Descent Performance

Descent Performance (flight-mechanics/performance/descent-performance)

Use when the task is descent analysis for planning: descent gradient and angle, rate of descent, glide range, best glide speed, step-down descent distance, segment time, and descent fuel for a fixed-wing aircraft.

Domain quick reference

• Descent gradient: the vertical path slope tan(gamma), dimensionless; percent = gradient * 100. A 3 deg path is a 5.24% gradient, about 318 ft per nautical mile (the standard instrument glide slope).
• Descent angle: gamma = atan(gradient) in degrees, the inverse of the gradient.
• Rate of descent: RoD = groundspeed * gradient in m/s, for a constant-gradient path. On shallow paths V * sin(gamma) agrees; the gradient form is exact for the path slope.
• Glide range: range = E * height_to_lose in m, the horizontal distance covered per unit height lost in a glide, where E = L/D (aerodynamic efficiency) in steady gliding flight.
• Best glide speed: v = sqrt(2 W / (rho * S * CL_LDmax)) in m/s, the speed at which the glide ratio is maximum, from weight, air density, wing area, and the lift coefficient at maximum L/D.
• Top of descent distance: d = height_to_lose / gradient in m, the horizontal distance at which a constant-gradient step-down must start to reach the target height.
• Descent segment time: t = height_to_lose / RoD in seconds, at a constant rate of descent.
• Descent fuel: m_fuel = fuel_flow * t in kg, from the average fuel flow (idle or flight-idle thrust) over the segment.
• Units are SI throughout: forces in N (weight W = mass * g0), speeds in m/s, angles in degrees, height in m, time in s, fuel in kg.
• Descent performance sits in the FAR-25 / CS-25 transport context for descent and emergency-descent considerations; the mathematics here is standard flight mechanics.

Workflow

1. Fix the descent strategy: constant-gradient step-down (VNAV style) or a glide leg (engine-out case).
2. Convert the path angle to the descent gradient with descent_gradient, or a given slope to its angle with descent_angle_from_gradient; verify it is positive.
3. Compute the rate of descent with rate_of_descent from the groundspeed and the gradient.
4. For a glide leg, estimate the glide range with glide_range and the best glide speed with best_glide_speed from weight, density, wing area, and CL at max L/D.
5. Plan the step-down: top of descent distance with top_of_descent_distance, segment time with descent_time.
6. Compute the descent fuel with descent_fuel from the average fuel flow and the segment time.
7. Check the profile against the arrival constraint and the fuel reserve before gating.

Pitfalls

• Mixing mass and weight in best_glide_speed: W is the weight in newtons (mass * g0), not mass in kg, or the speed comes out low by sqrt(g0).
• Using the air speed instead of the groundspeed for rate of descent: the path is flown over the ground, so RoD = groundspeed * gradient.
• Feeding the gradient as percent: gradient is dimensionless (tan); percent is * 100. Convert before computing RoD or the TOD distance.
• Taking the angle for the gradient: descent_gradient takes degrees and converts inside; never pre-convert to radians.
• Using the full descent height for one step-down leg: each leg loses only its own height step; plan leg by leg.
• A zero gradient means level flight: no descent, no glide range, no TOD distance; the functions raise, not divide by zero.
• Dividing instead of multiplying for glide range: range = E * height_to_lose, not E / height.

Behavior contract (gate 3)

The descent gradient, angle, rate of descent, glide range, best glide speed, TOD distance, segment time, and descent fuel logic is exercised by the gate 3 contract test: scripts/test_descent_performance.py against scripts/descent_performance_logic.py (stdlib unittest, offline). Run: python3 scripts/test_descent_performance.py

Compliance

• Standards referenced, not reproduced: FAR-25 is US government work (public domain) and CS-25 is a free EASA download; descent performance from the path slope and glide ratio is common flight-mechanics methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.