Weighty New Years Resolutions

[Dollytrolley]

Problem is, nobody knows what any of the items weigh so best case is a WAG (wild ass guess)

Ooosooo grasshopper.....now we get to the rest of the story......junk in junk out....

 

So perhaps we might petition Big5er to get his part of DOT to make each truck and trailer carry a current Certified weight and balance just like the other strong-arm section of DOT does with the FAA who requires ALL civil have a current weight and balance. Just a bit more Truck &Trailer Government could solve our problems......

 

So......indeed how much you want to know about your weight and balance is tempered by how much care and detail you are WILLING to input into your weight and arm listings.......

 

Math is math .......only as good as the level of detail you are willing to attain.

 

Now in the "perfect world of aerospace" the weight and balance numbers are obtained by ......"Official-Wild-A$$-Guess" (OWAG)

 

This OWAG is obviously the ......answer.....so no male driver is allowed in the truck until he attains the FAA OWAG weight of 188 lbs (winter) or 183 lbs (summer).....or you can do what the airlines do....fill up the bird and takeoff.....sorta....

 

At the end of the day the the world tends to operate on WAG or maybe OWAG or.......EWAG (Estimated Wild A$$ Guess)....

 

Of course there is Hugh Heffner....he said...."ignorance is bliss....I did not know that I could NOT start a magazine with a old typewriter and $800 borrowed from my aunt".....

 

Drive on.......(Steve...remind me....how much does a gallon of vodka weigh)

[NoDirectionHome]

 

 

.(Steve...remind me....how much does a gallon of vodka weigh)

http://www.aqua-calc.com/calculate/food-volume-to-weight/substance/alcoholic-blank-beverage-coma-and-blank-distilled-coma-and-blank-vodka-coma-and-blank-80-blank-proof

[Alie&Jim's Carrilite]

http://www.aqua-calc.com/calculate/food-volume-to-weight/substance/alcoholic-blank-beverage-coma-and-blank-distilled-coma-and-blank-vodka-coma-and-blank-80-blank-proof

But that is before the vodka is drunk..... Does a gallon of vodka weigh the same after being imbibed?

[Dollytrolley]

But that is before the vodka is drunk..... Does a gallon of vodka weigh the same after being imbibed?

so....R wee talkn bout drinked bye aah ....drunk? ?

 

Drive on.......(whach out fur drink'n , drunkz 2nite...)

 

Happy New Yearz....

[Dollytrolley]

Maybe this sketch for the trailer will help:

 

 

For additional items like more cargo bays, just measure from pin and provide the same info as noted for similar items.

 

Dave

Since Dave has made the effort to kindly sketch out the generic trailer configuration form to allow us to graphically record the various variable mass centers of the trailer it brings out one of the "elephants-in-the-room" and that is....individual tire position weights....

 

Individual tire position weights come in two configurations......baseline trailer configuration is the first and loaded trailer configuration second.

 

At various times in numerous threads Trey and Susan have commented on various aspects of individual tire position weights on many of the RV units that they weigh for owners. Make no mistake .....this can indeed be a large elephant when when we address Weight in the process of defining and recording RV weight & balance calculations.....

 

In Oregon ODOT leaves all of the public scales operational 24/7 so it is moderately easy to obtain individual tire position weights if you are willing to take the time and effort to position each individual tire on the scale platform one at a time (you do get some backup practice).

 

As Trey and Susan have mentioned in various posts many RV owners are shocked at the wide differences of individual tire position weights on their RV once each tire position is weighed......

 

Now to address this......"tire position elephant"........I was thinking about assigning the task of building a 3D weight and balance auto calculating live data software program to Stekay since we all know Sr Engineers are Overpaid and Underworked so it just makes sense to give Steve something to do......the problem with the 3D concept is that each owner would have to keep weight and location detailed in a manner that is simply not going to happen in RV operations.

 

So.......how do we deal with the ....."elephant".... Most folks ignore the "elephant" ....

 

I have recorded the "baseline" individual tire position weights and then when I calculate my weight and balance I down-rate my axle capacities to account for my highest individual tire position weight. Now this works well for me because our stone simple small toy hauler is pretty light at baseline and I keep it below 80% Gross even when Dolly the paint horse is riding in her horse module in the back of the garage. This works well to keep our individual tire position weights well below axle and tire load ratings. We offload every pound we can out of the trailer and transfer it to the tandem truck.....while this works well for our odd rig it is less practical for the larger trailers....

