Takeoff Planner: Density Altitude & Crosswind Calculator

Density altitude uses a dry ideal gas and the ISA troposphere: $H=T_0/L$, $n=g/(R L)$, $p/p_0=(1-h_p/H)^n$, $\sigma=(p/p_0)T_0/T$, and $h_D=H[1-\sigma^{1/(n-1)}]$. Constants are $T_0=288.15$ K, $L=0.0065$ K/m, $g=9.80665$ m/s² and $R=287.05287$ J/(kg·K). The field/QNH option uses the ISA altimeter relation, $h_p=h+H[1-(Q/Q_0)^{1/n}]$, with $Q_0=1013.25$ hPa. These equations are derived here from hydrostatic balance and the ideal-gas law; the PHAK density-altitude example independently checks the result.

Wind projections are $H_w=V\cos(\theta)$ and $X_w=V\sin(\theta)$, where $\theta$ is wind FROM direction minus runway heading. Apply the same projection to gust speed. Reciprocating the runway reverses both signs. The largest adverse tailwind of the steady/gust envelope is used for distance.

The Koch nomogram is implemented by digitizing its temperature axis, pressure-altitude axis, and two correction scales (FAA P-8740-02 archived source s3, p.3). The straight line is read at 340/456 of the horizontal axis separation. Linear interpolation is between digitized chart ticks, not a fitted aircraft model. Approximate graphical precision is about 5% in the distance multiplier and 4 percentage points in climb fraction. The separate climb comparison multiplies the entered sea-level rate by the retained fraction. No below-baseline benefit or extrapolation above the digitized 260% distance increase is allowed.

Generic landing factors are $1.05^{\max(h_p,0)/1000\,ft}$ and $1.05^{\max(T-15\,°C,0)/10\,K}$, interpreting the CAA increments multiplicatively. AFM/POH atmosphere-corrected mode sets both atmosphere factors to one. Surface multipliers follow CAA Safety Sense 09 (August 2024), p.15, also found in historical SSL7 p.8. The nominal wet-grass pair is 1.30 takeoff / 1.35 landing. SSL7 warns that very short slippery wet grass can increase landing distance by up to 60% (factor 1.60); that is not treated as a universally sufficient factor. The wet-grass qualifier defaults to short/slippery/uncertain. While checked, the final landing surface factor, landing distances and margins are unavailable; takeoff retains the wet-grass factor. Adverse slope is linearly interpolated to 1.10 at 2% grade. Tailwind is linearly interpolated to 1.20 at 10% of lift-off speed; larger ratios are rejected. No favorable slope or headwind credit is taken. Multiply atmosphere × surface × slope × wind, then apply the CAA general factors 1.33 and 1.43. Margin = usable available distance − factored total distance.

Distances are total takeoff distance to 50 ft and total landing distance from 50 ft to a stop, not ground roll. Each baseline is unfactored and dry, level, zero wind at the entered mass and configuration. Baseline defaults and the 700 ft/min climb baseline are illustrative, not a named aircraft.

Koch generic mode applies only as an educational approximation for light normally aspirated piston airplanes. Generic landing elevation uses pressure altitude as a proxy for the CAA elevation increment. Negative altitude and colder-than-baseline temperature receive no landing improvement. Use AFM/POH mode to avoid these generic atmosphere assumptions.

The steady wind and gust have one FROM direction. Wind and runway headings use one common north reference; no magnetic-variation correction is inferred. Personal crosswind threshold is chosen by the user. Reciprocal selection reverses slope, but available lengths are entered independently for the chosen direction and must be updated when the direction changes.

The drawing's assumed roll fraction and ten-second animation are illustrative only. Its 50 ft marker is the distance-definition reference, not a surveyed obstacle. Horizontal lengths share a scale; height is exaggerated. General factors lengthen the distance bars, not a predicted aircraft trajectory.

EDUCATIONAL ESTIMATE — AFM/POH and official aircraft and aerodrome data govern. Not for flight planning. This tool does not demonstrate compliance or a safe go/no-go decision. The cited CAA factors are guidance from historical SSL7 (June 2005) and current attached SS09 (August 2024), reviewed for this build on 26 October 2026; check current official guidance and applicable rules.

Dry-air ISA tropospheric calculation, within the altitude and temperature input limits. Humidity, wind shear, turbulence, gust-direction variability, runway width, obstacle position, aircraft weight changes, configuration changes, engine condition, pilot technique and braking differences are not modeled. No aircraft, engine-out climb, accelerate-stop, TORA/ASDA or regulatory dispatch analysis is performed. The available takeoff length assumes no separate clearway or stopway; enter usable LDA separately.

Slope is limited to ±2% grade. CAA generic tailwind interpolation is limited to 10% of lift-off speed. Koch points beyond the digitized takeoff scale suppress generic takeoff distance and margin, with blank Koch comparison cards. Landing remains available when its own factors are supported. Exceeding the tailwind limit suppresses both distance/margin pairs. These are warnings, so valid atmosphere and wind results stay visible. The AFM/POH baseline option avoids generic atmosphere corrections. The wet-grass option assumes firm soil and grass up to 20 cm. Its short/slippery/uncertain qualifier defaults to checked; only explicitly confirmed ordinary wet grass uses the nominal 1.35 landing factor. Slippery short wet grass has no generic landing estimate here, because SSL7 notes increases up to 60%. Soft ground, mud, snow, standing water and contaminated surfaces require specific official data and are not offered. Factors for total distance must not be treated as ground-roll factors: SSL7 explicitly warns that ground-run effects may be greater.