Tutorials · four forces

Four forces in steady flight

Hypothetical 172, ISA, sea level

Lift Thrust Drag Weight Resultants Along-path lengths at 3×, weight kept vertical

Aircraft designed by Magnific, mirrored

Show net forces (should sum to zero for steady flight)

Net force is zero. Level: thrust exactly balances drag.

Trim angle of attack 0.0° Power 75%

Drag (CD₀) 0.034

Advanced

Total drag CD 0.038 = parasite 0.034 (airframe 0.034 + flaps 0.000) + induced 0.004

Airframe drag (CD₀) 0.034

Flaps

Flaps +0.00 CL, +0.000 CD · Total CL 0.26

Weight 900 kg

Airspeed: 115 kt
Vertical speed: +50 fpm
Flight path: +0.2°
Lift / drag: 6.7
Stall speed: 44 kt

01 Learning opportunities

Start where the page opens, in level flight. Lift equals weight and thrust equals drag, and the two resultants lie exactly over one another. That is what "steady" means: the net force is zero.
Add power and leave the trim alone. The flight path tilts up while the airspeed hardly changes. Power sets the climb or descent; attitude sets the airspeed.
Read the lift label in that climb. It is a little less than weight, not more. A climb is not extra lift; it is thrust carrying part of the weight, L = W cos γ.
Pull the power to idle. The nose goes down and the forward part of weight now does what thrust was doing, pulling the aeroplane along its path against drag.
In that glide, change the weight. The glide angle does not move, only the speed. The glide angle depends on lift over drag alone, which is why the best-glide speed rises with weight but the distance covered does not change.
Raise the trim slowly, at any power. Airspeed falls and lift over drag changes with it. Keep going past the critical angle and the readout turns red: lift falls away, drag climbs, and the only steady state left is a steep descent. The stall is an angle, not a speed.
Open Advanced and add drag or flap. More drag at the same power means a shallower climb or a steeper descent at the same speed. Flap adds lift and drag together, which is why it lowers the stall speed without improving the climb.
Untick and retick "Show net forces". Whatever you set, the two resultants stay equal and opposite. Every steady state, climbing, level or descending, is one with no net force on the aeroplane.

Model and aeroplane details (not required for pilot learning outcomes)

02 The model

Steady, unaccelerated flight, with thrust taken to lie along the flight path and γ positive in a climb. Across the path the lift carries the weight's component, and along it the thrust carries drag plus the rest of the weight:

L = W cos γ
T = D + W sin γ

At a fixed trim angle of attack the lift and drag coefficients are fixed, so E = L/D is too. That leaves one unknown, the flight path angle:

sin γ + cos γ / E = T / W
γ = asin( T / (W·R) ) − φ,   R = √(1 + 1/E²),   φ = atan(1/E)

Airspeed follows from the lift the wing has to make, V = √(2 W cos γ / ρ S CL). Thrust is simply the power lever times a maximum of 1,800 N, the same at any speed: a real propeller gives more thrust when slow and less when fast, which is why this model climbs more slowly and runs faster than the handbook. Up to the stall the lift coefficient is 0.085 per degree from a zero-lift angle of −3°, and drag is CD₀ plus the flap increment plus CL² / (π·AR·e). Past the critical angle the lift coefficient falls by 0.05 per degree and parasite drag grows with the square of the degrees beyond it, so lift over drag collapses and the steady state becomes a steep, mushing descent.

Every force is drawn from the centre of gravity, and the picture is stretched three times along the flight path: thrust and drag would otherwise be slivers beside lift and weight, since a 172 flies at a lift-to-drag ratio around ten. Stretching the whole picture rather than two arrows keeps vector sums honest, so the two resultants, lift + thrust and drag + weight, are the diagonals of the parallelograms the dashed construction lines complete and come out equal and opposite in every steady state. The stretch would make weight lean in a climb or descent, so the whole picture is then turned until weight points straight down; the horizon tilts a little instead. Forces are labelled in kilograms-force, the mass that would weigh as much.

03 The aeroplane

The numbers are a Cessna 172 approximation, a 180 hp fixed-gear 172S at sea level in the standard atmosphere, tuned to the Pilot's Operating Handbook within roughly five to ten per cent. Airspeeds are true at sea level, not indicated. For teaching, not flight planning.

Parameter	Value	Why
Wing area	16.2 m² (174 ft²)	published
Aspect ratio	7.37 (35.8 ft span)	published
Oswald efficiency	0.70	typical strut-braced high wing
CD₀ clean	0.034	fixed gear and struts; tuned to top speed
Flaps 10 / 20 / 30 / 40°	+0.20 / 0.40 / 0.55 / 0.62 CL	typical single-slotted flap; 40° as on the older 172s
	+0.008 / 0.022 / 0.045 / 0.075 CD
Maximum CL, clean	1.75	gives a 50 kt clean stall
Maximum thrust	1,800 N (184 kgf)	constant with speed; a stand-in for 180 hp
Past the stall	−0.05 CL per degree, +0.003 CD per degree²	textbook shape
Gross weight	2,550 lb (1,157 kg)	published

Check	Model	POH
Best rate of climb	~570 fpm at ~90 kt	~730 fpm at Vy 74 KIAS
Top speed, level, full power	~137 kt	~126 kt
Stall, clean	50 kt	~48 kt
Stall, flaps 30°	44 kt	~40 kt
Glide ratio, idle	~11:1	~9:1, with a windmilling propeller

Known gaps: with thrust constant the best-climb speed comes out high and the climb rate low, the top speed high, and the flap-30 stall a few knots fast. Pitching moment and trim change with flap are ignored, as is any offset of the thrust line from the flight path.