A Lippincott planimeter traces a closed diagram with a moving arm and disc. Explore its main parts, then use an indicated area, diagram length and spring scale to calculate mean height and mean effective pressure.
Lippincott Planimeter Ideal Indicator-Diagram Calculator
Enter planimeter-indicated diagram area, diagram length and indicator spring pressure scale. The result is ideal mean height and mean effective pressure; no wheel-slip, arm-bias or calibration correction is assumed.
Equation Used
- A is the indicated closed-diagram area in square inches.
- L is diagram length in inches and S is the indicator spring scale in psi per inch.
- Calibration, zeroing, orientation, repeated traces and instrument condition are outside the model.
The tracer follows a closed loop while the arm and disc illustrate the instrument arrangement. Enter an independently measured diagram area for the calculation; the animation does not measure that area.
Documented Lippincott arrangement
In Hiscox figure 156, R is the stationary point, T is the tracer, c is a smooth round arm carrying a scale, and D is a disc free to move on that scaled arm. The operator traces the closed indicator diagram and reads the instrument according to its calibrated scale.
The animation identifies those parts and follows a schematic loop. Its disc motion is explanatory only; it is not a numerical simulation of the mechanical integration.
Indicator-diagram measurement
Contemporary steam-engine practice used planimeter-indicated area to obtain mean diagram height and mean effective pressure. Actual use requires the correct instrument, scale, zeroing, orientation and tracing procedure.
Ideal diagram arithmetic
A is indicated area, L diagram length and S the indicator spring scale. The equation converts a valid area reading; it does not create or calibrate that reading.
Arithmetic example
For A=8 in², L=4 in and S=50 psi/in, mean height is 2 in and ideal MEP is 100 psi.
Model boundary
No numerical allowance is made for wheel condition, arm geometry, scale error, zero error, paper movement, tracing speed or failure to close the loop. Repeatability and calibration must be assessed from the instrument and method.
Lippincott planimeter questions
Does the animation calculate area from its drawn path?
No. Enter the area indicated by the real or independently modeled measurement.
Are slip and arm-bias corrections available?
No. The calculation assumes a valid indicated area. Instrument error and corrections require calibration and the applicable operating method.
Does MEP equal engine power?
No. Power also requires cylinder geometry, cycle rate and the applicable indicated-power convention.
Primary and contemporary references
- Hiscox, Modern Steam Engineering, The Indicator and Its Work: planimeter area, diagram length and indicator spring-scale method.
- Hiscox, Mechanical Movements, figure 156: R, T, c and D component description.
- US Patent 689,978, A. C. Lippincott: planimeter specification and drawings.
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