CAA NZ CPL Theory - Principles of Flight & Aircraft Performance cheat sheet
CAA NZ CPL Theory - Principles of Flight & Aircraft Performance · Keep the key ideas within reach.
Principles of Flight
Lift L = ½ρV²SCL; induced drag Di = ½ρV²S·CL²/(πAe), so induced drag varies inversely with V² at constant weight.
Total drag = parasite drag (varies with V²) + induced drag (varies with 1/V²); minimum drag occurs where parasite and induced drag are equal, at CL = √(CD0·πAe).
At constant weight and altitude, minimum drag speed is 1.32 times minimum power speed (V_mp = V_md/√3).
Load factor n = L/W = 1/cos φ in a level banked turn; stall speed increases with √n, so a 60° bank raises Vs by 41%.
Rate of climb depends on excess power (T−D)V/W; angle of climb depends on excess thrust (T−D)/W.
Critical angle of attack is the only direct cause of stall; it is unaffected by weight, bank, density altitude or CG.
Static stability requires a negative dCm/dCL; positive static stability plus positive dynamic stability gives short-period and phugoid damping.
Mach crit is the free-stream Mach number at which local flow first reaches M=1; swept wings and thin sections raise Mcrit.
Adverse yaw arises from asymmetric induced drag on the downgoing wing in a turn; aileron differential and rudder coordinate the roll.
Aircraft Performance
Density altitude = pressure altitude + 120 × (OAT − ISA temperature at that pressure altitude); ISA lapse is 1.98 °C per 1000 ft up to 36,090 ft.
Take-off and landing distances increase by roughly 10% per 1000 ft density altitude and by 10% for each 10% increase in weight beyond the AFM reference.
Headwind component = wind speed × cos(angle between wind and runway); crosswind component = wind speed × sin(angle).
V1 is decision speed, VR rotation speed, V2 take-off safety speed; V1 must be ≥ VMCG and ≤ VR.
Balanced field length is achieved when V1 is chosen so that accelerate-stop distance equals accelerate-go distance.
Climb gradient % = (ROC ft/min × 60) / (groundspeed in kt × 6076) × 100, or approximately (ROC/GS) × 100 when ROC is in ft/min and GS in kt × 101.3.
Service ceiling is where ROC falls to 100 ft/min; absolute ceiling is where ROC is zero.
Landing distance is measured from 50 ft screen height to full stop on a dry, level, paved runway at AFM reference conditions.
Weight and Balance
Moment = weight × arm; CG arm = total moment / total weight.
Weight shift formula: ΔCG = (weight moved × distance moved) / total weight.
Adding or removing weight: new CG = (old total moment ± added moment) / (old total weight ± added weight).
Empty weight, basic empty weight, zero fuel weight and maximum take-off weight are distinct; MZFW limits payload before fuel is added.
Forward CG increases longitudinal stability and elevator effectiveness but lengthens take-off run and raises stall speed slightly; aft CG reduces stability margin and stick force.
Datum, arm and station are measured in the AFM; arms forward of the datum are negative.
The CG envelope is bounded by forward and aft limits that vary with weight; the aft limit is often set by stability and the forward limit by elevator authority in landing flare.
Percentage MAC = (CG arm − LEMAC) / (MAC length) × 100.
Flight Planning and Fuel
Fuel required = trip fuel + taxi fuel + contingency (usually 5% of trip) + alternate fuel + final reserve + additional fuel.
Final reserve for a VFR CPL flight is 30 minutes at holding speed; IFR final reserve is 30 minutes at 1500 ft above the alternate.
Endurance = usable fuel / fuel flow; range = TAS × endurance, corrected for wind.
Specific range = (TAS in nm/h) / (fuel flow in kg/h); maximum specific range occurs at the tangent from the origin to the power-required curve.
Piston engine fuel flow varies roughly with power; lean mixture reduces flow but must respect CHT and detonation limits.
Pilot-observed ISA deviation: pressure altitude from QNH setting, then density altitude from OAT and pressure altitude.
Pounds to kilograms: 1 kg = 2.2046 lb; 1 imperial gallon avgas = 6.7 lb ≈ 3.04 kg; 1 US gallon = 6.0 lb.
Wind effect: groundspeed = TAS ± headwind/tailwind component; time = distance / groundspeed.
Loading and Performance Limitations
Maximum take-off weight, maximum landing weight, maximum zero fuel weight and maximum ramp weight each limit a different phase; the lowest applicable limit governs.
Structural limit load factors for the normal category are +3.8 g and −1.52 g at or below design cruising speed, decreasing to +2.5 g at VD.
Utility category permits +4.4 g and −1.76 g; aerobatic category permits +6.0 g and −3.0 g.
VNE is the never-exceed speed; VNO is maximum structural cruising speed; VA is design manoeuvring speed and decreases with √(weight).
VA is the speed above which full deflection of a single control can overstress the airframe; turbulence penetration speed is normally VB or below VA.
Floor loading and baggage compartment limits must be checked separately from the CG envelope.
Runway limit, obstacle clearance, brake energy and tyre speed are operational limits not captured by the AFM weight limits.
A forward CG combined with aft-loading error can push the aircraft outside the envelope at low weight even when MTOW is respected.
Principles of Flight
Lift L = ½ρV²SCL; induced drag Di = ½ρV²S·CL²/(πAe), so induced drag varies inversely with V² at constant weight.
Total drag = parasite drag (varies with V²) + induced drag (varies with 1/V²); minimum drag occurs where parasite and induced drag are equal, at CL = √(CD0·πAe).
At constant weight and altitude, minimum drag speed is 1.32 times minimum power speed (V_mp = V_md/√3).
