[Study Help] Basic Radar Plotting Aid

For reasons I’d rather not elaborate, I recently had to re-do my D5 exams. We’re talking all the courses, the whole shibang. If you think it sounds like fun to go back to school for a while so you can stun your peers with your grey beard and worldly wisdom, I can inform you that it wears off real soon after establishing that true virgins do indeed make terribly dull company, and the mind invariably drifts towards whiskey. In a bid to retain my sanity in the face of lethal boredom, I took it upon myself to solve the radar plot using trigonometry, and developed an algorithm that runs on my TI graph calculator.

Somewhat surprisingly, radar plotting was one of the “problem subjects” that saw a lot of my fellow students frustrated. If you’re also pulling your hair out over how difficult graphical vector addition can be, or if you (like me) are just annoyed at the inescapable measurement errors, you may find my little creation handy for double checking your work. Thus I present to you the BRPA, written in Texas Instruments Basic:

If you go to the program menu on your TI calculator, select new, and type in the above, you should end up with a functional program that does the following:

-Prompts for T, time between readings. In the study material that is basically always 6, but I decided not to hard code it in case you somehow have a different value
-Prompts for V, own ship speed over ground
-Prompts for K, own ship course over ground
-Prompts for B, target bearing
-Prompts for R, target range
-Returns nonsensical output, please ignore
-Prompts for B
-Prompts for R
-Returns CPA, TCPA, target SOG and COG, all rounded to two decimal places.

At this point the program is stuck in a loop, assuming you keep taking readings of the same target at the same time interval, and updates the output accordingly. I’ve tested it on all the example problems we were given, and it seemed to work correctly for all of those. As a funny side note, the answer key was sometimes significantly off on the CPA, sometimes in excess of 20%.

Now some important caveats:
Make sure your calculator is set to degrees (radians is default on most), and please don’t use this for anything without a sanity check. I don’t have the USB cable for my calculator, so the code has been manually transcribed; if it doesn’t run, I probably forgot a parenthesis or somesuch. I have not attempted to deal with targets moving away from own ship, since those didn’t show up in my data set (for some reason), but the way I built it I suspect that it’ll give you correct CPA and time since CPA as TCPA, but I haven’t tested it. Due to the pen and paper way I developed this, there is glaring potential for optimization. Due to the use of division in the intermediary steps, targets on a constant bearing result in a divide by zero, and due to the use of tangent, targets with relative course parallel or perpendicular to own ship result in out of domain error. The only way I can see to fix that is by testing for edge cases and outputting preset values, which sounds tedious, so I haven’t.

If there is any interest, I can sanitize the output, add some exception handling, maybe even a graphical interface, etc. If anyone wants to grab this and port it to whatever (Casio? iOS?), please go right ahead, no attribution required (but don’t blame me when the code blows up). The right arrow is the assignment symbol in TI basic, so substitute = and invert the statement for most common languages.

Anyway, hope someone gets use of this, and don’t hesitate to ask :slight_smile:


I felt the same when we were required to do a refresher course for STCW95 under our regulations covering BRM, Computers and ship stability programmes, ship simulater and other subjects . When I did my unlimited mechanical computers existed in the military and hand held calculator with the 4 basic mathematical functions was $1000. I still use a slide rule in the workshop.
I was a bit more fortunate that because it was mandatory there were a few more grey beards to sink a few with.
I will see if I can port it to an HP11C, a nice project for a rainy day in lookdown.

1 Like

Not bad. I wasn’t able to get that done. Tried that for a final project in a BASIC class, some time ago, long enough back they were using a IBM 360. When I told the instructor I’d run out of time and hadn’t been able to make it run he told me it was a very ambitious and passed me anyway.

Wikipedia tells me HP quit making those 30 years ago.

1 Like

I first used an HP calculator as a desk top for Hydro graphic work in the late 60’s and got used to Reverse Polish Notation. I brought my first HP in Houston, it had a rechargable battery that lasted no time at all. If I want to produce a graph I use Excel otherwise I am happy with the HP I have and I still use my Grandfathers tools, he was a carpenter, and many of those are over 100 years old.

1 Like

I don’t know what method my son used, but finished radar renewal a few months ago just before classes got cancelled this year… He had to renew because he was just short of seatime due to medical crap. He passed. Now we wait for USCG approval or not on 5 year license renewal.

Thanks :grinning: When I showed my teacher and told him I intended to use it on the exam, he just rolled his eyes, which had become his standard reaction to my opening my mouth. I can’t really blame the guy.

