This partial calculator normalizes a selected signed block coordinate by a selected half-link travel and projects that coordinate by the cosine of an entered angle. It visibly flags selections outside the stated half-travel. It does not calculate valve cutoff, lead, lap, port opening, steam expansion or engine performance.
Stephenson Valve Gear - Selected Link-Coordinate Projection Ledger
Explore a selected signed block coordinate, normalized half-travel, and cosine projection.
Equation Used
- x, L and projection angle are entered values.
- L is positive and defines the stated half-travel.
- Selections with |x| greater than L are preserved and visibly flagged.
- The cosine operation is only a selected coordinate projection.
- Complete valve-gear geometry, events, loads and safety are excluded.
The secondary figure is a selected slot-coordinate ledger, not a valve-gear reconstruction.
Selected link-coordinate ledger
The signed normalized coordinate is x/L. Its magnitude is |x|/L. The selected cosine factor is cos(theta), and the signed projected coordinate is (x/L)cos(theta). If |x| exceeds L, the selected coordinate lies outside the stated half-travel and is flagged rather than clamped.
What the calculator determines
Use it only to inspect the entered coordinate ratios and projection. The slot figure is a coordinate diagram, not a Stephenson valve-gear reconstruction.
Selected relationships
q=x/L; |q|=|x|/L; k=cos(theta); q_p=qk.
Selected-input example
At x=75 mm, L=75 mm and theta=25 degrees, q=1, |q|=1, cos(theta)=0.906308 and projected q is 0.906308.
Not a valve-event model
Eccentric throws and phases, link curvature, eccentric rods, suspension point, die-block geometry, rocker ratio, valve travel, lap, lead, port dimensions, cutoff, compression, release, steam conditions, loads and safety are excluded.
Questions
Is projected coordinate the steam cutoff?
No. Historical and engineering references show that link-block position influences motion, but valve events require the complete gear and valve geometry.
What does outside selected half-travel mean?
It means |x|/L exceeds one for the entered coordinate definition; the calculator does not silently clamp it.
Does the angle represent eccentric advance in a real engine?
It is only an entered projection angle here because the rest of the eccentric and valve geometry is absent.
Authoritative references
- University of Illinois Library: Cylinders, Valves, and Valve Gears — identifies the link block, eccentrics, rods and reversing positions in Stephenson gear.
- Cornell Library: The Modern Steam-Engine — describes intermediate link positions changing valve motion and expansion.
- University of Chicago Library: Steam and Steam Engines — shows that valve motion depends on the full reversing-link and eccentric arrangement.
References & Further Reading
- Wikipedia contributors. Stephenson valve gear. Wikipedia
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