Gust and maneuver loads on a fixed-wing UAS

On a manned light aircraft the maneuver load factor usually sets the wing design. On a small fixed-wing UAS it often doesn’t, and the reasons are wing loading and how close to stall the aircraft cruises. This post works the standard gust formulation for one specific airframe, shows where the gust case overtakes the maneuver case, shows where the airframe stalls before the formula’s number is ever reached, and identifies which parts of the manned-aircraft method carry over to a 10 kg aircraft at 100 m and which don’t.

The airframe we’re using

We picked the Applied Aeronautics Albatross because it’s a commercial fixed-wing UAS and the manufacturer publishes most of its numbers.

If the 57 km/h stall speed was measured below MTOW, the stall speed at 10 kg is higher and every stall-limited number below gets smaller. At MTOW, 57 km/h implies a C_Lmax of about 0.93, which is on the low side for a clean wing and is one reason to suspect the stall figure is at a lighter weight.

For scale, a Cessna 172 has a wing loading around 670 N/m².

The maneuver case

NATO AEP-83, the Light Unmanned Aircraft Systems Airworthiness Requirements published under STANAG 4703 and the NATO airworthiness code for fixed-wing UAS under 150 kg, asks for a positive symmetric limit maneuvering load factor of at least 3.8 and a negative limit of at least −1.5 (UL5.2), and allows lower values if the flight control system makes them impossible to exceed. Those are the normal-category numbers from the FAA’s small-airplane airworthiness standard, 14 CFR Part 23 (in the text that applied before the 2017 rewrite), and from EASA CS-VLA, the European Certification Specifications for Very Light Aeroplanes, carried across.

There’s a second constraint the standard doesn’t need to state because it’s physics: the wing can’t make more lift than C_Lmax allows. At any speed V the most load factor available is

At V_C = 18 m/s, n_stall = (18 / 15.8)² = 1.3. The aircraft cruises at 1.14 times its stall speed and can’t pull 3.8 g at cruise no matter what the autopilot commands; it stalls at 1.3. The speed where 3.8 g first becomes reachable is 15.8 × √3.8 = 31 m/s, which is the aircraft’s maneuvering speed V_A. At V_Cmax = 36 m/s, n_stall = 5.2.

Wing root bending moment for the 3.8 g case, taking the lift distribution as roughly elliptical so the spanwise center of pressure sits at 4/(3π) of the semispan: M_root = n × (W/2) × 0.424 × (b/2) = 3.8 × 49.05 × 0.636 = 119 N·m per wing, before inertia relief from the wing’s own mass. The Albatross wing is forward-swept and tapered, so the real distribution isn’t elliptical.

The gust case, as the standard writes it

AEP-83 UL5.3 assumes the aircraft meets vertical and lateral gusts in level flight, with the gust velocities to be set by rational analysis of the intended use. If you don’t do that analysis it gives defaults: 15.2 m/s (50 ft/s) at V_C and 7.6 m/s (25 ft/s) at V_Cmax, up to 6096 m. Those are the Part 23 and CS-VLA values, and every manned light aircraft for decades has been designed to them.

The load factor increment from a discrete gust uses the Pratt formula, written in section 23.341 of Part 23 and section 341 of CS-VLA. In SI:

where K_g is the gust alleviation factor, K_g = 0.88 μ / (5.3 + μ), and μ is the mass ratio, μ = 2 (W/S) / (ρ c a g). The alleviation factor is there because a real gust ramps up over a distance and the aircraft starts responding (climbing, pitching) before the full gust velocity arrives. Light, short-chord aircraft respond faster and get more alleviation.

For the Albatross: μ = 2 × 143.5 / (1.225 × 0.228 × 5.46 × 9.81) = 19.2, so K_g = 0.69.

The two results are equal because the product V × U_de is 274 m²/s² in both cases: the standard halves the gust velocity, and this aircraft’s V_Cmax is twice its V_C. Both are above the 3.8 maneuver case. This is the effect of wing loading: Δn scales with 1 / (W/S), so an aircraft with a quarter of a Cessna’s wing loading sees, all else equal, four times the gust increment from the same gust, before K_g takes some of it back.

Where the formula stops working

Not all of those load factors are reachable.

Stall caps the V_C case. A 15.2 m/s vertical gust at 18 m/s forward speed changes the angle of attack by atan(15.2 / 18), about 40 degrees. The wing stalls long before that. The most lift it can make at 18 m/s is n_stall = 1.3. The discrete gust formula assumes the lift curve stays linear through the gust, which is fine when the gust-to-airspeed ratio is small (a Cessna at 60 m/s in the same gust sees a 14 degree change) and isn’t fine here. AEP-83 UL47.4 addresses this: it requires the applicant to characterize the aircraft’s response to the UL5.3 gust including the possibility of stalling, and to set operating limits if needed.

