Mass & Balance: Part 1

追加: 2026-04-29

[00:00:01]All right. So, today we will be looking at mass and balance. I mean, I actually wanted to make uh videos of numericals because I got so many requests, but I feel like I should give some pretext as to what we're going to talk about. Um, I'm sure many of you know what I'm talking about if you're looking for these videos, but I want the satisfaction of me saying um or explaining these terms. So we're going to see the theory part of mass and balance in brief and then we will get to the numericals and I think this should be like a three or four part um video series like a playlist of mass and balance. Now if you know me uh when it comes to nav I prefer u IC sorry Oxford and u we will be looking at definitions first.

[00:00:49]So for example, let us start with like when you consider an airplane, there are different masses at different point of times based on how you load or what you load in it. Right? So when the question is talking about a certain kind of mass, you should know what is included in it and what is not included in it for your calculations. Right? And why are these important? this every single flight you take you should do mass imbalance because whenever it is overweight it will structurally damage your aircraft and that's not something that you want obviously right so mass imbalance the first weight that we have or mass that we have is basic empty mass know it's like when you buy a car or bike for the first time and you get it from the showroom right so they give you with some things like the manuals and uh I don't know spare tire I'm not sure but so This is when the aircraft's manufacturer gives the aircraft to the owner or operator and what is included.

[00:01:50]So the standard mass of the airplane structure itself and it has things like your uh just write this down emergency oxygen equipment, pyrochnics like the flare guns and things like that. um unusable fuel other usable fuel uh fuels like lubricating oil uh supplementary electronic equipment and I don't know if I mentioned fire extinguishers I forgot but yeah that as well so these are the things which come under basic empty mass so these things plus the aircraft standard mass is your basic empty mass so to this basic empty mass if you add variable load you get something called as dry operating mass. Now what is variable load? Variable load includes three things. Okay, it includes includes crew and their baggage. So crew and their baggage both flight crew and cabin crew.

[00:02:45]It includes catering equipment and also the lavatory chemicals.

[00:02:52]So if you are asked a question as to what is in a variable load, these are the things which are in the variable load. So you get something called as the dry operating mass because this is ready to be operated but there is no fuel in it right. So to this dry operating mass you could add either of two things. Okay what is that? So if you add let's say traffic load or also called as payload just another name for the same thing. What is payload? If you and I are flying as passengers in this aircraft, then you and like our weight and whatever cargo we are um carrying. So all this commercial uh mass you could say. So if you add that to the dry operating mass, you get something called the zero fuel mass.

[00:03:38]Zero fuel mass because this aircraft has everything except for the usable fuel that you need to fly this plane to whatever place it is going. or to this dry operating mass you could add takeoff fuel. Now take off fuel just doesn't mean that you know you just hold the pump and just pump how muchever fuel you want. There are different types of fuel as well which we will see in some time.

[00:04:03]But the fuel that you need to take off if you add that but without the payload.

[00:04:08]Okay, that is called as operating mass.

[00:04:12]Okay, so DOM plus traffic load gives you zero fuel mass or DOM plus takeoff fuel gives you operating mass. So to this zero fuel mass if you just add takeoff fuel you get takeoff mass or to the operating mass if you add traffic load you get takeoff mass. Sometimes uh you will see something called a word called as useful load.

[00:04:38]Useful load is just takeoff fuel and traffic load put together in like one block. So DOM plus useful load gives you takeoff mass. Okay. Now to this takeoff mass if you subtract trip fuel. See in takeoff mass there are different types of fuel. One of it is trip fuel. What is trip fuel? Trip fuel is how much fuel?

