Leveling 1

[Equestion]

Good day all

I am struggling to get my head around this one
The situation is as follow;

If an aircraft is being weighed with 3 scales ( one at Each main Landing gear and one at the nose Landing gear) at a given and known angle for eg 4 degrees, is it possible to predict the GC at 0 Degrees?

I would like to know is there a way of applying maths as an iterative method to solve it?

A bit of background to why the question arose, I weighed an A/C getting the following readings:
In Situation A I got 3131 KG on the Main LG and 275Kg on the Nose LG, the angle was measured at 4.8 Degrees.

In Situation B I got 3035 KG on the Main LG and 363 Kg on the Nose LG, the angle was measured at 2 Degrees. Situation B was created by deflating the Nose LG strut slightly. See pics below to illustrate situation A and B better.

 

[rb1957]

if you know the height of the CG you'd be a long way there ...

another day in paradise, or is paradise one day closer ?

 

[Equestion]

Can you please elaborate on what you mean?

I know the Height of the CG. It is about 2300mm heigh.

I don't quite understand how to mathematically predict the weight shift if the angle would be 0 Degrees?
Is it possible to "predict" how much weight will be on the nose LG at 0 Degrees?

Thanks for the interest and help.

Kind regards

E

 

[WKTaylor]

Suggest You refer to FAA handbook that includes weight and balance.

In general, the aircraft must be leveled** fore-aft and laterally for a 'by-the-maintenance-book' weight and balance [W&B] measurement. Otherwise the measurement 'is-what-it-is'... especially with acft that presume leveling and have no estimated CG height location.Leveling is unique to each aircraft type and is determined by the designer/manufacturer.

NOTES

Small acft may be weighed on wheels [struts and tires balanced/nominally extended and within by-the-book 'level limits']. Larger acft, empty, may be weighed on jacks [acft specifically leveled by the jacks] with load sensors. Very large/heavy acft may be weighed on in-ground roll-over-scales... much like heavy trucks are weighed at highway check-points... on specially leveled/calibrated hangar or apron areas.

W&B measurements can be affected by unbalanced landing gear strut extension and improper tire inflation, adjustable seat [miss]placement, unknown fuel/oil loads, 'special equipment', uneven/sloping ground**, wind, etc ... among other factors.

** CAUTION: uneven/sloped ground, wind exposure, laterally unbalanced loads, etc pose 'a safety issue/threat' when acft are jacked: possibility of 'slipping/sliding/jumping' off the jack-points, causing structural damage.

Certain acft, such as tail-wheeled aircraft... that have a significant tail-down attitude on the ground... may also have the W&B measured in that tail-down attitude for 'most severe aft CG'... but generally that is all factored-into the 'leveled-acft W&B' for operations.

FAA-A-8083-30 AMT Handbook - General, Chapter 4 Aircraft Weight and Balance.

https://www.faa.gov/regulations_policies/handbooks_manuals/aircraft/amt_handbook/

Regards, Wil Taylor

o Trust - But Verify!
o We believe to be true what we prefer to be true. [Unknown]
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation,Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", Homebuiltairplanes.com forum]

 

[rb1957]

if you know the height of the CG (hint, above the ground plane) then you should be able to account for the inclination of the ground plane. 2nd hint, weight acts vertically down but the CG height is normal to the ground.

another day in paradise, or is paradise one day closer ?

 

[berkshire]

You have something else going on with your weighment . Regardless of the angle of the aircraft the total weigh should be the same when all three scales are summed up. you have an 8 kilo difference.
B.E.

You are judged not by what you know, but by what you can do.

 

[rb1957]

except that the scales are normal to the ground plane and the weight is vertically down (I think there's a cosine term in there).

another day in paradise, or is paradise one day closer ?

 

[Compositepro]

The measurements you have done allow you to calculate x and y location on the ground, above which the center of gravity is located. If you take the same measurements at a different inclination of the plane you will get a second line that passes through the CG. Where the two lines intersect is your CG. Changing the inclination enough so that you can accurately locate the CG may be difficult.