This won’t show up on any curriculum, except maybe ARPA making class. What they teach is the old pencil and plotting sheet method. I find it more than a bit silly, because I can guarantee you that not a single one of the current crop of mariners will ever use it. What I’ve done here is basically to create a cheat so that you can annoy your teachers with far too many decimal points.

1 Like

Never mind the teacher; that’s an offense against the universe. Those extra decimals are lies.

1 Like

That’s what I was wondering. Outside of engineering or scientific stuff unless you run into one at work how many people would use RPN?

I ran into it when I got hired as rodman for an engineering company. One of the jr engineers there used to spend a lot of time reducing hand written “cut and fill” data and the like from field notes on a HP desktop calculator.

However he was a binge drinker and sometimes missed work for days at a time. So the boss told him to show me how to do it for the days when he didn’t show up. That’s how I ended up with a 11C.

Now however if RPN is preferred there are RPN calculator apps for smartphones. The keyboard layout is not the same as the 11C but the display also shows what’s in the stack which is helpful at times.

Between the smartphone and the computer less demand for calculators like this outside of exams or classrooms I’d think.

This forum does a great job of teaching me how little I know at times. I’ve only owned a smart phone in retirement so much of what I use it for has been discovered by accident. Grandkids of an age to teach me are in the US and Trump has sorted that out last night.
I use the calculator function in its most basic form because in the scientific mode the buttons are too small and obtaining correct answear is problematic. I suffer from the fat finger syndrome from too much wire splicing as a young man.

1 Like

I agree, the calculator is much easier to use than the phone app. The HPs especially, the keys have good tactile feedback.

My 11c quit working a while back and I got a 32S II to replace it. Wikipedia says 32S was discontinued in 2002 so it must have been about then.

At this point however I wouldn’t trust anything from HP.

I know I’m supposed to like matlab, but I can solve basic problems much faster with my trusty TI-84. Part of that is the habitude born from going to college with a TI-81, which has relegated interface interactions to the subconscious, and part of it is the fact that single purpose tools always outperform their multi role counterparts.

On a semi related side note, the above problem could be solved much more efficiently by leveraging the graph, matrix and vector math functions, but this was a pen-and-paper challenge. Also, doing so would have rendered the code basically non-portable.


The trusty old calculator still have their niche.

I used my programmable HP for all my CG exams. They make you take the batteries out so any saved programs are lost but it only takes about a minute or less to reenter the formula from Bowditch which is available in the exam room

Once I had the program entered I’d test it on the example problem in Bowditch and if the answer came out correct I could be confident it would do the exam question correctly. Probably takes about the same time to work out the problem by hand but with the calculator no need to recheck. Also if there is an error less likely to be one of the incorrect choices on the exam.

I’d take a cheap non-programmable Casio as well in the case they wouldn’t let me use the HP but I never had to use it.


We were not allowed calculators until we sat our Masters Unlimited so sitting for second mate and chief mate exams it was all about speed and accuracy with 7 figure log tables. only non programmable calculators were permitted. I think things have changed now.

Yea they have changed. I assume you were allowed to use slide rules before calculators were allowed? What will be interesting is to see what happens moving forward. NOAA is stopping production of all raster charts. At the least, USCG would have to move to paper ENC charts. But maybe they will go a step further and go digital?

Sliderules were allowed and I’ve still got the one I used. I keep it in the workshop.

Being currently stuck at home, I’ve been going through Bowditch to relieve boredom. I’m all stopped at some of the mathematics you used to use before calculators. Stuff I was never even introduced to in school. Logarithms, haversines, secants and cosecants. It cracks me up that most of the V2 tables are only there because calculators didn’t exist. Yet this is still what USCG expects modern mariners to use.

Maybe I’m not grasping what you guys are experiencing, or what it is the course requirements… Son did radar renewal and used both paper plotting sheets and the radar on the premises. Used a calculator and triangles. Maybe I’ve been away too long. And correct, I did not use radar plotting sheets onboard once I passed the renewal test.

At the time I tested I believe the rules allowed what’s called manually programmable calculators. This is from an internet search"

as they meet all other requirements. All manually programmable calculators must have simple erasure capability in order to be permitted.

If I had to test now I think I’d use a non-programmable scientific calculator with a display big enough to show the entire formula. I think that would minimize the chance of error and be faster than programming the calculator during the exam. .

1 Like

Unless the exam room staff is of a certain age, would they even recognize a programmable calculator, or know that such things exist?