Algorythm for determining average wind direction

[solarengineer]

Hey List, I'm building a windspeed and direction datalogger and hit a snag on determining the average wind direction.

I'm sampling once per second and averaging every minute to get average wind direction every minute.

wind direction is with 0, 90, 180 and 270 degrees denoting N,W,S,E respectivly.

The standard add the 60 samples and devide by 60 is fine up until winds come from north east and north west during the 60 second sample time.

example.

Seconds        direction degrees

1.               10
   
2.               15
   
3.               12
   
4.               355
   
5.               5
   
6.               358
   
7.               9
   
8.               5
   
9.               352
   
10.              6
    
    

average direction (10+15+12+355+5+358+9+5+352+6) = 1127/10 = 112.7 degrees!

This is in the wrong direction. the winds were coming from 352 to 15 degrees and around 8 or 9 degrees would be the proper ballpark.

My question is, how can you average the wind direction when it crosses back and fourth the zero(360) degree mark?

every other circumstance will average properly except that one.

Thanks for any ideas.

Jamie

[rossw]

For an "engineer" you're none too smart.

I faced this problem when I built my first substantial AWIS back in 1985, only then I was sampling wind to 1 degree, and doing so every 300 milliseconds (3 times/second)

I'm not an "engineer" so I am therefore rather dumb, so won't inflict my solution upon you, save to suggest two key words. "Sine" and "Cosine". Averaging the two provides a unique average vector.

R.

[Tio]

"wind direction is with 0, 90, 180 and 270 degrees denoting N,W,S,E respectivly."

Where I come from 90 equals E, and 270 equals W.

[solarengineer]

Oh what a relief, all i have to do is move.

[Tio]

LOL - yep.

Or just turn around.

[Tio]

Seriously though, I am not too smart on what you are doing - but you seem to be equating 360 to 0.

Zero to 359 might help you out some.

[WindJuggler]

There is a good explanation on this site: http://windmolensite.be/

Then click on Windrichting (wind direction) on the left-hand side of the page

It is in dutch but the math should remain the same.

Good luck

[frackers]

I'd make that 0, 90, 180, -90 for N, E, S, W. That get round the 'each side of North' problem... (the equivalent of two complement but in degrees!!)

[dpshort218]

You must use vector math as mentioned above. Simply using 0, 90, 180, and -90 moves the location of the error to around +- 180. Example: -179 and +179 averages to 0. Wrong direction! Stick with 0 to 359 degrees. You pick the N,S,E,& W directions the values represent.

Example:

Assume we have 3 readings of 359, 0, and 1 degrees. Simple reasoning tells us this should average to 0 degrees, not (0+1+359)/3 = 120 by simply averaging the values.

Let v be the wind velocity. If all you want is direction, assume a constant speed(v) of 1 and the v's go away. If you want to know the average direction where most of your speed comes from (the magnitude), you need to also measure the speed(v) for each direction recorded. This example sets v to a constant of 1 for simplicity. From trigonometry we get:

    Vector = (X,Y) where X = v * cos(Angle) and Y = v * sin(Angle)

    Vector 1(V1) = (v cos(359), v sin(359))   = (0.99985v, -0.01745v)

    Vector 2(V2) = (v cos(0),   v sin(0))     = (1v, 0v)

    Vector 3(V3) = (v cos(1),   v sin(1))     = (0.99985v, 0.01745v)

Add the 3 vectors by adding their X components together and their Y components together and divide by the number of readings(3) to get the resulting "average" vector:

(V1+V2+V3)/3 = ((0.99985+1+.99985)/3, (-0.01745+0+0.01745)/3) = (0.99990, 0)

So our average Vector(X,Y)  is (0.99990, 0)

The angle here is obvious since Y is 0 and X is positive(0.99990), the vector is along the positive X axis which is defined as 0 degrees.

