eytelwein.horizontal_curves.core.horizontal_curve_calculations module

Public API for horizontal curve calculations with unit handling.

This module provides the public interface for horizontal curve force calculations with comprehensive unit validation and conversion using the Pint unit registry.

eytelwein.horizontal_curves.core.horizontal_curve_calculations.force_component_towards_inside_curve_from_belt_tension(belt_tension: Quantity, idler_spacing: Quantity, horizontal_curve_radius: Quantity, unit: str = 'newton', precision: int = 2) → Quantity[source]

Calculate the force component towards the inside of the curve from belt tension.

This function provides the public API for horizontal curve force calculations with comprehensive unit handling and validation. It implements research-based methodologies for belt conveyor horizontal curve analysis.

The force component is calculated as:

F = T * L / R

Where: - F is the force component towards the curve center - T is the belt tension - L is the idler spacing - R is the horizontal curve radius

Parameters:

  • belt_tension (Quantity) – Belt tension at the location of interest. Must have force dimensions [N].

  • idler_spacing (Quantity) – Distance between consecutive idler sets. Must have length dimensions [m].

  • horizontal_curve_radius (Quantity) – Radius of the horizontal curve. Must have length dimensions [m].

  • unit (str, optional) – The unit for the returned force. Default is “newton”.

  • precision (int, optional) – The number of decimal places for the results. Default is 2.

Returns:

Force component towards the inside of the curve with the specified unit.

Return type:

Quantity

Raises:

  • pint.DimensionalityError – If input quantities do not have the correct dimensions.

  • ValueError – If horizontal_curve_radius is zero or negative. If the output unit is invalid.

Examples

>>> import eytelwein.main.units as u
>>> belt_tension = 5000 * u.ureg.newton
>>> idler_spacing = 1.2 * u.ureg.meter
>>> curve_radius = 50 * u.ureg.meter
>>> force = force_component_towards_inside_curve_from_belt_tension(
...     belt_tension, idler_spacing, curve_radius
... )
>>> print(f"Force towards curve center: {force:.1f}")
Force towards curve center: 120.0 newton

Notes

Sign convention: Positive force indicates direction towards the inside of the curve, following standard mathematical conventions for centripetal forces.

eytelwein.horizontal_curves.core.horizontal_curve_calculations.force_component_towards_inside_curve_from_belt_tension_sections(belt_tensions: Quantity | ndarray, idler_spacings: Quantity | ndarray, horizontal_curve_radii: Quantity | ndarray, unit: str = 'newton', precision: int = 2) → Quantity[source]

Calculate force components towards the inside of curves for multiple conveyor sections.

This function computes the force components based on belt tensions, idler spacings, and horizontal curve radii for multiple sections using research-based methodologies, with vectorized calculations for performance.

The force component is calculated as:

F = T * L / R

Where: - F is the force component towards the curve center - T is the belt tension - L is the idler spacing - R is the horizontal curve radius

Parameters:

  • belt_tensions (Quantity or np.ndarray) – The belt tensions for each section (typically in newtons). Can be a single Quantity or a numpy array of Quantities.

  • idler_spacings (Quantity or np.ndarray) – The idler spacings for each section (typically in meters). Can be a single value applied to all sections or section-specific values.

  • horizontal_curve_radii (Quantity or np.ndarray) – The horizontal curve radii for each section (typically in meters). Can be a single value applied to all sections or section-specific values.

  • unit (str, optional) – The unit for the returned force array. Default is “newton”.

  • precision (int, optional) – The number of decimal places for the results. Default is 2.

Returns:

Array of force components towards the inside of curves for each section with the specified unit.

Return type:

Quantity

Raises:

ValueError – If there is an error in converting units. If array dimensions don’t match. If any horizontal curve radii are zero or negative. If the output unit is invalid.

Examples

>>> import eytelwein.main.units as u
>>> import numpy as np
>>> belt_tensions = [3000, 4000, 5000] * u.ureg.newton
>>> idler_spacing = 1.2 * u.ureg.meter
>>> curve_radii = [40, 50, 60] * u.ureg.meter
>>> forces = force_component_towards_inside_curve_from_belt_tension_sections(
...     belt_tensions, idler_spacing, curve_radii
... )
>>> print(f"Forces: {forces:.1f}")
Forces: [90.0 96.0 100.0] newton

Notes

This function supports NumPy broadcasting, allowing for flexible combinations of scalar and array inputs following standard mathematical conventions.

eytelwein.horizontal_curves.core.horizontal_curve_calculations.restraining_force_from_dead_weights(total_force_from_belt: Quantity, total_force_from_material: Quantity, method: str = 'conventional', unit: str = 'newton', precision: int = 2) → Quantity[source]

Calculate the total restraining force from dead weights acting toward the outside curve.

This function provides a unit-aware interface for calculating the combined restraining force that acts toward the outside of horizontal curves due to the dead weights of the belt and conveyed material. This force opposes the centripetal force required for the belt to follow the curved path and must be balanced by appropriate belt tension and guiding forces.

Parameters:

  • total_force_from_belt (Quantity) – Total lateral force component from belt weight acting toward outside curve

  • total_force_from_material (Quantity) – Total lateral force component from material weight acting toward outside curve

  • method (str, optional) – Calculation methodology. Currently supports: - “conventional”: Standard method from Grimmer & Kessler (1987) Teil I - “improved”: Enhanced method from Grimmer & Kessler (1987) Teil II Default is “conventional”.

  • unit (str, optional) – Output unit for the force. Default is “newton”.

