Trig functions & Private Pilot Test

My simple calculator is an HP 15C which has trig functions on it. I showed it to the proctor several days in advance and, with a smile, explained how it worked, how I was used to it, and how I wanted to make sure it was OK. He was fine with it, but I imagine not all would be.

And, since you're going tomorrow, be prepared to use a more basic calculator.

The standards are here:

https://www.faa.gov/regulations_pol...fm/go/document.information/documentID/1031967

This is the relevant stuff:

calculators.jpg





Nochmal said:
I scheduled my written for tomorrow and just called the exam place to confirm whether or not I can use a trig calculator on the exam. It was a little unclear in some of the way the regs are written.

Answer: No, I cannot use the trig calculator, but I can use an aviation-specific calculator that does all the calculations for you like magic in a black box. Or you can use an E6B which is a piece of **** and hard to be accurate with.

That is frankly, stupid. So, those of us who do calculations from first principles are disadvantaged to those who spend some extra money and buy and learn how to use a device that takes all the understanding out of it.

Sorry, this is just a rant, but man am I angry...
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Nochmal said:
Thank you...mostly I posted to hopefully find out I wasn't alone. I'll go slog my way through the 1920s approach with a slide rule. Grin and bare it while my trusty HP 32S (I had a 15C but gave it to my sister when I went to grad school and she was in college) sits in the car. :(
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That’s sick. You should be ashamed.

I’d give away my sister before I’d ever part with my 15C. I’ve made my living with that little jewel for 3 decades.
 
Nochmal said:
I scheduled my written for tomorrow and just called the exam place to confirm whether or not I can use a trig calculator on the exam. It was a little unclear in some of the way the regs are written.

Answer: No, I cannot use the trig calculator, but I can use an aviation-specific calculator that does all the calculations for you like magic in a black box. Or you can use an E6B which is a piece of **** and hard to be accurate with.

That is frankly, stupid. So, those of us who do calculations from first principles are disadvantaged to those who spend some extra money and buy and learn how to use a device that takes all the understanding out of it.

Sorry, this is just a rant, but man am I angry...
Click to expand...

I took my Private and several years later, Instrument written tests, both using my left-over-from-college HP41CV scientific calculator with only about 50 buttons but several hundred builtin functions. I was nice and pulled the battery out, waved it around and made sure the proctor saw it. Then put it back in, turned it on and showed them the "0.0000" display.

It was far easier to use this calculator than struggle to relearn how to use parentheses and equals signs. Don't remember if I ever used a trig function, but it was nice to multiply how I'm used to (9<enter>4×) instead of the old way (9×4=).

Yes, I still use it at home and at work, and have emulators on my phone and tablet. But it's better with real buttons that I can feel when pushing, I make fewer mistakes that way.
 
MBDiagMan said:
Sorry to be combative, but I feel that if you’re not smart enough to use an E6B, you should probably do yourself and your potential passengers a favor, and find something to do with your time other than flying.
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The wind triangle side of an E6B is a party trick to graphically do the trig without having to understand the math behind it. Personally I like to understand the math behind it. I haven't used an E6B in decades and have no plans to start.

Somewhere in the debris of my desk I have a Mach wheel that I do know how to use, do you think you'll allow me to share the sky with you?

Nauga,
who thinks it's as easy as pi
 
nauga said:
. . . it's as easy as pi
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Which my HP has beat into my head through simple repetition is 3.141592654

The E6B even tells you how to spin, mark and respin to figure wind correction and groundspeed. But it's a simple calculation as long as you have basic trig functions on your calculator. But I don't want to use my trusty HP in the air . . . .
 
Half Fast said:
That’s sick. You should be ashamed.

I’d give away my sister before I’d ever part with my 15C. I’ve made my living with that little jewel for 3 decades.
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Hard to argue with you on that point...although I have been quite happy with the 32S I replaced it with in the early 90s. It's gotten me through much more challenging examinations than this silly FAA pilot test.

FWIW, I had checked the FAA requirements before starting my studying and I also had checked with my CFI. It's pretty clear that my 32S should be allowed, so I assumed it would be. But when I signed up with PSI today, they sent me the following, which is why I called the test center:

Allowed Materials
All models of aviation-oriented calculators may be used, including small electronic calculators that perform only arithmetic functions (add, subtract, multiply, and divide). Simple programmable memories (which allow addition to, subtraction from, or retrieval of one number from the memory) are permissible. Also, simple functions, such as square root and percent keys, are permissible. Applicants may use scales, straightedges, protractors, plotters, navigation computers, blank logsheets, holding pattern entry aids, and electronic or mechanical calculators that are directly related to the test. For more detailed information, please consult: http://www.faa.gov/training_testing/testing/test_guides/​

Apparently PSI has stricter regulations than the FAA...including in the FAA link they have there. I'm tempted to show up with my 32S and walk them through the FAA regs, but I'm guessing that'll just make as many enemies as it appears to have done here. One of the biggest things I've noticed about aviation so far is the high fraction of people who are very proud and defensive of their Luddite perspectives.
 
