Bridge & Saddle forces calculator

This calculator separates the steady loads present when the guitar is tuned from the dynamic forces generated by a plucked string. It uses a simplified fixed-bridge model in which the speaking strings are parallel to the soundboard and the saddle and string anchor belong to the same bridge assembly.

Static loading — full string set

Break angle
The break angle is set by the vertical drop from the saddle to the string anchor and by their horizontal separation. In the diagram, D1 is the saddle height above the soundboard, D2 is the horizontal saddle-to-anchor distance, and D3 is the anchor height above the soundboard.

Saddle downbearing
The break angle creates a local downward force that keeps the strings seated on the saddle. The calculator estimates it as total string tension multiplied by the sine of the break angle. The string anchor applies an equal opposing vertical component to the bridge assembly, so this value is not a net downward force on the complete bridge or soundboard.

Static bridge moment
For the complete fixed bridge, the forces produced by the string segment between saddle and anchor are equal, opposite and collinear. They affect downbearing, contact conditions and the local stress distribution, but cancel in the global force and moment balance. Under the assumptions of this calculator, the equivalent static bridge moment is therefore total string tension multiplied by saddle height. This steady moment preloads and deforms the soundboard; it does not provide the vibrational energy that produces sound.

Dynamic forces — selected string

When a string is plucked, its changing direction and length generate time-varying forces at the bridge. These dynamic forces transfer part of the energy introduced by the player to the guitar body.

Peak transverse force
This is the estimated maximum force at the bridge in the direction of the pluck, perpendicular to the string axis. It depends on the selected string tension, pluck displacement and pluck position. The real force waveform contains a fundamental and higher harmonics whose relative levels depend strongly on where the string is plucked.

Peak longitudinal force
Plucking slightly increases the total length of the string and therefore its tension. The calculator estimates the maximum resulting tension increase from the string axial rigidity and the geometry of the displaced string. In a simple single-mode interpretation this produces a mean tension increase and a component at twice the fundamental frequency; real string behaviour is more complex.

Static downbearing is necessary to maintain reliable string–saddle contact. The sound-producing energy, however, is transmitted by the time-varying forces. Once stable contact is established, increasing break angle does not itself add vibrational energy.

Many thanks to Michael Kennedy, whose observations contributed to the refinement of this model.