  • precision (int, optional) – Number of decimal places for the result. Default is 2.

Returns:

Total restraining force from dead weights acting toward outside curve with specified unit.

Return type:

Quantity

Raises:

ValueError – If input parameters are invalid, method is unknown, or unit conversion fails.

Notes

The calculation combines the lateral force components from belt and material weights that act toward the outside of horizontal curves. These forces arise from the natural tendency of dead weights to move radially outward in curved paths due to inertia.

Mathematical formulation: F_restraining = F_belt + F_material

Where: - F_belt: Total lateral force from belt weight toward outside curve - F_material: Total lateral force from material weight toward outside curve

Physical interpretation: - This force represents the total centrifugal effect of dead weights - Must be balanced by belt tension and guiding forces for stable operation - Positive values indicate force magnitude toward outside curve - Critical for determining required belt tension and curve radius limits

The restraining force is fundamental to horizontal curve design as it determines: 1. Minimum required belt tension to maintain belt path 2. Maximum allowable curve radius for given operating conditions 3. Guiding force requirements for stable belt tracking

Examples

>>> import eytelwein.main.units as u
>>> from eytelwein.horizontal_curves import restraining_force_from_dead_weights
>>>
>>> result = restraining_force_from_dead_weights(
...     total_force_from_belt=450.25 * u.ureg.newton,
...     total_force_from_material=184.77 * u.ureg.newton,
...     method="conventional"
... )
>>> print(f"Total restraining force: {result:.2f}")
Total restraining force: 635.02 newton

References

Grimmer, K.-J. und F. Kessler: Teil I - Traditional calculation approaches. Grimmer, K.-J. und F. Kessler: Teil II - Enhanced calculation procedures.

eytelwein.horizontal_curves.core.horizontal_curve_calculations.restraining_force_from_tilted_idlers(force_component_inside: Quantity, force_component_center: Quantity, force_component_outside: Quantity, method: str = 'conventional', unit: str = 'newton', precision: int = 2) → Quantity[source]

Calculate the restraining force from tilted idlers towards the outside curve.

This function provides a unified interface for calculating the resultant restraining force that acts to guide the belt towards the outside of horizontal curves when idler rolls are suitably tilted. It supports both conventional and improved methodologies with comprehensive unit handling and validation.

Parameters:

  • force_component_inside (Quantity) – Force component acting on the inside wing roll from tilted idler friction [force]

  • force_component_center (Quantity) – Force component acting in the center section from tilted idler friction [force]

  • force_component_outside (Quantity) – Force component acting on the outside wing roll from tilted idler friction [force]

  • method (str, optional) – Calculation methodology: - “conventional”: Standard method from Grimmer & Kessler (1987) Teil I - “improved”: Enhanced method from Grimmer & Kessler (1987) Teil II Default is “conventional”.

  • unit (str, optional) – Output unit for the force. Default is “newton”.

  • precision (int, optional) – Number of decimal places for the result. Default is 2.

Returns:

Net restraining force from tilted idler friction effects with specified unit.

Return type:

Quantity

Raises:

ValueError – If input parameters are invalid, method is unknown, or unit conversion fails.

Notes

This function implements the Method A architectural pattern with method parameter dispatch, providing a unified interface that dispatches to the appropriate private implementation based on the specified method.

The calculation combines force components from tilted idler friction effects following the standard force balance methodology for horizontal curve analysis:

F_net = F_inside + F_center - F_outside

Where the subtraction of the outside component reflects the opposing nature of forces in horizontal curves.

Available calculation methods: 1. Conventional Method (method=”conventional”):

  • Based on Grimmer & Kessler (1987) Teil I

  • Traditional calculation approaches

  1. Improved Method (method=”improved”): - Based on Grimmer & Kessler (1987) Teil II - Enhanced calculation procedures with improvements to conventional methods

Examples

>>> import eytelwein.main.units as u
>>> from eytelwein.horizontal_curves import restraining_force_from_tilted_idlers
>>>
>>> result = restraining_force_from_tilted_idlers(
...     force_component_inside=530.29 * u.ureg.newton,
...     force_component_center=87.49 * u.ureg.newton,
...     force_component_outside=433.01 * u.ureg.newton,
...     method="conventional"
... )
>>> print(f"Net restraining force from tilted idlers: {result:.2f}")
Net restraining force from tilted idlers: 184.77 newton

References

Grimmer, K.-J. und F. Kessler: Teil I - Traditional calculation approaches. Grimmer, K.-J. und F. Kessler: Teil II - Enhanced calculation procedures.

eytelwein.horizontal_curves.core.horizontal_curve_calculations.tilted_idler_friction_force_center(total_weight_force_material: Quantity, inclination_angle: Quantity, belt_width: Quantity, troughing_angle: Quantity, banking_angle: Quantity, belt_width_on_center_wing_roll: Quantity, belt_width_on_inside_wing_roll: Quantity, belt_width_on_outside_wing_roll: Quantity, friction_variation: Quantity, friction_coefficient_tilted_idler: Quantity, normal_force_on_idler_roll: Quantity | None = None, method: str = 'conventional', center_roll_load_factor: Quantity | None = None, unit: str = 'newton', precision: int = 2) → Quantity[source]

Calculate the friction force from conveyed material acting on tilted idlers at the center section.

This function calculates the friction force arising from the interaction between conveyed material and tilted idlers positioned at the center section of a troughed belt conveyor system operating in horizontal curves. The center section calculation uniquely combines effects from all three belt sections (center, inside, outside).