But to make sure the math works for all average vectors you use this:

tan(Angle) = Y/X  which gives: Angle = inverse tan(Y/X) or

Our average angle = inverse tan(0.99990) = 0 degrees as expected

It is important to point out that the angles calculated using tan will always be from -90 to +90 degrees. You must keep up with which quadrant this vector is in to make sense of the angle.  Quadrant 1: 0 - 90 degrees, Quadrant 2 90 - 180, Quadrant 3: 180 - 270, Quadrant 4 270 - 360(0)    

 Q2    90  Q1

180    +     0

 Q3   270  Q4

If we used 179, 180, 181 degrees we would have ended up with (-0.99990,0)  Our angle would still be 0. This is why you must keep up with the quadrant of the resulting "average" vector. This  vector(-0.99990,0) is along the X axis in the negative direction, so the angle is 180. For numbers where X or Y are 0, the angle is 0, 90, 180, or 270. For all other answers, simply plot the point in the proper quadrant 1, 2, 3, or 4 as shown above. Here is the corrected Average Angles for each of the 4 possible sign values of the resulting Average Vector( X,Y) in each quadrant:

Quadrant 1:  (+X, +Y)   Angle is always positive. Average Angle =   0 + Angle.

Quadrant 2:  (-X, +Y)   Angle is always negative. Average Angle = 180 - |Angle|

Quadrant 3:  (-X, -Y)   Angle is always positive. Average Angle = 180 + Angle

Quadrant 4:  (+X, -Y)   Angle is always negative. Average Angle = 360 - |Angle|

Final Example: You calculate your "Average" vector and end up with (4, -3). This is in quadrant 4. Your angle using inverse tan(-3/4) is -36.8699 degrees. Your "Average" angle would be 360 - |-36.8699| = 360 - 36.8699 = 323.1301 degrees.

[SparWeb]

I would approach the problem from "a different direction", but I'm also surprised that you call yourself an "engineer" without being able to think of this:

Create a statistical histrogram with 36 "bins", each 10 degrees wide.  Bin "1" is from 0-9 deg, Bin "2" is from 10 to 19 degrees, etc.

Count data in each bin, plot on histogram, or make one of those cute "flower" shaped graphs.

Preserve the raw direction information in your data file, (at each reading interval) with the wind speed, and you can now bias the direction stats with the ENERGY available in that direction.

In other words, don't forget that it's possible for strong wind to come from one direction occasionally, and light wind from a different direction all the rest of the time.  The difference, in terms of energy, could be the equal, or go either way.

[rossw]

Here's something not entirely dis-similar to your "buckets" concept, except I'm using 17,280 of them

This is built from 5-second wind-vectors over a 24-hour period. (I also do it for other timeframes and windspeeds depending on application) but it provides a very good "at a glance" view of the recent wind, trend and character. Once you get used to what its telling you, it's a great tool.

[Stonebrain]

Hey,this is really tough stuff.

Still I don't get it.

If half of the time the wind is from the south and half of the time from the north,

is the mean direction frome the east or from the west? LOL!

Reallity is that 'mean direction' just doesn't mean anything.

Rossw.shows the way to go.

cheers,

stonebrain

[TomW]

Stone;

Its a trick question, I know.

I say "there is no wind".

If thats wrong I invoke the other dimension. Its a wind from above.

Or none.

T

[solarengineer]

regarding the engineer slams, I don't have the codespace for the vector math, and the 14bit micro takes forever to do vector math. The obvious I already know. a different approach is what I was after.  

So I'm off to go change my name to dumbass and wipe my butt with my degrees.

Thank you to those that posted helpfull Ideas.

Thanks Ross for helping me realize i'm stupid. now I can save so much time by not designing anything else otherwise it's sure not to work.

What a relief!

[TomW]

solar;

Maybe you should have been up front with the limitations rather than use them as a defense after the fact for failing in your ill defined question or mentioning at that time what you now claim "you knew"?

I can change your userid in about 5 seconds. I don't suggest it in this case as the name violates some convention, I am sure.

Remember, you are the one that flaunted "engineer" then for some unknown reason neglected to provide a proper set of project guidelines and limitations that could reasonably be expected from a real engineer.

At this point I think you may be justified in seeking a refund for those sheepskins?

All we know of you is what we read from you.

I am no engineer, I worked for years fixing up circuits after engineers screwed the pooch on designing them. High end Electrical Engineers with yards of degrees, in fact. So I earned my right to scoff at those that wave the title around to cover their butts.

Just to put it into perspective. Much text trimmed to keep it civil. This time.

You spelled "algorithm" wrong, by the way.

TomW

[solarengineer]

Tom. we've never spoken before so it's unfortunate you chose a fight with yet another of a countless number of users instead of being descent. People leave this board constantly because of being bullied or whatever. It used to be a good board, 80% of the time all you do is whine.

I didn't need to be upfront with my limitations because i didn't want to seed the conversation in any specific direction. WHAT I DIDN'T NEED IS TO BE CALLED STUPID!

It's easy to that on a board. In person good luck.

