Fundamentals
| Quantity | Formula | Maximum at |
|---|---|---|
| Rate of Climb (RoC) | RoC = (excess power) / weight — in ft/min | Vy (best rate) |
| Climb angle / gradient | sin γ = excess thrust / weight — in % or degrees | Vx (best angle) |
Vx vs Vy — comparison
| Speed | Maximises | When |
|---|---|---|
| Vx (best angle) | Altitude per horizontal distance | Obstacle clearance after take-off (short runway with trees/buildings ahead) |
| Vy (best rate) | Altitude per time | Cruise climb to cruising altitude (normal climb) |
In piston aircraft Vx < Vy (typically 5–10 KIAS difference). With altitude both converge; at absolute ceiling they are equal.
Factors affecting RoC and gradient
| Factor | Effect |
|---|---|
| Rising mass | both ↓ (more load for same excess power) |
| Rising density altitude | both ↓ (engine produces less, wing needs more TAS for lift) |
| Flaps extended | RoC ↓ and gradient ↓ — best climb with flaps fully retracted |
| Tailwind | gradient ↓ (over ground), RoC unchanged (airmass) |
Wind and climb gradient — through air vs over ground
Important distinction between two definitions of the climb angle:
| Concept | Definition | Effect of headwind |
|---|---|---|
| Airmass climb gradient | sin γ = (T − D) / W — function of thrust, drag, weight | NOT affected by wind. At the same speed (constant IAS) and configuration, climb angle relative to the airmass is always the same. |
| Ground climb gradient | altitude / ground distance — function of ground speed | Headwind increases the ground-based climb angle (slow GS, same RoC → steeper ground angle). |
→ AFM climb gradient is the airmass value (for performance charts). So when a pilot flies a straight line at constant speed, headwind does NOT affect the climb gradient (through the air).
For practical obstacle clearance, the ground-based angle matters — and headwind helps there.
Ceilings
| Term | Definition |
|---|---|
| Absolute ceiling | Altitude where RoC = 0 ft/min — aircraft cannot climb further |
| Service ceiling | Altitude where RoC = 100 ft/min = 0.5 m/s for SEP piston aircraft — the usual AFM value |
| Service ceiling for twin-engine | RoC = 50 ft/min |
| Service ceiling for jet airliners | RoC = 300 ft/min |
So the service ceiling of an SEP PPL aircraft is defined as the altitude where it can still climb at 0.5 m/s (= 100 fpm). Above this altitude normal cruise is hardly practical (low reserve, engine at its limit).
Example: Cessna 172 climb performance
- Sea level ISA: climb rate ~730 fpm at Vy = 79 KIAS.
- 5000 ft DA: ~530 fpm.
- 10 000 ft DA: ~330 fpm.
- Service ceiling: ~13 500–14 000 ft (POH).
- Absolute ceiling: ~15 000 ft (typical, variant-dependent).