UAV Camera Bracket Bolt Check
A UAV carries a 4.5 kg electro-optical camera on a bracket that projects 0.35 m forward from the mounting plate. The bracket is fastened by four M4 bolts arranged in a 60 mm (fore-aft) by 40 mm (lateral) rectangular pattern. The aircraft can accelerate forward at 6 g. Assume the camera mass acts at the bracket tip and the bolt group resists the resulting moment as a couple shared equally by the two bolts on the tension side; the lever arm between the tension and compression bolt rows is 60 mm. Each bolt's allowable tensile load is 1.2 kN, and the design requires a safety factor of 1.5 on the combined tensile and shear load per bolt. The forward inertia force is shared equally by all four bolts in shear. Take g = 9.81 m/s². The structural engineer must check whether the bolt pattern is adequate, and whether moving the camera 50 mm closer to the plate would change the verdict.
1. Calculate the per-bolt combined tensile and shear load and compare it with the allowable load including the safety factor.
Read the worked answer
Inertia force F = m × a = 4.5 × 6 × 9.81 = 264.87 N. Moment about the bolt plane M = F × 0.35 = 92.70 N·m. The couple force total is M ÷ 0.06 = 1545 N, shared by two tension bolts, so tensile load per bolt = 772.5 N. Shear per bolt = 264.87 ÷ 4 = 66.2 N. Combined load = √(772.5² + 66.2²) = 775.3 N. The allowable with the required safety factor is 1200 ÷ 1.5 = 800 N. Since 775.3 N < 800 N, the bracket passes, but the margin is only 24.7 N, about 3% of the allowable. That is a thin margin for assumptions about mass location, dynamic factors, and bolt preload.
2. Recompute the per-bolt load if the camera is moved 50 mm closer to the mounting plate. Does the verdict change?
Read the worked answer
The new moment arm is 0.35 − 0.05 = 0.30 m. The inertia force is unchanged at 264.87 N, so M = 264.87 × 0.30 = 79.46 N·m. The couple force total is 79.46 ÷ 0.06 = 1324.3 N, and tensile load per bolt is 662.2 N. Shear remains 66.2 N per bolt. Combined load = √(662.2² + 66.2²) = 665.5 N. This is below the 800 N allowable by 134.5 N, a margin of about 17% of the allowable. The verdict remains 'pass', but the margin improves substantially. Moving the mass closer reduces the moment proportionally, which is why a 50 mm change cuts the tensile component by about 14%.
3. The bracket is rotated 90° so the 60 mm dimension is now lateral and the 40 mm dimension is fore-aft. Which dimension sets the moment lever arm, and what happens to the bolt tension?
Read the worked answer
The forward inertia force creates a moment about a lateral axis, so the resisting couple acts between the fore-aft bolt rows. The relevant lever arm is therefore the fore-aft spacing, not the larger 60 mm spacing. After rotation, that spacing is 40 mm. The moment remains 92.70 N·m. The couple force total is 92.70 ÷ 0.04 = 2317.5 N, and tensile load per bolt is 1158.75 N. Adding shear gives √(1158.75² + 66.2²) ≈ 1160.6 N. This exceeds the 800 N allowable, so the pattern fails. The orientation change is not cosmetic: it reduces the lever arm by one third and raises bolt tension by 50%.