Designing a Peak-Hour Traffic Monitoring Satellite Constellation for Hong Kong: A GMAT Tutorial

Introduction to Satellite Constellation Design for Traffic Monitoring

In this tutorial, we explore the engineering behind designing a satellite constellation to monitor vehicular traffic in Hong Kong during peak hours (07:00–09:00 and 18:00–20:00 local time). This is based on the AAE5208 Satellite Engineering lab assignment, where you must use GMAT to simulate a constellation that provides at least two passes over the target area (22.3°N, 114.2°E) during each critical window. The mission starts on 19 November 2025 and must operate for at least two years. We'll cover key concepts like orbit altitude, inclination, Walker constellations, delta-V budgeting, and cost minimization.

Why Satellite Constellations for Traffic Monitoring?

Traditional ground-based traffic cameras have limited coverage. Satellites can provide wide-area monitoring, but a single satellite's revisit time is too long. A constellation of multiple satellites can achieve the required revisit rate. For Hong Kong, a densely populated city with complex traffic patterns, a satellite constellation offers a cost-effective solution for real-time traffic data collection, helping to alleviate congestion and improve urban mobility—a trend seen in smart city initiatives worldwide.

Understanding the Requirements

Before diving into design, let's break down the key requirements:

• Target Area: 50 km × 50 km centered on Hong Kong (22.3°N, 114.2°E).
• Peak Hours: 07:00–09:00 and 18:00–20:00 Hong Kong Time (UTC+8).
• Revisit Rate: At least two passes per peak window.
• Mission Lifetime: Minimum two years.
• Spatial Resolution: GSD ≤ 1.0 m to distinguish individual vehicles.
• Launch Constraints: From Hainan Wenchang (19.6145°N, 110.9511°E) using CZ-12 rocket.
• Satellite Mass: Dry mass 500 kg, total launch mass 1000–4000 kg (including fuel). Propulsion: Isp 320 s, delta-V 2168–6511 m/s.
• Cost: Minimize total mission cost = m_total × Claunch + n_sats × Csat, where Claunch = 80,000 HKD/kg, Csat = 50 + 2 × m_total (million HKD, m_total in tons).

Step 1: Choosing Orbit Altitude and Inclination

Altitude affects spatial resolution, swath width, atmospheric drag, and launch cost. For GSD ≤ 1.0 m, we need a low altitude. Using a real-world camera like the WorldView-3 (panchromatic resolution 0.31 m at 617 km altitude) scaled to our requirements, a lower altitude improves resolution but increases drag. We'll assume a camera with half-cone field of view θ = 2° and sensor dimensions (longer side 10000 pixels, shorter side 5000 pixels).

From Equation (2): Wnadir = 2h tan(θ). For θ = 2°, tan(2°) ≈ 0.0349. To achieve a swath width covering the 50 km target, we need Wnadir ≥ 50 km. Thus h ≥ 50/(2*0.0349) ≈ 716 km. But this is too high for 1 m GSD. Let's compute GSD: GSD = (pixel size * h) / focal length. For a typical camera, GSD ∝ h. If we want GSD ≤ 1 m, we need h ≤ about 300 km for a camera with 0.5 m focal length and 5 µm pixel size. So we choose an altitude around 300 km to balance resolution and drag.

At 300 km, atmospheric drag is significant but manageable with propulsion for station-keeping. We'll need to justify altitude in the report. For inclination, a sun-synchronous orbit (SSO) provides consistent lighting, which is beneficial for traffic monitoring (consistent shadows). SSO typically has inclination around 97° for low altitudes. However, SSO may not be optimal for coverage during specific local times. We'll consider a lower inclination like 45° to increase revisit frequency over Hong Kong (latitude 22.3°N). A Walker constellation with 45° inclination can provide good coverage at mid-latitudes.

Step 2: Walker Constellation Design

A Walker constellation is denoted by i: t/p/f, where i = inclination, t = total number of satellites, p = number of equally spaced planes, f = relative phasing between planes. For our requirement of at least two passes per peak window, we need to simulate different configurations. Let's start with a simple design: 4 satellites in 2 planes (t=4, p=2, f=1). We'll use GMAT to verify coverage.

We'll set orbital altitude = 300 km, inclination = 45°, RAAN distribution: first plane RAAN = 0°, second plane RAAN = 180° (or 90° depending on phasing). Mean anomaly for satellites in each plane spaced 180° apart. We'll also consider adding more satellites to meet the revisit requirement.

