How Mathematical Modeling Powers China’s New Fujian Aircraft Carrier

Fujian Carrier Development Timeline

The Fujian carrier (hull number 18) is China’s first fully indigenous catapult‑based aircraft carrier. With a full‑load displacement of over 80,000 tonnes, a straight flight deck, electromagnetic launch and arresting gear, it entered service on 5 November 2025.

1. Construction Start (2018)

Construction began in 2018 after extensive theoretical research, design validation and key‑technology development. Major tasks included hull block assembly, electromagnetic catapult development and power‑system integration, representing a clean‑sheet design compared with earlier carriers.

2. Launch and Naming (June 17 2022)

The ship was launched and officially named "People’s Liberation Army Navy Fujian" (hull number 18) at Jiangnan Shipyard, marking completion of the hull and transition to outfitting.

3. Mooring Tests (Sept 2022 – 2023)

Mooring tests verified power, electrical, weapons, communications and navigation systems. In November 2023 the catapult weight‑test vehicle was successfully launched, confirming a key technology breakthrough.

4. Sea Trials (May – Sept 2024)

1 May – 8 May 2024 : First sea trial, testing power‑system reliability.

March 2025 : Seventh sea trial, focusing on electromagnetic compatibility of aircraft.

By September 2025 : Over 100 days of sea trials, catapult success rate >95%.

5. Aircraft Training (Sept 2025)

On 12 Sept 2025 the carrier passed through the Taiwan Strait for research and training. By 22 Sept three aircraft types (J‑15T, J‑35, KJ‑600) completed their first catapult launches and arrested landings, demonstrating full‑deck operational capability.

6. Commissioning (Nov 5 2025)

The carrier officially entered service, marking China’s “three‑carrier era” and a significant boost to blue‑water combat capability.

Mathematical Models in Fujian Carrier Development

The carrier’s design, construction and operation rely on a suite of mathematical models across multiple engineering domains.

1. Electromagnetic Launch System

Electromagnetic Induction and Lorentz Force

The linear induction motor follows Faraday’s law and the Lorentz force: F = B I L, where F is force (N), B magnetic flux density (T), I current (A) and L conductor length (m). Precise current control yields accurate launch forces.

Kinematics and Dynamics

Aircraft launch is modeled as uniformly accelerated motion. Using Newton’s second law, m a = F - D (mass , acceleration , thrust , drag ). For a 30‑ton aircraft accelerated to 70‑85 m/s in 2‑3 s, required acceleration is a = (v_f^2 - v_0^2) / (2 s) , where s is catapult length (< 100 m).

2. Energy Storage System

High‑power pulses are supplied by a super‑capacitor bank. Stored energy is E = ½ C V^2, with C capacitance (F) and V voltage (V). A single launch needs ~120 MJ; at 1000 V this requires ~240 F, achieved by thousands of graphene super‑capacitors in series‑parallel.

Charging and Discharging Characteristics

Charging follows a first‑order RC circuit: V(t) = V_{max}(1 - e^{-t/RC}). The Fujian carrier’s super‑capacitors charge in ~45 s, ready for the next launch interval.

3. Carrier Stability and Seakeeping

Roll Motion Equation

Roll dynamics are described by a second‑order differential equation: I_{xx} \, \ddot{\phi} + c \dot{\phi} + k \phi = M_{wave}(t), where I_{xx} is roll inertia, c damping, k restoring moment coefficient, and M_{wave} wave‑induced moment. Solving yields natural frequency and damping ratio, guiding hull form design to avoid resonance.

Deck Motion Compensation

Real‑time deck motion is estimated with a Kalman filter. State equation: x_{k+1}=A x_k + w_k, observation equation: z_k = H x_k + v_k, where x includes deck height and velocity, w_k process noise, v_k measurement noise. The filter provides feed‑forward control for the arresting gear.

4. Hull Hydrodynamics

Reynolds Number

Re = (ρ V L)/μ, with sea speed V≈15.4 m/s, length L≈316 m, water density ρ≈1025 kg/m³, dynamic viscosity μ≈1.0×10⁻³ Pa·s, giving Re ≈ 5×10⁹, indicating fully turbulent flow and a complex boundary layer.

Froude Number and Wave Resistance

Fr = V / √(g L). For the Fujian carrier, Fr ≈ 0.28, placing it in the regime where wave resistance is significant. Total resistance is decomposed into friction, wave, form and air components.

5. Aircraft Launch Scheduling Optimization

Integer Programming Model

Decision variable x_{ij}=1 if aircraft i uses catapult j. Objective: minimize makespan C_{max}. Constraints enforce one catapult per aircraft, minimum time gaps between launches on the same catapult, and binary nature of x_{ij}.

Queueing Theory Model

Landing operations are modeled as an M/M/1 queue: arrival rate λ (aircraft/min), service rate μ (recover‑time of arresting gear). Utilization ρ = λ/μ, average number in system L = ρ/(1‑ρ), average waiting time W = ρ/(μ‑λ). This guides optimal recovery intervals.

6. Radar Detection Model

Radar Equation

Maximum detection range:

R_{max} = \left( \frac{P_t G^2 λ^2 σ}{(4π)^3 S_{min}} \right)^{1/4}

, showing range ∝ fourth‑root of transmitted power and target radar cross‑section.

Phased‑Array Beam Steering

Beam angle θ relates to element phase shift Δφ by θ = \frac{λ}{d}\,\frac{Δφ}{2π}, where d is element spacing. Rapid electronic steering enables multi‑beam tracking.

7. System Reliability Model

Series Reliability

System reliability R_series = ∏_{i=1}^{n} R_i. With 100 components each having R_i=0.99, R_series ≈ 0.366, highlighting the need for high‑reliability critical parts.

Parallel Reliability

For redundant subsystems, R_parallel = 1 - ∏_{i=1}^{n} (1 - R_i). Three redundant units each with R=0.9 give R_parallel ≈ 0.999, demonstrating the benefit of redundancy.

Mean Time Between Failures (MTBF)

MTBF = 1/λ, where λ is failure rate. For λ = 1/1000 h⁻¹, MTBF = 1000 h. Designing for MTBF > 100 h ensures ≥ 95% reliability over a 100‑hour mission.