[00:04:58]Let's say it's a flight from Hyderabad to Bangalore and the uh alternate is Chennai. Okay. So how much fuel is needed for this aircraft to take off in Hyderabad and land in Bangalore is your trip fuel. Okay. See whatever fuel you carry to be able to fly from or near the vicinity of Bangalore to go to Chennai as your alternate if you divert that comes under alternate fuel. Okay. But only trip fuel is what I'm talking about. If you subtract the trip fuel from what you take off with that means you're landing right when you land only you would have spent your trip fuel. So that gives you landing mass or for starting the engine and for you to taxi from your stand or apron to the runway it takes some fuel. Right? So if you add startup SU startup and taxi fuel to take off mass you get something called as a ramp mass. What is ramp mass? It is a mass of the aircraft on the ramp or the airplane. Okay. So when you are trying to solve theory or even numericals trying to figure out which mass has what and what it doesn't have, I recommend keeping this image in your mind because it makes a lot of things easy. Okay. Now what are some things? Uh actually laboratory chemicals plus portable water is also included in this also. Okay. So takeoff mass in takeoff mass we have um two things okay you could have maximum structural takeoff mass or performance limited takeoff mass. Now what is the difference between both of them maximum structural takeoff mass is mentioned in the um handbook of that aircraft like like whatever manual comes with it. It is saying that for example uh Piper PA28 this aircraft maximum structural mass is 3,500 lb. Okay. Or maybe like 1,500 kes that is maximum structural takeoff mass.

[00:07:09]Anything beyond this in any condition will lead to structural failure of the aircraft. Now there is something called performance limited takeoff mass where as you uh go to different airports with different environment in terms of pressure, temperature, humidity and things like that. The performance of your aircraft changes as the environmental parameters change. Right?

[00:07:34]So when that changes, sometimes performance can increase, sometimes performance can decrease, right?

[00:07:38]Depending on the environment. So sometimes you might need to load an aircraft with less weight for that environment in which you're flying in. Okay. So that is performance limited takeoff mass. Okay.

[00:07:54]So most of the times it's anyway. So you have something called as regulated takeoff mass. This is what you consider when you are doing your final calculations. Okay. So regulated takeoff mass which one do you? Let's say if this is 1500 kg and this is 1,400 kg. Which do you consider for your calculations?

[00:08:15]Always the one which is lesser because it is okay to under load a plane than overload a plane. Right? So when you talk about regulated takeoff mass, you take the lowest between maximum standard uh maximum structural takeoff mass and the performance limited takeoff mass.

[00:08:35]All right. And there are also two things. One is design limit load and other is design ultimate load. Design limit load is so there is this thing called load factor.

[00:08:46]So uh load factor is the wings of a plane um are the reason why a plane is staying in the air.

[00:08:56]Right? Now, the more you load, the more mass you load into an aircraft, the more the wings are working, right, to keep the plane up in the air. So, load factor is how much load the wings are experiencing because of what you've loaded, because of the mass that you put in. I feel like I'm using the word load a lot. So, um, how do you calculate it?

[00:09:22]Think of it as G force. It's not exactly geforce, but a load factor. It's like if an aircraft is straight and level, let's say it is uh its mass is 2,000 kg.

[00:09:33]Straight and level, it feels 2,000 kg.

[00:09:35]But when an aircraft is turning or banking by 60°, okay, this in this case, the aircraft feels the load of 4,000 kg because the load factor in a 60° turn for any aircraft is around 2°. That sorry 2G.

[00:09:52]What does that mean? or two. What does that mean? In a 60° turn, the wings are or the aircraft is feeling twice its weight even when the mass is actually not increasing. Right? So you have something called design limit load which is the load factor an aircraft should not cross in normal conditions. And then you have the design ultimate load which is the load factor aircraft shouldn't cross in even emergency conditions. So there's a difference right? This is normal. This is emergency. Normally dul is 1.5 * dl. Just a piece of information that you can remember. Now what happens to weight of an air? Uh different things when weight of the aircraft increases.

