It's often stated that concave bottoms stiffen a board, but it seems clear that if a given board has volume removed to create a concave ( either deck or bottom as in #2 , or deck and bottom as in figure #3 ) that this will increase flex rather than decreasing it.If on the other hand the entire board is bent with the volume maintained to create either a domed deck and concave bottom or domed bottom and concave deck as in #4, then flex will be decreasedThe drawing shows four cross sections with the same maximum thickness, but not necessarily the same cross sectional area
The usual myth is that the concave represented by #2 will be stiffer than #1 which has no concave.The bent card theory ( i.e. the example where a card bent into for example a cylinder will be stiffer than one lying flat ) is often used in attempts to lend support to this myth, however the bent card example is equivalent to drawing #4 which is in fact a stiffer cross section. Bending the card acrossways is equivalent to bending the entire board crossways as in #4 but is not equivalent to hollowing out the bottom and bending the bottom skin only.When people put forward the theory that concave makes the board stiffer they are not usually talking about bending the entire board into a concave as in #4 but rather shaping away some of the bottom as #2, a process which makes the board more flexible !I thought that it would be a good idea to clear this matter up because 'concave makes the board less flexible' has been a persistent myth since at least 2004 when it was cultivated on Swaylocks.The reason why shaping away some of the bottom to make a concave makes a board more flexible is because it makes the board effectively thinner.. . .. . and the reason why bending the entire board into a concave makes it stiffer is because it makes the board effectively thicker.For any given skin laminate and core material, the main factor which controls the amount of flex is the effective thickness of the board.Because it's the effective thickness of the board which counts, we can thus safely say the following:1) For a given cross sectional area and a given width, introducing concave or convex will increase board stiffness (increases effective thickness)2) For a surfboard cross section of any given width and thickness, removing cross sectional area in order to create concave will increase surfboard flexibility ( reduces effective thickness)The four drawings I did assumed board cross sections of the same width and maximum thickness, I should have added another set which keeps the same width and cross sectional area but allows the maximum thickness to vary, it's a bit harder to draw though.A short answer is that it all depends
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The usual myth is that the concave represented by #2 will be stiffer than #1 which has no concave.The bent card theory ( i.e. the example where a card bent into for example a cylinder will be stiffer than one lying flat ) is often used in attempts to lend support to this myth, however the bent card example is equivalent to drawing #4 which is in fact a stiffer cross section. Bending the card acrossways is equivalent to bending the entire board crossways as in #4 but is not equivalent to hollowing out the bottom and bending the bottom skin only.When people put forward the theory that concave makes the board stiffer they are not usually talking about bending the entire board into a concave as in #4 but rather shaping away some of the bottom as #2, a process which makes the board more flexible !I thought that it would be a good idea to clear this matter up because 'concave makes the board less flexible' has been a persistent myth since at least 2004 when it was cultivated on Swaylocks.The reason why shaping away some of the bottom to make a concave makes a board more flexible is because it makes the board effectively thinner.. . .. . and the reason why bending the entire board into a concave makes it stiffer is because it makes the board effectively thicker.For any given skin laminate and core material, the main factor which controls the amount of flex is the effective thickness of the board.Because it's the effective thickness of the board which counts, we can thus safely say the following:1) For a given cross sectional area and a given width, introducing concave or convex will increase board stiffness (increases effective thickness)2) For a surfboard cross section of any given width and thickness, removing cross sectional area in order to create concave will increase surfboard flexibility ( reduces effective thickness)The four drawings I did assumed board cross sections of the same width and maximum thickness, I should have added another set which keeps the same width and cross sectional area but allows the maximum thickness to vary, it's a bit harder to draw though.A short answer is that it all depends 
