Design project: a small UAS

Six months after the Vertical Flight group formed, it holds the conceptual design review for the wildfire mapping and inspection aircraft, which the team has named Larkspur. Representatives of the state forest service and a regional power cooperative attend, along with Rachel Oduya for regulation, Teresa Nakamura for propulsion, Marcus Webb for structures, Hélène Lavoie for manufacturing and Sam Littlechild, who will fly it. Arjun presents. This lesson follows the design from requirements to a selected concept, using the methods of the whole course, and ends with the plan for the next phase. It is also the template for the course's own design project.

Requirements

Good requirements are specific, measurable and traceable to a need. The team turned the customers' wishes into the following set, agreeing which are firm and which are goals. The wildfire mission drives most of them: mapping a fire perimeter at night with thermal imagery, from launch sites that may be a gravel road or a small clearing, and sending images to the incident team within minutes. The inspection mission adds hovering close to towers and lines.

Two requirements pull against each other: the inspection hover favors a multirotor, while the 60-minute mapping endurance favors a wing. The group decided early that the firm requirements come from the wildfire mission and that inspection hover is a goal. If no single concept meets both, a regional power cooperative can use a commercial quadcopter for close inspection, as lesson 7 showed is practical, and Larkspur for long line patrols.

Concepts

The team considered five concepts. A conventional fixed-wing aircraft has the best endurance but needs a runway or launcher and recovery system; it failed the launch requirement. A hexacopter, the multirotor with useful redundancy, meets the launch and hover requirements easily. A quadplane, a lift-plus-cruise layout with four lift rotors on two booms, a pusher propeller and a wing, hovers for take-off and landing and cruises on the wing. A tail-sitter, which takes off pointing up and pitches over to fly on its wing, saves the mass of separate lift rotors but is hard to handle in gusty wind during the transitions and lands nose-up on rough ground. A tiltrotor uses the same motors for both phases but adds tilt mechanisms and complex transition control. After a qualitative screening against the requirements, the hexacopter and the quadplane went forward to quantitative sizing.

Sizing method

Small aircraft sizing works with mass fractions. The take-off mass is the sum of the payload, the avionics and systems (flight controller, radios, satellite receiver, ADS-B receiver, parachute), the propulsion system (motors, speed controllers, propellers), the structure and the battery. Writing the structure and battery as fractions of take-off mass, and the propulsion mass as a function of the installed power, which itself depends on the take-off mass, gives a fixed-point equation:

Iterating from a guess converges in a few steps. For the hexacopter, hover power from momentum theory sets the motor size for a thrust-to-weight ratio of 2, and forward flight at mapping speed needs about 95 percent of hover power, because the body and payload drag cancel most of the induced power relief at these modest speeds. For the quadplane, the lift motors are sized for a thrust-to-weight ratio of 1.6, enough for vertical flight in gusts, while cruise power comes from the wing: the wing area follows from a chosen wing loading, the lift coefficient from the cruise speed, and the drag coefficient from a parasite term, which includes the drag of the stopped lift rotors and booms, plus the induced drag of the wing. The endurance is the usable battery energy, after the quadplane's two minutes of vertical flight, divided by the cruise power.