[00:10:34]For example, um weight increases, performance reduces. What happens to takeoff and landing distance? They increase because heavier it needs to have a greater takeoff run. And if um mass is great, momentum is great. It takes longer time to come to rest. uh v_sub_1 increases, vr rotation speed increases, the v_sub_2 takeoff safety um climb speed and stopping distance increases, climb gradient, rate of climb and ceiling height will reduce. So rate of climb, ceiling height, climb gradient being high means your aircraft is performing well, right? But when weight is increased, performance generally reduces. So they reduce rate of descent will increase because you're heavier, right? So you fall down faster, stalling speed increases. See um I'll come back to the stalling speed later when we talk about CG because I feel like um a lot of people out there don't know exactly what stalling means. Next mass uh max speed reduces. See maximum speed is um if your minimum let's say from zero you can operate until let's say 160 180 knots but if your weight is more then that window u shortens maybe it'll come to like 140 150 because again weight increases performance reduces so your margins are smaller um what else drag will increase of course because greater weight greater lift is required induced drag I hope you know what that is range and endurance will reduce because you're using more fuel fuel for that given mass. Maneuverability, what happens? It reduces because the aircraft being heavy is less responsive to controls. The CG uh uh okay uh wing root stress, the stress that the wing root feels also uh increases because uh again greater weight wings are what is holding the aircraft up in the air. Um undercarriage loads, undercarriage is nothing but your landing. So loads on your landing gear will obviously increase if your mass increases, right?

[00:12:29]Now um there are different types of fuel. I think it is mentioned here in Oxford as well. Let me just quickly go to that page. So there are different types of fuel. For example, trip fuel, right? I mentioned trip fuel. That is the fuel um from your departure to your destination. And then you have so yeah this is very very important this thing that you see here. Please make a note of this. So 2% for venting. What is venting? You know that fuel vaporizes very quickly, right? So, and it expands and contracts when temperature increases and decreases. So, 2% of that fuel tank is left empty. So that this expansion, contraction and the vaporization of fuel can happen without having any kind of vacuum because if vacuum forms then fuel doesn't go into the um engine for combustion. You have the startup and taxi fuel. You have the trip fuel. See, startup and taxi fuel varies based on how far you have to taxi to go to the runway, right? U trip fuel depends on your departure and destination.

[00:13:32]Contingency fuel always keep this as 5%.

[00:13:34]So if your trip fuel is let's say 1,000 kg, your contingency fuel is 5%, 5% of that is 50 kg. Okay? So keep that in mind. Alternate it depends again how far is your alternate from your destination.

[00:13:47]final reserve uh for any unpredicted emergency and captain discretion it is the captain who sometimes might want to take more fuel. So the total this that is venting startup taxi all this is called as ramp fuel or block fuel. Block fuel is how much is the total fuel that you're putting in the aircraft. This is takeoff fuel. Okay. Because when you take off you would have spent startup and taxi fuel, right? So I hope you keep that in mind. Generally final reserve um I don't know where I got this information but it's in my notes. This is taken to be 45 minutes if I'm not wrong. And alternate fuel in the chapter of in Oxford flight planning and monitoring the textbook you have um a again see you have to do some amount of hard work I feel. So open that and there is one page in one of those chapters where there's a table of how much alternate fuel is needed to be taken for piston engine and turbine engine right uh and that also depends on where the alternator is and things like that so I mean some kind of effort you guys also have to put right now let's come to CG what is CG CG stands for center of gravity right the example example that I give is um so see the example that I give in my class are the examples I think of when I read it or study. Now, I remember this one scene from I think Endgame, Avengers Endgame where um Thanos talks to Gamora and there is this I don't know dagger or a knife that he holds on his index finger and he tries to balance it, right? Or why I'm not giving the spinning basketball is because I'm I want the object to be stationary. So this one scene I know maybe you can Google it or YouTube it but um if you watched it you know what I'm talking about. So see so what is Thanos trying to do in this case is taking this one thing I cannot look like find anything around me but let's say I take this pencil which I don't think is going to stand. So what I'm trying to do oh it is I'm trying to hold this pencil at its CG. I'm trying to put my finger under the place where all of the mass is being concentrated. Okay, I'm holding this pen by it CG. So what is CG? CG center of gravity. It is a place where the whole mass of the body is acting. So if you can hold, if you suspend that mass at that point, the whole thing will be balanced. Okay. So if I'm holding let's say I add on like some kind of magnet this side then it'll try to bend this way. So what will I do? I'll just go slightly this side to kind of balance out the mass left and right. That is center of gravity. And such thing exists for aircrafts as well. Okay. So in an aircraft you have a point which is the CG.

[00:17:02]Now the CG is it always constant? No.

