a pie-more like a soft cookie with some cornmeal crunch
INGREDIENT
WEIGHT (GRAMS)
VOLUME (CUPS)
All Purpose Flour
210 g
1 ½ cup
Stone Ground cornmeal
70g
½ cup
If you don’t like the crunch of the cornmeal, just sub flour.
Baking Powder
2 tsp
Salt
½ tsp
Unsalted Butter
130g
4 ½ ounces
Room Temp
Sugar
100g
½ cup
Egg
1 large
Egg Yolk
1
Almond Extract
½ tsp
Dough Weight 590g
In a small bowl, whisk together the flour, cornmeal, baking powder and salt.
In a mixer or food processor, mix the butter and 1/2 cup (100 grams) sugar together until smooth. Add the egg, egg yolk (keep the egg white from the second egg on hand for later) and almond extract and beat until combined.
Gradually add the flour mixture and mix until the dough just comes together. Consistency of a soft cookie dough.
Transfer about one-third of the dough (About 220g) to a piece of wax paper and shape it into a log about 1 -1 1/2 inches (5 cm) in diameter. Refrigerate/freeze it until needed.
Transfer the remaining dough to a buttered 9-inch (23-cm) tart pan with a removable bottom or a 9-inch (23-cm) springform pan.
Using your buttered hands, press the dough evenly into the bottom.
If using a tart pan, press the dough up the sides to the rim of the pan and set the tart pan on a baking sheet.
If using a springform pan, press the dough 3/4-inch (2-cm) up the sides of the pan.
Refrigerate/freeze the dough-lined pan until firm, at least one hour.
Jam or Marmalade
450g
1 1/3-1 ¾ c
Any flavor-lesser amt works well
Egg white for glazing
1 egg white
Whisk egg white with 1 tsp water and brush over top of tart dough for sheen
Water (for egg white glaze)
1 tsp
Whisk lightly into egg white
Sugar-white or coarse
2 tbsp
Sprinkle over egg-washed top
Preheat the oven to 375°F (190°C).
To assemble rest of tart:
Spread the jam or marmalade evenly over the dough in the pan.
Cut the chilled dough into very thin discs (1/8 in) with a sharp paring knife. Arrange them slightly overlapped in concentric circles over the jam to form a top crust. Start at the outside and work into center. A hole in the center is ok. Make sure you lay them a bit over the crust edges so there is no leakage of filling. When the first row is around-then lightly press the crust edge down to be even with the petal edge.
Egg wash and sprinkle with sugar.
Bake until the top crust is golden brown, about 25 minutes. Let cool completely.
Do ahead: This tart keeps beautifully for up to 3 days if well-wrapped at room temperature. David says that it’s pretty sturdy, so perfect to take along on a picnic.
Gooseberry sauce/jam (strained of seeds) was excellent. Not too sweet!
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and the inverse of .81 is 1.23456790. Ha! or you need 123% of what you had so multiple ingredients by same for larger...
Since I usually do not use the egg white wash, I believe I will just add 2 whole eggs and add a smidge (5g?0 more butter to compensate for the slightly less fat in the ratios. It should work fine.
Thanks everyone!