I figure it won’t hurt me to do a few minor math problems on paper and use the silly wheel a couple times to prove I understand how they work. Consider it part of the rite of passage if it makes you feel better. I don’t mind because I expect to become an instructor some day and a student might benefit from me knowing how it works.
 
I have tried to put myself in the shoes of a young person who never had to do trig without an electronic calculator. I would like to ask those of you who fall in that category if you ever wondered how a trig problem was solved with better than two place accuracy before the electronic calculator. Old timers please refrain from answering before the young folks have a chance to ponder the supposition.

Another way to ask the question, if you were isolated with no electronic calculator, with a pencil and paper, and no math education beyond high school algebra, geometry and trig, what would you need for a precise answer beyond pencil and paper.
 
Ha! You don't need no "trig calculator". All you need is a plotter: https://en.wikipedia.org/wiki/Wind_triangle

I bet none of you nerds could out-navigate a farmer I once gave a private flight test to. Watching him handle the diversion problem inflight was a thing of beauty. This penchant for accuracy, while knowing your flying skills can't even come close to the right side of a decimal point, is a real good laugh. Thanks for starting my day off with this thread. Lol, lol., lol.
 
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I'm just gratified to hear so many people still use stand alone calculators, and not their phones. My old solar powered TI is around somewhere, but haven't used it in years. Calculator app in my phone does everything I need.
 
Nochmal said:
Thank you...mostly I posted to hopefully find out I wasn't alone. I'll go slog my way through the 1920s approach with a slide rule. Grin and bare it while my trusty HP 32S (I had a 15C but gave it to my sister when I went to grad school and she was in college) sits in the car. :(
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You're definitely not alone. For my instrument checkride oral I brought in my cross country calculations using an Excel spreadsheet I had written that does the vector arithmetic explicitly. The DPE checked my spreadsheet with a few hypothetical values and pronounced it correct, and that was that.

And yes, I would trust that spreadsheet over an E6B any day. I still use it for flight planning when I have any doubt about whether I will need a fuel stop. Unfortunately, for the FAA written exams, the rules is the rules. :(
 
dmspilot said:
What is a trig calculator?

I used a basic scientific calculator which had trig functions on it on every written I've taken. Which is a lot.
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Interesting. My testing center said that all calculators were disallowed. I guess it is not forbidden at the FAA level, then.
 
Van Johnston said:
I'm just gratified to hear so many people still use stand alone calculators, and not their phones. My old solar powered TI is around somewhere, but haven't used it in years. Calculator app in my phone does everything I need.
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I can't stand the iOS calculator, the only calculator app I've ever used for anything is Panecal, and that mainly to show my students that they don't need to spend anything to have a calculator that can do trig functions and scientific notation.

I had an HP 15C for many years, but its memory registers started failing one by one until it became nearly useless. I still swear by RPN though, so last year I ordered a 35s online from Amazon. Not as good as the classic HP calculators (key layout is wonky IMO), but much better than any app.
 
Nochmal said:
On the Sporty’s practice tests there are always questions like:

Given wind X at Y and true air speed Z, how long will it take to fly from A to B.

Or:

What is the crosswind component on runway A if wind is X at Y.

Or anything to do with wind impact to flying...

Yes, an E6B will do it. Painfully, slowly and inaccurately. A trig calculator will do it swiftly, easily and accurately if you know basic vector algebra.

Also, if you’re right and I don’t need it, why ban it?
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Completely agree. Dirt simple with the trig calculator. The only reason I bought one of those electronic pilot’s calculators was for my commercial and instrument written tests. Much easier to use the RPN calc app on my phone in real life.

Also, those questions about g force and angle of bank. It’s easily calculated as 1/cos(bank angle). Instead they’ll give you that stupid plot with thick lines and faded numbers, ask the g force at 40 degrees, and have two answers that are within the plot line thickness as an answer. It’s a crap shoot trying to pull out the answer from the plot.

Weight and balance calcs are also easier with a calculator which has an add to stored memory function.

Oh, and stall speed increase factor equals square root of the load factor. When I took my instrument and commercial writtens, I wasn’t allowed to use my HP-15C even after I showed them that the memory was completely cleared.

