Weight and Balance- Private Pilot Written Test review practice

i'm working on putting together a playlist on my channel dedicated to students who may be preparing to take their faa pilot knowledge test because quite frankly i didn't enjoy studying for them either with matters about aircraft weight and balance these test questions can include scenarios and charts that closely resemble what you may encounter in real life practical flying while few other questions have less practical use for pilots this video will review three sample weight and balance questions that are known to be in the private pilot written test using various types of charts as previewed here there are some recurring themes and formulas with each weight and balance question to follow we will be observing the weight of an object multiplied by its distance from a reference point known as the arm will give us what is called a moment you can think of moment as the resulting force that tends to cause a rotation around a pivoting point we can easily demonstrate this in action using a seesaw for example this formula is often abbreviated to w times a equals m or even further abbreviated to wham in this part of the globe weight is pretty much always given in pounds well the unit for arm is given in inches symbolized by those two dots that look like quotation marks and moment is given in pound inches knowing these units associated with the different items in the equation helps us differentiate them from each other and lastly it would be helpful to understand some standard weights for fuel and oil the weight of fuel here is referring to gasoline not the heavier jet fuel standard weight for gasoline is at six pounds per gallon standard weight for oil is seven and a half pounds per gallon i recommend to memorize these standard weights as well because this information is not available during the written test though there is a small indirect way to find that out i'll show you that later too i thought it would make sense by starting with a question like this one that refers to a chart figure with a seesaw i will be featuring the applicable charts throughout the video but i want to encourage you to acquire your own copy of these charts and diagrams so you can fully view their information for yourself a free pdf of these charts in the testing supplements book is available on the faa website i will include the link in the video description below along with this figure the question asks if 50 pounds of weight is located at point x and 100 pounds at point z how much weight must be located at point y to balance the plank and we will have three answer options to select from with only one of them being correct we will look back at this figure and begin applying the given information from the question to figure out the weight of box y in this scenario the question gives us that box x weighs 50 pounds and box z weighs a hundred pounds by taking this information along with applying the weight times arm equals moment formula we will find how much the weight of box y would need to be i will add the given information to this picture to begin laying out this equation under box x on the farthest left side we have 50 pounds right next to that we have the weight of box y in a question mark and then on the far right side of the fulcrum we have box z weighing 100 pounds the arms for each box are provided including box y they are listed above near the top and starting from the top left side box x has an arm of 50 inches box y is sitting at 25 inches and on the other side box z is positioned at 100 inches all these arm measurements are taken in reference from the datum the middle dash line that happens to also line up with the fulcrum to visually illustrate the math as much as possible here i'll set up a simple drawing of our seesaw with a dashed line that connects the fulcrum and the datum a quick peek back at the question asks that the plank to be balanced in case you're wondering the plank is that board that sits horizontally in the seesaw if everything it holds is balanced basically when we're drawing out the math problem here we can imagine that there would be an equal sign right above the fulcrum so that the left side of the plank with box x and y would balance the right side of the plank with box z or more specifically the total moment on the right side would equal the total moment on the left side of the fulcrum now we can get to work and start on box x with our wham formula i have set up for box x 50 pounds multiplied by its arm length of 50 inches giving us 2 500 pound inches this is the moment for box x not very exciting so moving on to box y we are missing the weight so i will leave that indicated as y but since we have the 25 inches for its arm for now we have y multiplied by 25 or 25y cleaning this up a bit we have on the left side coming to 2500 plus y now it's wham time for the right side we take the hundred pounds of box c multiplied by its arm of a hundred inches this gives us ten thousand pound inches and this you know would be the dramatic moment for box z anyhow when we really boil down to what we have here essentially this is a basic algebra equation where we are solving for y for this video i assume most of us here will be familiar with performing this level of math but just in case you haven't or if it's been a while since you've last done this i will isolate y by taking the 2 500 and subtracting it from the 10 000 on the other side of the equation which leaves us with 7500 at this point we will still want to isolate y from being multiplied by 25 so to do that we will take the 25 and use it to divide the 7 500 on the other side of the equation we found that y equals 300 pounds which leads to answer option c for this question next up is another question that involves a different kind of chart this one happens to be figure number 34. question has also included this partially completed table of a list of items on an aircraft and their corresponding weights and moments right away we can fill the last two weights for the fuel and oil by using our standard weights remember that fuel weighs 6 pounds per gallon so here we can multiply our 38 gallons of fuel by 6 and find that this would weigh 228 pounds the last item below we see that this oil quantity is listed in quartz we know that there are four quarts in a gallon so essentially here we are looking at two gallons of oil and by standard oil weighs 7.5 pounds per gallon we can multiply that by our two gallons we have here which comes to 15 pounds but luckily we have this particular weight conversion already listed in the top half of figure 34 so we could have simply referred to this part of the chart too and with this information you could do the reverse