I asked a simple question, was at work and typed it fast like people do here all the time. Your right all you know of me is the questions I ask, so don't go attacking people based on assumptions. Thats all you do. you didn't need to chime in on this either but you smell a fight and it brings meaning to your life and your BRING IT ON kicks into play and here we are.

"you are the one that flaunted "engineer" then for some unknown reason neglected to provide a proper set of project guidelines"

 I never flaunted anything mouth, there again you generalize. I have 15 people that work for my company and every one of them has their own way of doing things, some better some worse and YES INCLUDING ME 2 ARE ENGINEERS. We don't build turbines and meterological equipment so again by asking my straight forward question there could have been 50 ways to do the same thing some better some worse without re inventing the wheel.

On the refund for my sheepskins, where the hell do you get off coming up with so much bull$#|+ to say? you wanna attack me do it in person or shut up! stop trying to be the cool moderator looking after everyones interests, what about mine?

you have a grudge against engineers, no doubt because you couldn't cut the mustard. You earned no right to attack anyone Tom only from a keyboard. My post wasn't meant to cover my butt for asking a simple question and being called stupid, it was to say f-off for the ignorant comment nothing more. I don't give two $#|+s about showing you or justifying my credentials.

You go ahead and keep feeling important and bullying everyone on the board until you do it to someone who lives around the block. You make the Dans look like crap by being such an bigmouth to everyone on this board.

Regardless tom I dont care, and don't threaten me with changing my user id. you can shove it for all I care and feel important again by removing another problem.

Every post I ever made here has been kind and courtious until this one. So I'll also make it my last.

They need to get rid of you!, too bad you came back after your whining a year or so ago about how the digital world is so unjust against tom. Lots of new people are looking for a place to learn and here they get bullied, not me man. try all you like!

"Just to put it into perspective. Much text trimmed to keep it civil. This time."

Ya thats funny tom. your the man! lucky me

I'm sure you'll just kill this post but no matter. You can go ahead and delete my account too if you like and get another tin star.

Now after all that you still don't know $#|+ about me and that really is to bad for you. you will naturally find all kinds of bad stuff about me now tho from my post and of course know the real me.

A simple question, polite responses or no responses would have avoided this whole matter. That and you minding your own business. All Rossw did was piss me off not much of a problem there but Tom...LMAO your just a bitter dope that loves attacking people on a regular basis the history of the board shows this. you have no business being a public figure. keep locking and discouraging everyone!!! and don't forget to crush and belittle newbies. you don't need them anyhow right!  

DanB, how far are you willing to let what you've accomplished here slide because of this guy? you really have a great site and I thank you for the time I've spent here and all your helpful comments. No-one likes to be called stupid and then have some fool tell you all the reasons why it's justified and pad it with crap. There is much to be proud of here! too bad the cancer is spreading. People want to have fun and learn.

To the rest of the list, Thanks everyone for all your help especially you Flux!

Tom, don't bother adding more to this if you want I'll give you a call.

It's too bad you felt the need.

[dpshort218]

solarengineer,

I wasn't trying to dumb down my answer with the long trig explanation. If you want very specific help though, you need to be a bit more specific with your question. You said you were designing a datalogger, but have not stated any limitations of your hardware. What micro are you using? Could you upgrade to one with more memory or power? I've used a 32 bit one from Coridium that is real easy to use. (http://www.coridiumcorp.com/) They have one with same pinouts as a Basic Stamp that can be programmed with their included Basic or C. Could a pc version written in VB or C be possible to use? Plenty of codespace. You say you don't have the codespace for vector math. How much accuracy do you need? For example, if every 5 degrees is enough, you might use a lookup table for the sines and cosines, add them together and divide by the number of readings. That would only require 142 numbers stored. Not too heavy on the code. I make no claim to be any sort of wind expert, but I would think the wind velocity would be of real interest as shown in the splatter graph displayed by someone else here. As an EE myself, don't feel too bad. I have wiped my own butt with my diploma on occasion! Had a few offers to place it where the sun don't shine too! Give me some specifics of your hardware and i'll offer some help. I did thermocouple readings in a 68HC11 once and avoided the polynomial math of the nonlinear thermocouples by using a lookup table.

[TomW]

Thats a fine fantasy you have there, really.

This post stays, no question.

As will all of your 160 others.

Did you actually read my comment?

I didn't think so.

I never called anyone stupid. You just called me a dope how nice of you!