 

So far my only "answer to considering the elephant" is to calculate each axles highest tire position into the baseline data and then apply a "fudge-factor" of say 15 to 20% to these weights as a down rate......

 

Anyone have any ideas on how to deal with the......"elephant"?

 

Drive on........(why are "elephants so......big)

[NoDirectionHome]

Cross connected (front/rear/left/right) air suspension will give you even weight distribution. To do so dynamically (go'in down the road) you need large enough diameter connecting tubes. You also would need some form of roll control so you don't tip over in a turn which would negate the even weight distribution except on a flat surface.

 

There's also this that gets pretty close fron to rear. I have it on one truck. http://www.hendrickson-intl.com/Truck/Vocational/HAULMAAX the ride is pretty awful though.

[I'mdonewiththis forum]

I have driven older International cabover trucks with a short wheelbase with the "hockey puck" suspension. To say they ride 'pretty awful' is kind of an understatement.

[rickeieio]

So, I just have to show my ignorance here............

 

DT, you've stated often that your goal is to stay below 80% of the rating on any given component, whether it be tire, axle, etc. I get that. Safety margins make for less stress, longer life. But how is the rating calculated in the first place? Is it a percentage of actual failure point? Hypothetical number taken from Grandpa Engineer's slide rule? ( used a slide rule in high school, cuz calculators were unobtanium.)

 

A little background of how ratings are determioned could help us common folk understand where we're going, and why.

[Dollytrolley]

So, I just have to show my ignorance here............

 

DT, you've stated often that your goal is to stay below 80% of the rating on any given component, whether it be tire, axle, etc. I get that. Safety margins make for less stress, longer life. But how is the rating calculated in the first place? Is it a percentage of actual failure point? Hypothetical number taken from Grandpa Engineer's slide rule? ( used a slide rule in high school, cuz calculators were unobtanium.)

 

A little background of how ratings are determioned could help us common folk understand where we're going, and why.

Rickooo......you used to love me....and now you ask hard questions....

 

Looking back over too many decades .....it seems to me that many "ratings" are determined by voodoo....sorta...

 

As far as my "personal-80%-de-rating" of the cheep 15 inch toy hauler is concerned all I can say is that since I have stayed below 80% of the listed sidewall rating I have had NO tire failures at all so.......am I just in a period of sustained luck.....or does my de-rate have real merit?

 

When I started this thread I knew that I would surely fall into the deep end of the pool with my lead boots on.....however I have been lucky in life to be rescued by folks with huge brains.....so.....maybe I'll get lucky here as well.

 

I wonder how many RV operators really desire to know their actual Operating Weight & balance......now I am fairly certain Rick as a farmer and RV operator you have never operated any rig overloaded or out of balance, however some HDT folks seem to having some overloads in their past lives that have steered them into purchasing class 8 trucks......a few folks seem to tend to be .....repeat offenders even with a class 8 truck....

 

Maybe Some of the tire-geeks on the forum might chime in about the finer points of tire and maybe axle / suspension ratings as well...

 

Drive on.......(what is your ratings?)

[rickeieio]

......now I am fairly certain Rick as a farmer and RV operator you have never operated any rig overloaded or out of balance,

 

Never. However, I've seen other folks do such things, which is why I went the HDT route. In the interest of full disclosure, I've come close to disaster more times than I care to admit. As I get older, I listen to folks like you and other learned folks on this forum, and so stay a little safer. Thank you all for educating us.

 

Something about old. bold pilots comes to mind.........

[Alie&Jim's Carrilite]

So, I just have to show my ignorance here............

 

DT, you've stated often that your goal is to stay below 80% of the rating on any given component, whether it be tire, axle, etc. I get that. Safety margins make for less stress, longer life. But how is the rating calculated in the first place? Is it a percentage of actual failure point? Hypothetical number taken from Grandpa Engineer's slide rule? ( used a slide rule in high school, cuz calculators were unobtanium.)

 

A little background of how ratings are determioned could help us common folk understand where we're going, and why.

