Course menu

Educational aerodynamic and performance model

Aircraft Performance & Forces Visualizer

Scenarios

Steady, unaccelerated flight at FL300. Lift equals weight, thrust equals drag. Confirm that L = W and T = D. Note the angle of attack and the L/D ratio.

HORIZONFLIGHT PATH γ 0.0°CGCPACNPWRPTLH-STABMAC 4.19 mLIFT 628 kNWEIGHT 628 kNTHRUST 87 kNDRAG 41 kNTAIL UPLOAD 5 kNWING M -148 kN·m NOSE-DOWNPITCH θ 2.3° · α 2.3°

Hover or tab onto CG, CP, AC, NP or the thrust line for an explanation.

Control console

Flight phase

γ = 0° · L = W and T = D at equilibrium

Mass and weight

W = m × g = 64,000 kg × 9.807 = 627.6 kN

41.4 t
9.0 t
13.6 t
25.0 % MAC

Thrust

Excess thrust = T available − T required = 45.5 kN

72 %
240 kN
-0.9 m

Airspeed and altitude

280 kt EAS · 458 kt TAS
30,000 ft

High lift devices and drag

Flaps

Slats
Landing gear
Speed brakes

Wing geometry

AR = b² / S = 35.8² / 124.6 = 10.29

35.8 m
125 m²

Wing loading 514 kg/m² · 5.04 kPa

Aircraft axes — demonstration

Ailerons → roll (longitudinal) · Elevator → pitch (lateral) · Rudder → yaw (vertical)

0.0°

Roll is visible in the front view, yaw in the top view and pitch trim in the side view.

Aircraft state

Flight phaseCRUISE
Altitude30,000 ftρ 0.4583 kg/m³ · σ 0.374
Airspeed280 kt EAS458 kt TAS
Mach number0.777
Dynamic pressure q12.71 kPa
Angle of attack α2.3°stall α 15.5° · margin 13.2°
Pitch attitude θ2.3°θ = α + γ
Flight path angle γ0.0°
Load factor n1.000 gn = cos γ in steady flight
Stall speed146 kt EASV/VS 1.91

Forces

Lift L627.6 kNC_L 0.396 of C_Lmax 1.45
Weight W627.6 kN64,000 kg
Thrust available86.8 kN
Thrust required41.3 kND + W sin γ
Total drag D41.3 kNC_D 0.0261
— parasite31.7 kNC_D0 0.0200
— induced9.6 kNC_Di 0.0061
W sin γ along path0.0 kN

L = ½ ρ V² S C_L = ½ × 0.4583 × 235² × 125 × 0.396 = 627.6 kN

D = ½ ρ V² S C_D , C_D = C_D0 + C_L²/(π e AR) = 0.0200 + 0.0061

W = m × g = 64,000 × 9.807 = 627.6 kN

T = D · L = W

Performance

Excess thrust45.5 kN
Excess power10.72 MW
Rate of climb3,363 fpmsustainable γ 4.2°
Climb gradient7.3 %
Lift/drag ratio15.20
Fuel flow6,906 kg/hspecific range 0.066 NM/kg

ROC = (T − D) × V / W = 45.5 kN × 235 / 627.6 kN

Stability and moments

Moments are taken about the CG. Positive is nose-up.

CG25.0 % MAC
CP30.6 % MAC
Aerodynamic centre25.0 % MAC
Neutral point42.0 % MAC
Static margin17.0 % MAC
Wing lift moment-147.8 kN·mnose-down
Thrust moment78.1 kN·mnose-up
Tail force4.9 kNupload
Tail moment69.7 kN·m
Net moment (trimmed)0.00 kN·m
Longitudinal stabilitySTABLE

M = F × d ; static margin = x_NP − x_CG = 17.0 % MAC

With the CG ahead of the neutral point, an increase in angle of attack produces extra lift behind the CG, generating a nose-down moment that opposes the disturbance — positive static stability. Moving the CG aft reduces that restoring moment and the tail download needed for trim, which reduces trim drag but erodes stability.

Model assumptions

  • Steady, symmetric flight: no acceleration along or normal to the flight path.
  • Parabolic drag polar, C_D = C_D0 + C_L²/(π e AR); no compressibility rise.
  • Linear lift curve up to the critical angle of attack.
  • Thrust available = rated static thrust × throttle × σ^0.7 (flat rated, no ram effects).
  • ISA troposphere; density from pressure altitude and ISA deviation.
  • Neutral point fixed at 42 % MAC, aerodynamic centre at 25 % MAC, tail arm 3.4 MAC.

Real-time performance graphs

Lift vs airspeed

Lift requiredWeight
0.00188.3376.6564.9753.2100175250325400NOWEAS (kt)Force (kN)

In steady flight the lift required is fixed by W cos γ — the wing achieves it with a different C_L at each speed.

Drag vs airspeed

ParasiteInducedTotal
0.0022.945.768.691.4100175250325400V_MD 210NOWEAS (kt)Drag (kN)

Induced drag falls with V², parasite drag rises with V². Their sum is minimum at V_MD, the best L/D speed.

Thrust required vs available

RequiredAvailable
0.0025.150.375.4100.5100175250325400V_MAX 400BEST ROC 280NOWEAS (kt)Thrust (kN)

The vertical gap between the curves is excess thrust. It closes at maximum level-flight speed and is greatest around the best angle-of-climb speed.

Power required vs available

RequiredAvailable
0.008.0316.124.132.1100175250325400MAX EXCESS POWEREAS (kt)Power (MW)

Excess power divided by weight is the rate of climb, so the widest power gap gives the best ROC speed.

Lift coefficient vs angle of attack

C_L
0.000.430.871.301.74-6.01.48.81624α_CRIT 15.5°NOWα (deg)C_L

Linear up to the critical angle of attack, then the flow separates and C_L breaks down. Slats extend the usable range; flaps shift the whole curve up.

Drag polar

C_D vs C_L
0.000.380.761.141.520.00.00.10.10.1NOWC_DC_L

Parabolic polar C_D = 0.0200 + C_L²/(π × 0.80 × 10.29). The tangent from the origin touches at best L/D, currently 15.2.

This visualization uses simplified aerodynamic relationships for educational purposes. Actual aircraft performance depends on aircraft-specific aerodynamic data, engine performance, atmospheric conditions, compressibility effects, configuration, and flight manual limitations. Never use these figures for real flight planning.