Load factor n = L/W = 1/cos φ in a level banked turn; stall speed increases with √n, so a 60° bank raises Vs by 41%.
Rate of climb depends on excess power (T−D)V/W; angle of climb depends on excess thrust (T−D)/W.
Critical angle of attack is the only direct cause of stall; it is unaffected by weight, bank, density altitude or CG.
Static stability requires a negative dCm/dCL; positive static stability plus positive dynamic stability gives short-period and phugoid damping.
Mach crit is the free-stream Mach number at which local flow first reaches M=1; swept wings and thin sections raise Mcrit.
Adverse yaw arises from asymmetric induced drag on the downgoing wing in a turn; aileron differential and rudder coordinate the roll.
Aircraft Performance
Density altitude = pressure altitude + 120 × (OAT − ISA temperature at that pressure altitude); ISA lapse is 1.98 °C per 1000 ft up to 36,090 ft.
Take-off and landing distances increase by roughly 10% per 1000 ft density altitude and by 10% for each 10% increase in weight beyond the AFM reference.
Headwind component = wind speed × cos(angle between wind and runway); crosswind component = wind speed × sin(angle).
V1 is decision speed, VR rotation speed, V2 take-off safety speed; V1 must be ≥ VMCG and ≤ VR.
Balanced field length is achieved when V1 is chosen so that accelerate-stop distance equals accelerate-go distance.
Climb gradient % = (ROC ft/min × 60) / (groundspeed in kt × 6076) × 100, or approximately (ROC/GS) × 100 when ROC is in ft/min and GS in kt × 101.3.
Service ceiling is where ROC falls to 100 ft/min; absolute ceiling is where ROC is zero.
Landing distance is measured from 50 ft screen height to full stop on a dry, level, paved runway at AFM reference conditions.
Weight and Balance
Moment = weight × arm; CG arm = total moment / total weight.
Weight shift formula: ΔCG = (weight moved × distance moved) / total weight.
Adding or removing weight: new CG = (old total moment ± added moment) / (old total weight ± added weight).
Empty weight, basic empty weight, zero fuel weight and maximum take-off weight are distinct; MZFW limits payload before fuel is added.
Forward CG increases longitudinal stability and elevator effectiveness but lengthens take-off run and raises stall speed slightly; aft CG reduces stability margin and stick force.
Datum, arm and station are measured in the AFM; arms forward of the datum are negative.
The CG envelope is bounded by forward and aft limits that vary with weight; the aft limit is often set by stability and the forward limit by elevator authority in landing flare.
Percentage MAC = (CG arm − LEMAC) / (MAC length) × 100.
Flight Planning and Fuel
Fuel required = trip fuel + taxi fuel + contingency (usually 5% of trip) + alternate fuel + final reserve + additional fuel.
Final reserve for a VFR CPL flight is 30 minutes at holding speed; IFR final reserve is 30 minutes at 1500 ft above the alternate.
Endurance = usable fuel / fuel flow; range = TAS × endurance, corrected for wind.
Specific range = (TAS in nm/h) / (fuel flow in kg/h); maximum specific range occurs at the tangent from the origin to the power-required curve.
Piston engine fuel flow varies roughly with power; lean mixture reduces flow but must respect CHT and detonation limits.
Pilot-observed ISA deviation: pressure altitude from QNH setting, then density altitude from OAT and pressure altitude.
Pounds to kilograms: 1 kg = 2.2046 lb; 1 imperial gallon avgas = 6.7 lb ≈ 3.04 kg; 1 US gallon = 6.0 lb.
Wind effect: groundspeed = TAS ± headwind/tailwind component; time = distance / groundspeed.
Loading and Performance Limitations
Maximum take-off weight, maximum landing weight, maximum zero fuel weight and maximum ramp weight each limit a different phase; the lowest applicable limit governs.
Structural limit load factors for the normal category are +3.8 g and −1.52 g at or below design cruising speed, decreasing to +2.5 g at VD.
Utility category permits +4.4 g and −1.76 g; aerobatic category permits +6.0 g and −3.0 g.
VNE is the never-exceed speed; VNO is maximum structural cruising speed; VA is design manoeuvring speed and decreases with √(weight).
VA is the speed above which full deflection of a single control can overstress the airframe; turbulence penetration speed is normally VB or below VA.
Floor loading and baggage compartment limits must be checked separately from the CG envelope.
Runway limit, obstacle clearance, brake energy and tyre speed are operational limits not captured by the AFM weight limits.
A forward CG combined with aft-loading error can push the aircraft outside the envelope at low weight even when MTOW is respected.
Principles of Flight
Lift L = ½ρV²SCL; induced drag Di = ½ρV²S·CL²/(πAe), so induced drag varies inversely with V² at constant weight.
Total drag = parasite drag (varies with V²) + induced drag (varies with 1/V²); minimum drag occurs where parasite and induced drag are equal, at CL = √(CD0·πAe).
At constant weight and altitude, minimum drag speed is 1.32 times minimum power speed (V_mp = V_md/√3).
Load factor n = L/W = 1/cos φ in a level banked turn; stall speed increases with √n, so a 60° bank raises Vs by 41%.
Rate of climb depends on excess power (T−D)V/W; angle of climb depends on excess thrust (T−D)/W.
Critical angle of attack is the only direct cause of stall; it is unaffected by weight, bank, density altitude or CG.
Static stability requires a negative dCm/dCL; positive static stability plus positive dynamic stability gives short-period and phugoid damping.
Mach crit is the free-stream Mach number at which local flow first reaches M=1; swept wings and thin sections raise Mcrit.
Adverse yaw arises from asymmetric induced drag on the downgoing wing in a turn; aileron differential and rudder coordinate the roll.
