This revision keeps the documented key, wippen, jack, hammer and escapement sequence while limiting calculations to a declared displacement map.
Grand-Piano Declared Travel Explorer
Choose key dip, a declared hammer-to-key travel ratio and a let-off gap. The worksheet reports the resulting prescribed travel positions without claiming to model action dynamics.
Equation Used
- Hammer rest-to-string travel is defined as H=R times total key dip K.
- The jack is prescribed to disengage when the remaining hammer gap equals L.
- After let-off, the displayed hammer completes the final prescribed gap without jack contact.
- The animation is a topological schematic, not a dimensioned reconstruction.
- Force, velocity, energy, friction, compliance, inertia, repetition behavior, tone, regulation and repair are excluded.
Replaces an internally inconsistent velocity formula with a transparent declared displacement map and schematic escapement sequence.
Key motion reaches the hammer through an escapement action
US patent 6232537B1 describes key motion transmitted through a wippen and jack to a hammer knuckle. As the hammer approaches the string, the escapement lets it leave the jack so it can strike and return rather than being held against the string.
The animation shows that sequence schematically. It prescribes positions from a simple travel map and does not solve the actual multibody contacts or dynamics.
A documented grand-action topology
US patent 7342159B2 identifies the familiar grand-action component set: key, wippen, repetition lever, jack and hammer. Smithsonian documentation shows historical action models with key, hammer, escapement, backcheck and string.
This page is for understanding the motion sequence, not regulating, diagnosing or modifying an instrument.
A declared displacement map
Total hammer travel H is defined as declared ratio R times key dip K. Let-off is prescribed when the remaining hammer gap is L, so key travel at let-off is (H-L)/R and remaining key travel is L/R.
The formula is internally consistent because hammer travel is derived from K and R rather than entered independently. It does not predict hammer velocity, force or energy.
A declared travel example
With 10.0 mm total key dip, R=4.7 and a 2.0 mm let-off gap, declared hammer travel is 47.0 mm. Let-off occurs after 9.57 mm of key travel, leaving 0.43 mm of prescribed key travel. The jack-driven portion is 95.7% of hammer travel.
Travel arithmetic is not action dynamics
Peer-reviewed measurements show that piano-action timing depends on dynamic key and hammer motion. A real model needs body inertias, changing lever geometry, unilateral contacts, spring forces, friction and impact.
The former velocity equation was internally inconsistent and even changed form mid-example. Its force, efficiency, tone, dynamic-range, regulation, repair and brand claims are removed.
Grand-piano action worksheet questions
Is R a measured action ratio?
No. It is a declared constant used only for this displacement map.
Does the model predict hammer velocity or tone?
No.
Does the let-off gap specify how to regulate a piano?
No.
Why show the jack moving aside?
That illustrates the documented escapement function: the hammer leaves jack contact before the string.
Grand-piano action references
- US patent 6232537B1: key, wippen, jack, hammer knuckle and escapement sequence.
- US patent 7342159B2: modern grand-action component topology.
- Smithsonian, Early Pianos: museum action model and escapement description.
- Goebl, Bresin and Galembo, JASA 2005: measured temporal behavior of grand-piano actions.
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