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If I did my calculations right, the following chart provides the approximate weight of various sizes of smoothbore octagonal steel barrels in pounds per inch of barrel length. (A barrel with a rifled bore would weigh slightly less.) To convert pounds to kilograms, multiply pounds by 0.4535924.
The chart is best viewed on a computer monitor. Example calculations are included below the chart.
Example calculations
The following equation was used for calculating the octagonal area, where G4 is one half of the octagonal barrel size across the flats and 0.4142136 is the tangent of 22.5 degrees: =(0.4142136*G4)*G4*8
The following equation was used for calculating barrel weight per inch of barrel length, where G$5 is the octagonal area, F9 is the bore diameter, and 0.2836 is the weight per cubic inch of steel: =(G$5-((F9/2)^2*PI()))*0.2836