[00:17:05]The CG moves. Now how does it move? It moves based on the weight or the load that you put in the plane. You load more weight in the front. The CG moves front.

[00:17:17]You load more weight in the back. CG moves back. Exactly like the seessaw example. If it popped into your head.

[00:17:23]Okay. Now if you are like when you're flying the plane and you would like to know about the CG like you cannot look at it you cannot physically see the CG right you have to calculate it and when you're calculating you should be able to figure out its position right so how will you tell like will you tell the CG is behind the pilot seat or will you tell it's between the cockpit and control that's very weak right so there's generally a datim that DATM datm is like a reference this DATM can be anywhere it depends on the manufacturer but let's say this is like a propeller aircraft and the datim is here okay this red line is a datim CG is always measured as the distance between so CG and DATM the distance between CG and DATM is called as arm okay so this is CG and sometimes like I said it moves forward backward but does that mean you can load the aircraft any way you want like you load your car, bike, train, bus. No, there are certain limits that the manufacturer sets saying this is the forward limit of CG. This is the aft. After means backward, rare. The manufacturer will tell the forward limit and after limit of CG are 40 and 55 in from the DATM respectively. What does that mean? You loading your weight into this aircraft should not make the CG move out of these limits. It should stay within the limits. Okay. Anytime you have the CG very like out of the forward limit or after limit some things happen which we'll talk about. But what is a CG? It is a place where uh total weight of the aircraft is set to act. And this so when you are looking I'm sure you every time you look a plane you open flight at 24 right the path that you see is the path that the CG makes also it is a point where aircraft manure. So all the like banking and climbing, pitching up, pitching down, loing, it all happens at CG. Like CG is the point where all of it pivots. I'm hoping you know pivot as well through friends. I'm kind of a CG this geek. Um so it is also the point where all the three axis of an aircraft pass through. Right? So these are um some things that you have to remember about CG. Now what happens when CG is to forward or to backward? CG being too forward means imagine I just told you that CG is the point where all the flight acts like all the flight movement happens pitching yawing and rolling or banking. So let's say if the CG is forward what happens is the aircraft will want to kind of pitch downward because CG is here right? CG is forward. Aircraft will want to pitch downward because CG weight acts downward. So aircraft will want to pitch down. Because of that aircraft is very stable. Okay. But the negative thing here is it is not very maneuverable because it's very stable like it's completely forward. Now um also there are some other things for example stick forces. Stick forces means how much how much amount of controls you have to input to control or change the orientation of this plane. If it is more stable and less maneuverable, you have to put more stick forces to change it.

[00:20:53]So stick force is very high. Now drag is high. Why is drag high? Because the aircraft is like wanting to pitch down constantly. We want lift to counteract it, right? We want lift to counteract it. when we want lift to counteract it, we are trying to pitch up more and more.

[00:21:10]And I I I don't know if you know the concept of induced drag. Induced drag is the drag which causes because of lift, which is kind of ironic because the whole purpose of lift is you thinking that you know we're going to fly and we're not going to have enough drag.

[00:21:26]But think of it this way. Okay, you have some amount of lift. You have an aircraft which whose path is like this. But now you want more lift, right?

[00:21:36]So you increase the angle of attack of aircraft like this. Now let's say this is the lift that is being generated. Any vector that is not exactly x or y axis will have resultants. Correct? You have a vertical component of lift and you have a horizontal component of lift.

[00:21:58]Correct? And this is the path of the aircraft. As you can see the horizontal component of lift is acting backwards.

[00:22:04]Which force acts backwards? It is drag.

[00:22:07]So that's a very very um simplified example of induced drag because the whole concept here is mass imbalance and not uh technical general.

[00:22:17]So um yeah so drag increases stalling speed increases. Now this I will spend some time and explain because I really really hope you know what stall is. If you do, great. Now, what is stall? I want you guys to pause it, think uh or tell yourself the definition and let's see if it is right. Okay, if you said stall, uh stalling is when the aircraft does not produce lift and it falls out of the sky, you partially correct, partially wrong. Okay, stall happens when the aircraft does not produce.

