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How to use E6B

Mechanical E6B​

Structure​

  • Slide rule for mathematics and conversions
    • 10 on outer scale as Math Pointer
    • 60 on the inner scale as Rate Pointer
  • Sectional plotter and chart on the front
  • Wind correction angle for backside

Math​

  • Multiplication 5x7:
    • Line inner 50 with outer 10
    • Find outer 70
    • Read the number 35 inner (=35)
  • Multiplication 17*53:
    • Line inner 17 with outer 10
    • Find outer 53
    • Read the number 90 inner (=900)

Conversion​

  • Convert 100 nm to sm
    • Find NAUT & STAT on the outer scale (left of 70)
    • Line 10 on the inner scale with NAUT
    • Read the answer under the STAT (11.5 = 115 sm)
  • Convert 53 GAL to LBS
    • Find US GAL & FUEL LBS
    • Line up 53 with US GAL
    • Read the answer under FUEL LBS (32 = 320 lbs)
  • Density altitude 30C 1000ft (pressure alt)
    • On the right align +30C (left of 0C) with 1 (= 1000ft)
    • Read DENSITY ALTITUDE above (3 = 3000ft)
  • True Airspeed with 0C 10000ft (pressure alt) 160kts (CAS)
    • On the right align 0C with 10 (= 10000 ft)
    • Find 16 (= 160kts) on the inner scale
    • Read the answer on the outer scale (18.8 = 188kts)

Wind, Time, Fuel​

  • Wind Correction with True Course 360, TAS 130 kts, Wind 270 at 30 kts
    • Align Wind direction (270) with True Index.
    • Slide to one horizontal line. Draw a line up to mark the wind speed (30).
    • Rotate to align the True course (370) with True Index.
    • Slide the marked dot to TAS (130)
    • Ground Speed is under the grommet (127)
    • Wind Correction Angle is the line to the marked dot (13 left)
      • True heading will be 347.
  • Time En Route with dist 250nm, GS 127 kts
    • Line Time pointer 60 to 12.7
    • Locate the dist 25 on the outer scale
    • Read the result in the inner scale (1hr 58 min)
  • Fuel with rate 12.5Gal/hr
    • Line back Time pointer with the fuel burn rate (12.5)
    • Find the time en route (1hr 58min)
    • Read the result from outer scale (24.6 Gal).
  • Heading formula: TC + WCA -> TH + V -> MH + D -> CH
  • VOR: VHF Omnidirectional Range
    • Compass ring on charts around a VOR station uses magnetic north (same as runway number).
    • On a VOR, the circle is the plane having the course direction, and the niddle gives the position of the course.
      • Niddle is left means left of course. Left/Right only makes sense when the plane is towards the course direction.
      • Each dot represents 2deg. Actual distance off course depending on the distance to the station.
  • Magnetic Course:
    • East is least, west is best.
      • That is, variation of xxE is substracted from the true course to get magnetic course. xxW is added.

Weight and Balance​

  • 1 US Gal fuel is 6 lbs.

Extra: Why E6B Works​

Math part​

  • Consider a straight, additive slide rule. Suppose a1,a2a_1,a_2 on Scale A is aligned with b1,b2b_1,b_2 on Scale B.
    • Then we have a2−a1=b2−b1a_2 - a_1 = b_2 - b_1
  • Now suppose the scale is marked by logarithm. That is, number = e ^ length.
    • Then we have ratio equation a2/a1=b2/b1a_2 / a_1 = b_2 / b_1
  • Then, we make it circular, and make sure that one cycle is 10 times. That is, the starting mark 10 becomes 100 after one round. Thus, number xx is written at the angle 360∘×(lg⁡x−1)360^{\circ}\times(\lg x - 1), for 10≤x<10010\le x< 100.
    • The ratio equation holds no matter whether the start point is 1 or 10. So we get the two main scales.
  • The time scale is marked by considering the scale as 10min and casting it to hours. 60 min is 1 hour.
    • Even when using the time scale for hours reading, the inner scale can still be used to get the minute number.
      • For example, 4:00 is 24*(10min). The next short mark means 24.2 in the inner scale, thus 4:02.

Convertion Part​

  • Altimeter setting to altitude is about 970 per "Hg (inches Hg).
    • Estimate: PressureAlt = (29.92 - Altimeter) x 970 + Elevation
  • However, the relation between temperature and altitude is linear.
    • The standard setting is 15C at sea level with 29.92 "Hg. Thus, when the scales are reset (10 aligned with 10), pressure alt has a setting of 0 aligned with 15.
    • The temprature decreases 2C or 3.5F per 1000 feet (not corrected for pressure). This is how the left temprature scale is designed.
      • Note that the spread of temperature and dew point is 2.5C or 4.4F per 1000 feet.
    • The temperature correction is about 120 feet per C. That's how the right scales are designed.

Wind Part​

  • Basically cosine theorem.
  • The wind blows from the end of wind mark to the grommet. Thus, when the TAS is from 0 to the wind mark, the GS is from 0 to the grommet.