I'd say in the case of tires, axles, and suspension, the rating SHOULD have been the item of least strength, be it the shear rating of the hanger bolts, the bearing weight rating, tire rim weight rating, axle tube or chinese made tire. This number would/should be accurate if the item in question was actually tested to failure by random selection from multiple batches of product made. But it seems that today the computer tells us what a rating should be based on how the original prototype was developed, not how the actual product is manufactured in a factory cutting corners in a far off land.

[Dollytrolley]

I have some reservations about posting this "event" from my past life but it is directly related to Weight and Balance as well as "rating standards".

 

Back in the 80's a overfunded company came up with a very questionable concept for a small group of "special use aircraft".

 

This concept aircraft constituted of a +4,000 lb gross Pressurized recip single airplane with many, many, too many modifications installed on aircraft.

 

In the U S when you modify a civil aircraft you should obtain FAA approval of the modifications.

 

To obtain FAA approval of the modifications to the aircraft the "applicant" often must fly a series of tests at various weights and balance to PROVE acceptable aircraft performance AND CONTROLLABILITY.....

 

The test aircraft was a brand new ship of a basic design that had been in production for a long time however the pressurized version had only been in production for about 8 years.

 

I at the time operated a pressurized version but was not a huge fan of the airplane since it was fairly sluggish and had ponderous handling.....

 

I was engaged to fly some of the testing of the highly modified airplane and the firm was in a big hurry to obtain FAA approval(s).

 

As is the case with a brand new HIGHLY modified aircraft some bugs needed to be ironed out before actual FAA tests could be scheduled.....as the preparations dragged on the management became very impatient and so they hired some big brain engineering talent to draw up a formal "rational aerodynamics analysis" of the "predicted handling qualities" of the highly modified test aircraft.

 

I reviewed the "rational aerodynamics analysis" and had some misgivings about some "assumptions" but the FAA seemed OK with a proposed "abbreviated" handling testing of the aircraft weight and balance envelope.

 

In essence light aircraft weight and balance envelope is constrained on the forward limit by the ability of the aircraft to have acceptable nose UP pitch control and stall speeds within regulated limits and the aft limit of the C G envelope is defined by nose pitch DOWN authority and acceptable POSITIVE control stick forces.

 

The FAA arrived to witness the testing and the aircraft was ballasted to the proposed forward C G limit.....

 

The airport was not ideal for testing with a 3,600 ft runway and loaded to forward Gross C G the aircraft struggled off onsented and it took a LOT of effort to barely pass the test....marginal at best.

 

I was NOT happy with the aircraft performance and handling but the firm was gung ho and the FAA was ok with results so far.

 

I expressed a desire to move the aircraft to a longer runway airport for the next Aft C G testing but the firm was very unhappy with my request and the FAA said that they would have to reschedule for a later date. Here is where I made a HUGE mistake.....

 

I finally consented to fly the first aft C G test and the agreed to test loading ballast was secured into the aft cabin of the aircraft AND the aft baggage aux fuel tank was topped off to complete the loading.

 

With this FAR aft loading the aircraft would sit on its tail skid with the nose wheel off the ground but when I would get into the pilots seat with a heavy parachute on the nose wheel would just slowly touch the ground but the nose wheel centering device would not allow the nose wheel to be steered until the strut was depressed at least a inch down so in order to steer the nose wheel I had to start the engine and then apply moderate breaking to allow propeller thrust to depress the nose strut just enough to steer as needed.

 

I herded the pig to the end of the runway and ran the trim to most of the nose pitch down range and then stood hard on the brakes and then the adventure began......

 

With the far aft C G the nose wanted to pitch up aggressively but with the high gross weight I had to keep the nose pitched down enough to attain take off speed to make matters even worse I had to use.....BRAKES ....initially to keep the nose strut depressed to keep some steering until the aircraft attained enough speed for the rudder to provide directional control.....once I gained enough speed to get off the brakes i was having to apply more and more forward wheel force to keep the nose pitched down enough to takeoff......at about 2500 feet the airplane struggled off the runway but it took almost full forward wheel travel to keep the nose pitch from reaching stall position....for a fleeting second I considered aborting the takeoff but reducing power would only pitch the nose into a stall and too little runway remained to attain a successful abort.....so...

 

wheel full forward the nose remained too high for the airplane to attain a decent climb speed but it was attaining a limited positive climb rate in a mushing nose high attitude. Enen though it was a fairly cool day the engine temps were nearing red lines and it was imperative that I somehow shift the C G forward enough to get the nose pitch down enough to attain a speed to cool the engine and climb some.