The issue wouldn’t be such a big deal except that the test creators delight in having answers close enough to multiple decimal places and well within the line thickness on the tiny, faded plots given on the test suplement.

In the real world, for example, we certainly don’t have the current winds at altitude accurate to the nth degree, and approximations and rules of thumb can be used. The written tests, at least when I took them, seemed to be designed by people who have no real clue regarding what a pilot actually does and needs to do wrt computations and approximations.

Sent from my iPad using Tapatalk
 
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azure said:
I can't stand the iOS calculator, the only calculator app I've ever used for anything is Panecal, and that mainly to show my students that they don't need to spend anything to have a calculator that can do trig functions and scientific notation.

I had an HP 15C for many years, but its memory registers started failing one by one until it became nearly useless. I still swear by RPN though, so last year I ordered a 35s online from Amazon. Not as good as the classic HP calculators (key layout is wonky IMO), but much better than any app.
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The iPhone has pCalc https://www.pcalc.com/. It can be configured in RPN mode. And I agree, RPN is great. So much better than all those ridiculous parentheses that most calculators force one to use to get the order of operations correct.

Used to be fun when one of the non-engineering majors would ask to borrow my HP-15C in some of my humanities electives class. You could see the puzzled look appear on their faces when they started looking for the equals key. Some decided that maybe that was the function of the Enter key, since it was so large and prominent. They’d maybe try a simple calculation like 3*4:

Lessee, uh [3] [*], WTF?? [4] [ENTER] !!??!! This stupid calcuator is broken! They’d hand it back relatively quickly...


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Capt. Geoffrey Thorpe said:
What is the g force at 90 degrees of bank, and why don't the wings fall off when you do it?
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Alright, I’ll restate it pedantically for you with the additional caveats supplied:

In a _level turn_, the g force is 1/cos(angle of bank) assuming the wings are providing all of the lift and there is no lift being generated by the other portions of the plane. Happy now? Geeze...

Flying a level turn at 90 degrees angle of bank is not possible without lift being provided by something other than the wings. Sustained knife edge flight, for instance, relies on lift from the fuselage and/or on the raw power provided by the engine.




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azure said:
Thanks, wasn't aware of that one but will definitely check it out.
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Yes, sadly, my HP-15C is gathering dust these days. pCalc has replaced it for most of my engineering calculation needs these days, with Excel doing the rest. pCalc is not programmable, but it is handy, and it’s got RPN.

Loved that HP though. Rugged, powerful, and easy to use. One time I accidentally dropped it off of my 3rd story appartment balcony onto the pavement below. 30 years later, it still works beautifully, albeit with a few scratches and dings.


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jimhorner said:
Happy now?
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Not really.

We are told over and over that bank increases g forces - but it's not the bank. g forces have nothing to do with bank angle. g forces are caused by pulling on the stick.
Yes, it so happens that under one nearly impossible to achieve in real life scenario, the actual g force is equal to the inverse of the cosine of the bank angle - but how is this helpful?

The reason for being a dick about this, is that we are taught that if steep banks increase g which increases stall speed, then it stands to reason that shallow angles wouldn't increase the stall speed and shallow angles keep us safe. Result? Stall / spin on the base to final turn because someone is focused on bank angles and not how hard they are pulling.
https://en.wikipedia.org/wiki/Misdirection_(magic)
 
Hank S said:
I took my Private and several years later, Instrument written tests, both using my left-over-from-college HP41CV scientific calculator with only about 50 buttons but several hundred builtin functions. I was nice and pulled the battery out, waved it around and made sure the proctor saw it. Then put it back in, turned it on and showed them the "0.0000" display.

It was far easier to use this calculator than struggle to relearn how to use parentheses and equals signs. Don't remember if I ever used a trig function, but it was nice to multiply how I'm used to (9<enter>4×) instead of the old way (9×4=).

Yes, I still use it at home and at work, and have emulators on my phone and tablet. But it's better with real buttons that I can feel when pushing, I make fewer mistakes that way.
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Postfix notation - welcome to the world of HP Calculators!
 
flyingron said:
Which is word for word what I posted earlier.
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Was I being redundant? I included a link to the FAA Order (good thing for the OP to know about), and and I highlighted additional words in the Order that empower the proctor with the power to make "the final determination."
 
