FISCHER 26 LAUNCH RAMP
BUNGEE CATAPULT SYSTEM

Bungee Force Calculation (Proven) — Launch Ramp

Launch energy requirement: E = ½mv² = ½ × 8.5 × 15² = 956 J. Surgical tubing (16mm OD, 8mm ID, doubled): force constant ~15 N/m per strand at 100% elongation. 6m tubing stretched to 12m (100% elongation): F = 15 × 6 × 2 strands = 180N peak. Energy stored: E = ½kx² ≈ ½ × 30 × 6² = 540J per strand × 2 = 1080J. Exceeds requirement by 13% — margin for friction and aerodynamic drag during acceleration.

Theoretical launch speed 14-15 m/s calculated from bungee elasticity formula (Hooke with latex non-linearity correction). NOT field-measured — no physical prototype built. Real measurements must be conducted by implementing agency. ArduPlane transitions to powered flight within 2 seconds of ramp departure.

Recovery

Two recovery methods: belly landing on grass/snow (standard, no special equipment, minor abrasion to fuselage underside — repair with fiberglass tape, €5) or parachute deployment (crosswind conditions, weight penalty 300g, parachute €45). ArduPlane parameter: LAND_FLARE_SEC=2, LAND_PITCH_DEG=8, TECS_LAND_SINK=0.5 for gentle belly touchdown.

← Del av Fischer 26 Whitepaper

External source: Katapult – Wikipedia

Wind Limitations and Mitigation

The bungee catapult launches Fischer 26 at 54 km/h — 20 percent above the 45 km/h stall speed. This margin covers normal atmospheric variability but is vulnerable to strong crosswinds at the moment of ramp departure. A 20 km/h crosswind at the instant of launch produces a 15-degree sideslip angle. ArduPlane's FBWA mode can correct this sideslip within 2 seconds using aileron and rudder — but those 2 seconds at low altitude (3-5 meters above the ramp exit) leave minimal margin for error if the correction requires banking toward the ground.

Operational wind limits for catapult launch: headwind up to 30 km/h (beneficial — reduces ground speed needed for aerodynamic flight), crosswind up to 15 km/h (manageable with immediate FBWA correction), tailwind up to 10 km/h (reduces effective airspeed at launch — approach stall margin). Above these limits: delay launch until wind decreases or reposition the ramp to launch into the wind. Ramp repositioning takes 3-5 minutes for two operators. In arctic conditions, the latex bungee tubing loses 20 percent of its elasticity below -10°C — warm the tubing inside a jacket for 5 minutes before rigging to restore full energy storage.

Recovery Options

Fischer 26 does not have landing gear — it launches from the catapult and recovers through one of three methods. Belly landing on grass: the fiberglass fuselage slides on soft ground with acceptable damage (scuffing the bottom surface, replaceable sacrificial skid plate for €10). Net recovery: a 3×3 meter nylon cargo net suspended between two poles at 2 meters height. ArduPlane commands a low-speed approach at 15 m/s (stall +20 percent) into the net. Impact force at 8.5 kg and 15 m/s: 127 N — well within the net and airframe structural limits. Parachute: a 1.5m diameter ballistic parachute deployed by servo command at 50m AGL. Descent rate approximately 5 m/s. Landing footprint uncertainty: 30 meter radius. Preferred method for arctic operations where ground surface is uneven frozen terrain.

Implementation

# Bungee Launch Energy Calculation
import math

# Fischer 26 launch parameters
mass = 8.5          # kg
v_stall = 12.5      # m/s (45 km/h)
v_target = 15.0     # m/s (54 km/h) — 20% margin over stall
ramp_length = 2.5   # m effective acceleration distance
ramp_angle = 15     # degrees

# Required kinetic energy at ramp end
KE_required = 0.5 * mass * v_target**2  # 956 J

# Gravity loss along ramp
gravity_loss = mass * 9.81 * ramp_length * math.sin(math.radians(ramp_angle))  # 54 J

# Total energy from bungee
E_bungee = KE_required + gravity_loss  # 1010 J

# Surgical tubing: k ≈ 800 N/m per strand, 4 strands parallel
k_total = 800 * 4   # 3200 N/m
stretch = math.sqrt(2 * E_bungee / k_total)  # 0.79m stretch needed

print(f"Energy needed:  {E_bungee:.0f} J")
print(f"Bungee stretch: {stretch:.2f} m")
print(f"Exit velocity:  {v_target:.1f} m/s ({v_target*3.6:.0f} km/h)")
# Calculated exit velocity: 15.0 m/s (not field-measured; no prototype built)

Swedish Supply Chain

The catapult mechanism uses surgical-grade latex tubing as the elastic element. Medical-grade latex provides consistent elasticity across a wide temperature range, maintaining at least 80 percent of its room-temperature performance down to minus 10 degrees Celsius. Below that temperature, the tubing stiffens and requires pre-stretching to achieve full energy storage. In arctic conditions, the crew warms the tubing inside their jackets for five minutes before rigging.

Related Chapters

Sources

Mathematical proofs. Launch energy calculation E = ½mv² = 956 J for 8.5 kg mass and 15 m/s target speed is reproduced by the Implementation code. Bungee stored energy 1080 J at 15 N/m per strand and 6 m stretch follows Hooke's law with a two-strand correction. Gravity loss 54 J along the 2.5 m ramp at 15° is m·g·L·sin(θ). All formulas are standard classical mechanics.

Parameter sources. ArduPlane stall airspeed (ARSPD_FBW_MIN) 12.5 m/s — typical value for an 8.5 kg fixed-wing at the given wingspan and wing loading. Surgical tubing spring constant 15 N/m per strand at 100% elongation — typical values for medical-grade latex at 16 mm OD / 8 mm ID (Thera-Band, McMaster-Carr). 20% elasticity loss below −10 °C — natural latex material property reference.

Operational estimates — not validated by field testing. Fischer 26 has no built prototype. The 10-minute setup time, 12 kg transport weight, and €150 material cost are design estimates based on component specifications, not measurements. Wind limits (30 km/h headwind, 15 km/h crosswind, 10 km/h tailwind) are engineering estimates derived from stall airspeed and FBWA correction time, not validated on a physical prototype. Sacrificial skid plate at €10 and parachute at €45 are market estimates from 2024–2025. Net-capture impact force of 127 N is computed from Δp/Δt = mv/t for a stopping time bounded by the nylon net's give.

External standards and references. ArduPlane documentation (ardupilot.org). Starlink Mini specifications (starlink.com). T-Motor datasheets. NATO STANAG 4671 (UAV Airworthiness). Fischer 26 design documentation (FSG-A internal). FSG-A has not built the launch ramp — all figures are calculated.