Exact Quilt Fill Quantity

[Peter McDonough]

Here is a way to find out the exact quantity of down needed to fill a quilt. The formulation shown below is good for a 2 inch thick layer revolved around a 2 foot radius.

The basic idea is to determine the area between the two lines I used to construct a basic quilt shape and revolve that area halfway around the x-axis.

QUILT EQUATIONS
Foot:
y=x^(.5)+1
y=x^(.5)+1.167

Body:
y=0.0283x+1.83
y=0.283x+2

Area/Volume Calcuation
(S will be used as integral sign)

Volume =
=(3.14/2) { S (x^(.5)+1.167)^2-(x^(.5)+1)^2 + S (0.283x+2)^2-(0.0283x+1.83)^2}

The first integral is evaluated from 0 to 0.723 and the second is from 0.723 to 6.

Volume = (3.14/2)(0.3985 + 3.60654) = 6.29109 ft^2

Fill Calculation

6.29109(12^3) = 10871 cubic inches

10871 / 800 = 13.6 oz

It should be simple to replace thickness layer with another thickness(like 1 inch or 1.5 inches), or to make the sleeping bag longer or shorter than 6 feet(just change the linear slope so that it intersects that point).

I hope this is useful for you guys.

[Author]

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