Aircraft Performance
Density altitude = pressure altitude + 120 × (OAT − ISA temperature at that pressure altitude); ISA lapse is 1.98 °C per 1000 ft up to 36,090 ft.
Take-off and landing distances increase by roughly 10% per 1000 ft density altitude and by 10% for each 10% increase in weight beyond the AFM reference.
Headwind component = wind speed × cos(angle between wind and runway); crosswind component = wind speed × sin(angle).
V1 is decision speed, VR rotation speed, V2 take-off safety speed; V1 must be ≥ VMCG and ≤ VR.
Balanced field length is achieved when V1 is chosen so that accelerate-stop distance equals accelerate-go distance.
Climb gradient % = (ROC ft/min × 60) / (groundspeed in kt × 6076) × 100, or approximately (ROC/GS) × 100 when ROC is in ft/min and GS in kt × 101.3.
Service ceiling is where ROC falls to 100 ft/min; absolute ceiling is where ROC is zero.
Landing distance is measured from 50 ft screen height to full stop on a dry, level, paved runway at AFM reference conditions.
Weight and Balance
Moment = weight × arm; CG arm = total moment / total weight.
Weight shift formula: ΔCG = (weight moved × distance moved) / total weight.
Adding or removing weight: new CG = (old total moment ± added moment) / (old total weight ± added weight).
Empty weight, basic empty weight, zero fuel weight and maximum take-off weight are distinct; MZFW limits payload before fuel is added.
Forward CG increases longitudinal stability and elevator effectiveness but lengthens take-off run and raises stall speed slightly; aft CG reduces stability margin and stick force.
Datum, arm and station are measured in the AFM; arms forward of the datum are negative.
The CG envelope is bounded by forward and aft limits that vary with weight; the aft limit is often set by stability and the forward limit by elevator authority in landing flare.
Percentage MAC = (CG arm − LEMAC) / (MAC length) × 100.
Flight Planning and Fuel
Fuel required = trip fuel + taxi fuel + contingency (usually 5% of trip) + alternate fuel + final reserve + additional fuel.
Final reserve for a VFR CPL flight is 30 minutes at holding speed; IFR final reserve is 30 minutes at 1500 ft above the alternate.
Endurance = usable fuel / fuel flow; range = TAS × endurance, corrected for wind.
Specific range = (TAS in nm/h) / (fuel flow in kg/h); maximum specific range occurs at the tangent from the origin to the power-required curve.
Piston engine fuel flow varies roughly with power; lean mixture reduces flow but must respect CHT and detonation limits.
Pilot-observed ISA deviation: pressure altitude from QNH setting, then density altitude from OAT and pressure altitude.
Pounds to kilograms: 1 kg = 2.2046 lb; 1 imperial gallon avgas = 6.7 lb ≈ 3.04 kg; 1 US gallon = 6.0 lb.
Wind effect: groundspeed = TAS ± headwind/tailwind component; time = distance / groundspeed.
Loading and Performance Limitations
Maximum take-off weight, maximum landing weight, maximum zero fuel weight and maximum ramp weight each limit a different phase; the lowest applicable limit governs.
Structural limit load factors for the normal category are +3.8 g and −1.52 g at or below design cruising speed, decreasing to +2.5 g at VD.
Utility category permits +4.4 g and −1.76 g; aerobatic category permits +6.0 g and −3.0 g.
VNE is the never-exceed speed; VNO is maximum structural cruising speed; VA is design manoeuvring speed and decreases with √(weight).
VA is the speed above which full deflection of a single control can overstress the airframe; turbulence penetration speed is normally VB or below VA.
Floor loading and baggage compartment limits must be checked separately from the CG envelope.
Runway limit, obstacle clearance, brake energy and tyre speed are operational limits not captured by the AFM weight limits.
A forward CG combined with aft-loading error can push the aircraft outside the envelope at low weight even when MTOW is respected.
Principles of Flight
Lift L = ½ρV²SCL; induced drag Di = ½ρV²S·CL²/(πAe), so induced drag varies inversely with V² at constant weight.
Total drag = parasite drag (varies with V²) + induced drag (varies with 1/V²); minimum drag occurs where parasite and induced drag are equal, at CL = √(CD0·πAe).
At constant weight and altitude, minimum drag speed is 1.32 times minimum power speed (V_mp = V_md/√3).
Load factor n = L/W = 1/cos φ in a level banked turn; stall speed increases with √n, so a 60° bank raises Vs by 41%.
Rate of climb depends on excess power (T−D)V/W; angle of climb depends on excess thrust (T−D)/W.
Critical angle of attack is the only direct cause of stall; it is unaffected by weight, bank, density altitude or CG.
Static stability requires a negative dCm/dCL; positive static stability plus positive dynamic stability gives short-period and phugoid damping.
Mach crit is the free-stream Mach number at which local flow first reaches M=1; swept wings and thin sections raise Mcrit.
Adverse yaw arises from asymmetric induced drag on the downgoing wing in a turn; aileron differential and rudder coordinate the roll.
Aircraft Performance
Density altitude = pressure altitude + 120 × (OAT − ISA temperature at that pressure altitude); ISA lapse is 1.98 °C per 1000 ft up to 36,090 ft.
Take-off and landing distances increase by roughly 10% per 1000 ft density altitude and by 10% for each 10% increase in weight beyond the AFM reference.
Headwind component = wind speed × cos(angle between wind and runway); crosswind component = wind speed × sin(angle).
V1 is decision speed, VR rotation speed, V2 take-off safety speed; V1 must be ≥ VMCG and ≤ VR.
