E6B Calculator: Wind Triangle and Flight Fuel Planner

Airspeed conversion

Pressure altitude sets static pressure through the standard troposphere relation $p=p_0(1-bh)^{5.255876}$, with $b=6.8755856\times10^{-6}\,\mathrm{ft}^{-1}$. SFTE Handbook chapters 3 and 4 supply the atmosphere and subsonic pitot-static relations. Constants are $p_0=101325$ Pa, $T_0=288.15$ K and $a_0=340.294$ m/s. For dry air with $\gamma=1.4$, impact pressure is $q_c=p_0[(1+(V_C/a_0)^2/5)^{3.5}-1]$. Then $M=\sqrt{5[(1+q_c/p)^{2/7}-1]}$ and $V_T=M a_0\sqrt{T/T_0}$. Temperature is converted to kelvin with its offset. Known-TAS mode bypasses this conversion.

Wind triangle

Following FAA PHAK chapter 16, printed pp.16-14–16-16 (attached extract pp.6–8), all wind directions are from, and all bearings are true. With $\beta=\text{wind-from}-\text{course}$, headwind is $W\cos\beta$ and crosswind from the right is $W\sin\beta$. Cancellation of the lateral velocity gives $\mathrm{WCA}=\arcsin(W\sin\beta/V_T)$. True heading is course plus WCA, wrapped to 0–360°. Groundspeed is $V_G=V_T\cos(\mathrm{WCA})-W\cos\beta$. Each leg uses $t=D/V_G$ and $F=q t$.

Fuel accounting

Sum destination-leg fuel, add the optional destination-to-alternate leg, add a user contingency on those two cruise quantities, add the ground/extra-climb/approach allowance, and add the final reserve. The reserve is normal-cruise fuel flow multiplied by the selected 30 or 45 minutes plus additional reserve time. The fuel margin is starting usable fuel minus that total. The profile deducts the extra allowance before cruise and protects alternate fuel, contingency and final reserve at destination.

Animation

The arrows share one speed scale in a course-up frame. During the one-minute playback, the air-only and ground markers move linearly; their orange connector is the wind displacement. The static vector sum, not the playback position, sets every heading, time and fuel result.

Aviation display units

Planning-table speeds and speed result cards use kt, and leg-table distances use NM in every display mode. Divide physical speed by the one-knot step and distance by the one-nautical-mile step to obtain these fixed-unit values; 1 kt = 1.852 km/h and 1 NM = 1.852 km. Heading, time and fuel calculations continue to use their declared physical units.

• U.S. airplanes on a training route ending at the first intended landing; no refuelling between its one to three legs. The alternate is a separate continuation after destination.
• User-supplied cruise flow and usable fuel are authoritative; the defaults are illustrative training inputs, not performance data for a particular aircraft.
• Steady, horizontally uniform wind, constant cruise speed and constant fuel flow per leg. The additional fuel allowance represents effects not already included in a cruise leg.
• CAS is IAS corrected externally for instrument and position error. OAT is static air temperature, not an uncorrected total-air-temperature indication. Pressure altitude is the standard-atmosphere pressure coordinate.
• The airspeed model uses dry ideal air and isentropic subsonic pitot flow. Exact unit definitions use 1 NM = 1852 m and the engine's US gallon = 3.78541 L.
• A contingency percentage is a planning choice; it is not a percentage prescribed by the cited reserve rules. Final reserve remains separate from contingency.

AVIATION TRAINING ONLY — NOT FOR NAVIGATION OR OPERATIONAL DISPATCH.

Airspeed conversion is restricted to pressure altitudes −1,000 to 30,000 ft, OAT −70 to +60 °C, and Mach below 0.8 on every active leg. A valid course requires crosswind no greater than TAS and strictly positive forward groundspeed. Infeasible cases are blocked; numerical guards only keep diagnostics finite and do not create a valid solution.

U.S. airplane reserve logic follows 14 CFR 91.151(a) and 91.167(a)–(b), using eCFR text current through 22 October 2026, checked on 26 October 2026. VFR day requires destination plus at least 30 minutes at normal cruise; VFR night requires 45 minutes. IFR requires destination, the alternate unless every exception condition in 91.167(b) is met, then 45 minutes. Selecting no alternate does not establish that the exception applies. Check against the rules in force.

No helicopter, rotorcraft, commercial-operator or non-U.S. reserve rules are implemented. Magnetic/compass headings, runway crosswind limits, climb/descent profiles, holding, missed approaches, terrain, traffic, weather updates and aircraft operational limitations are not evaluated. A nonnegative fuel margin only satisfies this numerical budget; it is not a finding of legal or operational fitness.