What loads act on a multirotor arm
Thrust, gyroscopic moment, landing impact, and vibration all show up at the arm. A walk through which ones set the design and which you can defer, worked on a Holybro X500 V2.
The arm is the simplest structural part on a multirotor, which can make it easy to account for thrust alone and miss the important loads. This post ranks every load that reaches the arm on one specific, widely used frame, shows the hand calculation for each, and says which ones you can leave out of the model without losing anything.
The frame we’re using
We picked the Holybro X500 V2 because it’s a common PX4 development platform, Holybro publishes the mechanical drawings and a STEP file, and the stock motor and prop are known. The numbers below come from Holybro’s product documentation and, for the motor, from the datasheet of the OEM-equivalent LigPower AIR2216II, since Holybro doesn’t publish its own thrust table.
| Parameter | Value | Source |
|---|---|---|
| Frame kit mass | 610 g | Holybro |
| Takeoff mass used here | 3.2 kg (weight 31.4 N) | Holybro’s payload statement (about 1 kg payload at 70 percent hover throttle on 4S) implies roughly 3.2 kg all-up; the ReadyMadeRC listing quotes “up to 3,200 g” |
| Wheelbase | 500 mm | Holybro |
| Arm length, hub center to motor axis | 250 mm | Computed, wheelbase divided by 2 |
| Arm section | 16 mm OD carbon tube; ID not published, taken as 14 mm | Holybro |
| Landing gear | Separate carbon tube assembly on the center body, not on the arms | Holybro |
| Motor | Holybro 2216 920KV, 63 g, 16 mm x 16 mm M3 bolt pattern | Holybro docs, reseller listings |
| Propeller | 1045 (10 in x 4.5 in), two blades, 13 g | Holybro; LigPower datasheet for mass |
| Max static thrust per motor | 1,332 g (13.1 N) at 9,857 rpm, 16.4 A, 260 W electrical, on 4S at 16 V | LigPower AIR2216II datasheet |
| Hover thrust per motor at 3.2 kg | 800 g (7.85 N), around 70 percent throttle | Computed from takeoff mass |
Tube section properties for 16 mm OD, 14 mm ID: I = 1331 mm⁴, Z = 166 mm³, J = 2662 mm⁴.
(1)One aside is that the X500’s landing gear bolts to the center plates, so on this frame the arms don’t need to withstand landing. That changes the ranking compared with a frame that has legs on the arm tips, and we show both cases below.
The loads
Each load is written as a moment at the arm root, where the tube enters the fiber-reinforced nylon connector at the center body. The tube itself has a lot of headroom, as the ranking shows.
1. Thrust bending
The most commonly modeled. Thrust acts upward at the motor axis, 250 mm from the root, so the root moment is T times L.
At hover: 7.85 N × 0.25 m = 1.96 N·m. Bending stress = M/Z = 1960 N·mm / 166 mm³ = 11.8 MPa.
(2)At max thrust: 13.1 N × 0.25 m = 3.27 N·m, or 19.7 MPa.
(3)Use max thrust, not hover, and use it at full pack voltage. The LigPower table is at 16 V, which is 4.0 V per cell; a freshly charged 4S pack sits at 16.8 V and thrust at full throttle will be a bit above 1,332 g. The datasheet also says its numbers are for reference only, so if you have a thrust stand, use your own.
2. Landing reaction, if the gear were on the arms
On the X500 it isn’t, so this line is hypothetical for this frame. It’s here because a lot of frames do put the legs on the arm tips, and the number is large enough to change the design. For a moderately hard landing at n = 5 on the gear, the vertical reaction per leg is n × W / 4 = 5 × 31.4 / 4 = 39 N.
Root moment: 39 N × 0.25 m = 9.8 N·m, or 59 MPa in the tube.
(4)That’s three times the max thrust case. If the legs are on the arms, landing sets the arm design and thrust doesn’t. On the X500 the same load goes into the center plates instead, so the arms can stay light and the 2 mm carbon plates take the force of the landing instead.
3. Gyroscopic moment
A spinning prop resists being tilted. When the aircraft pitches or rolls at rate Ω, each prop puts out a moment M = I_p × ω × Ω, where I_p is the prop’s moment of inertia about its spin axis and ω is prop speed.
Nobody publishes I_p for a 1045 prop. Treating the 13 g prop as a uniform rod, I_p = (1/12) × 0.013 × 0.254² = 7.0 × 10⁻⁵ kg·m². Real props carry most of their mass near the hub, so this is an upper bound.
At 9,857 rpm (1,032 rad/s) and a pitch rate of 200 deg/s (3.5 rad/s): M = 7.0 × 10⁻⁵ × 1032 × 3.5 = 0.25 N·m.
(5)Which way it acts depends on how the aircraft is rotating relative to the arm. If the pitch axis runs along the arm, the moment twists it. If the axis runs across the arm, the moment bends it sideways. On an X frame like the X500 every arm sits at 45 degrees to both axes and gets some of each.
Torsional stress in the tube: τ = M × c / J = 250 × 8 / 2662 = 0.8 MPa.
(6)Negligible for the tube. It matters at the motor mount bolts, which you can read about here.
