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Add plan for next 10 quantities & units
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‎.github/prompts/next-10-quantities-plan.md‎

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# Plan: Next 10 Quantities
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## Existing Quantities (28)
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Acceleration, AmountOfSubstance, Angle, Area, Data, DataRate, Density, ElectricalResistance, ElectricCharge, ElectricCurrent, ElectricPotential, Energy, Force, Frequency, Impulse, Length, LuminousIntensity, Mass, MassFlowRate, Momentum, Power, Pressure, SpecificEnergy, Temperature, Time, Velocity, Volume, VolumetricFlowRate.
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---
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## Theme 1: Rotational Mechanics (3 quantities)
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These extend the existing kinematic/dynamic quantities into the rotational domain. `Angle` already exists as a dimensionless quantity, making these natural next steps.
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| # | Quantity | Dimension | SI Unit | Rationale |
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|---|---------|-----------|---------|-----------|
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| 1 | **Torque** | Force × Length (M·L²·T⁻²) | N·m | Ubiquitous in mechanical engineering. Dimensionally identical to Energy but semantically distinct (rotational vs. translational). |
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| 2 | **AngularVelocity** | Angle / Time (T⁻¹) | rad/s | Fundamental rotational kinematic quantity. Bridges Angle and Time. |
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| 3 | **AngularAcceleration** | Angle / Time² (T⁻²) | rad/s² | Completes the rotational kinematic trio alongside Angle and AngularVelocity. |
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**Dependencies:** Torque needs `IForce` × `ILength`; AngularVelocity and AngularAcceleration need `IAngle` and `ITime`. All dimension interfaces already exist.
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**New dimension interfaces needed:**
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- `ITorque : IProduct<IForce, ILength>, IMultiplicity<ITorque, One>, IDerivedQuantity`
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- `IAngularVelocity : IProduct<IAngle, IDimension<ITime, Negative<One>>>, IMultiplicity<IAngularVelocity, One>, IDerivedQuantity`
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- `IAngularAcceleration : IProduct<IAngle, IDimension<ITime, Negative<Two>>>, IMultiplicity<IAngularAcceleration, One>, IDerivedQuantity`
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**Suggested implementation order:** AngularVelocity → AngularAcceleration → Torque
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---
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## Theme 2: Electromagnetic Quantities (4 quantities)
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The library currently has ElectricCurrent, ElectricCharge, ElectricPotential, and ElectricalResistance. These four additions complete the core electromagnetic set, covering all remaining SI derived electromagnetic units with special names.
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| # | Quantity | Dimension | SI Unit | Rationale |
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|---|---------|-----------|---------|-----------|
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| 4 | **ElectricalConductance** | 1 / Resistance | S (Siemens) | Inverse of ElectricalResistance. Commonly used in circuit analysis. Completes the resistance/conductance duality. |
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| 5 | **Capacitance** | Charge / Potential (I²·T⁴·M⁻¹·L⁻²) | F (Farad) | Fundamental passive circuit element quantity. |
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| 6 | **MagneticFlux** | Potential × Time (M·L²·T⁻²·I⁻¹) | Wb (Weber) | Prerequisite for MagneticFluxDensity. Fundamental electromagnetic quantity. |
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| 7 | **MagneticFluxDensity** | MagneticFlux / Area (M·T⁻²·I⁻¹) | T (Tesla) | Key quantity for electromagnetic applications (motors, sensors, MRI). |
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**Dependencies:** ElectricalConductance is the inverse of ElectricalResistance (already exists). Capacitance needs ElectricCharge and ElectricPotential (both exist). MagneticFlux needs ElectricPotential and Time (both exist). MagneticFluxDensity needs MagneticFlux (new) and Area (exists).
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**New dimension interfaces needed:**
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- `IElectricalConductance : ILinear<IElectricalConductance>, IDerivedQuantity` (with `IInvertible` linking to `IElectricalResistance`)
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- `ICapacitance : ILinear<ICapacitance>, IDerivedQuantity`
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- `IMagneticFlux : IProduct<IElectricPotential, ITime>, IMultiplicity<IMagneticFlux, One>, IDerivedQuantity`
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- `IMagneticFluxDensity : IProduct<IMagneticFlux, IDimension<ILength, Negative<Two>>>, IMultiplicity<IMagneticFluxDensity, One>, IDerivedQuantity`
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**Suggested implementation order:** ElectricalConductance → Capacitance → MagneticFlux → MagneticFluxDensity
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---
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## Theme 3: Photometry & Fluid Dynamics (3 quantities)
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These fill important practical gaps: photometry builds on `LuminousIntensity` (which currently has no derived quantity using it), and dynamic viscosity extends the existing fluid mechanics quantities.