Step 3: Launch Strategy and Delta-V Budget

We launch from Hainan Wenchang (19.6°N). The CZ-12 can deliver up to 10,000 kg to 300 km LEO. Our satellites have total launch mass between 1000 and 4000 kg each. For a constellation of 4 satellites, total mass = 4 * 2000 kg = 8000 kg (if we choose 2000 kg each), which is within capacity. We may need multiple launches if mass exceeds capacity.

Delta-V budget: From parking orbit (200 km) to final orbit (300 km) requires a Hohmann transfer: ΔV ≈ 0.1 km/s (small). Inclination change from 19.6° to 45°: ΔV = 2V sin(Δi/2) ≈ 2 * 7.7 km/s * sin(12.7°) ≈ 3.4 km/s. This is large but within our delta-V capability (2168–6511 m/s). We'll need to perform inclination change at apogee of transfer orbit. Alternatively, we can launch directly into desired inclination if launch site latitude allows; Hainan at 19.6°N can achieve inclinations down to 19.6° but not higher without a plane change. So we need a plane change maneuver.

Phasing maneuvers to establish constellation: After injection, satellites need to be spaced in true anomaly. Using differential mean motion, we can drift to correct positions. ΔV for phasing is typically small (< 100 m/s). Station-keeping for two years: at 300 km, drag causes about 2 km altitude loss per year; ΔV for drag compensation ≈ 10–20 m/s per year. Total ΔV budget ≈ 3500 m/s (inclination change) + 200 m/s (phasing and station-keeping) = 3700 m/s, which is feasible with fuel load of about 2000 kg (total mass 2500 kg, dry 500 kg, fuel 2000 kg). Using ΔV = Isp * g0 * ln(m0/mf) = 320 * 9.81 * ln(2500/500) ≈ 320*9.81*1.609 ≈ 5050 m/s, which is sufficient.

Step 4: Cost Optimization

Cost per satellite: Csat = 50 + 2 * m_total (million HKD, m_total in tons). For m_total = 2.5 tons, Csat = 50 + 2*2.5 = 55 million HKD. Launch cost: Claunch = 80,000 HKD/kg * 2500 kg = 200 million HKD per satellite. Total mission cost for 4 satellites = 4 * (200 + 55) = 1020 million HKD. To minimize cost, we can reduce satellite mass (e.g., use 1000 kg total mass) but then delta-V capability drops to 2168 m/s, which may not be enough for inclination change. We need to find a balance.

Consider using a higher altitude (e.g., 500 km) to reduce drag and inclination change ΔV? Actually, inclination change ΔV depends on velocity, which decreases with altitude. At 500 km, velocity ≈ 7.6 km/s, ΔV for 25.4° change ≈ 2*7.6*sin(12.7°) ≈ 3.35 km/s, slightly lower. But higher altitude increases GSD (worse resolution). To meet GSD ≤ 1 m, we need a larger camera or lower altitude. We'll stick with 300 km.

Another cost-saving approach: use fewer satellites with better phasing. Simulate in GMAT to see if 3 satellites can achieve two passes per window. If not, 4 satellites is the minimum.

Step 5: GMAT Simulation Setup

In GMAT, create a spacecraft with dry mass 500 kg, fuel mass 2000 kg, Isp 320 s. Set orbit elements: SMA = 6378 + 300 km, eccentricity 0, inclination 45°, RAAN = 0° for first satellite, 180° for second (if in different plane). Mean anomaly: 0° for first, 180° for second in same plane. Propagate using J2 perturbation and drag (use a simple drag model). Define the target area as a ground target at Hong Kong. Use the Coverage tool to compute passes during peak hours. Adjust number of satellites and phasing until you get at least two passes per window.

For the launch segment, you can simulate a simplified ascent: start from parking orbit at 200 km, then perform a Hohmann transfer to 300 km, followed by inclination change at apogee. Use finite maneuvers in GMAT.

Example: Walker 45°: 4/2/1

Let's test a Walker 45°: 4/2/1 constellation. That means 4 satellites, 2 planes, phasing factor 1. In GMAT, set up two planes with RAAN difference 180°. In each plane, two satellites with mean anomaly difference 180°. Propagate for one day and check coverage over Hong Kong during peak hours. You may find that this configuration provides about 3–4 passes per window, exceeding the requirement. Then you can reduce to 3 satellites (e.g., 3/3/1) and check again. The goal is to minimize cost while meeting requirements.

Conclusion

This tutorial walked through the key steps in designing a satellite constellation for traffic monitoring: understanding requirements, choosing orbit parameters, designing a Walker constellation, planning launch and maneuvers, and optimizing cost. Use GMAT to iterate and validate your design. Remember to justify your choices in the technical report. Good luck with your AAE5208 lab!