When instruments fail and the horizon is a blur, a slide rule bezel can buy decisive minutes.
Mid-flight, with fuel gauges flickering and electronics unreliable, the pilot often faces a simple, urgent question: how much fuel will remain by the time of landing or diversion? In that moment, a slide rule bezel—on an E6B-style flight computer or a watch with a slide rule—serves as a mechanical, immediate fallback.
The bezel turns known fuel flow rates and elapsed time into a usable fuel remainder in a few quick rotations. It is not a precision meter; it provides a fast, reasonably accurate estimate suitable for short-term decisions: diversion planning, declaring minimums, or buying time to reach a safer situation.
How the bezel multiplies and divides
Why alignment equals multiplication
A slide-rule-style bezel uses logarithmic scales: each position on the ring corresponds to the log of a number, not the number itself. Physically, equal distances on the scale represent equal ratios. When the movable ring is rotated, those distances add or subtract, so lining one mark up with another effectively adds their logs—which is exactly how multiplication (and division) works.
Think of it this way: placing the ring so its “1” lines up with 10 and reading 2.5 on the outer scale produces 25 on the inner scale because log(10)+log(2.5)=log(25).
Decimal-place ambiguity and precision
The bezel only gives the mantissa (the digits), not the exponent. That creates decimal-place ambiguity: an alignment that reads “12” might mean 1.2, 12, or 120. Resolve the ambiguity by estimating the expected magnitude before using the bezel (fuel capacity, typical burn rates, time remaining).
Also expect limited precision—usually 2–3 significant digits—because of scale graduation, parallax, and wear. Treat bezel results as quick approximations, not instrument-grade values.
Tips:
- Estimate magnitude first to place the decimal point.
- Round conservatively for fuel planning.
- Cross-check with a secondary method when possible.
Bezel arithmetic gives fast, approximate multiplication and division. Always pick the decimal place from context and treat results as rough guidance, not precise instrument readings.
Core fuel math
The fundamental equation is simple: fuel = flow × time. Flow is a rate (for example, gallons per hour or pounds per hour); time must be in hours. The bezel implements this multiplication by using its logarithmic scales to add exponents.
How to do it on the bezel
- Set the index (the 1 on the C scale) to the flow rate on the D scale. This primes the bezel for multiplication by the chosen rate.
- Find the time in hours on the C scale. Under that mark on the D scale is the fuel consumed.
Important: if time is given in minutes, convert to hours first (minutes ÷ 60). For example, 15 minutes = 0.25 hours.
Examples:
- 12 GPH for 45 minutes → 12 × 0.75 = 9 gallons. On the bezel: align 1 to 12, read at 0.75.
- 200 lb/hr for 20 minutes → 200 × (20/60) ≈ 66.7 pounds.
If the flow is in GPH, label results as gallons. If in lb/hr, label as pounds. To convert between mass and volume, divide or multiply by fuel density (use aircraft data; Jet A ≈ 6.7–6.9 lb/gal as a rough value).
Memorized three-step bezel routine (plus decimal note)
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1. Set the index to the fuel flow
Rotate the bezel so the index mark (the ‘1’ or single-dot) lines up with the fuel-flow reading on the fixed scale (e.g., 12 GPH or 800 lb/hr). This establishes the multiplier baseline.
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2. Read elapsed time on the opposite scale
Locate the elapsed minutes on the fixed minute scale and read the number directly under that minute on the bezel. That readout is the fuel burned for that interval in the flow’s units (subject to decimal placement).
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3. Do a quick sanity check
Mentally compute flow × minutes/60 (for example, 12 GPH × 30/60 = 6 gal) to confirm the bezel result. If the two disagree, reset and repeat; a fast mental check prevents gross errors.
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Decimal placement shorthand
Remember common minute→hour equivalents to place the decimal: 6 min ≈ 0.1 h, 12 ≈ 0.2, 15 = 0.25, 30 = 0.5. Use these to translate the bezel’s raw number into gallons or pounds.
Practice until reflexive. Short timed drills on the ground cement the routine—compare bezel outputs to a stopwatch and the linked timing holds with a chronograph and bezel.
Start with simple checks: 5, 10 and 30 minutes. Verify both GPH and lb/hr flows. If under pressure, rely on the three-step routine plus the mental check.Two numeric bezel examples
Piston example — GPH × minutes
Flow: 12.5 GPH for 45 minutes. Rotate the bezel so 12.5 on the outer scale sits under the 60 index on the inner scale. Find 45 on the inner scale; read the aligned value on the outer scale — about 9.375. Write the answer as 9.4 gallons. Decimal placement confirmed by simple check: 12.5 × 45/60 = 12.5 × 0.75 = 9.375.
Turbine example — lb/hr × minutes
Flow: 1800 lb/hr for 22 minutes. Because the bezel shows 1–10, use 1.8 to represent 1800 (keep the ×1000 in mind). Place 1.8 under 60, find 22 on the inner scale and read roughly 0.66 on the outer. Restore the thousand multiplier: 0.66 × 1000 = 660 lb consumed. Context rule: carry any kilo/milli multipliers from the original rate when interpreting the bezel mantissa.
Quick tip: when in doubt, do a fast mental check (rate × time/60) to confirm decimal placement.
Convert hourly burn into range and reserves
Convert an hourly burn into per‑nm consumption by dividing the hourly flow by groundspeed (knots = nm/hr). Example: 12 gph ÷ 120 kt = 0.10 gal/nm. If groundspeed is unknown, use estimating groundspeed with basic tools to get a usable knot value.
Estimate remaining range from fuel on board: Range (nm) = remaining fuel (gallons) ÷ gal per nm. Example: 30 gal ÷ 0.10 gal/nm = 300 nm. The same math applies to lb/hr (pounds per nm).
Always subtract required reserves before computing range. Convert reserve minutes to hours and multiply by the hourly burn to get reserve fuel to withhold.
Switch to instrument‑derived endurance as soon as reliable sensors or GPS are available—particularly when estimates approach legal or safety limits or winds are variable. If bezel and instruments differ substantially (about 10%), trust the instruments.
Follow regulatory minimums, then add margin.
Convert minutes to fuel: reserve fuel = flow × (minutes/60).
Round estimates down (assume worse groundspeed); if unsure, land earlier.
Common bezel mistakes and quick corrections
It provides a quick, low‑precision estimate; decimal place and exponent are omitted.
Treat bezel results as rough guidance for decisions, not as loggable measurements.
Using the wrong scale or reversed orientation yields values off by factors of ten.
Always align indices and verify with a short timed burn or known quantity.
Flow changes with power, mixture, altitude, and configuration; bezel inputs must reflect current or averaged flow.
Re‑check estimates after climbs, descents, or power changes and use short intervals when uncertain.
Memorize this one‑column bezel cheat sheet
Run this checklist after any bezel estimate
- Compare the bezel result to fuel gauges and recent logbook burns.
- Confirm decimal placement using expected endurance or remaining distance.
- Add regulatory and conservative reserves; recalculate if fuel state changes.
Memorize the cheat sheet and follow the checklist immediately after every estimate. The bezel gives fast, low‑precision answers; treat them as decision aids, not absolute readings. When in doubt, err on the side of more fuel and cross‑check with instruments or a second method.
Step-specific issue: step 3 in the memorized routine (multiplying the two readings) doesn’t feel as ‘memorized’ for me. I keep fumbling with the bezel alignment under stress.
Nice walkthrough — the three-step bezel routine is actually way easier than I expected. Used it on a sim when my GPS glitched and it saved me a bunch of time.