A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: The cocked hat
From: Joel Jacobs
Date: 2004 Apr 4, 09:41 -0400
From: Joel Jacobs
Date: 2004 Apr 4, 09:41 -0400
Henry, Thank you very much. You stated the complete argument much better than I just did, though I think any more than three sights is an over kill. Joel Jacobs ----- Original Message ----- From: "Henry C. Halboth"
To: Sent: Sunday, April 04, 2004 1:15 AM Subject: Re: The cocked hat > In my experience at sea, before other means of position finding were > available offshore, conventional wisdom suggested the EFFORT to observe > at least four stars (including planets), one each bearing respectively > south, north, east, and west, or as close thereto as possible, so as to > average out opposing horizon conditions. The sea horizon is seldom > consistent at all points of the compass and discrepancies readily show up > in utilizing this method - judgement being of course necessary in not > using a portion of the horizon which may be obviously unsuitable. > > Obviously conditions do not always permit of such niceties and one must > do what one can. It was, however, quite customary to pre-compute and > observe at least five bodies, even if only to have a reserve in the event > that some proved obviously in error, i.e, wrong body, poor horizon, time > error, sextant reading error, etc. By the way, pre-computation is > essential to accurate star sights - if you wait until you can see them > it's too late to expect a good horizon on average, telescope power > notwithstanding. > > With a well calibrated sextant, a good horizon, the correct time, and > careful calculation, "cocked hats" of any great significance or magnitude > were not the usual thing - if they occasionally were, judgement as to the > value of the individual sights and as to the reliability of the fix as a > whole were seen as more of a consideration than efforts to calculate, by > whatever means, an MPP. If two sights are correct and a third is in > error, calculating an MPP by any method is not going to provide a more > correct position, especially if one can be evaluated out. If it is a > matter of serious concern, it seems the careful navigator will carry > his/her (almost slipped on that one) reckoning forward from each > intersection of the fix to insure s/he is not standing into danger - > assuming of course a "cocked hat" of a magnitude requiring calculation of > an MPP. > > Just thought I'd put my oar in. > > Henry > On Sat, 3 Apr 2004 22:07:05 -0500 Robert Eno writes: > > I'll throw my two bits' worth in. I agree with Joel and in fact what > > he > > describes is more or less the method that I have employed for quite > > a few > > years. > > > > I'll take it a step further: I generally examine my intercepts > > before > > plotting them out, discarding the obviously wonky ones. I do, > > however, > > average out sights taken on land with a bubble attachment because > > bubble > > attachments are inherently inaccurate and in my experience, it is > > better to > > take multiple observations of a few stars and average them out. > > > > I was persuaded, some years ago, that the 3 star fix is overrated. > > Better to > > take two observations of two stars. This is not an an original idea > > on my > > part: my inspiration comes from a little-known book -- Arctic Air > > Navigation -- by a former RCAF Air Navigator, Keith Greenaway:. In > > his book > > Greenaway writes: > > > > "Navigators who use asto continually prefer 2-star fixes with each > > star > > sighted twice, rather than 3 star fixes with each star sighted only > > once. > > Although an extra sight is required, time is actually saved, because > > only > > two stars have to be located, the course setting of the sextant > > changed only > > once, and the tables entered for two stars only. It is also easier > > to detect > > inaccurate computation or observation as shown in Fig. 27". > > > > Figure 27 shows two parallel LOP's spaced very closely and two > > parallel LOPs > > at right angles to the former, spaced far apart. The figure beside > > it shows > > a classic "cocked hat". The caption to the figure reads: "Comparison > > of a > > 2-star and a 3-star fix. In the case of the 3-star fix, it is not > > obvious > > which sight may be in error, while in the case of the 2-star fix it > > is > > immediately apparent which star should be re-sighted or sight > > computations > > checked". > > > > While it is true that I have quoted from a book pertaining to Air > > Navigation, I have used this technique, successfully both on land > > and at > > sea. > > > > As for MPPs, I cannot argue with George and Herbert about the > > efficacy of > > performing the necessary statistical computations to arrive at this > > figure. > > I have read only a little on MPPs but I certainly agree that it is a > > very > > real and very valid concept. Nevertheless, for purposes of practical > > navigation, who is really going to perform this exercise while at > > sea? In > > reality, navigators will simply take the centre of the cocked hat or > > the > > intersection of two lines of position. > > > > I believe that the two times two star technique described by > > Greenaway is a > > reasonable compromise. > > > > Robert > > > > > > > > ----- Original Message ----- > > From: "Joel Jacobs" > > To: > > Sent: Saturday, April 03, 2004 7:58 AM > > Subject: Re: The cocked hat, again. Was: "100 Problems in Celestial > > Navigation" > > > > > > > In an off group exchange with Herbert Prinz, to which I have added > > a few > > > words to for clarity, I said this: > > > > > > "It is really a matter of personal judgment. The navigator's > > selection of > > an > > > MPP will vary as to how reliable or accurate the navigator thinks > > the > > sights > > > were based in the conditions he encountered when taking the > > sights. A > > > mathematical solution may not be appropriate." > > > > > > I submit that this is what George is correctly introducing. > > > > > > Let me add this thought. When I took the USCG Celestial Exam, year > > ago, > > one > > > of the questions had a series of sights that when plotted, had one > > sight's > > > LOP distant from the others. If you answered the question > > including that > > > sight in your calculations, even by averaging, you were wrong. If > > you > > > rejected it as a bad sight, you were right. As a matter of pride, > > I got > > > 100%. Of course I was a lot younger and sharper. > > > > > > Joel Jacobs > > > > > > > >