Parameters:

  • total_weight_force_material (Quantity) – Total weight force of the conveyed material

  • inclination_angle (Quantity) – Inclination angle of the belt conveyor

  • belt_width (Quantity) – Total width of the belt

  • troughing_angle (Quantity) – Troughing angle of the belt

  • banking_angle (Quantity) – Banking angle of the belt in the horizontal curve

  • belt_width_on_center_wing_roll (Quantity) – Effective width of the belt supported by the center section

  • belt_width_on_inside_wing_roll (Quantity) – Effective width of the belt supported by the inside wing roll

  • belt_width_on_outside_wing_roll (Quantity) – Effective width of the belt supported by the outside wing roll

  • friction_variation (Quantity) – Friction variation factor (dimensionless)

  • friction_coefficient_tilted_idler (Quantity) – Friction coefficient for material-idler interaction (dimensionless)

  • normal_force_on_idler_roll (Quantity, optional) – Additional normal force acting on the idler roll. Default is 0.0 * u.newton.

  • method (str, optional) – Calculation methodology. Currently supports: - “conventional”: Standard method from Grimmer & Kessler (1987) Teil I - “improved”: Enhanced method from Grimmer & Kessler (1987) Teil II Default is “conventional”.

  • center_roll_load_factor (Quantity, optional) – Load factor for center roll. If None and method=”improved”, defaults to 0.9. Ignored for conventional method.

  • unit (str, optional) – The unit for the returned force. Default is “newton”.

  • precision (int, optional) – Number of decimal places to round the result to. If None, no rounding is applied.

Returns:

Friction force component from material on center section tilted idlers with specified units.

Return type:

Quantity

Raises:

ValueError – If unit conversion fails, if belt widths are invalid, if weights are negative, or if calculation parameters are outside valid ranges.

Notes

The center section friction force calculation is unique as it considers the combined influence of all three belt sections. This comprehensive approach accounts for the complex load distribution that occurs in horizontal curves.

Mathematical formulation combines three components: 1. Center component: (w_center/w_total) * F_material * cos(β) * cos(α) 2. Inside component: (w_inside/w_total) * F_material * sin(λ + β) * sin(λ) * cos(α) 3. Outside component: (w_outside/w_total) * F_material * sin(λ - β) * sin(λ) * cos(α)

Final calculation: F = f_var * μ * (F_center + F_inside + F_outside + F_normal)

Where: - f_var is the friction variation factor - μ is the friction coefficient for tilted idler interaction - λ is the troughing angle, β is the banking angle, α is the inclination angle - w_*/w_total are the width ratios for each section - F_material is the total material weight force - F_normal is the additional normal force on the idler roll

Examples

>>> import eytelwein.main.units as u
>>> from eytelwein.horizontal_curves import tilted_idler_friction_force_center
>>>
>>> # Basic calculation with SI units
>>> force = tilted_idler_friction_force_center(
...     total_weight_force_material=200.0 * u.ureg.newton,
...     inclination_angle=0.0 * u.ureg.radian,
...     belt_width=1.0 * u.ureg.meter,
...     troughing_angle=20.0 * u.ureg.degree,
...     banking_angle=2.0 * u.ureg.degree,
...     belt_width_on_center_wing_roll=0.4 * u.ureg.meter,
...     belt_width_on_inside_wing_roll=0.3 * u.ureg.meter,
...     belt_width_on_outside_wing_roll=0.3 * u.ureg.meter,
...     friction_variation=1.0 * u.ureg.dimensionless,
...     friction_coefficient_tilted_idler=0.3 * u.ureg.dimensionless
... )
>>> print(f"Center friction force: {force:.2f}")
Center friction force: 28.19 newton

References

Grimmer, K.-J. und F. Kessler: Teil I - Traditional calculation approaches. Grimmer, K.-J. und F. Kessler: Teil II - Enhanced calculation procedures.

eytelwein.horizontal_curves.core.horizontal_curve_calculations.tilted_idler_friction_force_inside(total_weight_force_material: Quantity, inclination_angle: Quantity, belt_width: Quantity, troughing_angle: Quantity, banking_angle: Quantity, belt_width_on_inside_wing_roll: Quantity, friction_variation: Quantity, friction_coefficient_tilted_idler: Quantity, normal_force_on_idler_roll: Quantity, wing_roll_load_factor: Quantity | None = None, method: str = 'conventional', unit: str = 'newton', precision: int = 2) → Quantity[source]

Calculate the friction force from conveyed material acting on tilted idlers at the inside wing roll.

This function provides a unit-aware interface for calculating the friction force component that results from conveyed material acting on tilted idlers positioned at the inside wing roll of a troughed belt conveyor operating in a horizontal curve.

Parameters:

  • total_weight_force_material (Quantity) – Total weight force of the conveyed material

  • inclination_angle (Quantity) – Inclination angle of the belt conveyor

  • belt_width (Quantity) – Total width of the belt

  • troughing_angle (Quantity) – Troughing angle of the belt

  • banking_angle (Quantity) – Banking angle of the belt in the horizontal curve

  • belt_width_on_inside_wing_roll (Quantity) – Effective width of the belt supported by the inside wing roll

  • friction_variation (Quantity) – Friction variation factor (dimensionless)

  • friction_coefficient_tilted_idler (Quantity) – Friction coefficient for material-idler interaction (dimensionless)

  • normal_force_on_idler_roll (Quantity) – Additional normal force acting on the idler roll

  • wing_roll_load_factor (Quantity, optional) – Load factor for enhanced calculation accuracy in improved method. Default is 1.1 if not provided.

