Mass&Balance Question

[bsal]

I've come across a question in the Oxford ATPL book on mass and balance which I just cannot get.

Q. An aeroplane with a two wheel nose gear and four main wheels rests on the ground with a single nose wheel load of 725kg and a single main wheel load of 6000kg. The distance between nose wheels and the main wheels is 10 metres. How far is the CG in front of the main wheels?

A.The CG is 57cm in front of the main wheels.

How do you work this out?

[CJ Driver]

Most of the question is pointless mathematics to confuse you, and has very little to do with how you would calculate mass and balance. Nevertheless, the answer is as follows...

If they told you the mass of the aircraft it would be far too easy, so instead they tell you that it has 6 wheels, four big ones and two little ones. The big ones each carry 6000 kg and the little ones each carry 725kg, and they would like you to add them up.

Using your trusty calculator you will find that the four big ones therefore carry 24000 kg between them, whilst the two little ones carry 1450 kg, for a total mass of 25450 kg between all six wheels.

At which point it is fairly simple to observe that the little wheels are carrying 5.7% of the total mass, so the C of G must be 5.7% of the distance between the big and little wheels. You're told that the total distance is 10 metres, so we'll accept 57cm as the answer, and move on to the next one :)

[bsal]

Thanks for that, I got as far as 25450kg :hmm: after that the question totally confused me! :ok:

[bishop99]

Only did those dreadful questions about a year and half ago, and that confused me!

Enjoy the rest of them.........

[bsal]

Haha I will...can't wait to be finished ATPL's

[Sudan19]

that was in my exam i remember. its a :mad: .

can't remember the answer though it was time ago.

[BOAC]

"A picture is worth a thousand words"

This is very basic maths! If you get stumped by a question like this, ALWAYS sketch it out!

Mark the c of g as 'X' cm from the nose, or in front of the main wheels if you prefer.

Note down the relevant loads on front and main bogies ie 1450/24000.

Work out the moments around your 'notional' c of g, 'X'.

Since the a/c does not tip on its tail, they must be equal

With X marked from nose:-
1450 x X=(10-X) x 24000 (10 is distance between legs)

Solve for X (metres)

[james ozzie]

Lets all stay with SI units! (no more hectalitres please)

[john_tullamarine]

Some thoughts ..

(a) Most of the question is pointless mathematics to confuse you, and has very little to do with how you would calculate mass and balance.

The arithmetic is simple and precisely how you do calculate mass and balance sums (although you appear to know that from the remainder of your commentary) ... the question simply tries to make a fairly boring moment sum a little bit more interesting .. even instructors and examiners get a tad tired of the same old same old all the time ...

(b) presuming that the isolated wheel loads are uniform, the nose and main loads can be assumed to act through the respective centroids (as has been observed in several posts)

The solution is very simple if some of the very basics are kept in mind ... BOAC's exhortation to draw a piccy, invariably, is good advice ... if I may be so bold as to simplify his comments/solution a tad further ...

(a) note that the position of the calculation datum has no effect on the significance of the answer (although the numbers will relate to whatever datum is chosen)

(b) we are interested in finding out the distance of the CG ahead of the mains ... so, would it not make sense to put the datum at the main centroid load ? This also has the advantage of making the moment sum only involve the nose assembly moment (as the main is at the datum .. ie zero moment regardless of load).

Hence ..

CG = total moment/total mass

= (1450*10) / 25450

= 0.57 m

= 57 cm in front of the mains.

either you keep in mind that the CG is in front of the mains, or you can be very clever and use a minus arm for the nose assembly load .. or however you like to keep track of the sense of the moments ...

[no more hectalitres please .. bring back the slug and poundal, I say !!]

[Old Smokey]

Oh dammit! The given correct answer is wrong!:ugh:

The correct answer is .5697446 M, or 56.97446 CM if you think smaller:ok:

Pedantic hat off now.

I seem to recall see-saw examples in Primary 6 mathematics, you know the type, one heavy kid, one lighter one, how far from the see-saw pivot point did the heavier kid have to move to maintain balance. Hardly ATPL stuff, or maybe the Queensland Primary School system in the 50's was ahead of it's time.:D

I'd have used more complex words such as fulcrum, equilibrium, etc., but I feared Kevin 07 Rudd (aka John_Tullamarine) reaching for his newly discovered thesaurus.:}

You just can't please some people, I remember (from an earler life) a discussion with the venerable J_T wherein I argued that the ISA Sea Level atmospheric density WAS .002031769 Slugs per Cubic foot, against some similar, but slightly different value proferred by his good self. I guess that he didn't go to school in Queensland (land of the pedantics).:ok:

Was it you J_T, who suggested that I removed the word "concatenated" from a Performance Manual where I'd "stringed" several single digit V1 corrections together? The grounds were that "the troops would never understand it". Actually, I still do it, and the "troops" do SEEM to understand it (after being issued with the Queensland Thesaurus, as approved by Johannes Bjelke Petersen).:ok:

Best Regards (and bored fartless in sand land),

Old Smokey

[john_tullamarine]

.5697446 M

..actually, I was going to round it off to "about half a yard" but I realised that there would be those about of the pedant persuasion who might take exception to such Southerner excesses .... I am still quite certain in my conviction that metrication is but a passing fad and we shall, again, return to the glories of multiple unit systems which take 7.5 years to comprehend ..

