String tension exerts a downward force on the bridge and top of a stringed musical instrument with a floating bridge and tailpiece, such as violin family instruments, archtop guitars, and mandolins. The downforce exerted is a function of the tension of the strings and the angle at which the strings break over the bridge. This angle is referred to (naturally enough) as the breakover angle. The formula for calculating downforce is given below.
Last updated: Tuesday, September 11, 2018
The formula for determining downforce on the bridge is:
This formula is an application-specific variant of the more general formula used to calculate the resultant of two concurrent forces.
Note that tension can be in any units you like and downforce will be in the same units. If you are using the calculator to figure out the total downforce on the bridge of an instrument be sure to add the string tension values from all the strings and use that value. Note also that the equation makes use of a function sin() which expects its argument in radians. If you intend to use this equation to calculate "by hand" or using a handheld calculator, be sure the sin() function you use expects radians. Of course, you can use the calculator above without having to worry about any of this.
Information on string tension of various types and sizes of strings is available from D'Addario Strings in their catalog. The breakover angle is measured as per the following diagram of the side view of the bridge of a bass viol.
It can be seen that the bigger the breakover angle the more downforce is exerted on the bridge and top. Violin family instruments have particularly big breakover angles and exert considerable force on the bridge and top.