Balanced field length is achieved when V1 is chosen so that accelerate-stop distance equals accelerate-go distance.
Climb gradient % = (ROC ft/min × 60) / (groundspeed in kt × 6076) × 100, or approximately (ROC/GS) × 100 when ROC is in ft/min and GS in kt × 101.3.
Service ceiling is where ROC falls to 100 ft/min; absolute ceiling is where ROC is zero.
Landing distance is measured from 50 ft screen height to full stop on a dry, level, paved runway at AFM reference conditions.
Weight and Balance
Moment = weight × arm; CG arm = total moment / total weight.
Weight shift formula: ΔCG = (weight moved × distance moved) / total weight.
Adding or removing weight: new CG = (old total moment ± added moment) / (old total weight ± added weight).
Empty weight, basic empty weight, zero fuel weight and maximum take-off weight are distinct; MZFW limits payload before fuel is added.
Forward CG increases longitudinal stability and elevator effectiveness but lengthens take-off run and raises stall speed slightly; aft CG reduces stability margin and stick force.
Datum, arm and station are measured in the AFM; arms forward of the datum are negative.
The CG envelope is bounded by forward and aft limits that vary with weight; the aft limit is often set by stability and the forward limit by elevator authority in landing flare.
Percentage MAC = (CG arm − LEMAC) / (MAC length) × 100.
Flight Planning and Fuel
Fuel required = trip fuel + taxi fuel + contingency (usually 5% of trip) + alternate fuel + final reserve + additional fuel.
Final reserve for a VFR CPL flight is 30 minutes at holding speed; IFR final reserve is 30 minutes at 1500 ft above the alternate.
Endurance = usable fuel / fuel flow; range = TAS × endurance, corrected for wind.
Specific range = (TAS in nm/h) / (fuel flow in kg/h); maximum specific range occurs at the tangent from the origin to the power-required curve.
Piston engine fuel flow varies roughly with power; lean mixture reduces flow but must respect CHT and detonation limits.
Pilot-observed ISA deviation: pressure altitude from QNH setting, then density altitude from OAT and pressure altitude.
Pounds to kilograms: 1 kg = 2.2046 lb; 1 imperial gallon avgas = 6.7 lb ≈ 3.04 kg; 1 US gallon = 6.0 lb.
Wind effect: groundspeed = TAS ± headwind/tailwind component; time = distance / groundspeed.
Loading and Performance Limitations
Maximum take-off weight, maximum landing weight, maximum zero fuel weight and maximum ramp weight each limit a different phase; the lowest applicable limit governs.
Structural limit load factors for the normal category are +3.8 g and −1.52 g at or below design cruising speed, decreasing to +2.5 g at VD.
Utility category permits +4.4 g and −1.76 g; aerobatic category permits +6.0 g and −3.0 g.
VNE is the never-exceed speed; VNO is maximum structural cruising speed; VA is design manoeuvring speed and decreases with √(weight).
VA is the speed above which full deflection of a single control can overstress the airframe; turbulence penetration speed is normally VB or below VA.
Floor loading and baggage compartment limits must be checked separately from the CG envelope.
Runway limit, obstacle clearance, brake energy and tyre speed are operational limits not captured by the AFM weight limits.
A forward CG combined with aft-loading error can push the aircraft outside the envelope at low weight even when MTOW is respected.
Principles of Flight
Lift L = ½ρV²SCL; induced drag Di = ½ρV²S·CL²/(πAe), so induced drag varies inversely with V² at constant weight.
Total drag = parasite drag (varies with V²) + induced drag (varies with 1/V²); minimum drag occurs where parasite and induced drag are equal, at CL = √(CD0·πAe).
At constant weight and altitude, minimum drag speed is 1.32 times minimum power speed (V_mp = V_md/√3).
Load factor n = L/W = 1/cos φ in a level banked turn; stall speed increases with √n, so a 60° bank raises Vs by 41%.
Rate of climb depends on excess power (T−D)V/W; angle of climb depends on excess thrust (T−D)/W.
Critical angle of attack is the only direct cause of stall; it is unaffected by weight, bank, density altitude or CG.
Static stability requires a negative dCm/dCL; positive static stability plus positive dynamic stability gives short-period and phugoid damping.
Mach crit is the free-stream Mach number at which local flow first reaches M=1; swept wings and thin sections raise Mcrit.
Adverse yaw arises from asymmetric induced drag on the downgoing wing in a turn; aileron differential and rudder coordinate the roll.
Aircraft Performance
Density altitude = pressure altitude + 120 × (OAT − ISA temperature at that pressure altitude); ISA lapse is 1.98 °C per 1000 ft up to 36,090 ft.
Take-off and landing distances increase by roughly 10% per 1000 ft density altitude and by 10% for each 10% increase in weight beyond the AFM reference.
Headwind component = wind speed × cos(angle between wind and runway); crosswind component = wind speed × sin(angle).
V1 is decision speed, VR rotation speed, V2 take-off safety speed; V1 must be ≥ VMCG and ≤ VR.
Balanced field length is achieved when V1 is chosen so that accelerate-stop distance equals accelerate-go distance.
Climb gradient % = (ROC ft/min × 60) / (groundspeed in kt × 6076) × 100, or approximately (ROC/GS) × 100 when ROC is in ft/min and GS in kt × 101.3.
Service ceiling is where ROC falls to 100 ft/min; absolute ceiling is where ROC is zero.
Landing distance is measured from 50 ft screen height to full stop on a dry, level, paved runway at AFM reference conditions.
Weight and Balance
Moment = weight × arm; CG arm = total moment / total weight.
Weight shift formula: ΔCG = (weight moved × distance moved) / total weight.