Been great having you.

Good luck in your engineering career.

I hope Dan fires me, too.

TomW

[MattM]

Just trying to understand what you said, don't take anything I say as an insult.  When you said 5 degree accuracy wouldn't that only need be 72 positions stored?  I figure 10 degree accuracy at 36 positions.  I'd think 5 degree accuracy at twice that.

Now to go off topic, I'm pretty sure to do this sort of math on a chip you'd use the integer bits as your range, translating the maximum number available in the integer as the 0/360 point.  This is how they do it in 3D modeling to keep the math simplified.

[finnsawyer]

Oh, lighten up.  Take your lumps like the rest of us.  I don't know how much programming space you have, but you have four unique quadrants to consider.  The signs of the sine and cosine tell you which quadrant you are in.  In quadrant one and three the product of the signs will be positive, in the other two negative.  Which of the actual functions is negative or positive then is the key to how to handle the 180 switch.  In your case you would impose the signs from the direction (quadrant) in which the vane is pointing for each data point.  That is, ++, +-,--,-+.  Then proceed accordingly.  All high level programming languages can get you the sign.

Some years ago I became interested in writing a 3-D rendering program (basically a walk around in a labyrinth).  It necessitated keeping track of just the type of information you are dealing with to render the views.  Gets rather complicated.

[PHinker]

   This is a nice way to display windspeed direction and magnitude in a single picture.  The color coding for the timestamp is clever as well!  What does the plot in the lower left corner represent?  Some sort of energy in the wind or produced or ??

I'm going to steal this representation for a data logger I'm writing for my own use.  Did this come from a package or is it something you developed, Rossw?

[rossw]

Yes, I can claim this as 100% original work. To the best of my knowledge, nobody anywhere else in the world was using a similar time+vector display of this kind.

I came up with it in response to wanting to "get a handle on" the wind conditions at a location I was entirely unfamiliar with. I've since had a (now retired) meterologist of many years experience look at it. His initial take was that he didn't like it. However, he called me back a day later, the more he thought about it, and looked at it, the more he liked it. He'd spent so many years reading the two strip graphs "two-in-hand" - one for direction and one for speed - that he didn't see need for yet another form, however he realised that this presentation actually gives him MUCH more information, more quickly.

The little graph at the bottom is simply a standardised (scaled) wind run gauge against time. It lets me see at a glance if the wind is trending up, down or much the same.

RossW

[Bruce S]

Folks;

   I just read this entire post and I am sure someone is going to fire back at me for this but here goes anyway.

I read the post from solarengineer and pretty sure he's not going to bother chimming in but ANYWAY.

I very sure in one respect, rossw started this by calling him "none too smart" then sparweb chimmed in with being surprised . UHhh people why ?

He did ask a quick question , maybe not a complete as some needed but the name calling was not even warrented, much less needed. He asked a question.

BTW: I have two engineering degrees Medical elec, and Mech ( the second one took me 20 years to complete), and I have to ask for help too, we can't be held to remember everything we've been taught.

Am I taking up for him? possibly , but probably don't need to other than others here saw what he was asking and helped, without the name calling...

Rossw since you started this put down arena, and touted your program for being so good, is it up for review? or a closed will cost money venture?

Attack me if you like, I can take it and will be here until asked to leave.

Bruce S

 

[rossw]

Didn't (don't) want this to degenerate into an all-in brawl, but we're sure heading this way.

Background: My parents both have more degrees than I care to count. So does my brother. So does my wife.

I, somewhat like TomW I guess, worked in some very technical fields working intimately with some very well paid and highly qualified people who loved to rub everyones nose in the icky brown stuff if they didn't have at least the same paper qualifications they did.

That kinda got me really pissed at people who flaunted their "engineer" status.

Over the next 30 years I encountered more and more of these types in industry as I went around doing my job, and being increasingly surprised at how often these people were just plain WRONG. Often times, their mistakes cost hundreds of thousands of dollars (millions in some cases). In some cases, their mistakes cost lives... but invariably, they played the "blame game" well and always avoided any responsibility.

The initial question being asked was oh-so-typical of a very recent issue (the day before) from another so-called expert I had to deal with. The person I had to deal with then asked a question and presented a small (but insufficient) sample of data which they should have been able to see for themselves in little more than a heartbeat WHY it wasn't going to work... yet still had to waste a couple of hours of my time to teach him from first principles why it wouldn't work and how to fix his stuffup (different field to here). It also annoys me that the company this guy works for pays me a pittance, and makes me justify my bill to them for this consulting work, yet happily pay this "expert" $250K/year for stuff I'd consider anyone with a very basic understanding of netmasks and routing would do easily.