4. Motor torque reaction
The motor spins the prop one way and the arm gets pushed the other way. Torque Q = P / ω. The datasheet gives electrical power: 260 W at max thrust, not shaft power. Using electrical power gives an upper bound: Q = 260 / 1032 = 0.25 N·m. Shaft torque is lower by the motor efficiency, by about 0.20 N·m.
This moment acts about the motor’s vertical axis, so it bends the arm sideways, in the plane of the frame. On a round tube it’s 0.25 N·m against a 3.27 N·m thrust moment, so it’s negligible on its own. The two reasons it stays on the list anyway are firstly that it reverses sign between CW and CCW motors, so the connector at the root sees opposite in-plane moments on adjacent arms. And secondly, that on a flat plate arm, which the X500 doesn’t have, the in-plane and out-of-plane stiffnesses can differ by a factor of fifty, and it needs to be included.
5. Tip mass inertia during maneuvers
The motor and prop at the tip weigh 76 g, plus the ESC if mounted there. With 13.1 N per motor against 31.4 N of weight, the X500 at 3.2 kg has a thrust-to-weight ratio of 1.66, so the hardest it can accelerate upward is 0.66 g and the highest load factor it can pull is 1.66. The tip mass then pulls down on the arm with 0.076 × 1.66 × 9.81 = 1.2 N.
Root moment: 1.2 N × 0.25 m = 0.31 N·m, opposite to the thrust moment, so in a climb it relieves the arm slightly. In a hard pitch reversal the sign can flip. Put it in the model as a mass at the tip rather than a force so the solver applies the correct direction.
6. Aerodynamic drag on the arm
At 15 m/s forward flight, a 16 mm tube 250 mm long with a drag coefficient around 1.0 sees roughly 0.55 N spread along its length. Root moment about 0.07 N·m. It can be left out.
7. Vibration
The two-blade 1045 at 9,857 rpm drives the arm at 164 Hz (once per revolution, from imbalance) and 329 Hz (twice per revolution, from blade passing). At hover, around 7,800 rpm from the datasheet curve, those are 130 Hz and 260 Hz. If the arm’s first bending mode lands near any of those, the static results above don’t apply, because the arm is resonating. Holybro doesn’t publish a natural frequency for the X500, so this has to come from a modal run or a tap test.
The ranking
Root moment on the X500 at 3.2 kg, largest first:
| Load | Root moment (N·m) | Tube stress (MPa) | Notes |
|---|---|---|---|
| Landing, n = 5, if gear were on the arm | 9.8 | 59 | Not on this frame; governs on frames with legs at the tips |
| Max thrust | 3.27 | 19.7 | Governs on the X500 |
| Tip mass inertia, 1.66 g | 0.31 | 1.9 | Relieves thrust bending in a climb |
| Gyroscopic, 200 deg/s | 0.25 | 0.8 (torsion) | Matters at the motor mount, not the tube |
| Motor torque reaction | 0.25 (upper bound) | 1.5 | In-plane bending, reverses on adjacent arms |
| Arm drag, 15 m/s | 0.07 | 0.4 | Leave out |
Two things come out of this table.
The tube has a large margin. Even the hypothetical landing case puts 59 MPa into a tube whose material fails at well over a thousand MPa in bending: Rock West quotes flexural strengths of 1,810 MPa for T300 and 1,670 MPa for T700S roll-wrapped laminate. A thin-wall tube usually fails by local buckling or ovalization before the laminate strength is reached, so the real number is lower, but not by a factor of thirty. The root joint carries that same moment into a nylon connector and a pair of screws, and that joint is where the margin is smallest. Mesh refinement belongs there.
And the load cases worth running are combinations. Max thrust plus gyroscopic moment happens in every aggressive maneuver. Landing plus residual hover thrust happens on every touchdown, into the center plates on this frame. A single “max thrust” case on its own misses both.
What to do with this
Rank the loads for your own frame before you run anything. A short spreadsheet is enough to show which two or three cases deserve a solver run. Check where the legs attach first, because that decides whether the arm is a thrust problem or a landing problem. Then mesh the root joint properly and treat the tube as a beam.
Sources
Holybro X500 V2 product page and documentation, including the 3D CAD download.
https://docs.holybro.com/drone-development-kit/px4-development-kit-x500v2ReadyMadeRC X500 V2 frame listing, used for takeoff weight guidance.
https://www.readymaderc.com/products/details/87065-holybro-x500-frame-kitLigPower AIR2216II KV920 datasheet with T1045 thrust table, the OEM equivalent of the Holybro 2216 920KV.
https://cdn.robotshop.com/media/T/Tmo/RB-Tmo-266/pdf/ligpower_airgear_450ii_combo_set_multi_rotor_uav_p_datasheet.pdfRock West Composites T300 and T700S laminate datasheets.
https://www.rockwestcomposites.com/on/demandware.static/Sites-RWC-Site/Sites-rwc-master-catalog/-/wysiwyg/T300DataSheet_1.pdfhttps://www.rockwestcomposites.com/on/demandware.static/Sites-RWC-Site/Sites-rwc-master-catalog/-/downloads/T700SDataSheet.pdfNATO AEP-83 (STANAG 4703), Light Unmanned Aircraft Systems Airworthiness Requirements, Edition A, 2014. UL.5 and UL.6 on including propulsion and gyroscopic loads.
https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/391827/20140916-STANAG-4703_AEP-83_A__1_.pdf