Adding or removing weight: new CG = (old total moment ± added moment) / (old total weight ± added weight).
Empty weight, basic empty weight, zero fuel weight and maximum take-off weight are distinct; MZFW limits payload before fuel is added.
Forward CG increases longitudinal stability and elevator effectiveness but lengthens take-off run and raises stall speed slightly; aft CG reduces stability margin and stick force.
Datum, arm and station are measured in the AFM; arms forward of the datum are negative.
The CG envelope is bounded by forward and aft limits that vary with weight; the aft limit is often set by stability and the forward limit by elevator authority in landing flare.
Percentage MAC = (CG arm − LEMAC) / (MAC length) × 100.
Flight Planning and Fuel
Fuel required = trip fuel + taxi fuel + contingency (usually 5% of trip) + alternate fuel + final reserve + additional fuel.
Final reserve for a VFR CPL flight is 30 minutes at holding speed; IFR final reserve is 30 minutes at 1500 ft above the alternate.
Endurance = usable fuel / fuel flow; range = TAS × endurance, corrected for wind.
Specific range = (TAS in nm/h) / (fuel flow in kg/h); maximum specific range occurs at the tangent from the origin to the power-required curve.
Piston engine fuel flow varies roughly with power; lean mixture reduces flow but must respect CHT and detonation limits.
Pilot-observed ISA deviation: pressure altitude from QNH setting, then density altitude from OAT and pressure altitude.
Pounds to kilograms: 1 kg = 2.2046 lb; 1 imperial gallon avgas = 6.7 lb ≈ 3.04 kg; 1 US gallon = 6.0 lb.
Wind effect: groundspeed = TAS ± headwind/tailwind component; time = distance / groundspeed.
Loading and Performance Limitations
Maximum take-off weight, maximum landing weight, maximum zero fuel weight and maximum ramp weight each limit a different phase; the lowest applicable limit governs.
Structural limit load factors for the normal category are +3.8 g and −1.52 g at or below design cruising speed, decreasing to +2.5 g at VD.
Utility category permits +4.4 g and −1.76 g; aerobatic category permits +6.0 g and −3.0 g.
VNE is the never-exceed speed; VNO is maximum structural cruising speed; VA is design manoeuvring speed and decreases with √(weight).
VA is the speed above which full deflection of a single control can overstress the airframe; turbulence penetration speed is normally VB or below VA.
Floor loading and baggage compartment limits must be checked separately from the CG envelope.
Runway limit, obstacle clearance, brake energy and tyre speed are operational limits not captured by the AFM weight limits.
A forward CG combined with aft-loading error can push the aircraft outside the envelope at low weight even when MTOW is respected.
Principles of Flight
Lift L = ½ρV²SCL; induced drag Di = ½ρV²S·CL²/(πAe), so induced drag varies inversely with V² at constant weight.
Total drag = parasite drag (varies with V²) + induced drag (varies with 1/V²); minimum drag occurs where parasite and induced drag are equal, at CL = √(CD0·πAe).
At constant weight and altitude, minimum drag speed is 1.32 times minimum power speed (V_mp = V_md/√3).
Load factor n = L/W = 1/cos φ in a level banked turn; stall speed increases with √n, so a 60° bank raises Vs by 41%.
Rate of climb depends on excess power (T−D)V/W; angle of climb depends on excess thrust (T−D)/W.
Critical angle of attack is the only direct cause of stall; it is unaffected by weight, bank, density altitude or CG.
Static stability requires a negative dCm/dCL; positive static stability plus positive dynamic stability gives short-period and phugoid damping.
Mach crit is the free-stream Mach number at which local flow first reaches M=1; swept wings and thin sections raise Mcrit.
Adverse yaw arises from asymmetric induced drag on the downgoing wing in a turn; aileron differential and rudder coordinate the roll.
Aircraft Performance
Density altitude = pressure altitude + 120 × (OAT − ISA temperature at that pressure altitude); ISA lapse is 1.98 °C per 1000 ft up to 36,090 ft.
Take-off and landing distances increase by roughly 10% per 1000 ft density altitude and by 10% for each 10% increase in weight beyond the AFM reference.
Headwind component = wind speed × cos(angle between wind and runway); crosswind component = wind speed × sin(angle).
V1 is decision speed, VR rotation speed, V2 take-off safety speed; V1 must be ≥ VMCG and ≤ VR.
Balanced field length is achieved when V1 is chosen so that accelerate-stop distance equals accelerate-go distance.
Climb gradient % = (ROC ft/min × 60) / (groundspeed in kt × 6076) × 100, or approximately (ROC/GS) × 100 when ROC is in ft/min and GS in kt × 101.3.
Service ceiling is where ROC falls to 100 ft/min; absolute ceiling is where ROC is zero.
Landing distance is measured from 50 ft screen height to full stop on a dry, level, paved runway at AFM reference conditions.
Weight and Balance
Moment = weight × arm; CG arm = total moment / total weight.
Weight shift formula: ΔCG = (weight moved × distance moved) / total weight.
Adding or removing weight: new CG = (old total moment ± added moment) / (old total weight ± added weight).
Empty weight, basic empty weight, zero fuel weight and maximum take-off weight are distinct; MZFW limits payload before fuel is added.
Forward CG increases longitudinal stability and elevator effectiveness but lengthens take-off run and raises stall speed slightly; aft CG reduces stability margin and stick force.
Datum, arm and station are measured in the AFM; arms forward of the datum are negative.
The CG envelope is bounded by forward and aft limits that vary with weight; the aft limit is often set by stability and the forward limit by elevator authority in landing flare.
Percentage MAC = (CG arm − LEMAC) / (MAC length) × 100.
