Landing performance

Landing is the take-off run in reverse, with one important difference: the aircraft must arrive at the runway at a controlled speed and height, then get rid of all its kinetic energy in a known distance, whatever the weather has done to the runway surface. The airline flies into strips in western Kansas and Colorado where the runway is gravel for part of the year and covered in compacted snow or ice for another part, so landing distances drive many of its payload decisions. This lesson builds the landing distance from its parts, integrates the braked ground roll, and shows how operating rules and runway condition reports turn the aircraft's capability into the distance a dispatcher must plan for.

The parts of a landing

The certified landing distance is measured from a point 50 ft(15 m) above the runway threshold to the point where the aircraft comes to a stop. It has three parts. The approach segment covers the steady descent on the glide path, typically 3 degrees, from 50 ft down to the start of the flare. The flare is the gentle pull-up that reduces the descent rate to near zero just before touchdown, during which the aircraft also floats and slows a little. The ground roll begins at touchdown and includes a short free roll while the pilot lowers the nose, applies the brakes and selects reverse pitch or spoilers, followed by the braked deceleration to rest.

Approach speed and air distance

The pilot flies the final approach at the reference landing speed \(V_{REF}\), at least 1.3 times the stall speed in the landing configuration, \(V_{S0}\). That margin protects against gusts, wind shear and the extra lift needed in the flare. With full landing flaps, the Tern's maximum lift coefficient is about 2.6, so at its maximum landing weight of 6300 kg its sea-level stall speed is 134 km/h(72 kt) and \(V_{REF}\) is 174 km/h(94 kt). Touchdown happens at about 1.15 \(V_{S0}\), roughly 154 km/h.

On a 3 degree path, descending from 15 m to about 3 m, where the flare begins, takes about 230 m of horizontal distance. The flare and float add roughly 4 seconds at the average of the approach and touchdown speeds, about 180 m. So the Tern covers more than 400 m in the air before its wheels touch the runway. That air distance is a large part of the total, and it is very sensitive to piloting technique: crossing the threshold 10 km/h fast or 20 ft high, or floating for an extra two seconds, can add 100 m or more. Steeper approaches shorten the air distance, which is why some short-field aircraft are certified for approach angles of 4.5 degrees or more.

The braked ground roll

Once the aircraft is on its wheels, the decelerating forces are aerodynamic drag, wheel braking and any reverse thrust. Braking acts on the load the wheels carry, so dumping lift quickly after touchdown with spoilers or by lowering the nose firmly makes the brakes more effective. The braking coefficient \(\mu_B\) depends on the runway surface, the tires and the anti-skid system: around 0.35 to 0.4 on a dry paved runway for a modern system, about half that on a wet runway, and much less on snow, slush or ice.

A simple check uses energy. At touchdown, the Tern carries about \(\tfrac{1}{2}\times 6300\times 42.8^2 = 5.8\ \text{MJ}\) of kinetic energy. Most of it goes into heat in the brakes, which is why brake temperature limits appear in performance manuals and why quick turnarounds after heavy landings can be restricted. Reverse pitch on the propellers turns them into air brakes, taking load off the wheel brakes and adding deceleration that does not depend on runway friction, which matters most on slippery surfaces.

# Landing: air distance from 50 ft, flare, ground roll by integration, and factored field length
import math
g, S = 9.81, 28.0
def rho_at(h, dT):
    T = 288.15 - 0.0065 * h
    return 101325 * (T / 288.15) ** 5.2559 / (287.05 * (T + dT))
def landing(m, h=0, dT=0, mu_b=0.35, rev=0.0, label="", CLmax=2.6, slope=3.0):
    rho = rho_at(h, dT); W = m * g
    Vs0 = math.sqrt(2 * W / (rho * S * CLmax))         # stall speed, landing flaps (true airspeed)
    Vref, Vtd = 1.3 * Vs0, 1.15 * Vs0
    gam = math.radians(slope)
    s_app = (15.2 - 3.0) / math.tan(gam)                # steady approach from 50 ft down to about 3 m
    s_flare = (Vref + Vtd) / 2 * 4.0                    # about 4 s of flare and float while slowing
    s_free = Vtd * 2.0                                   # 2 s from touchdown to full braking
    V, s, dt = Vtd * 0.97, 0.0, 0.01
    while V > 0.5:                                       # braked ground roll with lift dumped
        q = 0.5 * rho * V**2
        D = q * S * (0.095 + 0.04 * 0.3**2)              # landing flaps, gear, spoilers
        F = D + mu_b * (W - q * S * 0.3) + rev * W       # braking on the wheel load; reverse as fraction of W
        V -= F / m * dt; s += V * dt
    total = s_app + s_flare + s_free + s
    print(f"{label:30s} V_REF {Vref*3.6:4.0f} km/h  air {s_app+s_flare:4.0f} m  ground {s_free+s:4.0f} m"
          f"  total {total:5.0f} m  factored {total/0.6:5.0f} m")
    return total
landing(6300, label="6300 kg, dry paved")
landing(6300, mu_b=0.20, label="6300 kg, wet paved")
landing(6300, mu_b=0.20, rev=0.08, label="6300 kg, wet, reverse pitch")
landing(6300, mu_b=0.15, label="6300 kg, firm gravel")
landing(6300, mu_b=0.08, label="6300 kg, compacted snow")
landing(6300, mu_b=0.05, rev=0.08, label="6300 kg, ice, reverse pitch")
landing(6300, h=1600, dT=15, label="6300 kg, 1600 m, ISA+15, dry")
# Energy check: kinetic energy at touchdown that the brakes must absorb
m, V = 6300, 1.15 * math.sqrt(2 * 6300 * g / (1.225 * S * 2.6))
print(f"Touchdown kinetic energy {0.5*m*V**2/1e6:.1f} MJ at {V*3.6:.0f} km/h")

