Power Ontology

# Power Ontology — Flow Algebra

URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/mechanical-measurements/power-ontology.html

FLOW PowerOntology {

  DOMAIN:
    Mathematical Ontologies
    -> Measurement & Units Ontologies
    -> Mechanical Measurements
    -> Power Ontology

  PURPOSE:
    Represent power as a measurable scalar physical quantity describing the rate at which energy is transferred, transformed, consumed, generated, or work is performed with respect to time, including mechanical and rotational power, instantaneous and average power, units, dimensional structure, efficiency, measurement conditions, uncertainty, and relationships to energy, work, force, velocity, torque and angular velocity.

  ENTITY Power {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: P
    DIMENSION: M * L^2 * T^-3
    SI_UNIT: watt
    SI_SYMBOL: W

    DEFINITION:
      power := rate_of_change(Energy, Time)

    INSTANTANEOUS_FORM:
      P = dE/dt

    WORK_FORM:
      P = dW/dt

    AVERAGE_FORM:
      P_avg = delta_E / delta_t

    PROPERTIES:
      is_scalar
      has_value
      has_unit
      has_dimension
      may_be_positive
      may_be_negative
      may_be_zero
      may_vary_with_time
      may_be_input_or_output
      may_have_uncertainty
  }

  ENTITY Energy {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: E
    DIMENSION: M * L^2 * T^-2
    SI_UNIT: joule
    SI_SYMBOL: J

    RELATION:
      derivative(Energy, Time) -> Power
  }

  ENTITY Work {
    TYPE: EnergyTransferQuantity
    SYMBOL: W_work
    DIMENSION: M * L^2 * T^-2
    SI_UNIT: joule
    SI_SYMBOL: J

    RELATION:
      derivative(Work, Time) -> Power
  }

  ENTITY Time {
    TYPE: BasePhysicalQuantity
    SYMBOL: t
    DIMENSION: T
    SI_UNIT: second
    SI_SYMBOL: s
  }

  ENTITY Force {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: F
    DIMENSION: M * L * T^-2

    RELATION:
      Force dot Velocity -> MechanicalPower
  }

  ENTITY Velocity {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: v
    DIMENSION: L * T^-1

    RELATION:
      Force dot Velocity -> MechanicalPower
  }

  ENTITY Torque {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: tau
    DIMENSION: M * L^2 * T^-2

    RELATION:
      Torque dot AngularVelocity -> RotationalPower
  }

  ENTITY AngularVelocity {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: omega
    DIMENSION: T^-1

    RELATION:
      Torque dot AngularVelocity -> RotationalPower
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: watt
      symbol: W

      equivalence:
        1 W = 1 J/s
        1 W = 1 kg*m^2/s^3
    }

    COMMON_ALTERNATIVES {
      milliwatt
      kilowatt
      megawatt
      gigawatt
      horsepower
      metric_horsepower
      foot_pound_force_per_second
    }

    CONVERSION_RULE:
      power_value(target_unit)
        = power_value(source_unit)
        * conversion_factor(source_unit, target_unit)
  }

  CLASSIFICATION {
    by_time_behaviour:
      instantaneous_power
      average_power
      constant_power
      variable_power
      peak_power

    by_mechanical_context:
      translational_mechanical_power
      rotational_mechanical_power
      shaft_power

    broader_context:
      electrical_power
      thermal_power
      optical_power
      acoustic_power

    by_system_role:
      input_power
      output_power
      generated_power
      consumed_power
      dissipated_power
  }

  RELATIONSHIPS {
    Power -> RATE_OF_CHANGE_OF -> Energy
    Power -> RATE_OF_WORK -> Work
    Power -> HAS_DIMENSION -> M*L^2*T^-3
    Power -> MEASURED_IN -> Watt
    MechanicalPower -> DOT_PRODUCT_OF -> Force
    MechanicalPower -> DOT_PRODUCT_OF -> Velocity
    RotationalPower -> DOT_PRODUCT_OF -> Torque
    RotationalPower -> DOT_PRODUCT_OF -> AngularVelocity
    EnergyTransfer -> INTEGRAL_OF -> PowerOverTime
    Efficiency -> RELATES -> OutputPower
    Efficiency -> RELATES -> InputPower
  }