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| # | Quantity | Dimension | SI Unit | Rationale |
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|---|---------|-----------|---------|-----------|
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| 8 | **LuminousFlux** | LuminousIntensity × SolidAngle (≈ cd) | lm (Lumen) | First derived photometric quantity. Makes `LuminousIntensity` practically useful. |
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| 9 | **Illuminance** | LuminousFlux / Area (cd·m⁻²) | lx (Lux) | Essential for lighting design and regulation. Builds on LuminousFlux. |
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| 10 | **DynamicViscosity** | Pressure × Time (M·L⁻¹·T⁻¹) | Pa·s | Fundamental fluid property. Extends the existing flow rate quantities (MassFlowRate, VolumetricFlowRate). |
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**Dependencies:** LuminousFlux needs `ILuminousIntensity` (exists); since solid angle is dimensionless by SI definition (like `IAngle`), LuminousFlux is essentially linear in luminous intensity. Illuminance needs LuminousFlux (new) and Area (exists). DynamicViscosity needs Pressure and Time (both exist).
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**New dimension interfaces needed:**
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- `ILuminousFlux : ILinear<ILuminousFlux>, IDerivedQuantity`
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- `IIlluminance : IProduct<ILuminousFlux, IDimension<ILength, Negative<Two>>>, IMultiplicity<IIlluminance, One>, IDerivedQuantity`
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- `IDynamicViscosity : IProduct<IPressure, ITime>, IMultiplicity<IDynamicViscosity, One>, IDerivedQuantity`
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**Suggested implementation order:** LuminousFlux → Illuminance → DynamicViscosity
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---
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## Overall Implementation Order
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Taking inter-dependencies into account:
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| Phase | Quantities | Notes |
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|-------|-----------|-------|
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| **Phase 1** | AngularVelocity, AngularAcceleration, ElectricalConductance | No new quantity dependencies; only existing dimension interfaces needed. |
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| **Phase 2** | Torque, Capacitance, LuminousFlux, DynamicViscosity | Independent of each other; can be done in parallel. |
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| **Phase 3** | MagneticFlux, MagneticFluxDensity, Illuminance | MagneticFluxDensity depends on MagneticFlux; Illuminance depends on LuminousFlux. |
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## Per-Quantity Checklist
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Each quantity requires:
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1. **Dimension interface** — add to `DerivedDimensions.cs` or `ElectricalDimesions.cs`
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2. **Quantity struct** — new `.ai.cs` file in `Quantities/`
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3. **SI derived unit** — e.g. `NewtonMetre`, `Siemens`, `Farad`, `Weber`, `Tesla`, `Lumen`, `Lux` in `Atmoos.Quantities.Units`
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4. **Physics extensions** — operator relationships in `Physics/`
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5. **Tests** — unit tests for conversions and arithmetic
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6. **Update readme** — add the quantity to the list in `readme.md`

‎.github/prompts/next-10-quantities-units-plan.md‎

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# Plan: Units for Next 10 Quantities
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Accompanies the [next 10 quantities plan](next-10-quantities-plan.md).
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## Overview
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Each new quantity needs at least one SI derived unit. Some quantities also benefit from metric, imperial, or non-standard units that are in common practical use.
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Quantities marked with **(compound only)** have no universally recognised named unit; they are expressed as combinations of existing units (e.g. `N·m`, `Pa·s`). They still need to work with the existing `Scalar<TUnit>`, `Product<T1, T2>`, and `Quotient<TN, TD>` creation patterns but do not require a new unit struct.
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---
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## Theme 1: Rotational Mechanics
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### 1. Torque — compound only
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Torque is dimensionally identical to energy (M·L²·T⁻²) but semantically distinct. The SI unit is the **newton metre** (N·m), which is *not* given a special name to preserve this distinction.
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| Unit | Symbol | Category | Conversion | Notes |
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|------|--------|----------|------------|-------|
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| — | N·m | (compound) | — | Expressed as `Product<Newton, Metre>`. No dedicated unit struct needed. |
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| — | lbf·ft | (compound) | 1 lbf·ft = 1.3558179483314 N·m | Expressed as `Product<PoundForce, Foot>`. Both units exist. |
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| — | lbf·in | (compound) | 1 lbf·in ≈ 0.1129848290276 N·m | Expressed as `Product<PoundForce, Inch>`. Both units exist. |
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**Implementation notes:**
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- The quantity struct uses `Product<TForce, TLength>` and `Quotient<TForce, TLength>` for `Of()` and `To()`.