 

First I moved my seat as fully forward as I could with my chest right up against the control wheel then I tooke EVERYTHING I could reach and started piling items on the glareshield .....the nose very slightly pitched down just a bit.....I was too low to bail out and I could never get the pressurized door open in time so......I released the leg straps for the chute and wiggled out of the shoulder straps and crammed the chute up onto the glareshield and the nose lowered a bit more and my airspeed increased a few knots and the poor but positive climb rate continued...sorta...next I switched fuel pump for the aft baggage aux fuel pump on and started pumping the fuel into the already full tip fuel tanks so the excess fuel was being pumped out of the tip tank vents overboard.....

 

The engine temps stabilized about 15% ABOVE redlines but I had no choice at this point.

 

Mean while the FAA pilot and flight test engineer were orbiting me in a wide arc and they knew that things were not going well because of the high pitch attitude and the full elevator position not allowing me any more pitch authority.. The FAA pilot had called on the radio but I had not responded because I was....BUSY....and I had pitched my headset and the hand mic up on the glareshield to shift some weight forward......

 

Gradually as I pumped more and more of the fuel out of the aft baggage fuel tank overboard the nose started to lower somewhat. After about 45 minutes of hellish floundering the sky I retrieved the hand mic from the glareshield and called the FAA pilot and told him that I was going to land at a nearby airport with a 8,000 ft runway....

 

In a moment the company engineer came up on the frequency and vetoed my decision to land at the other airport......

 

Finally I did something that I should have done at the beginning of the day......I keyed the mic and said "This IS 711Golf and we ARE landing on Runway 22 on a long straight in 3 mile final....."

 

The fast touch down with as heavy braking as the wing loading would allow and large amounts of engine power required in the last half of the roll out to keep the nose wheel steering operational simply melted the remaining brakes and I used over 6,000 feet of runway to get the pig to a halt in one shaky piece.....

 

Later that evening I was having dinner with a old but very talented pilot and after I told him about my screwy day and that I thought I was being paid too little.....Bill smiled and said "well Kid....you should have paid all of the people that were flying that aircraft UNTIL you finally got some guts and HAD to fly it yourself".....gulp

 

So you see I had some....."Experience" with Weight and Balance rating....of sorts....but I proved to NOT be a expert at the end of the day....

 

In the RV world it seems that Weight and Balance ratings are pretty much determined by how large a fifth wheel trailer the owner can afford to hitch up to his pickup.....wonders never cease...

 

At most I might get by with ciphering some Weight and Balance calculations but .....testing the results are better left to better.....drivers or pilots...

 

Drive on.....(Where is your ....C G?)

[Steve from SoCal]

That sounds like a poorly developed program, every CG test I have seen puts the ballast on a moving slide. P210?

 

Steve

[rickeieio]

January, 1970..... 1947 Bonanza (slightly upgraded engine), with so much avionics, it was rated for pilot (Dad) with 1/2 load of fuel and NO other ballast. So one cold day we add me, at 200#, two other guys at about 180# ea. and a tool box at a good 100# in the luggage compartment. Of course, full tanks. Lumbered out of Hamilton, OH and proceeded to Burke Lakefront in Clevelant, where a Cessna 210 waited, engine in a crate, as was the prop.

 

The 210 had force landed when the original prop decided to quit holding hands. Meanwhile, the engine shook a bit and twisted the mounts. All this was sitting in North American Rockwells hanger. When we told the "real mechanics" that we were going to assemble the pieces and take the plane home, before dark, they laughed. We did it. No FAA guys on site.

 

Last time I checked, that old Bonanza (3317V) was in Indianapolis. Sweet old bird. I had a lot of time in the right seat. The 210 burned in a hanger fire about 15 years later.

[Dollytrolley]

 

That sounds like a poorly developed program, every CG test I have seen puts the ballast on a moving slide. P210?

 

Steve

 

 

Sometimes "special programs" are hellish programs.

 

The sliding ballast devices have had "mixed" results......

 

My favorite ballast mitigation device is a shot tube in the belly of the aircraft so if testing becomes....."unpleasant"..... the trap door is tripped and a large percentage of the ballast falls free thereby shifting the C G forward and also reducing the aircraft weight at the same time.....Shot tube are expensive mods for pressurized aircraft though.

