For N identical angular windows evenly spaced around one revolution, pitch is 360°/N. Each pitch is covered for min(θ, pitch), so duty is 100 min(θ, pitch)/pitch. If θ reaches or exceeds pitch, coverage is continuous and there is no closed gap.
Ideal Evenly Spaced Rotary-Window Timing
Calculate ideal covered time, closed-gap time, angular duty and window-passage rate for evenly spaced rotor windows.
Equation Used
- Windows are identical and evenly spaced.
- Shaft speed is steady and positive.
- Port opening is represented by ideal angular coverage with zero edge thickness.
- Flow, pressure, leakage, inertia, deformation, wear and ratings are excluded.
If window angle reaches pitch, the ideal port is continuously covered; passage rate then does not represent distinct open-close pulses.
Ideal angular-window model
A rotor carries identical ideal windows at equal angular spacing. Shaft speed sets the time for one revolution, while window angle and count set the angular coverage within each pitch.
When window angle is smaller than pitch, the model has distinct open intervals and closed gaps. When it equals or exceeds pitch, adjacent windows overlap in angle and the ideal port remains continuously covered.
What the calculator determines
Select shaft speed, ideal window angle and number of evenly spaced windows. The calculator reports covered time per pitch, closed-gap time per pitch, total angular duty and window-passage rate.
It does not predict flow, leakage, pressure capacity, torque, shaft power, particle filling, engine breathing, port-edge dynamics, wear or safe operating speed.
Bounded timing identities
Pitch β = 360°/N. Covered angle α = min(θ, β). With revolution period T = 60/RPM, covered time per pitch is αT/360 and closed-gap time is (β − α)T/360. Duty is 100α/β and window-passage rate is RPM × N.
For θ ≥ β, duty is 100% and closed-gap time is zero. The reported covered time is then the continuously covered pitch interval, not a distinct isolated pulse.
Selected-input example
At 15,000 rpm, one 140° window gives a 4.000 ms revolution period, 1.556 ms covered time, 2.444 ms closed time and 38.889% angular duty. The passage rate is 15,000 windows per minute.
These are ideal angular-timing results only and do not establish mass flow, volumetric flow or engine performance.
Scope and correction boundary
The former calculator multiplied window angle by count and capped duty at 100%, but its open- and closed-time labels did not clearly define the overlap case. The corrected model explicitly evaluates coverage and gap within each angular pitch.
Unsupported speed, throughput, pressure, clearance, tolerance, material, product, failure, maintenance and performance claims, the fabricated pellet example and unrelated video are removed.
Questions
Does a larger window always create a longer isolated opening?
No. Once window angle reaches pitch, ideal coverage is continuous and there is no distinct closed interval.
Does passage rate equal an open-close cycle rate?
Only when windows are separated by closed gaps. With overlap, it is simply the geometric rate at which window centers pass the reference port.
Does angular duty determine flow?
No. Flow also depends on port area, pressure difference, fluid or material behavior, geometry, losses and system dynamics.
Is the selected speed a rating?
No. Use manufacturer limits and an application-specific analysis.
Technical references
- OpenStax Physics, Angle of Rotation and Angular Velocity — angular position, angular speed and period relationships.
- NIST Special Publication 811 — SI units and conversion guidance.
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