Flight Planning and Fuel
Fuel required = trip fuel + taxi fuel + contingency (usually 5% of trip) + alternate fuel + final reserve + additional fuel.
Final reserve for a VFR CPL flight is 30 minutes at holding speed; IFR final reserve is 30 minutes at 1500 ft above the alternate.
Endurance = usable fuel / fuel flow; range = TAS × endurance, corrected for wind.
Specific range = (TAS in nm/h) / (fuel flow in kg/h); maximum specific range occurs at the tangent from the origin to the power-required curve.
Piston engine fuel flow varies roughly with power; lean mixture reduces flow but must respect CHT and detonation limits.
Pilot-observed ISA deviation: pressure altitude from QNH setting, then density altitude from OAT and pressure altitude.
Pounds to kilograms: 1 kg = 2.2046 lb; 1 imperial gallon avgas = 6.7 lb ≈ 3.04 kg; 1 US gallon = 6.0 lb.
Wind effect: groundspeed = TAS ± headwind/tailwind component; time = distance / groundspeed.
Loading and Performance Limitations
Maximum take-off weight, maximum landing weight, maximum zero fuel weight and maximum ramp weight each limit a different phase; the lowest applicable limit governs.
Structural limit load factors for the normal category are +3.8 g and −1.52 g at or below design cruising speed, decreasing to +2.5 g at VD.
Utility category permits +4.4 g and −1.76 g; aerobatic category permits +6.0 g and −3.0 g.
VNE is the never-exceed speed; VNO is maximum structural cruising speed; VA is design manoeuvring speed and decreases with √(weight).
VA is the speed above which full deflection of a single control can overstress the airframe; turbulence penetration speed is normally VB or below VA.
Floor loading and baggage compartment limits must be checked separately from the CG envelope.
Runway limit, obstacle clearance, brake energy and tyre speed are operational limits not captured by the AFM weight limits.
A forward CG combined with aft-loading error can push the aircraft outside the envelope at low weight even when MTOW is respected.
Principles of Flight
Lift L = ½ρV²SCL; induced drag Di = ½ρV²S·CL²/(πAe), so induced drag varies inversely with V² at constant weight.
Total drag = parasite drag (varies with V²) + induced drag (varies with 1/V²); minimum drag occurs where parasite and induced drag are equal, at CL = √(CD0·πAe).
At constant weight and altitude, minimum drag speed is 1.32 times minimum power speed (V_mp = V_md/√3).
Load factor n = L/W = 1/cos φ in a level banked turn; stall speed increases with √n, so a 60° bank raises Vs by 41%.
Rate of climb depends on excess power (T−D)V/W; angle of climb depends on excess thrust (T−D)/W.
Critical angle of attack is the only direct cause of stall; it is unaffected by weight, bank, density altitude or CG.
Static stability requires a negative dCm/dCL; positive static stability plus positive dynamic stability gives short-period and phugoid damping.
Mach crit is the free-stream Mach number at which local flow first reaches M=1; swept wings and thin sections raise Mcrit.
Adverse yaw arises from asymmetric induced drag on the downgoing wing in a turn; aileron differential and rudder coordinate the roll.
Aircraft Performance
Density altitude = pressure altitude + 120 × (OAT − ISA temperature at that pressure altitude); ISA lapse is 1.98 °C per 1000 ft up to 36,090 ft.
Take-off and landing distances increase by roughly 10% per 1000 ft density altitude and by 10% for each 10% increase in weight beyond the AFM reference.
Headwind component = wind speed × cos(angle between wind and runway); crosswind component = wind speed × sin(angle).
V1 is decision speed, VR rotation speed, V2 take-off safety speed; V1 must be ≥ VMCG and ≤ VR.
Balanced field length is achieved when V1 is chosen so that accelerate-stop distance equals accelerate-go distance.
Climb gradient % = (ROC ft/min × 60) / (groundspeed in kt × 6076) × 100, or approximately (ROC/GS) × 100 when ROC is in ft/min and GS in kt × 101.3.
Service ceiling is where ROC falls to 100 ft/min; absolute ceiling is where ROC is zero.
Landing distance is measured from 50 ft screen height to full stop on a dry, level, paved runway at AFM reference conditions.
Weight and Balance
Moment = weight × arm; CG arm = total moment / total weight.
Weight shift formula: ΔCG = (weight moved × distance moved) / total weight.
Adding or removing weight: new CG = (old total moment ± added moment) / (old total weight ± added weight).
Empty weight, basic empty weight, zero fuel weight and maximum take-off weight are distinct; MZFW limits payload before fuel is added.
Forward CG increases longitudinal stability and elevator effectiveness but lengthens take-off run and raises stall speed slightly; aft CG reduces stability margin and stick force.
Datum, arm and station are measured in the AFM; arms forward of the datum are negative.
The CG envelope is bounded by forward and aft limits that vary with weight; the aft limit is often set by stability and the forward limit by elevator authority in landing flare.
Percentage MAC = (CG arm − LEMAC) / (MAC length) × 100.
Flight Planning and Fuel
Fuel required = trip fuel + taxi fuel + contingency (usually 5% of trip) + alternate fuel + final reserve + additional fuel.
Final reserve for a VFR CPL flight is 30 minutes at holding speed; IFR final reserve is 30 minutes at 1500 ft above the alternate.
Endurance = usable fuel / fuel flow; range = TAS × endurance, corrected for wind.
Specific range = (TAS in nm/h) / (fuel flow in kg/h); maximum specific range occurs at the tangent from the origin to the power-required curve.
Piston engine fuel flow varies roughly with power; lean mixture reduces flow but must respect CHT and detonation limits.