 

The sad side note to this mess is that the load I flew with was a transposed loading from another failed program and that pilot did manage to bail out but he perished when he drown when he was being rescued. The transposed loading was a protected document so the error was not found until my little joy ride uncovered the sad fact that the projected handling was derived from another loading profile......just hate when the paperwork almost kills meeee....

 

Drive on.....(is this the right load?)

[Dollytrolley]

For those of us who fell asleep in geometry class and went directly to work after school pumping gas, this exercise cries out for some illustrations or a graphic based demonstration. Since this website isn't great for that, maybe a link to a picture website might do the trick.

Some basic definitions of the terms would also be a help to the great unwashed.

 

Well Jeff I already had my first of a planed few baths of the new year so maybe I am not a part of the unwashed but I can't remember much so some folks might need to help me out here but here goes....

 

The basic concept of calculating RV longitudinal weight and balance intended to assist the RV operator to attain loading of the RV within limits of capacities of the tires, brakes, axles, suspension, frame,hitches and cargo compartments in such a manner to attain a safe balance for normal operations.

 

The method utilized in calculating the RV Weight and Balance involves establishing a Baseline RV weight and Center of Gravity by scale measuring the RV and then by calculation adding and subtracting various items utilized in the day to day life of the RV operations.

 

The terms utilized in the Weight and Balance calculations are:

 

WEIGHT is the mass of a object, for our purposes this will be defined in Pounds

 

DATUM is a arbitrary point from mass points are referenced from, for our purposes truck datum will typically be the front steer axle, trailer datum points will typically be the center of the hitch.

 

ARM is the distance from the datum measured in inches to the center of a mass listed.

 

MOMENT is a sum or sums of a item weight multiplied by that items arm.

 

CENTER GRAVITY is the point of balance of a mass or groups of masses at the combined balance point.

 

For our purpose we will list items added or subtracted to the baseline and then define the arm of each item and then calculate the moment of each item by multiplying the weight by the arm. Once all items are recorded then the sum of all weights are totaled and then the sum of all moments are totaled and the the moment total is divided by the weight total to arrive at a Center of Gravity number that represents the distance from the datum to the Center of Gravity.

 

Examples will be given in following posts.

 

Drive on......

[Dollytrolley]

For those of us who fell asleep in geometry class and went directly to work after school pumping gas, this exercise cries out for some illustrations or a graphic based demonstration. Since this website isn't great for that, maybe a link to a picture website might do the trick.

Some basic definitions of the terms would also be a help to the great unwashed.

 

Well Jeff as far as your suggestion regarding some illustrations and graphics it is perhaps the best way for many folks to get the "picture" of weight AND balance it is likely that some illustrations could help with explaining the subjects at hand.

 

For a few reasons I have resisted he occasional urge to post pictures on the forum however I might reconsider my self-imposed ban on posting graphics here......

 

Being geezer-lazy, I have hoped that some forum members might step up to the graphics chore and save my mangy hide in this task.....Star Dreamer has shined brightly with his nice graphic of a generic trailer loading template......thanks Star......I need to send you a gold star....

 

Being geezer-lazy I sometimes utilize a couple of VERY capable computer engineering programs that are free and are simply stunning in capability......these programs are products of AutoDesk the company that brought us Autocad and Solidworks and many other programs.....

 

The two engineer programs are called....ForceEffect.....and...ForceEffect Motion, these are free but have huge capabilities....using these programs for weight and balance computation is.....child's play and sorta fun.....the non-fun part is me trying to post some of the results here in the forum.....uuuug .......

 

Maybe some computer-geek like Derek (RV).....might come to the rescue and cobble up some graphic displays of various weight and balance configurations......

 

Or.......maybe....just maybe I might burn some midnite oil and cobble up a few graphic weight and balance configurations and then attempt the task of posting them here........I have posted ONE image per +1,000 posts here.....maybe it's time for image #2 ? ?

 

Drive on.......(maybe I am too geezer-lazy...)

[beyerjf]

The graphic does the trick. There also must be a CAD program out there somewhere that allows you to put in the various values, desired component design limits and watch everything change, kind of like a graphic excel spreadsheet. The definitions are also a big help.