In the issue here, an "engineer" should be (I'd have thought) quite clued up in math and trig, and that with only a small amount of thought, would have not only seen the problem, but the answer. Having worked this out for myself many years before - and without the benefit of such high-level education, I guess it was just a whole lot more of the "I'm an engineer but I'm too lazy to look for the answer, I'll just tell someone to give me the answer so I can do my job and look good" attitude I've come to loath and detest.

Respect is something you earn. A degree does not bestow respect, and indeed it has been my experience that the more qualified, the more arrogant and DISrespectful the individual becomes.

Its my experience that a degree means "I have been brainwashed. I have learned how not to THINK and REASON. I have passed the test that says 'if the answer is not in the book, then it cannot be done'"

Yes, there are exceptions, but you sure have to look hard for them.

If there had been "full and complete" detail in the original posting, and some indication of what had been done/tried and why it wasn't adequate, perhaps responses would have been different.

As to:  "Rossw since you started this put down arena, and touted your program for being so good, is it up for review? or a closed will cost money venture?" - which part did I claim as being so good?

Certainly, the time+vector display (which was in response to another posters comment anyway) demonstrates that (the link here is a real-time display, not a photoshopped fake of what someone might have done). I don't offer the code "for sale", it's not a money-making venture. I've never asked anyone for a cent for it, advertised it or touted for business. It has been reviewed by people within the Australian Bureau of Metorology, but if you feel the need to review it yourself, contact me directly.

[Volvo farmer]

OMG, This is beautiful!

Its my experience that a degree means "I have been brainwashed. I have learned how not to THINK and REASON. I have passed the test that says 'if the answer is not in the book, then it cannot be done'"

/guilty.

[dpshort218]

The 144 numbers is for storing both X and Y components of the vector points from a table based on X = cos(Angle) and Y =sin(Angle).  Each would be multiplied by the velocity recorded for the final vector(X,Y) points.  Then all you do is add up the Calculated X values and calculated Y values and divide by the count(60, I believe) And yes, it would be easier to deal with integer math so you might simply multiply the sin and cos numbers by 1000 for the table. (Realizing of course that the resulting X and Y values are units of 1000.) You can do the arctan from lookup tables also at the end to get back the angle. I'm not exactly sure what the datalogger is used for. I would tend to want to simply record a bunch of angles and windspeeds and then dump them into a pc and get a scattergraph like shown here by somebody else. I can see how one average angle could be very misleading. Of course if you are controlling something with the data in real time, that's a different story.

[finnsawyer]

A lot of this "non thinking" attitude may have resulted (here in the U. S.) from the dumbing down of the requirements for a B.S. degree.  That is, everyone is entitled to one, so let's make it easy enough.  By the time one reaches the Ph.D. level the requirement is for independent thinking or "thinking outside of the box".  This is necessary or the field can't advance.  It also leads to disappointment on the part of some of those minority individuals that have been pushed through to get the first degree, but then find they are not allowed to advance further because they just don't have a good grasp of the material.

None of this justifies RossW's put down of SolarEngineer.  No one can know everything or even keep track of everything they may have learned.  That's why we have reference books and maybe why we have this site.  Computer programming imposes it's own peculiar constraints and one has to learn them.  While RossW apparently has self worth issues he should leave them at Log-in.

[Bruce S]

Rossw;

Couple items: 1.) glad that you too are not wanting this to turn into an all-out brawl. Usually it turns up waisting everyones time.

My reason for saying what I said was for two parts, 1.) the first item you put up was a put down. 2.)The graph that you put showing off your program. As I looked at it I was very impressed with the detail and the time point coloring in the lower left.

Engineers: Try not to be too hard on us, some of us worked just as hard doing the very same grunt work, except in the field in which I work in (Medical) , if you don't have a degree you don't get listen to. I have enough credentials, letters of appreciatation enough to paper a wall 8x10x12, heck I can even put the A+ beside my name on my biz cards if I want to, but ALL that and $4.00 will only get me a good Cafe-moca at Starbucks. I don't like showing these unless trying to make a point.

I use the very same type of math day-in day-out for plotting R-R points on a EKG.

There are also other types of engineering degrees that once you're finished getting the paper, you almost never use the math again. Datamining comes to mind.