  • method (str, optional) – Calculation method to use. Either “conventional” or “improved”. Default is “conventional”.

  • unit (str, optional) – Output unit for the force. Default is “newton”.

  • precision (int, optional) – Number of decimal places for the result. Default is 2.

Returns:

Friction force component from material on inside wing roll tilted idlers.

Return type:

Quantity

Raises:

ValueError – If input parameters are invalid or unit conversion fails.

Notes

This calculation considers the interaction between conveyed material and tilted idlers in the inside wing roll position of a troughed belt conveyor system operating in horizontal curves.

The friction force arises from the normal force of material on the tilted idlers combined with geometric factors including troughing angle, banking angle, and belt width distribution.

Physical constraints checked: - All force inputs must be non-negative - Belt widths must be positive - Inside wing roll width must not exceed total belt width - Friction coefficients must be non-negative

Examples

>>> import eytelwein.main.units as u
>>> from eytelwein.horizontal_curves import tilted_idler_friction_force_inside
>>> force = tilted_idler_friction_force_inside(
...     total_weight_force_material=156.71 * u.ureg.newton,
...     inclination_angle=0 * u.ureg.degree,
...     belt_width=0.8 * u.ureg.meter,
...     troughing_angle=30 * u.ureg.degree,
...     banking_angle=1.46 * u.ureg.degree,
...     belt_width_on_inside_wing_roll=0.3025 * u.ureg.meter,
...     friction_variation=0.7 * u.ureg.dimensionless,
...     friction_coefficient_tilted_idler=0.416183 * u.ureg.dimensionless,
...     normal_force_on_idler_roll=0 * u.ureg.newton
... )
>>> print(f"Friction force: {force:.2f}")
Friction force: 12.75 newton
eytelwein.horizontal_curves.core.horizontal_curve_calculations.tilted_idler_friction_force_outside(total_weight_force_material: Quantity, inclination_angle: Quantity, belt_width: Quantity, troughing_angle: Quantity, banking_angle: Quantity, belt_width_on_outside_wing_roll: Quantity, friction_variation: Quantity, friction_coefficient_tilted_idler: Quantity, normal_force_on_idler_roll: Quantity, wing_roll_load_factor: Quantity | None = None, method: str = 'conventional', unit: str = 'newton', precision: int = 2) → Quantity[source]

Calculate the friction force from conveyed material acting on tilted idlers at the outside wing roll.

This function provides a unit-aware interface for calculating the friction force component that results from conveyed material acting on tilted idlers positioned at the outside wing roll of a troughed belt conveyor operating in a horizontal curve.

Parameters:

  • total_weight_force_material (Quantity) – Total weight force of the conveyed material

  • inclination_angle (Quantity) – Inclination angle of the belt conveyor

  • belt_width (Quantity) – Total width of the belt

  • troughing_angle (Quantity) – Troughing angle of the belt

  • banking_angle (Quantity) – Banking angle of the belt in the horizontal curve

  • belt_width_on_outside_wing_roll (Quantity) – Effective width of the belt supported by the outside wing roll

  • friction_variation (Quantity) – Friction variation factor (dimensionless)

  • friction_coefficient_tilted_idler (Quantity) – Friction coefficient for material-idler interaction (dimensionless)

  • normal_force_on_idler_roll (Quantity) – Additional normal force acting on the idler roll

  • wing_roll_load_factor (Quantity, optional) – Load factor for wing roll considering improved load distribution (dimensionless). Default is 1.1. Only used for improved method.

  • method (str, optional) – Calculation method to use. Must be one of [‘conventional’, ‘improved’]. Default is ‘conventional’.

  • unit (str, optional) – Output unit for the force. Default is “newton”.

  • precision (int, optional) – Number of decimal places for the result. Default is 2.

Returns:

Friction force component from material on outside wing roll tilted idlers.

Return type:

Quantity

Raises:

ValueError – If input parameters are invalid or unit conversion fails.

Notes

This calculation considers the interaction between conveyed material and tilted idlers in the outside wing roll position of a troughed belt conveyor system operating in horizontal curves.

The friction force arises from the normal force of material on the tilted idlers combined with geometric factors including troughing angle, banking angle, and belt width distribution.

Physical constraints checked: - All force inputs must be non-negative - Belt widths must be positive - Outside wing roll width must not exceed total belt width - Friction coefficients must be non-negative

Examples

>>> import eytelwein.main.units as u
>>> from eytelwein.horizontal_curves import tilted_idler_friction_force_outside
>>> force = tilted_idler_friction_force_outside(
...     total_weight_force_material=156.71 * u.ureg.newton,
...     inclination_angle=0 * u.ureg.degree,
...     belt_width=0.8 * u.ureg.meter,
...     troughing_angle=30 * u.ureg.degree,
...     banking_angle=1.46 * u.ureg.degree,
...     belt_width_on_outside_wing_roll=0.1825 * u.ureg.meter,
...     friction_variation=0.7 * u.ureg.dimensionless,
...     friction_coefficient_tilted_idler=0.216 * u.ureg.dimensionless,
...     normal_force_on_idler_roll=0 * u.ureg.newton
... )
>>> print(f"Friction force: {force:.2f}")
Friction force: 4.11 newton
eytelwein.horizontal_curves.core.horizontal_curve_calculations.tilted_idler_friction_force_outside_improved(total_weight_force_material: Quantity, inclination_angle: Quantity, wing_roll_load_factor: Quantity, belt_width: Quantity, troughing_angle: Quantity, banking_angle: Quantity, belt_width_on_outside_wing_roll: Quantity, friction_variation: Quantity, friction_coefficient_tilted_idler: Quantity, normal_force_on_idler_roll: Quantity | None = None, unit: str = 'newton', precision: int = 2) → Quantity[source]

Calculate the friction force from conveyed material acting on tilted idlers at the outside wing roll - improved method.

