Effective Runway Slope
Calculate a runway's effective slope, S = (max elevation − min elevation) ÷ length · 100, from the highest and lowest elevations along the runway centerline and its length. The effective slope is the difference between the highest and lowest points of the longitudinal profile divided by total length — a global measure of the incline the aircraft faces. It feeds directly into the runway length correction (+10% length per 1% effective slope), since an uphill runway needs more takeoff acceleration distance. ICAO limits effective slope by runway code (typically 1-2% max for higher codes) and also limits local slopes and their rate of change for safety. Geometric design minimizes effective slope and smooths transitions, balancing earthwork and drainage. Enter the maximum and minimum elevations and the runway length.
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Effective runway slope
The effective slope of a runway is S = (maximum elevation − minimum elevation) ÷ length · 100 — the difference between the highest and the lowest point of the runway's longitudinal profile, divided by the total length and expressed as a percentage. It is a global measure of the gradient an aircraft faces along the whole runway, and not the local gradient of any single segment. This parameter feeds directly into the runway length correction: every 1% of effective slope calls for another 10% of length, because an uphill runway eats up more distance during the takeoff acceleration. ICAO caps the effective slope according to the runway category (code number) — typically 1% at most for code 3 and 4 runways (the largest ones) and up to 2% for the smaller ones — and also caps the local slope of each segment and the rate of change between segments, so the aircraft neither loses contact with the ground when crossing a hump (the 'undulating runway' effect) nor puts excessive loads through the landing gear. The geometric design of the runway aims to minimize the effective slope and to smooth the vertical transitions with curves, balancing that against earthwork volume and drainage requirements (the runway also needs a transverse fall to shed rainwater). Enter the maximum and minimum elevations and the runway length.
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Runway Hourly Capacity
Estimate a runway's hourly capacity, C = 3600 ÷ T, from the average occupancy or separation time between successive operations T (seconds). A runway's capacity — the maximum operations (landings and takeoffs) per hour — is one of the most important airport planning parameters, setting the airport's traffic limit. The time T is governed by minimum wake-turbulence separation, runway occupancy time (from touchdown to clearing via a rapid-exit taxiway), air traffic control procedures and the aircraft mix. Well-run single runways reach about 40-60 operations per hour; capacity rises with parallel runways, high-speed exits (reducing occupancy time) and optimized procedures. As demand nears capacity, delays grow nonlinearly (queueing theory), driving expansions or flow management (slots). Enter the average time between operations.
Approach Surface Height
Calculate the height of an approach surface (or other obstacle limitation surface) at a given distance, h = (gradient ÷ 100) · distance, from the ramp gradient (%) and the horizontal distance from the surface origin (m). Obstacle Limitation Surfaces (OLS) are imaginary inclined planes projected from runway thresholds and around runways, defined by ICAO, delimiting the airspace that must stay clear of obstacles for safe landing and takeoff. The approach surface, for example, rises at a typical 2% (1:50) gradient from the runway strip end; any object (building, antenna, tree, terrain) penetrating it is an obstacle to be removed, lowered, marked/lit or, ultimately, leading to operational restrictions. This calculation gives the maximum allowed surface height at each point, to compare with the actual height of existing or proposed obstacles around the airport — the basis of land-use control in airport protection zones and the assessment of new developments. Enter the gradient and the distance.
Take-Off Distance Available (TODA)
Calculate the Take-Off Distance Available, TODA = TORA + clearway, from the Take-Off Run Available (TORA) and the clearway length. TODA is one of the four declared distances of a runway, central ICAO operational concepts. The clearway is an obstacle-free rectangular area beyond the runway over which the aircraft can complete the initial climb to a minimum height — it extends takeoff distance without extra pavement, since the aircraft is already airborne. The declared distances (TORA, TODA, ASDA, LDA) are published for each runway threshold and used by pilots and dispatchers to verify, for each takeoff, that the aircraft — with its weight, configuration and the day's conditions — fits the available runway with required margins. Enter the TORA and the clearway length.
Corrected Runway Length (ARFL)
Calculate the corrected runway length from the aircraft reference field length (ARFL) and the three ICAO correction factors: L = L₀·(1 + 0.07·E/300)·(1 + 0.01·ΔT)·(1 + 0.10·S). The basic length L₀ (m) is required at sea level, ISA atmosphere and level runway; corrections increase it for: aerodrome elevation E (+7% per 300 m, as thin air reduces lift and thrust), temperature ΔT above ISA (+1% per °C, same density reason) and effective runway slope S (+10% per 1% slope, which hinders takeoff acceleration). This is fundamental in airport planning: it decides whether a runway can serve a given aircraft at a given airport. High-altitude, hot-climate airports need far longer runways — the same aircraft needs much more runway in La Paz or Brasília than at sea level. Enter the basic length, elevation, temperature difference and slope.
Takeoff Runway Distance Calculator
Estimates single engine aircraft takeoff distance from weight, pressure altitude and temperature using typical aircraft manual corrections.
Curve-Compensated Grade (Railway)
Calculate the compensated grade of a railway section on a curve, i_c = i − 700/R, from the actual section grade i (in ‰, per mille) and the curve radius R (m). When a grade coincides with a curve, the train faces both the climb resistance (gravity) and the extra curve resistance (added wheel-rail friction when changing direction). So the total resistance does not exceed that of the maximum tangent grade, the actual grade on the curve must be reduced (compensated) — subtracting a value equivalent to the curve resistance, commonly estimated as 700/R (in ‰, a usual empirical approximation; some manuals use 500/R or 600/R by gauge). Thus the compensated grade is the equivalent grade the train 'feels' including the curve. This is essential in railway geometric design: it keeps the required tractive effort uniform along the line, preventing a curve-on-grade from creating a critical point (a 'traction bottleneck') that would limit all trains' weight. The designer reduces the grade on curved sections to compensate. Enter the actual grade and the curve radius.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.