CPL Flight Performance and Planning cheat sheet

Lift L = ½ρV²SC_L; induced drag D_i = L²/(½ρV²πbe), so doubling speed cuts induced drag to about one quarter at constant lift.

Total drag = parasite + induced; minimum total drag occurs where parasite drag equals induced drag, at the speed for L/D_max (best glide).

V_MP (minimum power speed) is about 0.76 × V_MD (minimum drag speed); best endurance is flown at V_MP, best range at V_MD.

Load factor n = L/W = 1/cos(bank angle) in a level turn; 60° bank gives n = 2, raising stall speed by √2 (about 41%).

Stall speed scales as V_S = √(2W/(ρSC_Lmax)); V_S increases with √n, so V_S at 2 g is 1.41 × V_S at 1 g.

Density altitude rises with pressure altitude and temperature; a 10 °C temperature rise above ISA at a given pressure altitude adds roughly 120 ft per 1000 ft of elevation.

Power required = drag × TAS; power available from a piston engine falls with altitude while TAS for a given IAS rises, so excess power peaks near a mid altitude.

Rate of climb ROC = excess power/W = (P_avail − P_req)/W; climb gradient = ROC/groundspeed, so headwind steepens the gradient for a fixed ROC.

Moment = mass × arm; CG position = total moment ÷ total mass. Use a datum-referenced table and keep units consistent (kg·m or lb·in).

CG must lie within the forward and aft limits for the actual takeoff mass; forward limit protects controllability and rotation, aft limit protects stability and stall/spin recovery.

Zero fuel mass (ZFM) = takeoff mass − trip fuel; ZFM and landing mass each have their own maximum structural limits independent of MTOM.

Maximum takeoff mass may be limited by field length, climb gradient, obstacle clearance, tyre speed, or brake energy - the lowest of these governs.

Moving a mass m by distance d shifts CG by ΔCG = m × d / total mass; the shift is in the same direction as the mass movement.

Forward CG increases stall speed, elevators the rotation force, lengthens takeoff run, and reduces cruise range; aft CG improves performance but degrades stability.

Regulatory minimum floor loading: the CG of the loaded aircraft must be shown to remain inside limits for takeoff, in flight (fuel burn), and landing.

Lateral (spanwise) imbalance limits exist for fuel and payload; asymmetric loading increases control forces and can restrict fuel transfer.

Takeoff distance required (TODR) = ground roll plus airborne segment to 35 ft (or 50 ft for wet); it must not exceed TODA, and for commercial performance the screen height and net takeoff flight path apply.

Balanced field length: V1 is chosen so that accelerate-stop distance equals accelerate-go distance; increasing mass or reducing thrust raises V1 and lengthens both.

V speeds: V1 decision speed, VR rotation, V2 takeoff safety speed (≥1.13 V_S1 at 1 g or 1.2 V_S1 depending on configuration), V_MCG minimum control on ground, V_MCA minimum control airborne.

Headwind reduces ground roll; use the headwind component, not the reported wind. Tailwind increases TODR - many operators prohibit tailwind takeoffs beyond a stated limit.

Runway slope: uphill slope increases takeoff distance; a 1% upslope adds roughly 5–10% to ground roll depending on type.

Landing distance required = airborne segment from 50 ft plus ground roll with full braking; wet or contaminated runways add a factor (often 1.15) and reduce braking coefficient.

Density altitude increases true airspeed at a given IAS, so both takeoff and landing ground roll increase with elevation and temperature.

Contaminated runway (standing water, slush, snow, ice) degrades friction; hydroplaning speed ≈ 9 × √(tyre pressure in psi) knots.

Climb gradient (%) = 100 × (ROC in ft/min) / (groundspeed in kt × 101.3); a 500 ft/min climb at 120 kt groundspeed gives about 4.1%.

Net takeoff flight path = gross flight path minus a gradient decrement (typically 0.8% for two-engine, 0.9% for three-engine, 1.0% for four-engine aircraft).

Obstacle clearance during climb requires the net flight path to clear all obstacles by 35 ft vertically; the segment ends at 1500 ft above the takeoff surface.

Cruise altitude is limited by buffeting (low-speed and high-speed), thrust available, and maximum operating altitude where 1.3 g manoeuvre margin is retained.