 

[GregLocock]

That's the method we use to measure CGZ of cars. Statics 101

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[verymadmac]

In addition to the guidance for weighting,the one issue not mentioned so far is configuration control, if you don't record / define exactly what configuration is on the aircraft (cabin / galley / cockpit etc etc) when it is weighted there is not a lot of point really, same applies to documenting how the "As Prepared for Service" weight is calculated.

 

[Equestion]

Hi All

Thank you all for the insight and guidance thus far.

I take note of the above comments and appreciate it. But note the Configuration is known and controlled.

Just to recap:

This problem I'm trying to solve is only an investigation on my behalf, I'm trying to establish if it is possible to "predict " the Weight of the Nose LG and Main LG when one rotates the A/C virtually to ZERO degrees. In other words, I'm trying to solve the Nose LG weight and Main LG weight for Zero degree attitude when known values are available like when the aircraft is pulled on to scales, Weights recorded as well as the angle at which it is being weighed (Not Zero degrees).

Another fact that I would like to throw into this discussion is discussing the importance of why an Aircraft should be weighed at 0 Degrees attitude. that the whole point of this exercise isn't it?

Now taking all the advice into consideration this is what I've come up with, It feels that we are almost there, so close but yet so far.
It seems that there should be a way to use a ratio, of some sort, of the A/C in the known tilted attitude to "predict" the Zero degree attitude weight distribution of each wheel? Please advice and comment if I'm on the right track or completely missing the point.

I'm using the picture below as a guidance for illustrating the thinking process. It is Based on Situation A as illustrated in the top of this discussion.

Now

And that where I'm stuck.

Please feel free to Comment and give some further awesome guidance.

Thanks

E

 

[rb1957]

I'd draw the ground reactions normal to the ground and on the ground, and the a/c CG is the only point off the ground and the weight is vertical (ie where it intercepts the ground plane is affected by the inclination).

can I ask, is this work or school work ?

another day in paradise, or is paradise one day closer ?

 

[Equestion]

Hi rB1957 This is related to work, thanks for the advice keep it coming XD.

Regards

E

 

[rb1957]

did the rest of my comments make sense ?

I think sum(ground reactions) = Wt*cos(theta) ...

you say (original post) "3131 KG on the Main LG" ... as the sum of both MLG scales ?
at 4.8deg total wt is 3406kg ? so a/c wt is 3418kg
at 2 deg 3398kg ... well, there's your problem (with this method at least) ... a lower angle should have a higher sum reactions.

I'd suggest putting the plane on it's jacking points, properly leveling the plane, and getting the correct reactions.

another day in paradise, or is paradise one day closer ?

 

[Equestion]

rb1957 I totally understand that there is an 8KG difference. This might be due to a scale error it was a very hot day when the guys did this test... human error might also be a big factor. For all intended purposes the total A/C Weight can be assumed to be the same in Both cases A and B?

I can Confirm I mistyped at the beginning of B the correct recorded readings are:
at A, scale readings for both MLG= 3131Kg, NLG=275Kg Total Weigh = 3406Kg
For B, scale Readings were: for both MLG1=3037Kg, NLG = 363Kg and Total Weight = 3400Kg
So, all in all, there is a 6Kg Error that slipped in, I know it is unacceptable, but for the purpose of my question can we ignore this error.

If I understand you correctly.

In A A/C WT= 3406/Cos(4.8)=3418

and in B (If I assume that the ground reactions should have been the same in A and B, then

A/C WT=3406/cos(2)=3408KG so what is actually wrong then? Am I missing what you're saying?

Kind Regards

E

 

[rb1957]

no, the actual reactions should be different for different inclinations, but the sum should be Wt*cos(theta)

4.8deg sum reactions is 3406 ... a/c wt = 3406/cos(4.8) = 3418 kg
2 deg sum reactions is 3398 ... a/c wt is 3398/cos(2) = 3400 kg

if we add experimeter error into the mix then the difference between the two is negligible (within experimeter noise)

another day in paradise, or is paradise one day closer ?