I have an HP28s and a HP32s. The 28s is non-functional due to a broken battery retainer, and the 32s is just... well if I actually do a hand calc, i'm using Excalibur on the PC, otherwise it's getting done on a spreadsheet. I don't think I've touched a hand calculator in years.
 
murphey said:
But how many people remember the sqrt of 2?
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But all you need to remember is that at 30 degrees off the nose, the crosswind is half the wind. At 45 degrees it's 70 percent, and at 60 degrees it's almost all. Either that or use the E6B or the crosswind component chart. Remember that, in real life, you'll never know the exact angle or speed of the wind at the moment you are approaching to land. I realize that these calculations use trig, but I'll bet there are many people who have been pilots for years who don't.
 
Capt. Geoffrey Thorpe said:
Not really.
Yes, it so happens that under one nearly impossible to achieve in real life scenario, the actual g force is equal to the inverse of the cosine of the bank angle - but how is this helpful?

]
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Ummm, we’re discussing the FAA written test and the use of calculators and the type of calculator used on that test. Right? That is the thread topic doncha know. My point, and I believe the OP’s point, is that it’s a lot simpler to use a calculator with trug functions (and a square root function) to get the silly multiple precision answers that the FAA is looking for on those tests than to read the blurred, wide plot lined old plots the FAA provides in the supplements.

I would , however, disagree with your assertion that a coordinated level turn is a rarity in real world conditions. In a coordinated level turn (don’t know about you, but I perform that maneuver frequently), guess what, the g loading is 1/cos(bank angle). That’s basic physics and can be easily shown with some simple trig calculations. You can prove it in a plane with a g-meter.

As far as the usefulness of this knowledge, I agree that it’s not much beyond getting the multiple decimal point precision answer on the written.

I’m not saying one needs an engineering, math, or physics degree in order to be a successful pilot. All I’m doing is agreeing with the OP that it seems silly for the FAA (or to be more correct, some testing centers) to disallow more capable calculators while at the same time (and this is the important bit) asking questions which require a level of precision to the answer that we _never_ need in the real world of flying. I mean really, why calculate an ETA to the nth decimal place when we’ll never know the weather to that level of accuracy.



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Everskyward said:
But all you need to remember is that at 30 degrees off the nose, the crosswind is half the wind. At 45 degrees it's 70 percent, and at 60 degrees it's almost all. Either that or use the E6B or the crosswind component chart. Remember that, in real life, you'll never know the exact angle or speed of the wind at the moment you are approaching to land. I realize that these calculations use trig, but I'll bet there are many people who have been pilots for years who don't.
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Yeah, in real life I just take the Nike approach to crosswinds. Just do it.
 
jimhorner said:
In a coordinated level turn (don’t know about you, but I perform that maneuver frequently), guess what, the g loading is 1/cos(bank angle).
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To how many decimal places? And, to specifically get back to the test, studying what you need to know for the the test and learning what you should know to fly are not the same thing. 1/cos(bank) is an excellent example of that as you suggest.
 
An EFB may not be as precise, but in many situations it is much faster than an electronic equivalent. Set it once and everthing is “lined up”.

If a trigometric calculator is something more than sine, cosine, and tangent, than I have no clue why you would need that for the written?
You’re not launching the Space Shuttle here.
 
Ryanb said:
What in tarnation do you need a trig calculator for? The e6b is about as simple as it gets, most of which are basic mental calculations.
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I'm guessing to calculate cross wind components.
 
murphey said:
However....the testing site has the option to allow or disallow any electronic calculator, even if the FAA says it's ok to use. Details in the tiny small print somewhere in the FAR or AIM, I don't remember which.

As for an E6B - PITA. I still have my K&R slide rule Dad bought me when I started engineering school. Never learned to use it. The manual E6B is just another version of a slide rule. There are too many other resources to be limited to the slide rule. Fortunately, most E6B have the instructions for wind calculations printed on them, which is legal for all exams. That's right - if your E6B has the details, they can't disallow it.

On the other hand, the trig/wind problems can be fairly well managed by remembering this:
45 deg is 0.707 (sin or cos)
30 deg sin = 60 deg cos = 0.5
30 deg cos = 60 deg sin = 0.87

Don't remember the triangle picture for sin & cos? NASA has great examples.
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When I started college in 70, the only calculators available were three Wang consoles in a small lab. TI was out but cost a semesters tuition. The came HP 35 with RPN and a stack. Wow, dam near a computer. Well, were were still punching cards. I had a Picket metal and a Post bamboo. Probably could still multiply/divide and sqrt.
 
Gosh. It's scary to see all you engineer/science freaks geek out over your reverse Polish notation machines. (Yes, I know what you mean by RPN!) Brings back bad memories from my childhood. (My older brother was a physics major.)
 
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