[00:22:56]This is the key word enough lift. Okay, that is the key word here because for an aircraft to fly there are four forces. Lift, weight, thrust, drag. Right? Now when lift and weight are equal, it's straight in level. When weight is more, it falls down or it sinks. And when lift is more, it climbs. Right? So a stall happens when an aircraft's lift which is being produced is not enough to stay in a straight and level flight.

[00:23:31]Right? So what happens? Lift is not enough and the aircraft sinks. Right?

[00:23:35]Now when does this happen? Stalling is most of the time almost all of the time related to something called as your angle of attack. Now what is your angle of attack in an aircraft? You have a wing shape that looks something like this. Okay, this shape is called as I hope you know it aeropoil where this part is called as the leading edge and this part is called as the trailing edge or the ed. edge there. If you join a like the furthermost point of the leading edge to the backward most point with a straight line imaginary obviously you can't really open the wing and see it. This is called as a chord line or same forward or backward most point.

[00:24:22]What you can do is you can join it with a line which is cutting the wing into equal upper and lower parts. Okay, upper and lower, not a straight line, it's a curved line. So this is called as a camber line. Okay, now when you're flying, there is something called as a relative wind. Relative wind, see when you're running, I don't know if you jog um but when you're jogging or when you're walking in actually jogging, you face wind, right? Wind hits you from the front and wind always hits you based on where you're running. If you're running like this, wind hits you. If you're running like this, wind will hit you from here. Relative wind is something similar. So relative wind is always coming towards you in the opposite direction of your flight path.

[00:25:09]Okay? Now the angle that forms here.

[00:25:14]The angle of attack is the angle which is formed between the chord line and the relative wind. Now relative wind is always coming like this. But the aircraft can sometimes either pitch up or pitch down. So what is happening?

[00:25:32]Aircraft pitching up means your angle of attack is increasing. Pitching down means angle of attack is reducing.

[00:25:36]Right? Now I'm sure you know for an aircraft to take off it has to pitch up.

[00:25:42]Right? Correct. But does that mean it can pitch up how muchever it want and just keep attaining unlimited amount of lift? No. It can if I draw a table, okay, where this is the angle of attack on the y-axis and this is the lift produced on the x-axis or I think it's the opposite.

[00:26:09]Yeah, the lift is here. Angle of attack is on x axis. This is 2 8 10 16 so on and so forth. And this is lift. From zero onwards you have like it actually goes like this. But okay. So as you keep increasing your angle of attack what happens to lift? It increases. Keeps increasing increasing increasing. But there is one angle of attack which is called as the critical angle of attack where the lift after this you will not have any lift. That is why it's called as critical angle of attack. Beyond this angle of attack even if you increase you are not going to have lift. So lift now it drops. This is generally it happens at 16° generally most of the times a critical angle of attack is 16. Now why does this happen? Very simply why air aircraft uh sorry the aeraf foil air goes up air goes down high pressure low pressure pushes upward lift. Basic right? But what if your angle of attack is so high that all the air is just going below the wing. not enough pressure differential right so because of that you will not have lift beyond critical angle of attack now how does weight even affect our soling speed because until now whatever explanation we've seen we've only spoken about relative wind we've s we've seen about cord line and critical angle of attack and air flow mass is not something that we've seen until now so how does it even affect let's take an example okay your aircraft my aircraft craft.

[00:27:48]Let me try and draw a good aircraft. Uh, I think this is good enough. This is me.

[00:27:59]And this is you. Okay. What I'm doing is I'm actually um flying with a bunch of friends. Okay.

[00:28:10]I I have um two of my very close friends. We are flying to get some breakfast in Okchobee airport or maybe Flaggler. So, but you are flying solo.

[00:28:24]It's your uh solo cross country flight.

[00:28:26]All right. Now, in this case, whose mass is greater? Yours or mine? It's the same kind of aircraft. Let's say it's a Piper PA28. In this case, obviously I am heavier. Correct? If I'm heavier than you, whose aircraft will need more lift?