Pilot-observed ISA deviation: pressure altitude from QNH setting, then density altitude from OAT and pressure altitude.
Pounds to kilograms: 1 kg = 2.2046 lb; 1 imperial gallon avgas = 6.7 lb ≈ 3.04 kg; 1 US gallon = 6.0 lb.
Wind effect: groundspeed = TAS ± headwind/tailwind component; time = distance / groundspeed.
Loading and Performance Limitations
Maximum take-off weight, maximum landing weight, maximum zero fuel weight and maximum ramp weight each limit a different phase; the lowest applicable limit governs.
Structural limit load factors for the normal category are +3.8 g and −1.52 g at or below design cruising speed, decreasing to +2.5 g at VD.
Utility category permits +4.4 g and −1.76 g; aerobatic category permits +6.0 g and −3.0 g.
VNE is the never-exceed speed; VNO is maximum structural cruising speed; VA is design manoeuvring speed and decreases with √(weight).
VA is the speed above which full deflection of a single control can overstress the airframe; turbulence penetration speed is normally VB or below VA.
Floor loading and baggage compartment limits must be checked separately from the CG envelope.
Runway limit, obstacle clearance, brake energy and tyre speed are operational limits not captured by the AFM weight limits.
A forward CG combined with aft-loading error can push the aircraft outside the envelope at low weight even when MTOW is respected.
Principles of Flight
Lift L = ½ρV²SCL; induced drag Di = ½ρV²S·CL²/(πAe), so induced drag varies inversely with V² at constant weight.
Total drag = parasite drag (varies with V²) + induced drag (varies with 1/V²); minimum drag occurs where parasite and induced drag are equal, at CL = √(CD0·πAe).
At constant weight and altitude, minimum drag speed is 1.32 times minimum power speed (V_mp = V_md/√3).
Load factor n = L/W = 1/cos φ in a level banked turn; stall speed increases with √n, so a 60° bank raises Vs by 41%.
Rate of climb depends on excess power (T−D)V/W; angle of climb depends on excess thrust (T−D)/W.
Critical angle of attack is the only direct cause of stall; it is unaffected by weight, bank, density altitude or CG.
Static stability requires a negative dCm/dCL; positive static stability plus positive dynamic stability gives short-period and phugoid damping.
Mach crit is the free-stream Mach number at which local flow first reaches M=1; swept wings and thin sections raise Mcrit.
Adverse yaw arises from asymmetric induced drag on the downgoing wing in a turn; aileron differential and rudder coordinate the roll.
Aircraft Performance
Density altitude = pressure altitude + 120 × (OAT − ISA temperature at that pressure altitude); ISA lapse is 1.98 °C per 1000 ft up to 36,090 ft.
Take-off and landing distances increase by roughly 10% per 1000 ft density altitude and by 10% for each 10% increase in weight beyond the AFM reference.
Headwind component = wind speed × cos(angle between wind and runway); crosswind component = wind speed × sin(angle).
V1 is decision speed, VR rotation speed, V2 take-off safety speed; V1 must be ≥ VMCG and ≤ VR.
Balanced field length is achieved when V1 is chosen so that accelerate-stop distance equals accelerate-go distance.
Climb gradient % = (ROC ft/min × 60) / (groundspeed in kt × 6076) × 100, or approximately (ROC/GS) × 100 when ROC is in ft/min and GS in kt × 101.3.
Service ceiling is where ROC falls to 100 ft/min; absolute ceiling is where ROC is zero.
Landing distance is measured from 50 ft screen height to full stop on a dry, level, paved runway at AFM reference conditions.
Weight and Balance
Moment = weight × arm; CG arm = total moment / total weight.
Weight shift formula: ΔCG = (weight moved × distance moved) / total weight.
Adding or removing weight: new CG = (old total moment ± added moment) / (old total weight ± added weight).
Empty weight, basic empty weight, zero fuel weight and maximum take-off weight are distinct; MZFW limits payload before fuel is added.
Forward CG increases longitudinal stability and elevator effectiveness but lengthens take-off run and raises stall speed slightly; aft CG reduces stability margin and stick force.
Datum, arm and station are measured in the AFM; arms forward of the datum are negative.
The CG envelope is bounded by forward and aft limits that vary with weight; the aft limit is often set by stability and the forward limit by elevator authority in landing flare.
Percentage MAC = (CG arm − LEMAC) / (MAC length) × 100.
Flight Planning and Fuel
Fuel required = trip fuel + taxi fuel + contingency (usually 5% of trip) + alternate fuel + final reserve + additional fuel.
Final reserve for a VFR CPL flight is 30 minutes at holding speed; IFR final reserve is 30 minutes at 1500 ft above the alternate.
Endurance = usable fuel / fuel flow; range = TAS × endurance, corrected for wind.
Specific range = (TAS in nm/h) / (fuel flow in kg/h); maximum specific range occurs at the tangent from the origin to the power-required curve.
Piston engine fuel flow varies roughly with power; lean mixture reduces flow but must respect CHT and detonation limits.
Pilot-observed ISA deviation: pressure altitude from QNH setting, then density altitude from OAT and pressure altitude.
Pounds to kilograms: 1 kg = 2.2046 lb; 1 imperial gallon avgas = 6.7 lb ≈ 3.04 kg; 1 US gallon = 6.0 lb.
Wind effect: groundspeed = TAS ± headwind/tailwind component; time = distance / groundspeed.
Loading and Performance Limitations
Maximum take-off weight, maximum landing weight, maximum zero fuel weight and maximum ramp weight each limit a different phase; the lowest applicable limit governs.
Structural limit load factors for the normal category are +3.8 g and −1.52 g at or below design cruising speed, decreasing to +2.5 g at VD.
