Lesson previewBuild the Ho–Hc Intercept Chain1 section shown
Preview lesson
Build the Ho–Hc Intercept Chain
What you will learn
Calculate a signed altitude intercept from Ho and Hc, convert its magnitude to nautical miles and explain why the result is one position line rather than a fix.
The intercept method compares what was observed, Ho, with what would be calculated from one named assumed position, Hc. The difference gives a signed distance towards or away from the body's geographical position along azimuth Zn.
Ho belongs to the observation after the required altitude corrections. Hc and Zn belong to the same body, exact time and assumed position used for the reduction. Write those inputs together before comparing the two altitudes; a clean subtraction cannot repair mixed body, time or position data.
A one-minute difference in altitude corresponds to one nautical mile of intercept distance in the local position-line construction. Use the sign to choose direction and the magnitude for distance: Ho greater than Hc is towards the body; Ho lower than Hc is away.
The underlying equal-altitude locus is a circle around the body's geographical position. On the scale of an ordinary marine plot, the nearby part is represented by a straight position line perpendicular to Zn. That approximation and its uncertainty must stay visible; the line is not the yacht's unique position.
Intercept plot workbench
Keep altitude, direction, distance and time in one traceable plot
Compare six worked states. Each names its inputs, signed comparison, plotting action, result and limitation in text, so no meaning depends on colour or a memorised towards-or-away phrase alone.
- 1Corrected altitude Ho
- 2Calculated altitude Hc
- 3Intercept Ho − Hc
- 4Azimuth Zn
- 5Intercept point
- 6Perpendicular position line
Inputs to preserve
Constructed reduction: Ho 38°24.6′, Hc 38°18.2′ and Zn 118°T from the named assumed position.
- 1Compare altitudesHo − Hc = +6.4′
- 2Convert angular intercept+6.4′ = 6.4 NM along the altitude gradient
- 3Choose directionHigher Ho means 6.4 NM towards the body on Zn 118°T
- 4Draw the position lineThrough the intercept point, perpendicular to Zn: 028°/208°T
Result
The yacht is somewhere on the resulting position line at the sight time, subject to the observation, reduction and plotting uncertainty.
What it does not prove
A positive intercept does not prove that the assumed position, body, time, Ho, Hc, Zn or chart plot is correct.
Worked example
A constructed Sun reduction gives Ho 38°24.6′, Hc 38°18.2′ and Zn 118°T from the named assumed position.
- 1Calculate Ho − Hc = 38°24.6′ − 38°18.2′ = +6.4′.
- 2Convert the magnitude: 6.4′ corresponds to a 6.4 NM intercept.
- 3Because Ho is greater, move 6.4 NM towards the body along Zn 118°T.
- 4Through that intercept point draw the position line perpendicular to Zn, along 028°/208°T, and label the sight time.
Sense check: A higher observed altitude means the body appeared higher than it would from the assumed position, so the equal-altitude line must be closer to the body's GP.
| Evidence | Question | Output |
|---|---|---|
| Observation | What corrected altitude was actually observed? | Ho |
| Reduction | What altitude and direction belong to this AP and time? | Hc and Zn |
| Comparison | What is Ho − Hc? | Signed intercept and NM magnitude |
| Plot | Where is the intercept point and its perpendicular? | Timed position line |
Say the full intercept sentence
Before drawing, read the result aloud as magnitude, direction, azimuth and time rather than carrying an unsigned number to the chart.
1. Compare
State Ho greater or lower than Hc and retain the signed subtraction.
2. Direct
Say towards the body on Zn or away on its reciprocal.
3. Constrain
Describe the result as one timed position line, not a fix.
Sense check: Another navigator should be able to reconstruct both the intercept point and the line direction from the sentence.
Common mistake or limitation
- Using an unsigned Ho/Hc difference and then guessing towards or away from memory.
- Drawing the position line along Zn instead of perpendicular to it.
- Calling one position line a fix because it crosses the DR track.
Recap
- Intercept = Ho − Hc; retain the sign and use the magnitude as nautical miles.
- Ho greater than Hc is towards; Ho lower than Hc is away.
- The position line passes through the intercept point at right angles to Zn.
Optional quick check
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