Good luck believing the manufacturer's rated capacity of a given component in the RV world, and then staying to 80% of that. And making these determinations within some kind of cost benefit analysis is even a bigger challenge. My only real experience with these sorts of things was when I visited the Spacecraft plant and saw first hand how that entire trailer is built about twice as strong as needed, and the price reflects it.

 

Hands down the most efficient structure on the face of the earth is the lowly intermodal container. But don't even think about modifying anything about it lest you change the capacity of stacking 8 fully loaded (60,000 lbs each) on top of each other, causing the one on the bottom to bear almost 500,000 lbs, on a rocky sea no less. Some more design stuff to ponder since we seem to have that kind of time around here:

 

https://backspace00.wordpress.com/2013/12/29/stacking-shipping-containers-on-land/

[Pat & Pete]

It's pretty easy to post 'self made graphics' to this site .

 

Simply highlight and save your 'composition/illustration' as a .jpg and place it someplace easy to find in your computer . Then hit the More Reply Options and then the Choose File button , just below Attach Files . Find your .jpg and ...

 

But , you probably already know all that .

[Dollytrolley]

The graphic does the trick. There also must be a CAD program out there somewhere that allows you to put in the various values, desired component design limits and watch everything change, kind of like a graphic excel spreadsheet. The definitions are also a big help.

Good luck believing the manufacturer's rated capacity of a given component in the RV world, and then staying to 80% of that. And making these determinations within some kind of cost benefit analysis is even a bigger challenge. My only real experience with these sorts of things was when I visited the Spacecraft plant and saw first hand how that entire trailer is built about twice as strong as needed, and the price reflects it.

 

Hands down the most efficient structure on the face of the earth is the lowly intermodal container. But don't even think about modifying anything about it lest you change the capacity of stacking 8 fully loaded (60,000 lbs each) on top of each other, causing the one on the bottom to bear almost 500,000 lbs, on a rocky sea no less. Some more design stuff to ponder since we seem to have that kind of time around here:

 

https://backspace00.wordpress.com/2013/12/29/stacking-shipping-containers-on-land/

Jeff your description of a cad program with a excel like output is Exactly what Autodesk ForceEffect does in spades AND it also Auto-generates a Formal engineering report that is simply stunning......so..... The software can do the.....heavy lifting here (pun intended) ....so I guess I need to get off my Kiester and do some graphics......

 

Pat, yes I hear your advice regarding jpegs however most of my image files are bloated and so then I have to photo edit them down the size that fits the small limits of the forum postings.......better I bite the bullet and photobucket post here....here again I am pretty lazy....

 

Drive on.........(test drive ForceEffect....)

[Steve from SoCal]

One little point of attribution,

 

Solidworks is a Dassault product. Loyal Falcon driver and Solidworks fumbler.

 

Steve

[Dollytrolley]

One little point of attribution,

 

Solidworks is a Dassault product. Loyal Falcon driver and Solidworks fumbler.

 

Steve

Cee messeeer Steven I am weeee 0veeeree myeee pay grade here......

 

Next I'll claim that F0rD made bird with two too many engine zzz ......

 

I need more help than any three people u no......

 

Drive on........(who makes Yugo......?)

[Dollytrolley]

Does anyone with a Large fiver want to supply a example trailer for the next part of the weight and balance thread.....you could fill in the sketch boxes in the Star Dreamer trailer diagram sketch contained in this thread.

 

If you have detailed wheel and hitch weights that would be nice but the arm locations for each item listed on the Star sketch is the most important items and then capacities of fresh, grey, and black water tanks would be nice.

 

IF anyone desires to contribute you could email the data and if you wish to not be named that's fine.....I forget my own name most days...

 

Send your data to mmcdan3189@aol.com

 

Thanks,

 

Drive on.....(needing dat data...)

[Dollytrolley]

Group,

 

Forum post editor seems to hate having Excel data inserted so all text and numbers bunch together .....

 

Has anyone a method of posting excel data here.

 

Drive on......(so close but no excel...)

[Dollytrolley]

Group,

 

Please take a look at the attached Example Weight and Balance for a sample HDT singled with a Smart Car and a 44 ft toy hauler hitched with a Harley loaded in the garage.

 

For calculation of average trailer wheel base all axle loads are combined on the center axle.

 

Not sure if the attached PDF will load.....

 

Drive on....(???)

HDT_WtBal_C.pdf