6300 kg, dry paved             V_REF  174 km/h  air  415 m  ground  338 m  total   753 m  factored  1255 m
6300 kg, wet paved             V_REF  174 km/h  air  415 m  ground  506 m  total   921 m  factored  1535 m
6300 kg, wet, reverse pitch    V_REF  174 km/h  air  415 m  ground  389 m  total   805 m  factored  1341 m
6300 kg, firm gravel           V_REF  174 km/h  air  415 m  ground  626 m  total  1042 m  factored  1736 m
6300 kg, compacted snow        V_REF  174 km/h  air  415 m  ground  994 m  total  1409 m  factored  2348 m
6300 kg, ice, reverse pitch    V_REF  174 km/h  air  415 m  ground  675 m  total  1090 m  factored  1817 m
6300 kg, 1600 m, ISA+15, dry   V_REF  193 km/h  air  435 m  ground  406 m  total   841 m  factored  1402 m
Touchdown kinetic energy 5.8 MJ at 154 km/h

Reading the results

On a dry paved runway at maximum landing weight, the Tern lands in about 750 m(2470 ft) from 50 ft. More than half of that is the air distance, which barely changes from one surface to another. The ground roll changes a great deal: it grows by half on a wet runway, nearly doubles on gravel, and triples on compacted snow. Reverse pitch recovers much of the loss on wet or icy surfaces, because its force does not depend on friction. At a high, warm airport, the higher true airspeed for the same indicated speed lengthens both air distance and ground roll, by about 12 percent at 1600 m and ISA+15.

Operating margins

The distance demonstrated in certification flight tests is flown by test pilots, in calm conditions, on a carefully measured runway, with aggressive braking. Airline pilots on a gusty night at the end of a long duty day will not repeat it. Operating rules therefore add margins at dispatch. For many commercial operations, the rule is that the aircraft must be able to land within 60 percent of the runway available at the destination, which is the same as multiplying the demonstrated distance by about 1.67. Where the runway is expected to be wet, a further 15 percent is commonly added. The details depend on the aircraft's certification basis and the kind of operation, set out in FAA operating rules (14 CFR Parts 91 and 135), but the principle is consistent: dispatch with enough runway that an ordinary landing has a wide margin.

The dispatch check is made before departure, using forecast conditions. At the time of arrival, crews make a second assessment using the actual runway condition and wind, with a smaller margin, typically about 15 percent over the expected landing distance. If the runway has deteriorated, the crew may need to hold, divert or wait for the runway to be cleared or treated.

Runway condition reports

Braking on a contaminated runway is difficult to predict, and many landing accidents have happened where crews received vague or out-of-date reports of conditions. The industry responded by standardizing how airports describe runway surfaces. In the United States, the Takeoff and Landing Performance Assessment took effect on October 1, 2016, introducing a runway condition assessment matrix that converts the type and depth of contaminant in each third of the runway into a runway condition code from 6, for dry, down to 0, for nil braking. Canada adopted the closely aligned ICAO Global Reporting Format in 2021. Pilots can report braking action, and those reports can downgrade the code.

Each code links to braking performance data the manufacturer supplies, so the crew can look up a landing distance for the reported conditions. The Tern's performance engineers at Prairiewind Aerospace must produce those data for each code, using flight tests on wet runways and agreed models for the contaminated cases, much like the program's braking coefficients.