Linear Algebra and estimating effects of windspeed and direction on Navigation.

I have set myself a project: Use Linear Algebra to estimate effect of wind-speed and direction on Navigation, specifically the calculation of groundspeed and “track made good”. This is the essence of Wind finding and application to the real world of navigation in the air by bomber command.

I HATED Linear Algebra. I was 17 years-old in first-year university when I took the course (it was mandatory) and I didn’t do well. I got an adjudicated pass, I believe. However, it is the real essence of what the navigator did. So I need to educate myself. I will build a spreadsheet to assist in the calculations.

There are of course resources on the web. I am starting by review the examples outlined here:

https://www.raeng.org.uk/publication...aft-navigation

I presume that you are “all up to speed” having reviewed DTC Bennett’s book *The Complete Air Navigator*? ;-)

Jim

Re: Linear Algebra and estimating effects of windspeed and direction on Navigation.

Jim, Just the words Linear Algebra had me blanching. I thought I would stick to the simple graph. Have fun. Regards, Terry

Re: Linear Algebra and estimating effects of windspeed and direction on Navigation.

Terry: Chuckle! I found it more difficult than I had hoped, and I got sidetracked by other topics and have set it aside for now. But believe me! I have continued respect for what these navigators accomplished in the heat of battle.

Jim

Re: Linear Algebra and estimating effects of windspeed and direction on Navigation.

Jim (*et al*)

There are a number of navigational computer programs on the internet. Some are ‘fixed’ in their use, but some are – basically – on Excel spreadsheets. These you can download and ‘play about’ with to make them do what you want. If you put your mouse over any box you will see the Peruvian nose-flute music that lies in that cell. Beyond me!

I start any investigation in daylight, with no wind/weather, and unlimited vis. I then “fly” the sector, and compare the times/distances with the figures given by FSX, and the various reports. I then gradually insert the winds, temps, time of day, etc, and re-“fly” the sector each time. By comparing the end figures it usually becomes fairly apparent which data are accurate – and which not.

But, as you say, what an 18-yr old (at the outbreak of war) who may have been an apprentice in a telephone company, and who enlisted in the RAF, was expected to do (after a few courses!) at the Nav’s table of a Lancaster whilst being shot at by all and sundry is beyond comprehension!

HTH

Peter Davies

Re: Linear Algebra and estimating effects of windspeed and direction on Navigation.

Absolutely Peter! I have a decent quantitative background from my work as a biologist in fisheries. I'm since retired and a mentally challenged these days (LOL). However I have been able to manage to put together the calculation of Great Circle Distances and Headings/bearings plus string arithmetic into a spreadsheet for dad's routes. It's been quite useful to derive all of this for some 31 routes with 10+ turning points for dad's operations. It would have been very "cumbersome" to say the least to do all of this using an online calculator.

BTW, this spreadsheet is available for anyone who wants to use it.

Jim

Jim

Re: Linear Algebra and estimating effects of windspeed and direction on Navigation.

Peter, If we take your telephone company apprentice, we also have to remember that he could be on a six-minute fixing cycle; so not a lot of time to spare. I suspect that was why you see or hear of so little astro nav being attempted. I read in that very interesting website "One Night in December" that an astro fix could take up to 20 minutes straight and level flying! rEGARDS, tERRY

Re: Linear Algebra and estimating effects of windspeed and direction on Navigation.

Terry,

The V-Bombers used astro-nav. They used it on the last leg of a long flog round the N Atlantic. That last leg (done on radio/radar silence) terminated in dropping a mythical Bomb (often, IIRC, the 'target' was the NW corner of Barnsley railway station!!). They would have to nav from their astro-fix (some way out over the Oggin) and using the fcast Met winds. We, in Met, discovered (illegal!!!) ways of getting the latest winds to 'our' crews. If one of 'our' Sqns won the Bombing Trophy we would get invited to their celebration. Met were just as much a part of their team as the Fitters/Mechs, etc, that kept the a/c serviceable.

Eventually, one of those SIGINT SUs discovered what we were doing - and stopped it (spoilsports!).

An exceptionally ancient Nav ('O' brevet and Pathfinder wings) tried to explain to me the mysteries of astro-nav, etc, but I'm afraid my eyes glazed over pretty quickly then - as they would now!!

HTH

Peter Davies

Re: Linear Algebra and estimating effects of windspeed and direction on Navigation.

Peter, mention was made on the One Night in December site of the V-Bombers and astro nav during a competition. The writer who was an F4 and Nimrod navigator with the RAF noted in regard to astro nav, "But this was a rare talent, I once took a three-position star fix when navigating in the back of a Nimrod, and was so satisfied that I had managed to establish our position as somewhere over the UK that I decided to quit whilst I was ahead!" I have looked at it, and like you ended up with a glazed stare. Regards, Terry