What is a gradient?
A gradient is the ratio of vertical to horizontal distance of a flight path. It describes how steeply an aircraft climbs or descends.
Formula:
Gradient (%) = (Height gained / Horizontal distance) × 100
or
Gradient (°) = arctan(Height gained / Horizontal distance)
Climb gradient
Definition: ratio of height gained to horizontal distance flown.
Example 1: 100 ft gained over 1 000 ft horizontal → Gradient = (100 / 1 000) × 100 = 10%.
Example 2: climb from 0 to 1 000 ft over 5 NM:
- 1 000 ft / (5 NM × 6 076 ft) = 1 000 / 30 380 ≈ 3.3%.
Key certification gradients (CS-23 for Class B):
- Take-off climb segment: after reaching V2 (Class A) or Vy (Class B) a minimum climb performance must be achieved.
- All-Engines-Operating (AEO) climb gradient at Vy: typically 3–10% at MTOM.
- One-Engine-Inoperative (OEI) for multi-engine Class B: no minimum required; often even descent possible.
Descent gradient
Definition: ratio of height lost to horizontal distance flown.
Approach application:
- 3° standard approach corresponds to about 5.2% gradient or 318 ft/NM.
- Steep approaches in IFR (e.g. London City) up to 5.5° ≈ 9.6%.
Rule of thumb for a 3° glidepath:
- Descent rate (fpm) = Groundspeed (kt) × 5.
- At 100 kt GS → descent rate = 500 fpm.
- At 120 kt GS → 600 fpm.
Gradient vs climb/descent rate
| Quantity | Unit | Use |
|---|---|---|
| Gradient | % or ° | Geometric slope (independent of speed) |
| Rate of Climb (RoC) | ft/min, m/s | Height per time (speed-dependent) |
| Rate of Descent (RoD) | ft/min, m/s | Height lost per time |
Conversion gradient ↔ rate:
Rate (fpm) = Gradient (%) × Groundspeed (kt) × 0.6128
simpler (for PPL estimates):
Rate (fpm) ≈ Gradient (%) × Groundspeed (kt)
Example: 5% gradient at 80 kt GS → about 80 × 5 × 0.6128 = 245 fpm (rounded 250).
Obstacle clearance
In take-off climb the aircraft must respect specific obstacle-clearance gradients:
- Class A (transport): precisely defined OEI gradients in each segment.
- Class B PPL: simplified — the AFM gives typical take-off distance over a 15 m / 50 ft obstacle (Take-off Distance Required, TODR).
Practical relevance for PPL(A):
- For take-off from a mountainous area or at high density altitude the available gradient drops dramatically — obstacles at runway end become dangerous.
- Concrete calculation from AFM performance tables or charts.
Example calculation
Scenario: C172 departing runway 27 (800 m long), obstacle 60 m high at 1.5 km from runway end. MTOM, density altitude 4 000 ft.
From AFM:
- Take-off Distance Required (TODR) to 50 ft = 650 m.
- Climb gradient after take-off at 70 kt = approx. 6% (AEO, MTOM, DA 4 000 ft).
Check:
- TODR 650 m ≤ TODA 800 m → ✓
- Height at 1 500 m from 50-ft point: 1 500 × 0.06 = 90 m above 50 ft = 90 + 15 m = 105 m total height.
- Obstacle 60 m → margin 45 m available. ✓
But account for wind/temperature effects!