.002031769 Slugs per Cubic foot

a dreadfully sad, but nonetheless statistically predictable, consequence of all Queenslanders' having been being weaned onto that dreadful XXXX stuff .... rather than Put-Hair-On-Your-Chest Hunter Black (or the equally beneficial and efficacious Guinness for those who hail from Mutt-land) ..... the lighter XXXX fraction, quite indubitably, led to an understated density value in the then locally extant engineering textbooks ....

but I feared Kevin 07 Rudd

I shall have to schedule a coffee with my good colleague Centaurus and remonstrate with him most severely .... I have an ominous fear that this association with the present political savant might just stick ... don't blame me .. I didn't vote for him.

removed the word "concatenated" from a Performance Manual

due to advancing senility I don't recall the specific events .. but the story has the ring of truth to it .... or, perhaps, PET ?

Trusting that life is treating your goodself well and that we shall see you in due course for an ale or ten ... I am determined to get the lovely Sally and myself to the Brekky Creek do this year ..... it is an historical fact that, after several libations ... I have the ability to slip into flawlessly idiomatic Gibberish ... whereupon I can dispense with the aforementioned Thesaurus.

.... or, as the highly esteemed JBP would have it ... "now don't you worry about that .. "


.. now that we've totally confused everyone ... are there any more questions about the original question ?

[galaxy flyer]

Just a comment from the Land of The Septics:

Eons ago, the FAA kept the written exams most secret and people struggled through the tests, sometimes learning the questions by taking them several times.

Lo, the mean spirited President Nixon shadowed the land and the Congress was unhappy with his secretive ways. They responded willfully with a law duly titled Freedom of Information Act, hereinafter referred to as FOIA. Citizens and exalted miscreants (aka lawyers) used to the new law to pry information from the government. Some government officials redacted the documents on grounds of "national security"-many requests were returned with articles "a", "an" and "the" the only readable words between strings of heavy black ink.

But, upon the sky, tests remained close held FAA material. Students of those skies studied, paid money to tutors and passed the tests. Until one day, a bright light used the FOIA to wrest the questions, thru a FOIA request,in the "public domain". Now students purchase books from the Goverment Printing Office with something like a thousand questions AND THE answers to the written exams required to fly. The minions at the FAA now merely have you answer questions 1,3,6, 10....798...999 and it is a test complete. It is mere rote memory now.

I dare say if that question were asked on an ATPL here, the answer would be either, "I can't program my PDA", "Call Dispatch", "how many can I miss" or "its level, so it's OK".

Land of Septics is now Land of the Anti-Pedantic.

J_T And I thought Queensland was the Land of Sunburned.

Bored in Beijing, but looking over my shoulder.

GF

[411A]

Well, when I did my ATPL written test (FAA), there were no especially easy answers, however, the practical side of the FAA was quite evident (using a DC-6 as the reference airplane), a quite handy loading chart was provided (copied directly from the Douglas DC-6 Load and Balance manual) which under all normal circumstances, would always be available to the respective crew member.

In every case thereafter, where the crew had to produce a load and trim sheet, this is the way it was done, in my particular case....
B377
DC6B
DC7
FH227
B707
L1011

All of 'em.
All you had to do was read and understand the manual, and fill out the trim sheet correctly.

Next question?:rolleyes:

[john_tullamarine]

It is mere rote memory now.

For many items, such is fine ... however

(a) some things, in general, require a deeper level of understanding to cover the oddball situation

(b) in respect of weight control ... the "specialists" ought to have a moderately deep understanding of the basics ..

All you had to do was read and understand the manual, and fill out the trim sheet correctly.

I concur with this sentiment in respect of routine pilot applications .. but see (b) above. In my experience, due to the variety of trimsheet design .. I have seen some very innovatively incorrect ways to complete trimsheets .... and the less that pilots get routine practice in doing the things .. the more will their basic skills atrophy.

Much the same as stick and rudder skills amongst the button pushing brigade ...

Not too sure what the answer to this problem is in an increasingly regimented world of aviation ...

[frontlefthamster]

All: Please forgive the thread drift in the following, but I wanted to put down some thoughts in response to John's general point about changing skills...

No answer is necessary, John, as the accident rate is acceptably low and the cost savings satisfactorily high.

Where we shall be in ten or twenty years' time, I cannot predict, but I am certain that by then the mean level of intelligence in the flight deck will be far below its current level (which in turn is far below where it was twenty years ago), and the consequences of that cannot be anticipated. Having intelligent people in the flight deck enables airlines to push their agendas effectively, even if those at the front are driving and supporting change unwillingly.

The industry is in a quandry, in a big way. The world of the professional pilot is some way downstream of where the real problems are ...

(I fear you and I are one step from being 'dinosaurs'; we must learn to adapt and survive, with our intellects and goals intact, despite the fact that our qualifications are perceived worthless outside our professional field).

[boofhead]

Ah, Old Smokey; I think you mean "land of the pedants".
Good try though...