So at V_C the wing’s structural load is capped at 1.3 g, and the gust case turns into a controllability question (does the autopilot recover from a gust-induced stall at 100 m, with a 40 degree angle of attack excursion) rather than a structural one.

The V_Cmax case is right at the boundary. At 36 m/s with U_de = 7.6 m/s the angle of attack change is about 12 degrees, close to where most airfoils stall, and n_stall = 5.2 sits just under the Pratt number of 5.4. So the wing load at V_Cmax is capped at about 5.2 g by stall, slightly below the formula. Either way it’s above the 3.8 maneuver case by roughly 37 percent, and that’s the case that governs the Albatross wing. If the store’s 40 m/s max speed is the right one instead, the Pratt number becomes 5.9 and the stall cap 6.4.

The 15.2 m/s figure itself is suspect at this altitude and size. The manned-aircraft gust velocities came from flight-load surveys on aircraft flying at altitude across weather systems. A small UAS below 120 m, in weather it’s legally allowed to fly in, sees a different atmosphere. The turbulence model in MIL-F-8785C, the US military flying qualities specification for piloted airplanes, as reproduced in its successor handbook MIL-HDBK-1797 and in the MathWorks Dryden model documentation, gives a low-altitude vertical turbulence intensity of σ_w = 0.1 × W_20, where W_20 is the wind at 20 ft: 15 knots for light turbulence, 30 for moderate, 45 for severe. That’s 0.8, 1.5, and 2.3 m/s RMS. A 3σ peak in severe low-altitude turbulence is about 7 m/s, close to the 7.6 m/s V_Cmax default and less than half the 15.2 m/s V_C default.

The mass ratio is moderate. At μ = 19 the Albatross is in the lower part of the range the K_g fit was built on, so the quasi-static assumption under the whole formula (that the load builds slowly enough for the structure to respond statically) still holds reasonably for a stiff carbon wing. For a long flexible wing on a high-endurance UAS it doesn’t.

Resulting V-n diagram

Reading it: the design point for the wing is the V_Cmax corner where the stall boundary and the gust line meet, not the maneuver limit. That’s the opposite of a typical manned light aircraft, where the maneuver corner at V_A usually governs.

Putting it into the model

Apply the gust case as a spanwise distributed pressure that matches your lift distribution, scaled so total lift equals n × W with n = 5.2, split per wing. Don’t apply it as a tip load or a single resultant at the center of pressure; both give the right root moment and the wrong stress everywhere else. Subtract inertia relief from the wing structure and anything mounted in the wing (servos, batteries in wing bays) by including those masses under n × g in the opposite direction.

Ultimate load is 1.5 times limit (AEP-83 UL2.3 for primary structure). Run the 5.2 g case and multiply the stresses by 1.5, or run 7.8 g directly if the model is linear; same answer.

The lateral gust (UL5.3 applies the same values sideways) loads the vertical tail and the fuselage in side bending. On the Albatross that goes through the tail boom into the fuselage, and should be included.

What to do with this

Work out n_stall at your cruise speed first. If it’s under 2, as it is for the Albatross, your gust problem at cruise is a stall recovery problem and the wing load question moves to V_Cmax. Then compute μ and K_g, draw the stall boundary before you draw the gust lines, and discard any gust point above it. Compare what’s left against the 3.8 maneuver case; on light airframes the gust case is usually larger. And decide whether the default gust velocities are right for your operating altitude.

Sources

1. Applied Aeronautics Albatross product page, FAQ, and store spec sheet.

   https://www.appliedaeronautics.com/faqhttps://store.appliedaeronautics.com/albatross-airframe/

2. diydrones Designer’s original Albatross specification, for wing area and root and tip chord.

   https://diydrones.com/profiles/blogs/introducing-the-albatross-uav-project

3. NATO AEP-83 (STANAG 4703), Light Unmanned Aircraft Systems Airworthiness Requirements, Edition A Version 1, September 2014. UL2.3 (ultimate factor), UL5.2 (maneuver load factors), UL5.3 (gust velocities), UL47.4 (gust-induced stall).

   https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/391827/20140916-STANAG-4703_AEP-83_A__1_.pdf

4. FAA 14 CFR 23.341 (pre-Amendment 23-64) and CS-VLA 341 for the discrete gust formula, K_g, and μ.

   http://www.pilotfriend.com/FARS/6/Sec.%2023.341.htm

5. Pratt and Walker “A Revised Gust-Load Formula and a Re-evaluation of V-G Data Taken on Civil Transport Airplanes from 1933 to 1950,” NACA Report 1206, 1954.

   https://ntrs.nasa.gov/search.jsp?R=19930090988

6. MathWorks MIL-F-8785C low-altitude turbulence model, as reproduced in the Dryden Wind Turbulence Model documentation.

   https://www.mathworks.com/help/aeroblks/drydenwindturbulencemodelcontinuous.html