Bridge & Saddle forces calculator

This calculator models the forces acting on a fixed flattop guitar bridge, separating them into static (constant) and dynamic (vibrational) components.

Static Forces (Full Set of Strings)

These are the constant loads present when the guitar is tuned to pitch. They result from the total string tension and the bridge/saddle geometry.

• Break Angle:

  This is the angle the string makes as it passes over the saddle toward the pin. It is determined by the vertical distance D3 and horizontal distance D2.

• Static Vertical Force:

  This value represents the downward force the string exerts directly on the saddle. This vertical force is compensated by the string anchor (pin/ball-end) that applies an opposite upward force on the bridge assembly. 

• Static Torque (Bridge Rocking Moment):

  This is the effective rotational moment that drives the soundboard and is the key force applied by the bridge. It is calculated from two primary contributions:

  1. The horizontal force component of the string tension acting at the saddle height.

  2. The force couple created by the downward force at the saddle and the opposing upward reaction at the pin anchor, separated by the pin-to-saddle distance.

Because of this, the geometry of the anchor point relative to the saddle directly affects the torque. If two pinned or pinless bridges place the anchor in the same location, their static torque will be the same.

Dynamic Forces (Single-String Estimate)

These are the peak vibrational forces generated when a string is plucked. They are responsible for driving the soundboard and producing sound.

• Peak Transversal Force
  The primary driving force at the fundamental frequency. It results from the changing slope of the vibrating string and depends on the static tension and pluck position.
• Peak Longitudinal Force
  A secondary force at twice the fundamental frequency, caused by the small increase in string tension that occurs when the string stretches during vibration. Its magnitude depends on the string’s longitudinal stiffness and the change in string length produced by the pluck.

Many thank to Michael Kennedy, that contributed with his observations to the refinement of this model.