 

[WKTaylor]

Equestion...

REF my previous post... where I get kinda 'anal' about jacking and leveling an aircraft 'by-the-book' so that there is NO measureable pitch [fore-aft] or roll [lateral] angular variability for W&B measurements...

Real world aircraft are rarely 'dry' of fluids. Trapped engine oil, fuel, hydraulic oil [tanks/accumulators], coolant, etc, [+ variations in fill-levels for all fluids] can/do affect W&B measurements/calculations.

When the aircraft is jacked/leveled to a consistent position... and equipment is precisely located/stowed... arbitrary variations are eliminated by being set to a 'normalized' position. However if the aircraft is arbitrarily 'off normal angle', then fluids do what fluids do: they flow to, and accumulate at, 'lowest points'... hence 'move [slide] their CG'. Variations within fluid cavity volumes can also aggravate this situation. Even simply 'folding or miss-locating a single seat', will/should be significant enough variation to affect measurements/calculations.

In the hypothetical world of a completely 'dry' aircraft [or where NO fluids are able to shift location due to gravity flow]... and all equipment is perfectly fixed... then OOOKKKaaay, various high-accuracy W&B measurements/calculations as noted above are possible/practical.

War Story.
When USAF changed fuels from JP-4 ['gasoline with oil'] to JP-8 to Jet-A++, variations in fuel density were significant enough to radically affect CG... and many aircraft actually require fixed ['dead-weight'] ballast changes to remain within 'normal' [jacked-leveled] CG range.

NOTE.
An 8-KG sum-difference between measurements for a ~3500-kG airframe is trivial and easily attributed to measurement accuracy [scales] and maintenance crew variations.

NOTE.
I am not used to seeing a 'main landing gear [MLG]' weights: there is USUALLY a weight measurement for each wheel [LDG] assy. I am used to seeing 'left MLG', 'right MLG' and 'nose [or tail-wheel] LG' weights.



Regards, Wil Taylor

o Trust - But Verify!
o We believe to be true what we prefer to be true. [Unknown]
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation,Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", Homebuiltairplanes.com forum]

 

[rb1957]

I guess you could use the two experiments separately and calculate the CG position for both and see how different they are ?

another day in paradise, or is paradise one day closer ?

 

[Equestion]

Thanks for the reply.

I get what you all are saying.

I only added the left-hand and right-hand MLG totals to get a so-called "MLG" for the purpose of this discussion as this was a 2-dimensional approach.

So if I take all the comments into account, it seems like I can conclude that it is... well rather pointless to try and pursue it any further? or maybe I can wander a bit further down this road as it is interesting though... I wonder how the US military handled the weighing process of the OV-10 Bronco as it was such a diverse a/c that accommodated a lot of different configurations?

I can take from the comments that it is essential to weigh an a/c in a lateral and longitudinal level attitude, mainly due to the fact that fluids will be fluids as WKTaylor mentioned, they flow and it will have an effect in the overall CG position. I will most definitely recommend that we rather move towards a jacking method as it is more precise and ultimately safer.

I must admit that I am all very new to M&B, I ventured down this path to investigate the possibility of using a purely mathematical approach to "predict" The CG at Zero Degrees.

WKTaylor thanks for the link to the FAA, interesting read I appreciate it. If there are any other links / Recommended books / interesting reads please post or PM me (If its possible on this Forum ).

rb1957 to get back to your comment, I do understand that the reaction should be higher as the angle get smaller.

If I understand you correctly I can use the "3406/cos(4.8) = 3418 kg" and with a ratio work back to what each LG position weigh?

Thanks again for all the insight and help.

Kind regards

E

 

[rb1957]

yes, you have two weighing "experiments". You can calc a CG position from both.

it seems "odd" that you are so sure of the CG height

another day in paradise, or is paradise one day closer ?