Specific range (nm per kg fuel) peaks at the speed for maximum L/D corrected for engine efficiency; long-range cruise is flown slightly faster than best specific range.

Step climb as fuel burns off reduces induced drag and improves range versus holding a constant lower altitude.

Descent: rate of descent (ft/min) ≈ groundspeed (kt) × gradient (%) × 101.3, or ≈ 5 × groundspeed for a 3° path.

Top of descent distance ≈ altitude to lose (ft) / (descent gradient in ft/nm); a 3° path loses about 318 ft per nm.

Trip fuel = fuel from takeoff to landing at destination; it excludes taxi, contingency, alternate, final reserve, and additional fuel.

Standard fuel plan: taxi + trip + contingency (typically 5% of trip) + alternate + final reserve (30 min holding at 1500 ft) + additional fuel + extra fuel.

Alternate fuel is the fuel to fly from destination to the chosen alternate via the planned route, including approach and landing, at the planned mass.

Final reserve is a fixed regulatory quantity (30 minutes holding for commercial aeroplanes); it must remain on board at landing and is not usable for planning.

Contingency fuel may be reduced under approved methods (statistical or decision-point) when an en-route alternate is available.

Equal-time point (ETP) and point of no return: distance to ETP = total distance × (groundspeed outbound)/(groundspeed outbound + groundspeed return).

Fuel required for a diversion must be recomputed at the actual mass and altitude; a lower mass reduces fuel flow and improves range.

Route planning must respect airway direction, level restrictions, and special-use airspace; check NOTAMs and AIP supplements for closures.

Read performance charts with the correct entry axis and interpolate between grid lines; never extrapolate beyond the chart boundary.

Density altitude = pressure altitude + 120 × (OAT − ISA temperature at that pressure altitude); use it as the entry for takeoff and climb charts.

Wind components: headwind = wind speed × cos(angle off runway); crosswind = wind speed × sin(angle off runway).

When interpolating between mass columns, interpolate linearly in the variable shown (distance or fuel); non-linear charts require reading at the nearest grid line.

Chart corrections: apply runway slope, wind, and contamination corrections in the order specified by the chart notes, usually as additive or multiplicative factors.

TAS from IAS requires pressure altitude and temperature; use the flight computer or the TAS chart, not a fixed percentage.

Fuel flow and endurance charts are read at cruise altitude and mass; endurance = usable fuel / fuel flow, range = endurance × TAS.

Always note the chart's assumed configuration (flaps, bleed, anti-ice) and correct if the actual configuration differs.

MTOM, MLM, MZFM, and maximum payload are structural limits; the operator must show the planned mass does not exceed any of them.

Takeoff alternate is required when the departure aerodrome weather is at or below the landing minima and no return is possible.

Destination alternate is required unless the destination has an approved instrument approach and the weather permits a visual approach and landing.

Weather minima for planning: ceiling and visibility at or above the applicable approach minima plus any operator margin; check TAF validity periods.

ETOPS rules apply to twin-engine operations beyond a specified distance from an adequate aerodrome; the diversion time is based on approved performance.

Performance-limited mass must be checked at every relevant obstacle and at the most critical segment of the takeoff flight path, not just at the runway end.

NOTAMs, AIP supplements, and volcanic ash or space weather advisories can close airspace or change minima; verify before dispatch.

Crew and aircraft recency, MEL items, and fuel policy must be confirmed before dispatch; a deferred item may impose performance penalties.

In-flight replanning compares fuel remaining against fuel required to the destination plus alternate plus final reserve; if below, divert or reduce consumption.

Fuel remaining at a waypoint = fuel at previous waypoint − fuel flow × time; update with actual flow, not planned flow.

If fuel on arrival would be below final reserve, declare minimum fuel; if below the fuel needed to reach a safe landing, declare MAYDAY FUEL.

Reclearance in flight allows the crew to amend the destination and fuel plan en route using updated weather and performance data.

Divert decision: compare fuel to destination + alternate versus fuel to the diversion aerodrome; choose the option that preserves final reserve.

Holding fuel burn = fuel flow at holding configuration × time; holding at low altitude and low speed increases flow and reduces endurance.

Fuel imbalance and transfer limits must be respected; crossfeed is used only per the aircraft's limitations.

Track actual fuel against the flight plan at each waypoint; a persistent negative trend requires early action, not waiting for the destination.