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- All torque units are compound: `Product<Newton, Metre>`, `Product<PoundForce, Foot>`, and `Product<PoundForce, Inch>`. No dedicated unit structs needed.
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### 2. AngularVelocity — compound only
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All angular velocity units are expressible as quotients of existing angle and time units. No dedicated unit structs are needed.
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| Unit | Symbol | Category | Conversion | Notes |
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|------|--------|----------|------------|-------|
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| — | rad/s | (compound) | identity | Expressed as `Quotient<Radian, Second>`. Both units exist. |
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| — | rev/min | (compound) | 1 rev/min = 2π/60 rad/s | Expressed as `Quotient<Turn, Minute>`. Both units exist (`Turn` has representation `"rev"`). |
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| — | °/s | (compound) | 1 °/s = π/180 rad/s | Expressed as `Quotient<Degree, Second>`. Both units exist. |
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**Implementation notes:**
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- The quantity struct uses `Quotient<TAngle, TTime>` for `Of()` and `To()`.
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- All angular velocity units are compound. The SI coherent form is `Quotient<Radian, Second>` (rad/s).
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- `Turn` already exists (in `NonStandard/Angle/Turn.ai.cs`) with `Representation => "rev"`, so `Quotient<Turn, Minute>` naturally produces "rev/min".
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### 3. AngularAcceleration — compound only
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Angular acceleration follows the same pattern as (linear) acceleration: it is expressed as a compound of existing units.
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| Unit | Symbol | Category | Conversion | Notes |
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|------|--------|----------|------------|-------|
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| — | rad/s² | (compound) | identity | Compound of `Radian` and `Second`. Both units exist. |
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**Implementation notes:**
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- The quantity struct uses a compound creation pattern analogous to linear acceleration.
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- No dedicated unit struct is needed; the SI coherent form is composed from `Radian` and `Second`.
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- Additional non-standard compound forms can be added later as needed.
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---
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## Theme 2: Electromagnetic Quantities
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### 4. ElectricalConductance — SI derived unit: siemens
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| Unit | Symbol | Category | Conversion | Notes |
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|------|--------|----------|------------|-------|
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| **Siemens** | S | SI Derived | identity | Named SI unit. Reciprocal of ohm. |
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**Implementation notes:**
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- `Siemens` implements `ISiUnit, IElectricalConductance, IInvertible<IElectricalResistance>`.
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- The `IInvertible` pattern mirrors how `Hertz` relates to `ITime`: `Siemens` is `1 / Ohm`.
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- Implements `ISystemInject<IElectricalResistance>` to inject `Ohm` as the base.
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### 5. Capacitance — SI derived unit: farad
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| Unit | Symbol | Category | Conversion | Notes |
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|------|--------|----------|------------|-------|
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| **Farad** | F | SI Derived | identity | Named SI unit for capacitance. |
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**Implementation notes:**
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- `Farad` implements `ISiUnit, ICapacitance`.
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- Practical capacitance values are typically very small (pF, nF, µF), so metric prefix support (`Si<Pico, Farad>()`, `Si<Nano, Farad>()`, `Si<Micro, Farad>()`) is essential — this is handled automatically by the prefix system.
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### 6. MagneticFlux — SI derived unit: weber
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| Unit | Symbol | Category | Conversion | Notes |
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|------|--------|----------|------------|-------|
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| **Weber** | Wb | SI Derived | identity | Named SI unit for magnetic flux. |
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| **Maxwell** | Mx | NonStandard | 1 Mx = 10⁻⁸ Wb | CGS unit, still occasionally encountered. |
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**Implementation notes:**
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- `Weber` implements `ISiUnit, IMagneticFlux`.
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- `Maxwell` implements `INonStandardUnit, IMagneticFlux` with `ToSi`: `self / 1e8` (rooted in `Weber`).
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### 7. MagneticFluxDensity — SI derived unit: tesla
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| Unit | Symbol | Category | Conversion | Notes |
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|------|--------|----------|------------|-------|
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| **Tesla** | T | SI Derived | identity | Named SI unit for magnetic flux density. |
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| **Gauss** | G | NonStandard | 1 G = 10⁻⁴ T | CGS unit, very widely used in practice. |
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**Implementation notes:**
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- `Tesla` implements `ISiUnit, IMagneticFluxDensity`.
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- `Gauss` implements `INonStandardUnit, IMagneticFluxDensity` with `ToSi`: `self / 1e4` (rooted in `Tesla`).
