The language of performance

Does the aircraft climb through air or over the ground?

Climb gradient is height gained divided by horizontal distance, expressed as a percentage. Angle is arctan(gradient/100). Rate of climb is vertical distance per time. In EASA examination convention, climb/descent angle refers to the air mass; flight-path angle refers to the ground.

Angle, gradient and rate

Climb gradient is height gained divided by horizontal distance, expressed as a percentage. Angle is arctan(gradient/100). Rate of climb is vertical distance per time. In EASA examination convention, climb/descent angle refers to the air mass; flight-path angle refers to the ground.

For a steady shallow climb, gradient ≈ ROC/(horizontal speed). In practical units: ground gradient (%) = ROC(ft/min) × 60 / [GS(kt) × 6,076.12] × 100. A headwind improves the ground gradient for the same air-relative climb; it does not generate extra engine power. The absolute ceiling is the altitude at which maximum achievable steady rate of climb becomes zero.

Available is not required

TORA is the declared ground run available. TODA adds the declared clearway to TORA; a clearway is a controlled area over which initial climb may occur. ASDA adds the declared stopway to TORA; a stopway is prepared for stopping after an abandoned take-off. LDA is the declared landing distance available. Do not invent extra TORA from a clearway or assume a stopway is available for landing.

Screen height defines the start or end of the measured airborne part. Common training cases use 50 ft for class-B take-off and landing, 35 ft for class-A dry take-off and 50 ft for normal landing. Class-A wet take-off distance can use 15 ft under the specific CS-25 definition while preserving the required V2 achievement by 35 ft. A screen height is not obstacle clearance.

Distance, time and fuel

Range is distance; endurance is time. Specific air range SR = TAS/fuel flow in NAM per unit of fuel; specific ground range SRG = GS/fuel flow in NGM per unit of fuel. Power is work per time: propulsive power equals thrust times TAS. Power available must be compared with power required at the same speed and units. Shaft power and propulsive power differ by propeller efficiency.

Why do hot, high and heavy demand more performance?

At low Mach, EAS ≈ TAS × √(density/sea-level density); IAS is an approximation to EAS when instrument, position and compressibility errors are small. At a fixed IAS and configuration the same lift coefficient supports the same weight. Lower density therefore means higher TAS. Drag against IAS is broadly unchanged at a fixed mass in this idealised incompressible comparison, but power required rises because power = drag × TAS. Against TAS, both the location and shape of the required curve change.

Separate IAS from TAS

At low Mach, EAS ≈ TAS × √(density/sea-level density); IAS is an approximation to EAS when instrument, position and compressibility errors are small. At a fixed IAS and configuration the same lift coefficient supports the same weight. Lower density therefore means higher TAS. Drag against IAS is broadly unchanged at a fixed mass in this idealised incompressible comparison, but power required rises because power = drag × TAS. Against TAS, both the location and shape of the required curve change.

A normally aspirated piston engine loses power with altitude. A constant-power propeller provides approximately ηP/V thrust: available thrust falls with speed. Turbojet thrust is comparatively flatter against speed in a limited low-Mach model, and its available power rises with speed. Real turbofans, turbocharged engines and flat-rated turbines need their actual engine schedules.

Mass and configuration reshape the curves

More mass requires more lift, increases induced drag at a given IAS and moves characteristic speeds upward approximately with √mass when other conditions match. Flaps and gear alter lift and drag; anti-ice and bleed extraction can reduce available thrust. A forward CG often increases balancing tail load and trim drag; approved performance must use its actual CG assumptions.

Pressure altitude, temperature, wind, runway slope and surface all matter. Anti-skid status changes usable braking, not lift-off lift. An upslope opposes acceleration; a wet or contaminated surface may reduce friction and add contaminant drag. Never correct all of these with one universal hot-and-high factor.

Can you make the performance decision?

Four original questions. Work from the stated conditions and review the reasoning.