# Larkspur concept trade: hexacopter against quadplane (lift rotors plus a pusher and a wing).
import math
rho, g = 1.225, 9.81
m_pay, m_avi = 1.5, 1.2                     # payload (RGB + thermal gimbal) and avionics, radios, parachute (kg)
e_spec, usable = 220.0, 0.80                # pack Wh/kg and usable fraction
eta = 0.85 * 0.95                           # motor x speed controller
def size(kind, f_batt):
    """Fixed-point sizing: take-off mass from fixed masses and mass fractions; return mass, span, endurance."""
    m = 10.0
    for _ in range(100):
        if kind == "hexacopter":
            f_struct, n, D = 0.24, 6, 0.53
            A = n * math.pi * (D / 2)**2
            P_h = m * g * math.sqrt(m * g / (2 * rho * A)) / 0.60 / eta
            P_cr = 0.95 * P_h                # forward flight at 12 m/s saves little: body drag offsets the induced-power relief
            m_prop = 0.20 * P_h * 2.0 / 1000 + 0.05 * n   # motors sized for T/W 2: 0.20 kg per kW, plus props
            span = None
        else:
            f_struct, n, D = 0.30, 4, 0.46
            A = n * math.pi * (D / 2)**2
            P_h = m * g * math.sqrt(m * g / (2 * rho * A)) / 0.60 / eta
            W_S = 160.0                      # wing loading (N/m^2)
            S = m * g / W_S; AR = 11.0; span = math.sqrt(AR * S)
            V = 22.0                         # mapping speed (m/s)
            CL = m * g / (0.5 * rho * V**2 * S)
            CD = 0.045 + CL**2 / (math.pi * 0.75 * AR)      # includes drag of the stopped lift rotors and booms
            P_cr = 0.5 * rho * V**3 * S * CD / 0.70 / eta
            m_prop = 0.20 * P_h * 1.6 / 1000 + 0.05 * n + 0.35    # lift motors (T/W 1.6) plus pusher system
        m_new = (m_pay + m_avi + m_prop) / (1 - f_struct - f_batt)
        if abs(m_new - m) < 1e-6: break
        m = m_new
    E = f_batt * m * e_spec * usable
    t_hover = 2.0 / 60 if kind == "quadplane" else 0.0     # two minutes of vertical flight per sortie
    t = (E - P_h * t_hover) / P_cr if kind == "quadplane" else E / P_cr
    return m, span, P_h, P_cr, t * 60
print(f"{'concept':11s} {'f_batt':>6s} {'mass kg':>8s} {'span m':>7s} {'hover W':>8s} {'cruise W':>9s} {'endur. min':>10s}")
for kind in ("hexacopter", "quadplane"):
    for fb in (0.25, 0.30, 0.35, 0.40):
        m, span, Ph, Pc, t = size(kind, fb)
        sp = f"{span:7.2f}" if span else "     --"
        print(f"{kind:11s} {fb:6.2f} {m:8.2f} {sp} {Ph:8.0f} {Pc:9.0f} {t:10.1f}")
print()
m, span, Ph, Pc, t = size("quadplane", 0.35)
print(f"Selected: quadplane, battery fraction 0.35 -> {m:.1f} kg ({m*2.2046:.0f} lb), span {span:.2f} m, {t:.0f} min")
print(f"Area mapped per sortie at 22 m/s with a 160 m swath and 20 % turns: {22*t*60*0.8*160/1e6:.1f} km^2")

concept     f_batt  mass kg  span m  hover W  cruise W endur. min
hexacopter    0.25     6.32      --      560       532       31.4
hexacopter    0.30     7.10      --      666       633       35.5
hexacopter    0.35     8.11      --      813       773       38.8
hexacopter    0.40     9.47      --     1027       976       41.0
quadplane     0.25     8.03    2.33     1130       319       59.3
quadplane     0.30     9.24    2.50     1396       368       72.0
quadplane     0.35    10.93    2.71     1795       435       84.6
quadplane     0.40    13.45    3.01     2450       535       97.0

Selected: quadplane, battery fraction 0.35 -> 10.9 kg (24 lb), span 2.71 m, 85 min
Area mapped per sortie at 22 m/s with a 160 m swath and 20 % turns: 14.3 km^2

The trade

The results are decisive. The hexacopter's endurance rises from 31 minutes at a 25 percent battery fraction to only 41 minutes at 40 percent, and the curve is already flattening: each extra kilogram of battery needs more power to lift. No reasonable hexacopter meets the 60-minute requirement. The quadplane's cruise power is a quarter of its hover power, so it reaches 59 minutes at 25 percent battery and 85 minutes at 35 percent. The team selected the quadplane at a 35 percent battery fraction: 10.9 kg take-off mass, a 2.7 m span, 85 minutes of endurance on a new battery and comfortably over 60 minutes at end of life, when capacity has fallen to about 80 percent and cold weather has taken more. At 22 m/s with a 160 m wide image swath and 20 percent of the time spent turning, one sortie covers about 14 km².

The quadplane's weakness is its hover power: 1.8 kW against 0.8 kW for the hexacopter at the same battery fraction, because its four lift rotors are smaller and more heavily loaded. That makes its battery work hard during the two vertical phases, at about 2C against 0.5C in cruise, which matters in the cold. It also means that long hovers near towers, the inspection goal, would use energy quickly. The team accepts this: two minutes of vertical flight per sortie is a small share of the energy, and the inspection goal will be met by a short hover capability plus close passes on the wing, with the commercial quadcopter for detailed tower work.

Checking the selected design

A concept is only credible when its key numbers survive cross-checks against the earlier lessons. The team ran five.

