LHA Method of Obtaining Three-Star Fix
The LHA technique allows you to solve the motion problem for a three-star fix by applying a correction to the assumed position rather than computing a numerical solution on the precomp. This eliminates mathematical motion calculations, therefore reducing the chance of math errors on the precomp. To accomplish a three-LHA fix, you must plan 4 minutes between the midtime of each shot. [Figures 12-4 and 12-5] Because LHA changes 1 degree for every 4 minutes, the precomp has three successive LHAs, 1 degree apart. To correct for off-time motion, adjust the assumed position based on true course (TC) and groundspeed (GS). If a shot is planned earlier than fix time, the assumed position is advanced (down-track). For shots planned later than fix time, the assumed position is retarded (up-track).
Figure 12-4. Typical example of the three LHA method. [click image to enlarge]
Figure 12-5. Plotting three LHA.
The example in Figures 12-4 and 12-5 shows the LHA method for a 12-8-4 early shooting schedule. This shooting schedule allows the fix and/or MPP to be resolved before the fix time. To adjust the assumed positions, plot the fix time assumed position and then advance it for 4 minutes of track and GS for each body. This satisfies motion of the observer. When shooting the selected bodies, take care to shoot them exactly on the prescribed times. This eliminates motion of the body.
A variation of advancing the assumed position is to use half motions. This enables you to plot all three LOPs from one assumed position. Table 1 from Pub. No. 249 lists corrections to position of the observer. Each correction is for 4 minutes of time. To use it, enter with your relative Zn (Zn-track) and GS. Now, look at the bottom of the table and note you can apply this correction to your tabulated altitude or observed altitude. It does not matter which you choose, but note that the sign changes dependent on where you apply it. Now, take the number and multiply it by the 4-minute increment of the shot. For example, Figure 12-6 shows the precomp for a 0300 fix using 3 LHAs and half motions. The 0248 shot, Alpheratz, relative Zn, and groundspeed were used to extract a +20 correction from Table 1. Because this shot is 12 minutes early, we need to multiply +20 by three before we apply it to the shot. Note the +60 correction was applied to the observed altitude and, therefore, kept its positive sign. The benefit of doing this is a reduction in plotting. See Figure 12-7 for the plotted LOPs. This technique can be applied to day celestial as well.
Figure 12-6. Half motions three LHA format.
Figure 12-7. Plotting a half motions observation. [click image to enlarge]