Payload installation and CG

Why this matters

UAT 321 taught how to compute total mass and CG position. This module answers the installer’s next questions: how far can the CG move while flight stays safe, and how should the camera be mounted so the image does not shake? The survey drone in this case switches between a mapping camera and a thermal camera depending on the mission, and each switch changes the CG and the vibration behaviour. The drone knowledge base’s unit on payload, CG and energy recommends calculating with checkable examples and confirming with thrust experiments. All numbers are hypothetical.

A moved CG loads the motors unequally

On an X quadcopter with the CG at the centre, all four motors carry equal weight. If the CG moves forward by $d$, the front motors must work harder to balance the moment about the CG (Quan, 2017). With the front and rear motors a fore-aft distance $a$ from the centre, each front motor’s thrust is $W(a+d)/(4a)$. The harder-working motor has less thrust left for attitude control, which may not be enough in a gust or a hard stop.

import math

G = 9.81
W = 3.2 * G                                   # N
A = 0.35 * math.cos(math.radians(45))          # m, fore-aft distance of motors from the centre
T_MAX = 1.8 * G                                # N per motor
LIMIT = 0.50

for d_cm in (0, 2, 4, 6):
    d = d_cm / 100
    tf, tr = W * (A + d) / (4 * A), W * (A - d) / (4 * A)
    share = tf / T_MAX
    print(f"CG +{d_cm} cm: front {tf:.2f} N, rear {tr:.2f} N, front motor at {share:.1%} of max -> {'ok' if share <= LIMIT else 'over limit'}")
d_max = A * (4 * LIMIT * T_MAX / W - 1)
print(f"largest CG offset within the limit: {d_max * 100:.1f} cm")

CG +0 cm: front 7.85 N, rear 7.85 N, front motor at 44.4% of max -> ok
CG +2 cm: front 8.48 N, rear 7.21 N, front motor at 48.0% of max -> ok
CG +4 cm: front 9.12 N, rear 6.58 N, front motor at 51.6% of max -> over limit
CG +6 cm: front 9.75 N, rear 5.95 N, front motor at 55.2% of max -> over limit
largest CG offset within the limit: 3.1 cm

Isolating payload vibration

Motors and propellers vibrate at the motor rotation frequency and at the blade-pass frequency (rotation frequency times the number of blades). A camera fixed rigidly to the frame shakes with it, blurring images and overworking the gimbal. The ArduPilot and PX4 documentation recommend fixing the sources first, such as balancing propellers and stiffening the frame, and then using an isolation mount. Isolation places the payload on rubber dampers, giving the system a natural frequency $f_n=\frac{1}{2\pi }\sqrt{k/m}$ under single-degree-of-freedom vibration theory (Gavin, 2026; Delli Carri). The undamped transmissibility is $T=1/|1-r^2|$ with $r=f/f_n$. Vibration is reduced when $r>\sqrt{2}$, and if $r$ is near 1 the vibration is amplified instead.

import math

M = 0.9                                        # kg
RPM, BLADES = 5000, 2
f_motor = RPM / 60
f_blade = f_motor * BLADES
print(f"excitation: motor {f_motor:.1f} Hz, blade pass {f_blade:.1f} Hz")

for name, k_each in (("soft", 2_000), ("stiff", 50_000)):   # N/m per damper
    fn = math.sqrt(4 * k_each / M) / (2 * math.pi)
    parts = []
    for f in (f_motor, f_blade):
        r = f / fn
        t = 1 / abs(1 - r * r)
        parts.append(f"{f:.0f} Hz: r {r:.2f}, T {t:.3f}")
    print(f"{name:<5} fn {fn:.1f} Hz | " + " | ".join(parts))

excitation: motor 83.3 Hz, blade pass 166.7 Hz
soft  fn 15.0 Hz | 83 Hz: r 5.55, T 0.034 | 167 Hz: r 11.11, T 0.008
stiff fn 75.0 Hz | 83 Hz: r 1.11, T 4.279 | 167 Hz: r 2.22, T 0.254

Mounting payloads so they can be inspected

• Use mounts designed to take loads in the flight directions, and lock screws with threadlocker or lock washers
• Route payload signal wires away from power wires, with enough slack for the gimbal to reach its full travel on every axis
• Put witness marks on critical screws so that loosening can be seen in the pre-flight check
• Record the mass, position and damper type of each payload variant in the configuration register (Module 5)

Module lab

Common mistakes

Summary

• A CG offset $d$ loads the motors on that side with $W(a+d)/(4a)$; the thrust margin sets the CG envelope
• Dampers isolate vibration when the excitation frequency is more than $\sqrt{2}$ times the natural frequency
• If the natural frequency is near the motor frequency, vibration is amplified
• Mount payloads so they can be inspected, with a safety lanyard, and record them in the configuration

Check your understanding

1. $W$ 30 N, $a$ 0.25 m and a CG offset of 0.05 m. What thrust does each front motor carry?
2. Mass 1 kg and total stiffness 4,000 N/m. What is the natural frequency?
3. With $r=3$, what is the transmissibility?
4. A motor at 6,000 rpm with a 3-blade propeller. What is the blade-pass frequency?
5. Why can dampers that are too stiff be worse than a rigid mount?