[00:28:43]Obviously m now the amount of throttle that we both can use is same while we are climbing yes but what I can change is angle of attack if you and I we want same amount of lift you are generating let's say 10 units of lift and with at let's say um 4° angle of attack okay let's say where straight and level flight uh this is called as optimum angle of attack 4° this is generally the angle of attack aircrafts make uh um when they are cruising. So you're at 4° generating 10 amounts of 10 units of lift. But at 4° the lift I am generating is only six units because my mass is very high. I'm being pulled down. So what will happen now? I will need to be flying at a greater angle of attack to get the same 10 amount of 10 units of lift. Right? So I want yours and my lift units to be equal. I don't care even if I'm at a slightly greater angle of attack of 8°. Okay. So here this is relative air flow. This is our angle of attack four. Okay. Now we are flying same kind of aircraft. So our critical angle of attack for both aircrafts are same. Correct? Which is let me use a different color. 16° 16° right? 16° is the critical angle of attack. We are again flying at the same speed. I am flying at a speed of 100 knots. You're also flying a speed of 100 knots. Okay. Now what's happening is you and I are racing to see who will stall first. Or I know please don't do this.

[00:30:23]But let's say um for experimental purposes we are doing this. What's going to happen? I am at 8°. I'm pitching up.

[00:30:32]Generally when I pitch up air speed reduces. Again, this is a concept in tech gen where we study about lift equation. But my speed will reduce as I'm pitching up. Uh so what's going to happen? Okay, a question for you. How many degrees should I pitch up to reach my critical angle of attack here?

[00:30:53]Eight. And how many degrees should you cross to reach critical angle of attack?

[00:30:58]12. Right? So for me crossing 8° takes 10 seconds and in 10 seconds I'm at a speed of 70 knots. I'm stalling at 70.

[00:31:09]But you are crossing 12°. This takes you 15 seconds.

[00:31:16]15 seconds means in 10 seconds you got to 70 but you have five more seconds and you're stalling at 60 knots.

[00:31:25]This is why stalling speeds are different. Okay, it depends on our weight. So I am stalling at 70 knots and you are stalling at 60 knots. This is what they mean by stalling speed increasing. Now um we are rotation speed obviously increases because you need greater lift to take off because your mass is high. Uh range will reduce if you have forward CG. Again coming back to the explanation of forward CG. Uh fuel consumption will increase because greater weight you're trying to keep a greater lift. So you are trying to put more um throttle or power. So that is um forward limit drag increases fuel consumption increases range and endurance reduce longitudinal stability increase. Longitudinal stability is so this is the longitudinal axis of the plane. And what did I say? Aircraft will want to pitch down. If it's pitching down it is stable. That is the longitudinal stability which is good.

[00:32:15]Also um there is something called as the tail down force. I don't know if it's in my notes. So tail down force also increases which is the force which acts here. This force tries to equalize with this pitch down force on second.

[00:32:30]Yeah. So this pitch down force is here.

[00:32:32]Tail down force is here. It tries to equalize with whatever um force is being acted on the front of the plane. Uh what else? Um spin recovery is easy. Um okay so after limit what happens exactly opposite after limit means have you ever seen um fighter jets? Of course you did.

[00:32:54]They're always like this right because their CG is after they are always in like a pitch up attitude because they want less stability. See stability means when you change the orientation of an aircraft it I'm sorry guys. Yeah it comes back to its original position.

[00:33:09]That is stability. We want that as passengers of a civil and commercial jets. want that but military doesn't want that. They want to be able to maneuver the aircraft in such a way that it's very very dynamic. It's very like like Mercury like just keeps going running or maneuvering left and right and um you want the controls to be very reactive if you're flying a fighter jet.

[00:33:34]So that's why they have off limit. So think of off limit as pitch up. pitch up. Um what happens to stability reduces, maneuverability increases, less stick force, you get greater output, uh stalling speed reduces. Um also BR rotation speed reduces, range reduces, fuel consumption reduces, everything pretty good, but again not too. Okay, so that is our um theory. I think this should be good enough. So I want to make two other parts. So one part the next part of the video will be um changing CG. So when you move weight from one part of the plane to the other part what happens and the third part will be what happens when you um sorry I lost my track of that uh third uh so third part will be doing the payload and traffic load questions.

[00:34:34]Okay. So keep watching.