math and figure out that the 15 pounds listed here would have led you to the seven and a half pound per gallon for oil just in case you may have forgotten the standard weight of oil but i still recommend just memorizing the standard weights and save yourself the math this question has two parts to it asking to determine the moment of the airplane as well as what category is applicable in this scenario now that we have all the weights figured out we will take a look at figure 34 in the upper half for now with this chart we will be able to take our known weights of each item such as the pilot passengers fuel etc and let these lines guide us to find each of their moments acting on the aircraft upon the left side of this chart you will see the vertical y-axis corresponding to weights we can begin at this area with the weight of our first item on the list which happens to be the combined weight of the pilot and front passenger the weight for this is 310 pounds so we can travel up the y-axis until we reach 310 pounds and then from there shoot straight across until we intersect the appropriate line for the pilot and front passenger once we have identified the point on the appropriate line from that point shoot directly down to hit a point on the x-axis to find the moment some people instead choose to first travel up diagonally along the appropriate line first and then look to align with the weight before shooting downwards towards the moment but as long as you arrive at the correct position on the moment axis it doesn't really matter which path you choose to take when starting out on this chart here i tried my best as humanly possible to be as straight and precise with my lines to get the most accurate reading i could manage here it looks like every other thin blue line represented the next full increment on the moment scale so here it looks to me about 11.75 the point here is take care in avoiding a sloppy reading with this chart as you can see a slight difference could sway us from selecting the right answer on the multiple choice test so i will enter my reading of 11.75 as the moment for the pilot and front passengers give it a try and check out what you come up with and continue the same work with this chart for the rear passengers and fuel we have left to work out feel free to pause this video and give yourself time to do this on your own or i'll just carry on and add what i came up with for them too so now that we have all the weights and moments completed in this chart all we need to do is add them up we will take all the weights in this column and find our total weight to come out to be 1999 pounds we will do the exact same thing for the moments column and yes we will subtract 0.2 for the oil as it is a negative number i came up with a moment of about 81.25 with these two numbers we will now use the bottom half of figure 34 this chart right here with this chart we should be able to determine if the airplane loading applies within the normal category or utility category similar to the line chart we worked with above we could start with drawing the total weight line across but since we also already know the moment you could start with that side too all we care about is the position of the point these two lines intersect somewhere within this red shape known as the envelope ideally i drew out the moment line coming upwards from about 81.25 we want to see where the point that the weight and moment lines cross and that will help us know part of the answer well at least it should you see i redrew my lines much thinner and attempt to be as accurate as possible but can you see the little green dot i made up there maybe it would help if we zoom in for a closer look even more closer and closer we'll keep going almost there a little bit more and there it is ah our little green dot now that we found the green molecule on the chart which side is it on yeah well that wasn't helpful honestly to me it looks way too close right on the line for my results for a written test question that provides answer options between it being either on the normal or utility side this is cutting it too close i believe this would make a poor quality multiple choice question i know we could get slightly different results if i went back in and redrew the lines maybe with the help of a microscope too but with these types of graphs we need to hand draw the lines and figure out the readings between the lines it's not the simplest of tasks so the main point i want to make here is don't rush and take your time being as neat and accurate as possible when you make these calculations especially on these graphs small discrepancies throughout the process can add up to be larger ones in the end result moving on let's take a look at these three answer options for this question the listed moments here are pretty close to each other too my result doesn't match any of them but i can try to find the closest option by finding the difference between each of them and consider the one that's closest to my result of 81.25 as for the second half of these answer options utility or normal category i'm feeling a little stuck with my point being like right on the line between normal and utility not clearly on either side for me sometimes we get ourselves in these situations and it's not a bad idea to go back in and try again see what result you get by trying the second time i'm sure if i also recalculated my moment right now i could get a slightly different number the next time we have been reading between the fine lines on these charts it's not a digital machine that spits out a number down to the decimal that would make our answers more consistent easily so looking at these three answer options i have to select the one that i think is best and with what i got right now it can be a tough call my moment is closest to matching answer option c it being 81.2 and in the normal category but at this point i'm also thinking about some general patterns i noticed on a lot of these written tests i often found that when you have part of the answer options outnumbering the other one such as here we have both a and b having the utility category listed i would have higher suspicions about their correct answer being in the utility category this would help me out since i can't distinctly tell from my own results of which category would be correct i would never say this is always the case but this is the general pattern i noticed in my experience with these kinds of written tests above all apply your own judgment and common sense too when you do all the work double check and make sure you were as accurate as possible sometimes you're still left with having to just pick the best answer amongst what is given so applying this i would