ECG overreads are another, there are at least 15 people here with Science Engineering degrees that can't spell trig without help, but can walk all over me when it capturing 3 and 4 models of a persons heart or brain.

MY main reason for jumping in on this was simply sometimes even the best, can't see the forest for the trees and like to hear from others points of view.

And the first thing that gets put up is a slam for being an engineer.

Time to go back to work now. Chile is calling

Cheers

Bruce S

[rossw]

Oh, FFS. Fine. I'll STFU.

If the original poster had spent ANY time researching the problem instead of asking for it to be damn well spoon fed to him, it wouldn't have happened either.

Don't tell me YOU never had a bad day.

I'll make it easy for you and clear off too. No wonder the place has gone to the dogs.

Get a life, and a thicker skin.

This has certainly done nothing to improve my take on engineers either. Narrow minded, self-centred, brain-dead, arrogant, oh never mind. I have more interesting thing to do elsewhere.

[SparWeb]

Jamie,

I didn't want to insult you either.  I made a little comment because I have always found it odd, watching your projects over the past two years or so, that you are much more interested in wind than in solar.  So I always wondered about the "solar" part of your handle, then you have a math blunder, and I found it too easy to jump on the "engineer" part.

I came back to the thread a day later and find that the point of the question and the answers are swamped by the snide comments.

I for one am sorry.  I thought I was kidding.

If I were you, however, I would think carefully about what the alias says about you, and the "prejudice" it creates.  Some people use their name, some use a word or numbers, but other people choose an expression that seems to give a flavour for who they are and their point of view.

I remember giving grief to people who have posted questions, partly because the question was stupid or unsafe, but also partly because they had ridiculous handles that gave them no credibility.

For the sake of your own credibility, you should try researching your questions before posting.  A look at the national Wind Atlas data website would turn up wind rose diagrams like I described.  After finding that, would you have needed to post your question?

To me, "Engineering" is a method of solving technical problems or improving on existing solutions.  It doesn't really have anything to do with math, it just often uses math to achieve the goal.  Not all engineers absorb that philosophy.  I for one have been working on it for 10 years, and my bias still shows through.

One last comment: whenever you get TomW all riled up, think of it as joining the club.  It seems everyone else has succeeded, but I can't.  Don't know what I'm doing so wrong that I haven't yet been able to cross swords with him!

Oh stop taking this so seriously guys.  It's all just words on a computer monitor!

[Bruce S]

IF you pointed this at me then!! BYE!!. I certainly won't miss the arrogance!!

Have a bad day !! hell yes I've had bad days even acted WRONG and lashed out at someone on here better than a year ago , BUT was adult enough to apologize.

Careful with the name calling your intelligance is showing.

tata

Bruce S

 

[vawtman]

Hi Bruce

 Your reply to Ross seems a bit out of character for you.I remember when you backed me up when i was in a bit of trouble.

 You seem a great guy and willing to help anyone you can with great advice.

Mark

[dpshort218]

As a fellow degreed engineer, I detect a fair amount of ill will here. I don't know anybody here, but the only thing I saw solar do was include "engineer" in is login name. If that is taken as rubbing your nose in his degree, get a life! He could have been a lot more specific up front, but why all the hate mail? Rossw, you had a very valuable plot, but you seemed to use it to show off instead of simply being helpful.

I will say about a degree what a high school teacher once told me many years ago. The degree simply shows an employer that you are "willing to make a lifetime commitment to learning". It says little about your brainpower, only that you are willing to use it. It says absolutely nothing about a person without one. It took me 28 years, raising 2 kids and a hip replacement to finally get mine. And yes, I am damn proud to have finally earned it. Electrical Engineering is such a broad and dynamic field that you can't possibly cover all topics in any 4 year program. I have been shunned in the past from opportunities because I did not have that degree. That's life! I don't want to use everything I learned in school every day. I'd go nuts. I can now find the area of a box using a triple integral. Big whoop! I would rather simply use L x W x H. BUT, there are some engineering jobs that you simply must use this level of math for. I bet the Apollo 13 Astronauts were very thankful that they got engineer-calculated re-entry numbers instead of "try this it might work" guesses. I have seen some very arrogant engineers. It isn't because of their degree, it's because they are arrogant people. Ever seen an arrogant doctor, lawyer, baseball player, or janitor? All jobs have their share of know it alls! As Forrest Gump said, that's about all I have to say about that.