Disk loading and hover: four 0.46 m rotors give 0.665 m² of disk; at 10.9 kg the disk loading is 161 N/m² and the induced velocity 8.1 m/s, giving an ideal hover power of 0.87 kW. With a figure of merit of 0.6 and drive efficiency of 0.81, the battery must supply 1.8 kW, matching the sizing code. Rotor speed for full thrust and motor Kv follow from lesson 7. The vortex ring band for vertical descent, from lesson 2, is about 2.4 to 12 m/s, so the flight controller limits vertical descent to 2 m/s below 30 m.

Battery: at 35 percent of 10.9 kg, the pack weighs 3.8 kg and stores about 840 Wh at 220 Wh/kg. A 12S configuration at about 44 V keeps the hover current near 41 A, about 2C for a pack of about 19 Ah. Lesson 8's cold-soak numbers say a pack started at −20 °C loses about a third of its usable energy and sags badly, so the pack has heaters powered from ground supply before launch and is insulated in flight.

Wing: the wing loading of 160 N/m² gives an area of 0.67 m² and, with an aspect ratio of 11, a span of 2.7 m and a mean chord of 0.25 m. The cruise lift coefficient at 22 m/s is 0.54, comfortably below stall, and the stall speed with a maximum lift coefficient of 1.3 is about 14 m/s. The Reynolds number based on chord is about 370 000, where airfoils designed for small uncrewed aircraft perform well.

Wind: a 12 m/s wind is 55 percent of the cruise speed, so flying crosswind the aircraft crabs at about 33 degrees and its ground speed downwind and upwind varies from 34 to 10 m/s. The mapping pattern is planned with lines across the wind where possible, and the endurance figure is derated by about 15 percent for windy days. In the vertical phases, the thrust-to-weight ratio of 1.6 leaves 60 percent of hover thrust in reserve for control in gusts.

Safety: the parachute weighs about 0.4 kg and, as lesson 11 showed, reduces impact energy by a factor of about 19. The independent geofence and flight termination unit, the ADS-B receiver and a strobe for night visibility are included in the 1.2 kg avionics budget. With these, the simplified SORA screen gave SAIL II for forest mapping.

Regulatory path and safety case

For US drone rules, Larkspur at 10.9 kg (24 lb) is a small UAS under Part 107. Wildfire mapping beyond visual line of sight needs a waiver under 107.205 while Part 108 remains unpublished. Because the state forest service is a public agency, its flights could also be conducted as public aircraft operations under a certificate of waiver or authorization, which is a common route for public-safety drones. Rachel will prepare the waiver application and safety case, including the detect and avoid concept, and will track Part 108; if it is adopted close to the proposal, a permit for the operation may replace the waiver. Within the fire's temporary flight restriction, the aircraft flies only under the incident's aviation plan.

The safety case brings the course together. It argues that the risk to people on the ground is acceptable because the operations are over sparsely populated land, the aircraft carries a parachute and an independent flight termination system, and its failure modes have been analyzed with defined contingencies; and that the risk to other aircraft is acceptable because flights are planned with the fire's air operations, stay below crewed traffic, broadcast or are tracked where possible, and descend quickly when an intruder is detected. Each claim must be supported by evidence: analysis, ground and flight tests, and the design and maintenance records of the aircraft.

Development plan

The conceptual design review closes with a plan. In the next three months, preliminary design will refine the mass estimate with real components, design the wing and booms, select the motors, propellers, speed controllers and cells, and model transitions in simulation. Marcus will run a structural analysis of the boom and wing joint, which carries the lift rotors' loads in hover and the wing bending in cruise. Hélène will plan a composite build of three prototypes. Teresa will run the battery and motor bench tests, including cold-chamber tests of the heated pack. Ground tests will verify thrust, endurance on a tether and the parachute deployment. Flight tests will begin with hover, move to transitions at altitude over a test range, and then to endurance and mapping trials. Each stage has success criteria traced to the requirements table, and each failure in test feeds back into the design.

Your design project

The course project asks you to repeat this process for a small uncrewed aircraft of your own choice, for a civil mission such as crop scouting, search and rescue support, bridge inspection or medical sample delivery. Write requirements with numbers and sources; screen at least three configurations; size at least two quantitatively with code like this lesson's, using momentum theory for hover, a power or drag model for forward flight, and a battery model with credible usable energy; check disk loading, battery C-rate, wing loading and stall speed of the selected design; identify the regulatory path in your country and the main hazards with their mitigations; and present a development and test plan. Present your results with the uncertainties stated: an endurance quoted as 85 minutes on a new battery at 20 °C is a different claim from 60 minutes at end of life in the cold.