Mass, Balance and the Camera Swap That Moves the Centre of Gravity
A 6.8 kg maximum take-off mass hexacopter has a documented empty mass of 3.9 kg and a maximum payload of 2.9 kg. The battery (1.6 kg) sits on a tray whose centre is 40 mm forward of the datum. The gimbal and camera (0.9 kg) mount on a rail; the rail's centre is 120 mm forward of the datum. The airframe's empty centre of gravity is 15 mm forward of the datum. You are asked to replace the 0.9 kg camera with a 1.5 kg camera and a 0.3 kg lens, both on the same rail, and to add a 0.4 kg telemetry module on a rear tray 200 mm aft of the datum. The aircraft's flight controller limits are set so that the centre of gravity must stay within 30 mm forward to 30 mm aft of the datum.
1. Determine whether the new configuration stays within the centre-of-gravity limits and within maximum take-off mass. Show your working.
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Work in moments about the datum, forward positive.
Masses. Empty airframe 3.9 kg (this already includes the battery tray structure but not the battery as a separate item - treat the stated empty CG as the airframe without battery, camera and module). Battery 1.6 kg, new camera 1.5 kg, lens 0.3 kg, telemetry 0.4 kg. Total = 3.9 + 1.6 + 1.5 + 0.3 + 0.4 = 7.7 kg.
Mass check. Maximum take-off mass is 6.8 kg, so 7.7 kg is over by 0.9 kg. The configuration is not legal or safe as proposed. This alone stops the plan.
Moment check (for completeness, using the airframe alone as 3.9 kg at +15 mm).
- Airframe: 3.9 × 15 = +58.5 kg·mm
- Battery: 1.6 × 40 = +64.0
- Camera: 1.5 × 120 = +180.0
- Lens: 0.3 × 120 = +36.0
- Telemetry: 0.4 × (−200) = −80.0
- Sum of moments = 58.5 + 64 + 180 + 36 − 80 = +258.5 kg·mm
- CG = 258.5 / 7.7 = +33.6 mm forward of datum.
That is 3.6 mm beyond the 30 mm forward limit. So the proposal fails on both mass and balance.
Conclusion. Reject the configuration. To fix it you must remove mass (smaller camera or lens, or drop the telemetry module) and move mass aft (shift the camera rail aft, or relocate the module further aft) until both total mass ≤ 6.8 kg and CG lies between −30 and +30 mm.
2. The client insists on the heavier camera. Propose a revised configuration and justify it numerically.
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The binding constraint is mass: 6.8 kg total. With airframe 3.9 kg and battery 1.6 kg, you have 1.3 kg for everything on the rails. A 1.5 kg camera plus 0.3 kg lens is already 1.8 kg, so the heavy camera cannot fly with this battery and airframe.
Options, each checked:
Option A - lighter camera, keep telemetry. Camera 0.9 kg, lens 0.2 kg, telemetry 0.4 kg: total = 3.9 + 1.6 + 0.9 + 0.2 + 0.4 = 7.0 kg. Still 0.2 kg over. Drop the telemetry module: 6.6 kg, within limits. Moments: 58.5 + 64 + 108 + 24 = 254.5; CG = 254.5 / 6.6 = +38.6 mm - too far forward. Move the camera rail aft so the camera centre sits at +60 mm: camera moment 0.9 × 60 = 54, lens 0.2 × 60 = 12; sum = 58.5 + 64 + 54 + 12 = 188.5; CG = 188.5 / 6.6 = +28.6 mm. Within the +30 mm limit, but with almost no margin.
Option B - heavy camera with a smaller battery. Camera 1.5 kg, lens 0.3 kg, no telemetry, battery reduced to 1.1 kg: total = 3.9 + 1.1 + 1.5 + 0.3 = 6.8 kg exactly - no margin, and reduced endurance. Moments: airframe 58.5, battery 1.1 × 40 = 44, camera 1.5 × 120 = 180, lens 0.3 × 120 = 36; sum = 318.5; CG = 318.5 / 6.8 = +46.8 mm - well outside the forward limit. Would require moving the rail aft by roughly 17 mm or more.
Recommendation. Option A with the rail moved aft is the cleaner answer: it meets mass with 0.2 kg margin and meets balance, though the CG margin is thin. Before flight, verify the actual CG on a balance rig rather than trusting catalogue masses, because camera, lens and cabling masses vary, and re-check after any rail adjustment. Also confirm the flight controller's CG limits are the certified ones, not just a convenience setting.