  SEMANTIC_EQUIVALENCE {
    "watt" ~= "W"
    "joule per second" ~= "J/s"
    "rate of energy transfer" ~= power
    "rate of doing work" ~= power
    power != energy
    power != work
    power != force
    power != torque
    power != efficiency
  }

  AVERAGE_INSTANTANEOUS_MODEL {
    AVERAGE_POWER:
      P_avg = delta_E / delta_t
      WHEN delta_t != 0

    INSTANTANEOUS_POWER:
      P = dE/dt

    RULE:
      average_power_over_interval
      NEED_NOT equal instantaneous_power_at_each_time
  }

  TRANSLATIONAL_MECHANICAL_POWER_MODEL {
    GENERAL_FORM:
      P = F dot v

    MAGNITUDE_FORM:
      P = F*v*cos(theta)

    PARALLEL_CASE:
      P = F*v

    PERPENDICULAR_CASE:
      P = 0

    CONDITIONS:
      force_and_velocity_evaluated_at_relevant_point_and_time
  }

  ROTATIONAL_POWER_MODEL {
    GENERAL_FORM:
      P = tau dot omega

    COLLINEAR_AXIS_CASE:
      P = tau*omega

    CONDITIONS:
      torque_and_angular_velocity_referenced_consistently
  }

  ENERGY_INTEGRATION_MODEL {
    GENERAL:
      delta_E = integral(P, dt)

    CONSTANT_POWER:
      delta_E = P * delta_t

    RULE:
      signed_power_integral determines_signed_energy_transfer
      under_consistent_sign_convention
  }

  EFFICIENCY_MODEL {
    DEFINITION:
      efficiency = useful_output_power / input_power

    SYMBOL:
      eta

    CONSTRAINT:
      input_power != 0

    IDEAL_BOUNDED_CASE:
      0 <= eta <= 1

    NOTE:
      system_definition_and_energy_accounting_scope
      MUST be specified for meaningful efficiency comparison
  }

  SIGN_CONVENTION_MODEL {
    positive_power:
      energy_transfer_direction_defined_as_positive_by_system_convention

    negative_power:
      energy_transfer_opposite_to_defined_positive_direction

    RULE:
      sign_interpretation REQUIRES explicit_or_inferable_system_convention
  }

  CONSTRAINTS {
    power_is_scalar_quantity = true
    dimensional_formula = M*L^2*T^-3
    SI_unit = W
    average_power_requires_nonzero_time_interval = true
    power_and_energy_are_not_semantically_equivalent = true
    power_and_work_are_not_semantically_equivalent = true
    efficiency_is_dimensionless_and_not_power = true
    mechanical_power_requires_consistent_force_velocity_geometry = true
    rotational_power_requires_consistent_torque_angular_velocity_reference = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE:
      Power

    DIRECT_OR_INSTRUMENTAL_MEASUREMENT:
      power_meter
      dynamometer
      wattmeter
      calibrated_power_sensor

    INDIRECT_MEASUREMENT:
      energy_change_over_time
      work_over_time
      force_dot_velocity
      torque_dot_angular_velocity
      electrical_voltage_current_model_when_applicable

    RECORD:
      numerical_value
      unit
      power_type
      input_or_output_role
      timestamp
      averaging_interval
      system_boundary
      sign_convention
      measurement_method
      instrument
      calibration_state
      uncertainty
      environmental_conditions

    UNCERTAINTY:
      measured_or_inferred_power = best_estimate +/- uncertainty
  }

  REASONING_RULES {
    IF energy_change_known AND time_interval_known AND time_interval != 0
      THEN average_power = energy_change / time_interval

    IF energy_function_known
      THEN instantaneous_power = derivative(energy, time)

    IF power_function_known_over_interval
      THEN energy_transfer = integral(power, time)

