Weight and balance problem - determining the CG?

[Sac Arrow]

I'm missing something. It's probably something totally stupid and I'll kick myself after someone points it out. I'm having a brain fart and I can't figure it out. Refer to the sample W&B for a 172R.


We end up with a total weight of 2450 lbs and a moment of 106.2 Kin-lbs. Fine. We go to the moment load envelope graph:

A weight of 2450 lbs and 106.2 Kin-lbs puts us in the normal category. We're done. We're legal to fly.

But we aren't done. Look at the same graph based on CG location and not moment.

Our allowable CG range is from 35" to 47" (and change) from the datum. But where is our total CG arm? We should be able to divide the total weight by the total moment and get it, right?

Wrong. If we divide 2450 by 106.2 we get 23.1" from datum. Not even close. If we extrapolate weight and the utility category line we should be further back than 40.5 inches.

What am I doing wrong? If I take say, my Arrow's W&B calculations and divide total weight by total moment I get the correct CG location. But for whatever reason, not here.

 

[Sac Arrow]

Check your units.

Can you expand on that?

Edit.... Ohhhhhhhhhhhh so I need to divide 106.2 x 1000 / 2450. That works. All right I'm an ignorant dumb s***t,

 

[Sac Arrow]

But thank you.

 

[MauleSkinner]

Can you expand on that?

Edit.... Ohhhhhhhhhhhh so I need to divide 106.2 x 1000 / 2450. That works. All right I'm an ignorant dumb s***t,

Now you can explain common errors to your students.

I was actually reformatting my response, and accidentally put the thread on ignore…so…lots of talent to go around here.

 

[Sac Arrow]

Now you can explain common errors to your students.

I was actually reformatting my response, and accidentally put the thread on ignore…so…lots of talent to go around here.

You know, honestly a part of me wants to delete the thread on shame, but on the other hand, how can a seasoned aviator and an engineer make such a stupid mistake?

I was sucked in to big-number itis. You expect to divide a big number by a smaller number to get an even smaller number because that is how you are used to working the problem.

"Check your units" to an engineer is akin to asking a doctor "Gee doc, that looks like a heart, not a lung."

Well, I said "Divide total weight by total moment." What is moment? It is weight x lever arm. You divide moment by weight to get lever arm. It's something you have to think about, unit wise. That should have been my first clue.

So kids, if W&B perplexes you, read this thread. If it still perplexes you, ask questions and we will try to clear things up.

 

[Capt. Geoffrey Thorpe]

It helps a lot that they throw in the random 1000 in the math. A lot.
It would help more if the put more divisions on the chart so that the whole thing just turns grey.

 

[Craig]

Sac: That's why the beat the crap out of you in Experimental Methods class with unit verification.... Hoping it gets solidly engraved in your thought process.

 

[Sac Arrow]

Sac: That's why the beat the crap out of you in Experimental Methods class with unit verification.... Hoping it gets solidly engraved in your thought process.

I understand how units work, I'm an engineer for fart's sake. It's sort of like how sometimes you forget your own name. Okay maybe you don't know. Welcome to my world.

 

[bnt83]

I hate that Cessna doesn't just use the actual moment but rather moment/1000 or whatever.

Its a dumb system.

 

[Half Fast]

Don’t beat yourself up too much. The chart probably threw you off by using weight instead of mass...

 

[Capt. Geoffrey Thorpe]

It's sort of like how sometimes you forget your own name.

Or call one of your kids by her sisters name.
Talk about a ****ed off daughter...

32.2 pounds mass per pounds force feet per second squared. That I will probably never forget.

 

[Dan Thomas]

I understand how units work, I'm an engineer for fart's sake. It's sort of like how sometimes you forget your own name. Okay maybe you don't know. Welcome to my world.

I'm not a professional engineer and I never had any problems with that. But I have made other stupid mistakes, as I am not a professional mathematician either. Doing W&B revisions on aircraft, where the datum is some spot on the airframe instead of out ahead of it somewhere, one has to watch negative numbers, weights installed ahead of the datum. Removing something there will result in a positive moment, like adding something behind the datum, and installing something extra ahead of the datum will result in a negative number. Lot of mechanics have made mistakes there, including me, and when we review W&B stuff that makes no sense, we find them.

Well, not a professional engineer. I'm an Aircraft Maintenance Engineer, the Canuck version of an A&P/IA, sort of. We have to take a lot more training than the American counterpart, do a longer apprenticeship, but we're still far from a PE of any sort.

The worst part about your mistake is making it public before you found it. Embarrassing. But it reminds us all that silly stuff can happen, and we can chase our tails a long time instead of stopping, walking away for a few minutes, then coming back and doing it again and realizing what we did.

 

[Half Fast]

That's why the beat the crap out of you in Experimental Methods class with unit verification

I still recall taking the Florida EI exam 30+ years ago. On the multiple choice portion, there were a couple of problems I had no clue how to actually solve, but there was only a single way to arrange the values in the problem statement so that both the numerical result and the units agreed with an answer choice.

(Frankly, a good portion of that exam was an exercise in test-taking skill rather than engineering skill.)

 

[Jim Carpenter]

What's a couple of decimal places, anyway?

 

[Craig]

Or call one of your kids by her sisters name.
Talk about a ****ed off daughter...

32.2 pounds mass per pounds force feet per second squared. That I will probably never forget.

Avogadro's number.... 6.023 x 10^23rd power.....

Sac: Laughing with you and not at you.....People's names trip me up more than anything else. Until I meet you several times, I'm liable to either mangle your name or not be able to recall it ten minutes after you tell me. My wife pokes at me often about the esoteric crap I can remember, but have to have a 5 item grocery list texted to me so that I don't forget something....

 

[Dan Thomas]

Sac: Laughing with you and not at you.....People's names trip me up more than anything else. Until I meet you several times, I'm liable to either mangle your name or not be able to recall it ten minutes after you tell me. My wife pokes at me often about the esoteric crap I can remember, but have to have a 5 item grocery list texted to me so that I don't forget something....

I understand that. I can spout the formulae for the volumes of several common shapes, but can't remember whether it was 1% or 2% milk my wife wanted. I used to know hundreds of part numbers and phone numbers by heart, before the days of computers and quick-dial stuff. Maybe if your new acquaintances had a number instead of a name, things would be easier....

 

[Half Fast]

I can spout the formulae for the volumes of several common shapes, but can't remember whether it was 1% or 2% milk my wife wanted.

Yep.

This husband must be an engineer:

The wife says: Go get a gallon of milk, and if they have bananas, get six.​

So, the husband leaves, and when he gets back he has six gallons of milk.​

The wife yells: What the hell?! Why did you buy six gallons of milk?!​

The husband replies: They had bananas!​