The intercept method: from altitude to position line
1The lesson in plain words
Compare the altitude you observed with the one you would see from an assumed position. The difference, the intercept, places your position line.
The idea
A corrected sextant altitude puts you on a circle of equal altitude around the body's geographical position (Celestial: the celestial sphere). That circle is huge, often thousands of miles across. Near you, a short piece of it is almost straight: a position line. The intercept method, published by Marcq St-Hilaire in 1875, finds that short piece without drawing the circle.
Assumed position
Choose an assumed position (AP) near your dead-reckoning position (DR). From the AP, calculate the computed altitude (Hc) and true azimuth (Zn), the body’s bearing clockwise from true north, for the exact sight time. Then compare Hc with your observed altitude (Ho): the sextant altitude after all corrections (Celestial: the sextant).
Towards or away
The intercept is Ho − Hc, in minutes of arc. Each minute is one nautical mile. If Ho is greater, you are nearer the body than the AP is: the intercept is towards. If Ho is smaller, you are farther away: the intercept is away. A memory aid: Ho Mo To, Ho more, towards.
Drawing it
From the AP, lay off the intercept along Zn if it is towards, or along the reciprocal of Zn if it is away. That end point is the intercept terminal point. Through it, draw the position line at right angles to the azimuth. At the time of the sight, you were somewhere on that line.
Why it works
Near the AP, a change of 1′ in altitude moves the circle 1 M along the azimuth. The method replaces the arc with a straight line, which is accurate when the intercept is short. If an intercept comes out very large, check your work, then rework the sight from a position nearer the result.
2Key data
- Intercept
- Ho − Hc, in minutes of arc = nautical miles
- Direction
- Ho > Hc: towards (Ho Mo To); Ho < Hc: away
- Position line
- At right angles to Zn, through the intercept terminal point
- You need
- Exact UT, Ho, an AP, and the body's GHA and Dec for that UT
- Spanish terms
- Recta de altura = position line; punto determinante = terminal point
3Key points
- 1
Intercept = Ho − Hc: one minute of altitude is one mile along the azimuth.
- 2
Ho greater than Hc: towards the body. Smaller: away. Ho Mo To.
- 3
The position line crosses the azimuth at right angles at the intercept terminal point.
- 4
Reduce every sight for its exact UT; the AP is only a convenient starting point.
4Frequent mistakes
Wrong: The position line runs along the azimuth.
Right: It runs at right angles to the azimuth. The azimuth only shows which way to lay off the intercept.
Wrong: An intercept is always laid off towards the body.
Right: When Ho is smaller than Hc you are farther away than the AP: lay it off along the reciprocal of Zn.
Wrong: The intercept is the distance from your real position to the AP.
Right: It is the distance from the AP to the position line, measured along the azimuth. Your position can be anywhere on the line.
5Practice case & exam keys
From your AP, Hc is 41°12.6′ and Zn 214°T. Your sight gives Ho 40°58.4′. A crew member lays off 14.2 M along 214° and draws the line along 214°. What two corrections do you make?
Show the answer
Ho is 14.2′ smaller than Hc, so the intercept is 14.2 M away: lay it off along 034°, the reciprocal. Then draw the position line through that end point at right angles to the azimuth, along 124°–304°. At the time of the sight you were somewhere on that line.
Exam keys
- Intercept method (Marcq St-Hilaire): intercept = Ho − Hc; 1′ = 1 M.
- Ho > Hc towards; Ho < Hc away (Ho Mo To).
- Position line at right angles to Zn, through the intercept terminal point.
- Inputs: exact UT, Ho, AP, and the almanac's GHA and Dec for that UT.
Finish this unit
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