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For beehive inner covers, canvas is becoming a more popular choice. While we are not beekeepers or authorities on the subject, a bit of research has shown that one of the reasons for choosing natural canvas is its breathability. We've heard that proper ventilation of the inner cover is important to allow evaporating water to escape and help prevent mildew.
Traditionally it seems that the most common inner cover material is wood, but recently we've had more and more beekeepers order our heavier canvas to make the hive's inner cover. #8 canvas in natural cotton has been recommended, but you may find that #6 or even #4 will work equally well. A general note on "numbered" duck canvas: The lower the number, the heavier, thicker and more rigid the material.