Editing Power units and hybrid systems

The modern Formula One power unit (PU) is a tightly integrated thermodynamic system consisting of a high-efficiency internal combustion engine (ICE) coupled with dual electric motor-generators and sophisticated control electronics. Since 2014, technical directives have enforced the hybridisation of propulsion systems, culminating in highly constrained yet optimised energy flow architectures.

== System Overview ==
The hybrid PU comprises six core components:

# 1.6L V6 Turbocharged Internal Combustion Engine (ICE)
# Motor Generator Unit – Heat (MGU-H)
# Motor Generator Unit – Kinetic (MGU-K)
# Turbocharger (TC)
# Lithium-Ion Energy Store (ES)
# Control Electronics (CE)

Each of these interacts through an optimised **energy transfer map**, constrained by fuel flow limits, maximum energy deployment, and component degradation models.

== Energy Conversion Flow Model ==
<nowiki>The PU’s energy efficiency can be modelled as a closed-loop system where input chemical energy is divided into mechanical, electrical, and waste heat outputs. Total efficiency \( \eta_{\text{PU}} \) is defined as:</nowiki>

<math>
\eta_{\text{PU}} = \frac{P_{\text{drive}} + P_{\text{ERS}}}{P_{\text{fuel}}}
</math>

Where:

* <math>P_{\text{drive}}</math> = shaft output from ICE
* <math>P_{\text{ERS}}</math> = net deployable power from ERS
* <math>P_{\text{fuel}}</math> = \dot{m}_{\text{fuel}} \cdot LHV \)

- <math>\dot{m}_{\text{fuel}}</math>: fuel mass flow rate (kg/s), limited to 100 kg/h - LHV: Lower Heating Value of fuel (~42.6 MJ/kg)

== ICE Output Modelling ==
Assuming ideal thermodynamic efficiency (Otto cycle), the ICE thermal efficiency is bounded by:

<math>
\eta_{\text{th,ideal}} = 1 - \left( \frac{1}{r^{\gamma - 1}} \right)
</math>

Where:

* <math>r</math>: compression ratio (~18:1 in F1 engines)
* <math>\gamma</math>: specific heat ratio (~1.33 for gasoline-air mix)

Actual ICE output torque \( T \) is derived from:

<math>
T = \frac{P_{\text{mean}} \cdot V_d}{4 \pi}
</math>

With:

* <math>P_{\text{mean}}</math>: brake mean effective pressure (BMEP)
* <math>V_d</math>: displacement volume (0.0016 m³)

Typical F1 ICE BMEP: ~20–24 bar under qualifying maps.

== MGU-H Dynamic Transfer Model ==
The MGU-H converts thermal energy from turbocharger exhaust into electrical energy. In simplified terms:

<math>
P_{\text{MGUH}} = \eta_{\text{MGUH}} \cdot \dot{m}_{\text{exhaust}} \cdot c_p \cdot (T_{turb\_in} - T_{turb\_out})
</math>

- <math>c_p</math>: specific heat capacity of exhaust gas (~1.1 kJ/kg·K)

- <math>\eta_{\text{MGUH}}</math> 30–38% in F1 conditions - MGU-H also regulates turbo RPM: up to 125,000 rpm

This electrical power is transferred either directly to the MGU-K or to the Energy Store (ES).

== MGU-K Deployment Curve ==
The MGU-K harvests up to 120 kW during braking and redeploys up to 4 MJ per lap. Optimal deployment maximises traction-limited exit speed, particularly in low-speed corners.

MGU-K deployment strategy is defined by:

<math>
E_{\text{K,deploy}} = \int_{0}^{t_{\text{lap}}} P_{\text{K}}(t) \cdot \delta(t) \, dt
</math>

- <math>\delta(t) \in \{0,1\}</math>: deployment status function - Controlled by SOC maps (State-of-Charge), ERS blending strategies, and gearshift timing

== Thermomechanical Constraints ==
The efficiency of ERS is bottlenecked by:

* Inverter thermal load: >100°C under regen
* Lithium-ion battery discharge envelope (C-rate)
* Charge air cooling effectiveness (for ICE knock control)

Heat rejection limits PU performance at high ambient tracks like Mexico City and Singapore. Engineers optimise:

* Radiator inlet pressure drop
* Intercooler latent capacity
* Surface area vs frontal drag trade-off

== Powertrain Efficiency Table ==
{| class="wikitable"
! Subsystem
! Conversion
! Peak Efficiency (%)
|-
| ICE (Shell fuel)
| Chemical → Mechanical
| 49.8
|-
| MGU-H
| Heat → Electric
| 35–38
|-
| MGU-K
| Kinetic ↔ Electric
| 90–94
|-
| ES (Li-ion)
| Electrical Storage
| ~95
|-
| Combined Lap Efficiency
| Total energy recovery + delivery
| 46–50
|}

== Control Electronics and Mode Switching ==
PU logic is encoded in the Control Electronics (CE) unit, which handles:

* Strat mode selection (maps torque, fuel mix)
* SOC (State-of-Charge) ERS curves
* Torque fill blending (MGU-K + ICE)
* Traction-limited energy blending
* Deployment overtake modes (e.g., Strat 10, Strat 5, ‘Attack’)

Teams run **lap-specific energy trace simulations** to maximise usable ERS within FIA constraints.

== Future Regulation (2026) Impact Model ==
Changes in 2026 include:

* Removal of MGU-H
* MGU-K power tripled to ~350 kW
* >50% of lap energy to be electric
* Synthetic fuels mandated

These changes imply:

<math>
P_{\text{elec,lap}} > P_{\text{ICE,lap}}
</math>

requiring reallocation of cooling mass flow, battery placement, and control logic redesign for KERS-only systems.

== See Also ==

* [[ERS Deployment Strategy]]
* [[Turbocharger Aeroelasticity]]
* [[FIA Fuel Flow Metering Model]]
* [[Hybrid Thermal Management]]
* [[FIA 2026 PU Regulations – Technical Summary]]

== References ==
<references />
* FIA Technical Regulations 2024 & 2026 Draft
* Mercedes-AMG HPP White Paper on PU Thermal Efficiency (2023)
* AVL RACING: “PU Simulation Techniques under Budget Constraints”, 2022
* Honda Racing Tech Briefing: MGU-H Torque and Vibration Suppression
* Racecar Engineering (Vol. 33 No. 4): “Heat Rejection vs Aero Compromise”
* AMuS Archives: “ERS Deployment by Circuit – Comparative Trends (2023)”

*

[[Category:Power Units]]
[[Category:Hybrid Systems]]
[[Category:Engineering Concepts]]
[[Category:Technical Analysis]]