Utility category permits +4.4 g and −1.76 g; aerobatic category permits +6.0 g and −3.0 g.
VNE is the never-exceed speed; VNO is maximum structural cruising speed; VA is design manoeuvring speed and decreases with √(weight).
VA is the speed above which full deflection of a single control can overstress the airframe; turbulence penetration speed is normally VB or below VA.
Floor loading and baggage compartment limits must be checked separately from the CG envelope.
Runway limit, obstacle clearance, brake energy and tyre speed are operational limits not captured by the AFM weight limits.
A forward CG combined with aft-loading error can push the aircraft outside the envelope at low weight even when MTOW is respected.
Principles of Flight
Lift L = ½ρV²SCL; induced drag Di = ½ρV²S·CL²/(πAe), so induced drag varies inversely with V² at constant weight.
Total drag = parasite drag (varies with V²) + induced drag (varies with 1/V²); minimum drag occurs where parasite and induced drag are equal, at CL = √(CD0·πAe).
At constant weight and altitude, minimum drag speed is 1.32 times minimum power speed (V_mp = V_md/√3).
Load factor n = L/W = 1/cos φ in a level banked turn; stall speed increases with √n, so a 60° bank raises Vs by 41%.
Rate of climb depends on excess power (T−D)V/W; angle of climb depends on excess thrust (T−D)/W.
Critical angle of attack is the only direct cause of stall; it is unaffected by weight, bank, density altitude or CG.
Static stability requires a negative dCm/dCL; positive static stability plus positive dynamic stability gives short-period and phugoid damping.
Mach crit is the free-stream Mach number at which local flow first reaches M=1; swept wings and thin sections raise Mcrit.
Adverse yaw arises from asymmetric induced drag on the downgoing wing in a turn; aileron differential and rudder coordinate the roll.
Aircraft Performance
Density altitude = pressure altitude + 120 × (OAT − ISA temperature at that pressure altitude); ISA lapse is 1.98 °C per 1000 ft up to 36,090 ft.
Take-off and landing distances increase by roughly 10% per 1000 ft density altitude and by 10% for each 10% increase in weight beyond the AFM reference.
Headwind component = wind speed × cos(angle between wind and runway); crosswind component = wind speed × sin(angle).
V1 is decision speed, VR rotation speed, V2 take-off safety speed; V1 must be ≥ VMCG and ≤ VR.
Balanced field length is achieved when V1 is chosen so that accelerate-stop distance equals accelerate-go distance.
Climb gradient % = (ROC ft/min × 60) / (groundspeed in kt × 6076) × 100, or approximately (ROC/GS) × 100 when ROC is in ft/min and GS in kt × 101.3.
Service ceiling is where ROC falls to 100 ft/min; absolute ceiling is where ROC is zero.
Landing distance is measured from 50 ft screen height to full stop on a dry, level, paved runway at AFM reference conditions.
Weight and Balance
Moment = weight × arm; CG arm = total moment / total weight.
Weight shift formula: ΔCG = (weight moved × distance moved) / total weight.
Adding or removing weight: new CG = (old total moment ± added moment) / (old total weight ± added weight).
Empty weight, basic empty weight, zero fuel weight and maximum take-off weight are distinct; MZFW limits payload before fuel is added.
Forward CG increases longitudinal stability and elevator effectiveness but lengthens take-off run and raises stall speed slightly; aft CG reduces stability margin and stick force.
Datum, arm and station are measured in the AFM; arms forward of the datum are negative.
The CG envelope is bounded by forward and aft limits that vary with weight; the aft limit is often set by stability and the forward limit by elevator authority in landing flare.
Percentage MAC = (CG arm − LEMAC) / (MAC length) × 100.
Flight Planning and Fuel
Fuel required = trip fuel + taxi fuel + contingency (usually 5% of trip) + alternate fuel + final reserve + additional fuel.
Final reserve for a VFR CPL flight is 30 minutes at holding speed; IFR final reserve is 30 minutes at 1500 ft above the alternate.
Endurance = usable fuel / fuel flow; range = TAS × endurance, corrected for wind.
Specific range = (TAS in nm/h) / (fuel flow in kg/h); maximum specific range occurs at the tangent from the origin to the power-required curve.
Piston engine fuel flow varies roughly with power; lean mixture reduces flow but must respect CHT and detonation limits.
Pilot-observed ISA deviation: pressure altitude from QNH setting, then density altitude from OAT and pressure altitude.
Pounds to kilograms: 1 kg = 2.2046 lb; 1 imperial gallon avgas = 6.7 lb ≈ 3.04 kg; 1 US gallon = 6.0 lb.
Wind effect: groundspeed = TAS ± headwind/tailwind component; time = distance / groundspeed.
Loading and Performance Limitations
Maximum take-off weight, maximum landing weight, maximum zero fuel weight and maximum ramp weight each limit a different phase; the lowest applicable limit governs.
Structural limit load factors for the normal category are +3.8 g and −1.52 g at or below design cruising speed, decreasing to +2.5 g at VD.
Utility category permits +4.4 g and −1.76 g; aerobatic category permits +6.0 g and −3.0 g.
VNE is the never-exceed speed; VNO is maximum structural cruising speed; VA is design manoeuvring speed and decreases with √(weight).
VA is the speed above which full deflection of a single control can overstress the airframe; turbulence penetration speed is normally VB or below VA.
Floor loading and baggage compartment limits must be checked separately from the CG envelope.
Runway limit, obstacle clearance, brake energy and tyre speed are operational limits not captured by the AFM weight limits.
A forward CG combined with aft-loading error can push the aircraft outside the envelope at low weight even when MTOW is respected.