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---
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## Theme 3: Photometry & Fluid Dynamics
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### 8. LuminousFlux — SI derived unit: lumen
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| Unit | Symbol | Category | Conversion | Notes |
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|------|--------|----------|------------|-------|
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| **Lumen** | lm | SI Derived | identity | Named SI unit. cd·sr, but sr is dimensionless. |
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**Implementation notes:**
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- `Lumen` implements `ISiUnit, ILuminousFlux`.
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- Since steradian (solid angle) is dimensionless, `LuminousFlux` is effectively linear in luminous intensity with its own named unit.
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### 9. Illuminance — SI derived unit: lux
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| Unit | Symbol | Category | Conversion | Notes |
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|------|--------|----------|------------|-------|
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| **Lux** | lx | SI Derived | identity | Named SI unit. lm/m². |
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| **FootCandle** | fc | NonStandard | 1 fc ≈ 10.7639 lx | Common in North American lighting practice. |
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**Implementation notes:**
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- `Lux` implements `ISiUnit, IIlluminance`.
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- `FootCandle` implements `INonStandardUnit, IIlluminance` with `ToSi`: `10.7639104167097 * self.RootedIn<Lux>()` (1 lumen per square foot).
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### 10. DynamicViscosity — compound only (pascal second)
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| Unit | Symbol | Category | Conversion | Notes |
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|------|--------|----------|------------|-------|
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| — | Pa·s | (compound) | — | Expressed as `Product<Pascal, Second>`. No dedicated named SI unit. |
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| **Poise** | P | NonStandard | 1 P = 0.1 Pa·s | CGS unit; often used as centipoise (cP = mPa·s). |
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**Implementation notes:**
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- Like Torque, DynamicViscosity has no special-name SI unit; it uses `Pa·s`.
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- `Poise` implements `INonStandardUnit, IDynamicViscosity` with `ToSi`: `self / 10`.
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- In practice, centipoise (cP) is extremely common. With `Poise` defined, `Si<Centi, Poise>()` would not work directly (Poise is non-standard, not metric). Consider also defining a metric `Poiseuille` (= 1 Pa·s) if prefix support is desired, though this name is rarely used.
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---
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## Summary Table
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| Quantity | Named SI Unit | Additional Units | Notes |
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|----------|--------------|------------------|-------|
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| Torque | — (N·m) | — (lbf·ft, lbf·in) | Compound only; all units are compounds of existing units |
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| AngularVelocity | — (rad/s) | — (rev/min, °/s) | Compound only; all units are quotients of existing angle and time units |
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| AngularAcceleration | — (rad/s²) | — | Compound only; analogous to linear acceleration |
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| ElectricalConductance | Siemens | — | Invertible with Ohm |
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| Capacitance | Farad | — | Prefix support critical |
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| MagneticFlux | Weber | Maxwell | |
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| MagneticFluxDensity | Tesla | Gauss | |
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| LuminousFlux | Lumen | — | |
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| Illuminance | Lux | FootCandle | |
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| DynamicViscosity | — (Pa·s) | Poise | Compound only |
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**Total new unit structs: 10** (6 SI derived + 4 non-standard)
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Five units originally planned as discrete structs are now compound-only, as all their components already exist:
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- RadianPerSecond → `Quotient<Radian, Second>`
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- RadianPerSecondSquared → compound of `Radian` / `Second`²
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- RevolutionsPerMinute → `Quotient<Turn, Minute>` (`Turn` exists with representation `"rev"`)
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- DegreesPerSecond → `Quotient<Degree, Second>`
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- PoundForceFoot → `Product<PoundForce, Foot>`
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## File Locations
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| Unit | Path |
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|------|------|
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| Siemens | `Units/Si/Derived/ElectricalConductance/Siemens.ai.cs` |
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| Farad | `Units/Si/Derived/Capacitance/Farad.ai.cs` |
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| Weber | `Units/Si/Derived/MagneticFlux/Weber.ai.cs` |
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| Tesla | `Units/Si/Derived/MagneticFluxDensity/Tesla.ai.cs` |
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| Lumen | `Units/Si/Derived/LuminousFlux/Lumen.ai.cs` |
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| Lux | `Units/Si/Derived/Illuminance/Lux.ai.cs` |
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| Maxwell | `Units/NonStandard/MagneticFlux/Maxwell.ai.cs` |
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| Gauss | `Units/NonStandard/MagneticFluxDensity/Gauss.ai.cs` |
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| FootCandle | `Units/NonStandard/Illuminance/FootCandle.ai.cs` |
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| Poise | `Units/NonStandard/DynamicViscosity/Poise.ai.cs` |

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