This function provides a dedicated interface for the improved calculation method of friction force component that results from conveyed material acting on tilted idlers positioned at the outside wing roll of a troughed belt conveyor operating in a horizontal curve.

Parameters:

  • total_weight_force_material (Quantity) – Total weight force of the conveyed material

  • inclination_angle (Quantity) – Inclination angle of the belt conveyor

  • wing_roll_load_factor (Quantity) – Load factor for wing roll considering improved load distribution (dimensionless)

  • belt_width (Quantity) – Total width of the belt

  • troughing_angle (Quantity) – Troughing angle of the belt

  • banking_angle (Quantity) – Banking angle of the belt in the horizontal curve

  • belt_width_on_outside_wing_roll (Quantity) – Effective width of the belt supported by the outside wing roll

  • friction_variation (Quantity) – Friction variation factor (dimensionless)

  • friction_coefficient_tilted_idler (Quantity) – Friction coefficient for material-idler interaction (dimensionless)

  • normal_force_on_idler_roll (Quantity, optional) – Additional normal force acting on the idler roll. Default is 0 N.

  • unit (str, optional) – Output unit for the force. Default is “newton”.

  • precision (int, optional) – Number of decimal places for the result. Default is None.

Returns:

Friction force component from material on outside wing roll tilted idlers (improved method).

Return type:

Quantity

Examples

>>> import eytelwein.main.units as u
>>> force = tilted_idler_friction_force_outside_improved(
...     total_weight_force_material=156.71 * u.ureg.newton,
...     inclination_angle=0 * u.ureg.degree,
...     wing_roll_load_factor=1.1 * u.ureg.dimensionless,
...     belt_width=0.8 * u.ureg.meter,
...     troughing_angle=30 * u.ureg.degree,
...     banking_angle=1.46 * u.ureg.degree,
...     belt_width_on_outside_wing_roll=0.1825 * u.ureg.meter,
...     friction_variation=0.7 * u.ureg.dimensionless,
...     friction_coefficient_tilted_idler=0.216 * u.ureg.dimensionless,
...     normal_force_on_idler_roll=0 * u.ureg.newton
... )
>>> print(f"Friction force: {force:.2f}")
Friction force: 5.22 newton
eytelwein.horizontal_curves.core.horizontal_curve_calculations.weight_force_belt_center(total_weight_force_belt: Quantity, inclination_angle: Quantity, belt_width: Quantity, banking_angle: Quantity, belt_width_on_center_section: Quantity, method: str = 'conventional', center_roll_load_factor: Quantity | None = None, unit: str = 'newton', precision: int = 2) → Quantity[source]

Calculate the weight force component acting on the center section of a troughed belt.

This function provides a complete unit-aware interface for calculating the weight force component that acts on the center section of a troughed belt conveyor in a horizontal curve, with comprehensive input validation and unit conversion capabilities.

Parameters:

  • total_weight_force_belt (Quantity) – Total weight force acting on the belt (belt + material) [force]

  • inclination_angle (Quantity) – Inclination angle of the belt conveyor [angle]

  • belt_width (Quantity) – Total width of the belt [length]

  • banking_angle (Quantity) – Banking angle of the belt in the horizontal curve [angle]

  • belt_width_on_center_section (Quantity) – Effective width of the belt supported by the center section [length]

  • method (str, optional) – Calculation methodology to use: - “conventional”: Standard method from Grimmer & Kessler (1987) Teil I - “improved”: Enhanced method from Grimmer & Kessler (1987) Teil II Default is “conventional”.

  • unit (str, optional) – Output unit for the force. Default is “newton”.

  • precision (int, optional) – Number of decimal places for the result. Default is 2.

Returns:

Weight force component acting on the center section with specified unit.

Return type:

Quantity

Raises:

ValueError – If unit conversion fails, parameters are invalid, or belt width constraints are violated.

Notes

The calculation accounts for the weight force distribution in the center section of a troughed belt system with banking. Physical constraints are enforced: - All forces must be non-negative - Center belt width cannot exceed total belt width - Angles are automatically converted to radians for calculation

Mathematical formulation: F_center = F_total * cos(α) * (w_center/w_total) * sin(β)

where: - F_center = weight force on center section - F_total = total weight force - α = inclination angle - w_center = belt width on center section - w_total = total belt width - β = banking angle

eytelwein.horizontal_curves.core.horizontal_curve_calculations.weight_force_belt_inside(total_weight_force_belt: Quantity, inclination_angle: Quantity, belt_width: Quantity, troughing_angle: Quantity, banking_angle: Quantity, belt_width_on_inside_wing_roll: Quantity, method: str = 'conventional', wing_roll_load_factor: Quantity | None = None, unit: str = 'newton', precision: int = 2) → Quantity[source]

Calculate the weight force component acting on the inside wing roll of a troughed belt.

This function provides a unit-aware interface for calculating the weight force component that acts on the inside wing roll of a troughed belt conveyor in a horizontal curve, with comprehensive input validation and unit conversion.

Parameters:

  • total_weight_force_belt (Quantity) – Total weight force acting on the belt (belt + material)

  • inclination_angle (Quantity) – Inclination angle of the belt conveyor

  • belt_width (Quantity) – Total width of the belt

  • troughing_angle (Quantity) – Troughing angle of the belt

  • banking_angle (Quantity) – Banking angle of the belt in the horizontal curve

  • belt_width_on_inside_wing_roll (Quantity) – Effective width of the belt supported by the inside wing roll

  • method (str, optional) – Calculation methodology: - “conventional”: Standard method from Grimmer & Kessler (1987) Teil I - “improved”: Enhanced method from Grimmer & Kessler (1987) Teil II Default is “conventional”.

  • wing_roll_load_factor (Quantity, optional) – Load factor for wing roll. Typical engineering range is 1.0 to 2.0 for most belt conveyor applications. Values outside this range may be used for research or special applications. If None and method=”improved”, defaults to 1.5 * u.dimensionless. Ignored for conventional method.

  • unit (str, optional) – Output unit for the force. Default is “newton”.

  • precision (int, optional) – Number of decimal places for the result. Default is 2.

Returns:

Weight force component acting on the inside wing roll with specified unit.

Return type:

Quantity

Raises:

ValueError – If input parameters are invalid, method is unknown, or unit conversion fails.

Notes

The calculation considers the geometric distribution of weight forces in a troughed belt system with banking. All angle inputs are converted to radians internally.

Available calculation methods: 1. Conventional Method (method=”conventional”):

  • Based on Grimmer & Kessler (1987) Teil I

  • Traditional calculation approaches

  1. Improved Method (method=”improved”): - Based on Grimmer & Kessler (1987) Teil II - Enhanced calculation procedures with improvements to conventional methods

Physical constraints checked: - Total weight force must be non-negative - Belt widths must be positive - Inside wing roll width must not exceed total belt width

eytelwein.horizontal_curves.core.horizontal_curve_calculations.weight_force_belt_outside(total_weight_force_belt: Quantity, inclination_angle: Quantity, belt_width: Quantity, troughing_angle: Quantity, banking_angle: Quantity, belt_width_on_outside_wing_roll: Quantity, method: str = 'conventional', wing_roll_load_factor: Quantity | None = None, unit: str = 'newton', precision: int = 2) → Quantity[source]

Calculate the weight force component acting on the outside wing roll of a troughed belt.

This function provides a complete unit-aware interface for calculating the weight force component that acts on the outside wing roll of a troughed belt conveyor in a horizontal curve, with comprehensive input validation and unit conversion capabilities.

Parameters:

  • total_weight_force_belt (Quantity) – Total weight force acting on the belt (belt + material) [force]

  • inclination_angle (Quantity) – Inclination angle of the belt conveyor [angle]

  • belt_width (Quantity) – Total width of the belt [length]

  • troughing_angle (Quantity) – Troughing angle of the belt [angle]

  • banking_angle (Quantity) – Banking angle of the belt in the horizontal curve [angle]

  • belt_width_on_outside_wing_roll (Quantity) – Effective width of the belt supported by the outside wing roll [length]

  • method (str, optional) – Calculation methodology to use: - “conventional”: Standard method from Grimmer & Kessler (1987) Teil I - “improved”: Enhanced method from Grimmer & Kessler (1987) Teil II Default is “conventional”.

  • unit (str, optional) – Output unit for the force. Default is “newton”.

  • precision (int, optional) – Number of decimal places for the result. Default is 2.

Returns:

Weight force component acting on the outside wing roll with specified unit.

Return type:

Quantity

Raises:

ValueError – If unit conversion fails, parameters are invalid, or belt width constraints are violated.

Notes

The calculation accounts for the geometric distribution of weight forces in a troughed belt system with banking. Physical constraints are enforced: - All forces must be non-negative - Outside belt width cannot exceed total belt width - Angles are automatically converted to radians for calculation

Mathematical formulation: F_outside = F_total * cos(α) * (w_outside/w_total) * sin(λ - β) * cos(λ)

where: - F_outside = weight force on outside wing roll - F_total = total weight force - α = inclination angle - w_outside = belt width on outside wing roll - w_total = total belt width - λ = troughing angle - β = banking angle

eytelwein.horizontal_curves.core.horizontal_curve_calculations.weight_force_material_center(normal_force: Quantity, banking_angle: Quantity, method: str = 'conventional', unit: str = 'newton', precision: int = 2) → Quantity[source]

Calculate the weight force component from material acting on the center section.

This function provides a unit-aware interface for calculating the weight force component that acts on the center section due to conveyed material in a troughed belt conveyor horizontal curve, with comprehensive input validation.

Parameters:

  • normal_force (Quantity) – Normal force acting on the center section from the conveyed material

  • banking_angle (Quantity) – Banking angle of the belt in the horizontal curve

  • method (str, optional) – Calculation methodology. Currently supports: - “conventional”: Standard method from Grimmer & Kessler (1987) Teil I - “improved”: Enhanced method from Grimmer & Kessler (1987) Teil II Default is “conventional”.

  • unit (str, optional) – Output unit for the force. Default is “newton”.

  • precision (int, optional) – Number of decimal places for the result. Default is 2.

Returns:

Weight force component from material acting on the center section with specified unit.

Return type:

Quantity

Raises:

ValueError – If input parameters are invalid, method is unknown, or unit conversion fails.

Notes

The calculation determines the lateral force component that results from the material weight acting on the center section of a troughed belt conveyor in a horizontal curve. The center section is only affected by banking angle, not troughing angle, since it remains horizontal.

Mathematical formulation for both methods: F_center = F_normal * tan(β)

Where: - F_normal: Normal force from material on center section - β: Banking angle

The center section calculation is simpler than wing roll calculations because it’s not influenced by troughing geometry - only by the banking of the entire belt cross-section. Both conventional and improved methods use the same formula for the center section since geometric considerations remain unchanged.

Examples

>>> import eytelwein.main.units as u
>>> from eytelwein.horizontal_curves import weight_force_material_center
>>>
>>> result = weight_force_material_center(
...     normal_force=1000.0 * u.ureg.newton,
...     banking_angle=5.0 * u.ureg.degree,
...     method="conventional"
... )
>>> print(f"Weight force: {result:.2f}")
Weight force: 87.49 newton

References

Grimmer, K.-J. und F. Kessler: Teil I - Traditional calculation approaches. Grimmer, K.-J. und F. Kessler: Teil II - Enhanced calculation procedures.

eytelwein.horizontal_curves.core.horizontal_curve_calculations.weight_force_material_inside(normal_force: Quantity, troughing_angle: Quantity, banking_angle: Quantity, method: str = 'conventional', unit: str = 'newton', precision: int = 2) → Quantity[source]

Calculate the weight force component from material acting on the inside wing roll.

This function provides a unit-aware interface for calculating the weight force component that acts on the inside wing roll due to conveyed material in a troughed belt conveyor horizontal curve, with comprehensive input validation.

Parameters:

  • normal_force (Quantity) – Normal force acting on the inside wing roll from the conveyed material

  • troughing_angle (Quantity) – Troughing angle of the belt

  • banking_angle (Quantity) – Banking angle of the belt in the horizontal curve

  • method (str, optional) – Calculation methodology. Currently supports: - “conventional”: Standard method from Grimmer & Kessler (1987) Teil I - “improved”: Enhanced method from Grimmer & Kessler (1987) Teil II Default is “conventional”.

  • unit (str, optional) – Output unit for the force. Default is “newton”.

  • precision (int, optional) – Number of decimal places for the result. Default is 2.

Returns:

Weight force component from material acting on the inside wing roll with specified unit.

Return type:

Quantity

Raises:

ValueError – If input parameters are invalid, method is unknown, or unit conversion fails.

Notes

The calculation determines the lateral force component that results from the material weight acting on the inclined inside wing roll of a troughed belt conveyor in a horizontal curve.

Mathematical formulation: - Conventional method: F_inside = F_normal * tan(λ + β) * cos(λ) - Improved method: F_inside = F_normal * tan(λ + β)

Where: - F_normal: Normal force from material on inside wing roll - λ: Troughing angle - β: Banking angle

The key difference between methods is that the improved method removes the cos(λ) factor present in the conventional method, providing enhanced accuracy based on refined geometric considerations.

Examples

>>> import eytelwein.main.units as u
>>> from eytelwein.horizontal_curves import weight_force_material_inside
>>>
>>> result = weight_force_material_inside(
...     normal_force=1000.0 * u.ureg.newton,
...     troughing_angle=30.0 * u.ureg.degree,
...     banking_angle=5.0 * u.ureg.degree,
...     method="conventional"
... )
>>> print(f"Weight force: {result:.2f}")
Weight force: 606.40 newton

References

Grimmer, K.-J. und F. Kessler: Teil I - Traditional calculation approaches. Grimmer, K.-J. und F. Kessler: Teil II - Enhanced calculation procedures.

eytelwein.horizontal_curves.core.horizontal_curve_calculations.weight_force_material_outside(normal_force: Quantity, troughing_angle: Quantity, banking_angle: Quantity, method: str = 'conventional', unit: str = 'newton', precision: int = 2) → Quantity[source]

Calculate the weight force component from material acting on the outside wing roll.

This function provides a unit-aware interface for calculating the weight force component that acts on the outside wing roll due to conveyed material in a troughed belt conveyor horizontal curve, with comprehensive input validation.

Parameters:

  • normal_force (Quantity) – Normal force acting on the outside wing roll from the conveyed material

  • troughing_angle (Quantity) – Troughing angle of the belt

  • banking_angle (Quantity) – Banking angle of the belt in the horizontal curve

  • method (str, optional) – Calculation methodology. Currently supports: - “conventional”: Standard method from Grimmer & Kessler (1987) Teil I - “improved”: Enhanced method from Grimmer & Kessler (1987) Teil II Default is “conventional”.

  • unit (str, optional) – Output unit for the force. Default is “newton”.

  • precision (int, optional) – Number of decimal places for the result. Default is 2.

Returns:

Weight force component from material acting on the outside wing roll with specified unit.

Return type:

Quantity

Raises:

ValueError – If input parameters are invalid, method is unknown, or unit conversion fails.

Notes

The calculation determines the lateral force component that results from the material weight acting on the inclined outside wing roll of a troughed belt conveyor in a horizontal curve.

Mathematical formulation: - Conventional method: F_outside = F_normal * tan(λ - β) * cos(λ) - Improved method: F_outside = F_normal * tan(λ - β)

Where: - F_normal: Normal force from material on outside wing roll - λ: Troughing angle - β: Banking angle

The key difference from the inside wing roll is the subtraction of banking angle (λ - β) instead of addition (λ + β), reflecting the opposite geometry effect.

The improved method removes the cos(λ) factor present in the conventional method, providing enhanced accuracy based on refined geometric considerations.

Examples

>>> import eytelwein.main.units as u
>>> from eytelwein.horizontal_curves import weight_force_material_outside
>>>
>>> result = weight_force_material_outside(
...     normal_force=1000.0 * u.ureg.newton,
...     troughing_angle=30.0 * u.ureg.degree,
...     banking_angle=5.0 * u.ureg.degree,
...     method="conventional"
... )
>>> print(f"Weight force: {result:.2f}")
Weight force: 403.83 newton

References

Grimmer, K.-J. und F. Kessler: Teil I - Traditional calculation approaches. Grimmer, K.-J. und F. Kessler: Teil II - Enhanced calculation procedures.

eytelwein.horizontal_curves.core.horizontal_curve_calculations.weight_force_of_belt(weight_force_belt_inside: Quantity, weight_force_belt_center: Quantity, weight_force_belt_outside: Quantity, method: str = 'conventional', unit: str = 'newton', precision: int = 2) → Quantity[source]

Calculate the net lateral weight force acting on the belt in a horizontal curve.

This function combines the weight force components from the inside wing roll, center section, and outside wing roll to determine the net lateral force acting on the belt due to banking and troughing effects in a horizontal curve.

Parameters:

  • weight_force_belt_inside (Quantity) – Weight force component on the inside wing roll [force units]

  • weight_force_belt_center (Quantity) – Weight force component in the center section [force units]

  • weight_force_belt_outside (Quantity) – Weight force component on the outside wing roll [force units]

  • method (str, optional) – Calculation methodology to use: - “conventional”: Standard method from Grimmer & Kessler (1987) Teil I - “improved”: Enhanced method from Grimmer & Kessler (1987) Teil II Default is “conventional”.

  • unit (str, optional) – Output unit for the result (default: “newton”)

  • precision (int, optional) – Number of decimal places for rounding (default: 2)

Returns:

Net lateral weight force acting on the belt [force units]

Return type:

Quantity

Raises:

ValueError – If input dimensions are incorrect or units are invalid

Notes

The calculation follows the sign convention where: - Inside and center forces contribute positively (toward curve center) - Outside force contributes negatively (away from curve center)

Mathematical formulation: F_net = F_inside + F_center - F_outside

This represents the net lateral force that must be balanced by the belt’s resistance to lateral movement in the horizontal curve.

Examples

>>> import eytelwein.main.units as u
>>> inside_force = u.ureg.Quantity(30.04, u.ureg.newton)
>>> center_force = u.ureg.Quantity(1.572, u.ureg.newton)
>>> outside_force = u.ureg.Quantity(27.93, u.ureg.newton)
>>> net_force = weight_force_of_belt(inside_force, center_force, outside_force)
>>> print(f"{net_force:.2f}")
3.68 newton
eytelwein.horizontal_curves.core.horizontal_curve_calculations.weight_force_of_material(inside_force: Quantity, center_force: Quantity, outside_force: Quantity, method: str = 'conventional', unit: str = 'newton', precision: int = 2) → Quantity[source]

Calculate the net lateral weight force acting on conveyed material in horizontal curves.

This function provides a unit-aware interface for combining the weight force components from inside wing roll, center section, and outside wing roll to determine the resultant lateral force acting on conveyed material in a troughed belt conveyor horizontal curve.

Parameters:

  • inside_force (Quantity) – Weight force component from material acting on the inside wing roll

  • center_force (Quantity) – Weight force component from material acting in the center section

  • outside_force (Quantity) – Weight force component from material acting on the outside wing roll

  • method (str, optional) – Calculation methodology. Currently supports: - “conventional”: Standard method from Grimmer & Kessler (1987) Teil I - “improved”: Enhanced method from Grimmer & Kessler (1987) Teil II Default is “conventional”.

  • unit (str, optional) – Output unit for the force. Default is “newton”.

  • precision (int, optional) – Number of decimal places for the result. Default is 2.

Returns:

Net lateral weight force acting on conveyed material with specified unit.

Return type:

Quantity

Raises:

ValueError – If input parameters are invalid, method is unknown, or unit conversion fails.

Notes

The calculation combines the three weight force components using the standard force balance methodology for horizontal curve analysis. The net lateral force represents the resultant effect of material weight distribution on belt behavior in horizontal curves.

Mathematical formulation: F_net = F_inside + F_center - F_outside

Where: - F_inside: Weight force component on inside wing roll - F_center: Weight force component in center section - F_outside: Weight force component on outside wing roll

The subtraction of the outside component reflects the opposing nature of forces in horizontal curves, where inside and center forces work together while the outside force opposes the resultant lateral movement toward the curve center.

Physical interpretation: - Positive result: Net force toward inside of curve - Negative result: Net force toward outside of curve - Zero result: Balanced forces, no net lateral effect

Examples

>>> import eytelwein.main.units as u
>>> from eytelwein.horizontal_curves import weight_force_of_material
>>>
>>> result = weight_force_of_material(
...     inside_force=530.29 * u.ureg.newton,
...     center_force=87.49 * u.ureg.newton,
...     outside_force=433.01 * u.ureg.newton,
...     method="conventional"
... )
>>> print(f"Net material weight force: {result:.2f}")
Net material weight force: 184.77 newton

References

Grimmer, K.-J. und F. Kessler: Teil I - Traditional calculation approaches. Grimmer, K.-J. und F. Kessler: Teil II - Enhanced calculation procedures.