be led to believe that answer option b would be the best answer in this case since 80.8 is closer to my 81.25 than the 79.2 and answer a this is also what the book states to be the correct answer i hope you don't get this odd question during your own written test but don't worry majority of the questions are much more reasonable and clearer than this one i just chose this particular question so i can share the answer selection method that has helped me more than once during testing let's get out of here and move on to the next and final question now we're looking at weight and balance tables these happen to be from figures 32 and 33. if it helps your motivation these don't involve reading between any fine lines and i'd say the worst is already behind us now but let's see what you think here it asks what effect does a 35 gallon fuel burn from the main tanks have on the weight and balance if the airplane weighed 2 890 pounds and the moment was 2452 at takeoff don't let yourself be too distracted by the moment indicated as being divided by a hundred here this representation occasionally is used to reduce the number of zeros or digits for the moment as they can increase to very large numbers especially for larger aircraft these are the three answer options to select from with every answer option here their first portion all state that the weight would be reduced and both options a and b say by 210 pounds answer option c however has a slight different wording of reduced to 2680 pounds we can see if this change of wording has any effect of the actual value of weight decrease for this option going back up top to the question it states that there is a 35 gallon loss of fuel from consumption so we can find out how much weight loss this would actually be by multiplying the 35 by the fuel standard weight of 6 pounds per gallon this will result in 210 pounds weight reduction indeed this confirms the answer options both a and b are on the right track for option c we need to take the airplane's weight before takeoff of 2890 pounds as provided in the question and subtract 210 pounds from it this comes to 2680 pounds and this says that though answer option c is made to look different from the weight reduction included in answer options a and b all these answer options include exactly the same quantity of weight reduction sometimes written test questions are set up like this that leaves us to distinguish the correct answer by comparing each answer option with their second half being the position of the cg or center of gravity at this point i'm suspecting that answer option b may be quickly eliminated because it includes the center of gravity would be unaffected in reality with a change of weight in an airplane's fuel tanks pretty much there will always be a change in the cg's position so let's see where the cg will end up moving in this case proceeding onto the tables we will start with figure 32. from this table we will be able to find the moment of the 35 gallon fuel in the main tanks this information is found in this spot right here in this area this particular area is specifically labeled at the top for the main wing tanks you can see that the area right below that i cropped off is information regarding the auxiliary wing tanks auxiliary wing tanks i could never say that word easily but the question is asking only for the main wing tanks not to be confused with each other so with this table we can identify the moment for the 35 gallons of fuel simply by traveling down the green gallons column to 35 and looking horizontally across to the right in the pink moment column which gives us a moment of 158. by the way just wanted to include a quick written test tip here that if you ever find yourself having forgotten the standard weight of fuel during your test you can take a look at this table and figure out that it would be six pounds per gallon by referring to the middle yellow weight column and dividing those numbers by their corresponding numbers in the green gallons column all of them would give you the result of six for example the very first row 30 divided by five is six you will be provided these same exact charts for your private pilot written test since the airman knowledge testing supplement book is the same exact book you will be provided during your test you can be as resourceful as you want with the information in this book returning to this question we now know that the moment for the 35 gallons of fuel was 158 pound inches we will need to find where the cg will move after this amount of fuel burns away we will take the original moment before takeoff which was 2452 and subtract the moment for the 35 gallons of fuel so 2452-158 will give us 2294 as our new moment after the fuel burn we will compare this number to the limitations that are listed out here on figure 33. with this table we are only going to seek out the listed weight of the airplane after the fuel burn and the associated range allowed for the moment the way this table is laid out is all the weights are colored yellow and incrementally increase towards the bottom of the page until it continues on this right side you will be better able to see the full image if you have downloaded the pdf the weight we will be looking for on this table is 2680 as we figured out from the beginning we got this when we subtracted the weight of 35 gallons of fuel from the airplane's weight before takeoff 2890-210 gives us 2680. with our new given airplane weight we can find if our moment fits within the minimum and maximum moment range we will soon have the moment of truth here we find that with a weight of 2680 our minimum moment is 2123 and the maximum moment is 2287. i just inserted a clip of the upper part of this table to include and match the titles of each column we're looking at in this close-up view here however our calculated moment is 2294. exceeding this table's maximum moment limit this would mean that rcg is beyond the aft limits and this is often referred to as the aircraft being tail heavy which is associated with less stability but for this video i should focus on answering this written test question so revisiting our three answer options the best answer looks to be a with a weight reduction of 210 pounds and the cg moving aft of the limits i would be pleased if this helped you teach yourself something new overall most other weight and balance problems follow the same patterns here in some form or another so will there be a part two to this video i don't know well you tell me if you comment or like this video i'll be watching the responses here till next time you

Channel: AIDYL CONCEPTS

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Length: 21min 31sec (1291 seconds)

Published: Fri Jun 25 2021