    IF constant_power AND time_interval_known
      THEN energy_transfer = power * time_interval

    IF force_vector_known AND velocity_vector_known
      THEN mechanical_power = dot_product(force, velocity)

    IF torque_vector_known AND angular_velocity_vector_known
      THEN rotational_power = dot_product(torque, angular_velocity)

    IF input_power_known AND useful_output_power_known AND input_power != 0
      THEN efficiency = useful_output_power / input_power

    IF force_perpendicular_to_velocity
      THEN translational_mechanical_power = 0

    IF torque_perpendicular_to_angular_velocity
      THEN rotational_power = 0
  }

  SYSTEM_BOUNDARY_MODEL {
    REQUIRE:
      define_system
      identify_input_power
      identify_output_power
      identify_losses_or_dissipation
      identify_sign_convention

    BALANCE:
      rate_of_system_energy_change
        = total_input_power - total_output_power
      UNDER defined_accounting_convention

    RULE:
      power_balance MUST preserve system_boundary_and_direction_semantics
  }

  TIME_MODEL {
    instantaneous:
      evaluated_at_specific_time

    average:
      evaluated_over_defined_interval

    sampled_measurement:
      includes_sampling_rate_or_averaging_window_when_relevant

    RULE:
      peak_power, average_power and instantaneous_power
      MUST_NOT be treated_as_interchangeable
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    SI_unit_confidence: 1.00
    energy_rate_relationship_confidence: 1.00
    mechanical_relationship_confidence: 0.99
    measurement_context_confidence: 0.98

    RULE:
      confidence decreases when power type, unit, time interval,
      system boundary, sign convention, measurement method,
      calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK time_interval_nonzero_for_average_power
    CHECK instantaneous_vs_average_semantics
    CHECK system_boundary_for_power_balance
    CHECK sign_convention
    CHECK force_velocity_geometry_for_mechanical_power
    CHECK torque_angular_velocity_reference_for_rotational_power
    CHECK efficiency_denominator_nonzero
    CHECK instrument_calibration_when_measured
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      identify_power_type
      identify_time_or_averaging_interval
      identify_system_boundary
      identify_sign_convention
      normalize_to_canonical_unit
      preserve_original_value_and_unit
      attach_timestamp
      attach_uncertainty
      update_power_state

    ON energy_transfer_event:
      record_initial_energy
      record_power_history
      integrate_power_over_time
      update_final_energy
      preserve_event_provenance

    ON input_output_change:
      update_input_power
      update_output_power
      update_loss_terms
      recompute_efficiency_when_valid
      update_system_power_balance

    ON revised_calibration:
      preserve_provenance
      recompute_affected_measurements
      update_confidence

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_entity: Power
    canonical_symbol: P
    canonical_dimension: M*L^2*T^-3
    canonical_SI_unit: W

    interpretation_order:
      identify_quantity
      identify_power_type
      identify_value
      identify_unit
      identify_instantaneous_or_average_context
      identify_time_interval
      identify_system_boundary
      identify_input_output_role
      identify_sign_convention
      identify_force_velocity_or_torque_angular_velocity_context
      identify_measurement_method
      identify_uncertainty
      validate_dimensions
      infer_energy_transfer_relationships

    ambiguity_controls:
      distinguish_power_from_energy
      distinguish_power_from_work
      distinguish_power_from_force
      distinguish_power_from_torque
      distinguish_power_from_efficiency
      distinguish_instantaneous_from_average_power
      distinguish_peak_from_continuous_power
      distinguish_input_from_output_power
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_mechanical_quantity_semantics

    parent_path:
      Ontologies
      -> Mathematical Ontologies
      -> Measurement & Units Ontologies
      -> Mechanical Measurements
      -> Power Ontology

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      dimensions
      units
      relationships
      constraints
      average_instantaneous_model
      translational_mechanical_power_model
      rotational_power_model
      energy_integration_model
      efficiency_model
      system_boundary_model
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      relationship_model_changes
      power_model_changes
      system_boundary_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW