Understanding Mass and Balance in Aviation

What forces amped on us during our flight? And what does a child's play part toy have to do with flying an aircraft? Let's find out! Hi I'm Grant and welcome to the fourth class in the Mass and Balance series. Today's class is a big one covering cargo loading and the importance of where we load cargo and passengers. We will see how to calculate the various forces on board. that are caused by the various masses on board. And by the end of the class you should be able to answer questions related to loading and moments that appear in the mass and balance exams. Cargo loading limitations come in three main forms. We have our maximum load limitations, we have our maximum linear load limitations, and we have our maximum area. Load limitations. Max load is what you would expect. It is a value of weight or mass that can be carried in the cargo hold. Very simple. Max linear load is a restriction on the amount of load that can be carried based on how much load can be handled by every unit length of the cargo floor. Think about it as having a plank of wood between two chairs. It will bend and eventually break if we place too much weight on it. It basically comes down to the structure of the frame supporting the floor panels. It's expressed as a mass over a distance so you get something along the lines of kilograms per meter or pounds per foot. Max area load is a restriction on the amount of mass that can be carried per unit area of floor in the hold. It's very similar to the linear load limit but instead of being one-dimensional it's two-dimensional and it's expressed as a weight or mass over an area so we're gonna end up with someone like kilograms per meter squared or pounds per square foot. Whichever is the most restrictive between max load, max linear load and max area load will be our limitation for that piece of cargo and if we can carry it or not. For example, a cargo hold has an area load limitation of 100 kilograms per meter squared. Our maximum load limitation is 250 kgs. If we have a box that weighs 50 kilograms and its dimensions are 1 foot by 2 foot by 3 foot, Can we carry load? Which limit is most restrictive and can we carry it? So first of all, we have our maximum load of 100kg, excuse me. First of all, we have our maximum load of 250kg and our box weighs 50kg. So we know the max load is not a limit for us. Next up we have to calculate the area of the box and which orientation we have to arrange it. So we've got a box that looks something like one foot by two foot by three foot. It looks something like that and we have to figure out which side will give us the lowest area load limitation. So let's calculate the areas. Area one. is going to be 1 by 2, area 2 will do 1 by 3 and area 3 will do 2 by 3. Our area load limit is in meters squared, this is in feet so we've got to convert. One foot I know from my unit conversions is 0.328 and two feet is going to be 0.656. I'll give this area one which is going to be 0.215 meters squared. Area two 0.328 times 0.984 that's going to give us 0.323 meters squared and lastly 0.984 times 0.656 and that's going to give us an area of 0.645 meters squared So we've got our areas, we've got our mass and we've got our mass limitation. We've got all that we need to do this calculation. So we take our 50 kilogram weight, divide it by our area and see if it exceeds 100 kilograms per meter squared. So for area one, 50 kilograms divided by 0.215. So we divide by 0.215. Area 2 we have 50 divided by 0.323 and area 3 we have 50 divided by 0.645. So for the first one if you do that calculation you should come up with 232.56 kg per meter squared. Second one we've got 154.78 kilograms per meter squared and lastly we've got 77.52 kilograms per meter squared. Area 1 exceeds our limit of 100 so we can't do that. Area 2 also exceeds that limit. Area 3 is okay. So we can carry this 50 kg box but only if we place it on its largest area side. If we place it on the 2 by 3 meter side it will be below that area limit. So we've just learned about how we load things, now we're going to talk about where we load them and why it's important. Aircraft forces operate around a focal point known as the centre of gravity and this is where our three axes of rotation meet. Our centre of gravity would be located there in the middle. Our pitch Roll and yaw were all centralised around this point on the aircraft. If you think about it on a single axis it would be equivalent to a play park seesaw or a teeter-totter as they call them in the states. The aircraft is designed to use a range of different centre of gravity positions and if the centre of gravity is outside of those positions the aircraft may become uncontrollable. The C of G, or the centre of gravity, is moved based on where things are loaded. So if there's more things in the front, the centre of gravity will be further forward, more things in the back, it will be further back. An example of bad center of gravity movement that fell outside of the allowable range is a flight called National Airlines 102 which I'll link down below. What happened in this flight is a bit of cargo came loose and moved aft during takeoff and it moved the centre of gravity so far aft that the centre of gravity was then outside the limits. This became a problem when it caused a pitch moment that was unrecoverable. It caused a nose up pitch moment that led to the stalling of the aircraft and led to a disaster. Now a nose up pitch moment that I just talked about. about would be a nose up movement around this center of gravity. A moment is something that causes rotation and it is expressed as a force times by the distance from the fulcrum or in the case of aviation it would be our center of gravity. There are a few methods for measuring the distance on aircraft, such as from a datum point or referring to certain parts of the aircraft as stations, but all calculations are the same. It's simply a force times the distance. We just have to find the distance in different ways. If we have two people exactly the same weight on either side of a seesaw it will not move unless they push with additional force. This is because by pushing they are making the moments no longer equal and therefore it causes a rotation. For example Mike weighs 70 kilograms and is sat two meters away from the center of the seesaw. Jenny is on the other side of the seesaw and weighs 50 kilograms. How far back will she have to sit to make the seesaw balanced? Now In all maths and balance questions to do with moments, you should draw the picture. Draw the effing picture. I always say it, said it during my exams that I sat myself, draw the effing picture. Never try and do these things in your head. Doesn't have to be exact, just rough. So we're thinking about a seesaw, here we go. Mike weighing 70 kilograms sat two meters away and we know Jenny is weighing 50 kilograms sat somewhere along here. Okay so we said that to calculate moments we have to do force times distance. We have a mass here which is not a force but because we're converting both to the same thing It isn't really necessary to bother with that conversion. We can just use force times mass because we're going to end up with the same proportions and same scaling of the values. So if we take our clockwise moments, so clockwise, they're considered positive. and we'll do our force times our distance but we're not going to bother with the conversion because it's unnecessary in this case. We'll do 70 times 2 and come up with a value of 140. That would be our moment for this direction. We know that if we want the anti-clockwise negative moments we have to have 50 kilograms times some distance. For this to be balanced the moments have to be equal so therefore positive moments equal the negative moments. So we have 140 equal to 50x. We solve for x, we'll end up with 2.8. So for this seesaw to be balanced, Jenny must sit 2.8 meters away all the way out here. If we apply this principle of moments to an aircraft, we can see this diagram. So thrust acts forward from the engines. and the weight acts downwards from our centre of gravity. Lift and drag both act through something called the centre of pressure. This is a point on the wing where the lift caused by the wing is averaged out as the amount of lift over the wing is not even over the whole surface. This is covered a lot more in Principles of Flight. The drag is also a byproduct of lift, something called induced drag, so this is thought to act through the center of pressure as well. You may have noticed that the center of gravity and the center of pressure are not in the same position. This is due to the aircraft design and therefore the design of the ...wing being fixed, so the centre of pressure remains relatively fixed, but the mass of an aircraft changes. So the centre of gravity changes position either forward or aft. The difference in position between the centre of pressure and centre of gravity causes rotation. Remember, the centre of gravity is where the aircraft rotates around, and if the centre of pressure is placed somewhere other than directly on top of the centre of gravity, it will cause a moment, a rotational moment. The moments will therefore need to be balanced out if the aircraft is not to rotate. This is best shown through an example. An aircraft of mass 10,000 kgs lift 98,100 newtons, thrust 100,000 kilonewtons and drag 50,000 newtons. Center pressure 2 meter math. Okay let's stop. Draw the f-ing picture. So here we go. I've drawn the picture out it makes it so much easier to understand. We have aircraft mass 10,000 kilograms. So we've got our centre of gravity acting straight down through that as our aircraft mass of 10,000 kg. We've converted it into weight for this case so we've timed it by 9.81, 98,100 newtons. Our lift is acting through our centre of pressure which is two meters aft of the C of G. It is a value of 98,100 newtons up there. Our thrust is acting through our engines which are one meter below the C of G and the value of a hundred thousand or a hundred kilonewtons. And our drag also acts through the center of pressure and it has a value of 50 kilonewtons. 50,000 units. So much easier to understand, draw the effing picture. So let's calculate the moments. Let's first look at our positive moments, our clockwise moments. So Our weight acts straight down through the center of gravity, there is no rotation caused by that. The only thing causing rotation clockwise is our thrust due to our engines being below the center of gravity. This is going to cause clockwise positive rotation. So again we can just take our force times our distance, we've got 100,000 multiplied by one and we end up with a value of 100,000 and this is going to be Newton meters. Next up we'll calculate our negative anti-clockwise moments. Drag is acting straight back through the centre of gravity, not causing any rotation. Our lift acting through the centre of pressure, two metres away, that is going to cause a rotation around. So we've got force times distance 98,100 times two. which gives us a value of 196,200 Newton meters. So we can see these are not balanced. We have a larger negative anti-clockwise moment than we do positive clockwise moment. So in this case our aircraft will be pitching down, we'll be pitching nose down. How do we solve this problem? Either we just have to reduce the lift or increase the thrust and that will balance out this motion. But if we are flying at this weight we need this much lift and if we're flying at this speed we need this much thrust. So how do we solve this problem? We need a counter moment. We get this counter moment from the tail of the aircraft out here. As we can see, in this case we need a counter moment, counter positive moment. of 96,200 newton meters because that's the difference between these two. How do we make it a positive moment from the tail? It must have to come down so we need this value here to be 96,200 newton meters and our tail is located seven meters back from our Centre of gravity. So this is our moment, this is our distance, what force is the tail having to apply? We know moments are equal to force times distance. So we have our moment of 96,200 equal to our force, we don't know, times our distance 7. So we take this 96,200 divided by 7 to find out what force we need from our tail. And in this case it would be 13,742.86 N worth of force from the tail. The distance of this counter moment tool known as the tail is fixed by nature of its design and therefore it can only produce a certain amount of downforce. This is why the center of gravity position being in a fixed range becomes so important. Let's take the example of the National Airlines flight from before. The center of gravity moved afterwards because the weight distribution changed, therefore making the center of gravity move backwards and the moment arm became shorter for the tail. So short in fact that the force produced by the tail at maximum force was not great enough to overcome that moment caused by the loose cargo and the changing centre of gravity position. This caused the aircraft to stall, which means losing sufficient airflow over the wings to cause lift. And by the time the pilots recovered that stall, it was too late and they were crashed into the ground. Other implications of a moving center of gravity follow the same principle of the balance arm changing length. For example, a forward CFG means that the balance arm is going to be longer, meaning tail is... way more effective at very low deflections. Therefore any change, any ripple in the air for instance, the tail is going to recover it really fast because it has much more of a moment due to the longer balance arm. Or in a more simple explanation, the longitudinal stability of the aircraft has increased. If the centre of gravity is too far forward however, it can lead to the tail and elevator needing to be displaced to the opposite direction throughout the whole flight to counteract the rotation that is caused by this forward CFG. The displacement of the tail and elevator can cause extra drag leading to an increase in fuel burn, lower speeds and a reduced range. To summarise, we have our cargo loading limitations which are max load, max linear and max area. Max load is the max load. Max linear, max per unit distance. Max area, max per unit area. Centre of gravity position. is in between a fixed range. If it moves too far forward we can get too far of a nose down motion and if it's too far backwards we can see that National Airlines flight disaster unfold. Moments. Positive is clockwise, negative is anti-clockwise and a moment is expressed as a force times a distance. For something to be balanced, the moments have to be balanced. If they are unbalanced, it will cause a rotation in that direction. The centre of gravity and centre of pressure are not located in the same location. So therefore, in normal aircraft there is an implicit rotation, an implicit moment that we counteract with the tail.

Today's class is a big one covering cargo loading and the importance of where we load cargo and passengers. We will see how to calculate the various forces on board. that are caused by the various masses on board.

And by the end of the class you should be able to answer questions related to loading and moments that appear in the mass and balance exams. Cargo loading limitations come in three main forms. We have our maximum load limitations, we have our maximum linear load limitations, and we have our maximum area.

Load limitations. Max load is what you would expect. It is a value of weight or mass that can be carried in the cargo hold.

Very simple. Max linear load is a restriction on the amount of load that can be carried based on how much load can be handled by every unit length of the cargo floor. Think about it as having a plank of wood between two chairs.

It will bend and eventually break if we place too much weight on it. It basically comes down to the structure of the frame supporting the floor panels. It's expressed as a mass over a distance so you get something along the lines of kilograms per meter or pounds per foot.

Max area load is a restriction on the amount of mass that can be carried per unit area of floor in the hold. It's very similar to the linear load limit but instead of being one-dimensional it's two-dimensional and it's expressed as a weight or mass over an area so we're gonna end up with someone like kilograms per meter squared or pounds per square foot. Whichever is the most restrictive between max load, max linear load and max area load will be our limitation for that piece of cargo and if we can carry it or not.

For example, a cargo hold has an area load limitation of 100 kilograms per meter squared. Our maximum load limitation is 250 kgs. If we have a box that weighs 50 kilograms and its dimensions are 1 foot by 2 foot by 3 foot, Can we carry load?

Which limit is most restrictive and can we carry it? So first of all, we have our maximum load of 100kg, excuse me. First of all, we have our maximum load of 250kg and our box weighs 50kg. So we know the max load is not a limit for us. Next up we have to calculate the area of the box and which orientation we have to arrange it.

So we've got a box that looks something like one foot by two foot by three foot. It looks something like that and we have to figure out which side will give us the lowest area load limitation. So let's calculate the areas. Area one.

is going to be 1 by 2, area 2 will do 1 by 3 and area 3 will do 2 by 3. Our area load limit is in meters squared, this is in feet so we've got to convert. One foot I know from my unit conversions is 0.328 and two feet is going to be 0.656. I'll give this area one which is going to be 0.215 meters squared. Area two 0.328 times 0.984 that's going to give us 0.323 meters squared and lastly 0.984 times 0.656 and that's going to give us an area of 0.645 meters squared So we've got our areas, we've got our mass and we've got our mass limitation.

We've got all that we need to do this calculation. So we take our 50 kilogram weight, divide it by our area and see if it exceeds 100 kilograms per meter squared. So for area one, 50 kilograms divided by 0.215. So we divide by 0.215.

Area 2 we have 50 divided by 0.323 and area 3 we have 50 divided by 0.645. So for the first one if you do that calculation you should come up with 232.56 kg per meter squared. Second one we've got 154.78 kilograms per meter squared and lastly we've got 77.52 kilograms per meter squared. Area 1 exceeds our limit of 100 so we can't do that.

Area 2 also exceeds that limit. Area 3 is okay. So we can carry this 50 kg box but only if we place it on its largest area side.

If we place it on the 2 by 3 meter side it will be below that area limit. So we've just learned about how we load things, now we're going to talk about where we load them and why it's important. Aircraft forces operate around a focal point known as the centre of gravity and this is where our three axes of rotation meet. Our centre of gravity would be located there in the middle. Our pitch Roll and yaw were all centralised around this point on the aircraft.

If you think about it on a single axis it would be equivalent to a play park seesaw or a teeter-totter as they call them in the states. The aircraft is designed to use a range of different centre of gravity positions and if the centre of gravity is outside of those positions the aircraft may become uncontrollable. The C of G, or the centre of gravity, is moved based on where things are loaded.

So if there's more things in the front, the centre of gravity will be further forward, more things in the back, it will be further back. An example of bad center of gravity movement that fell outside of the allowable range is a flight called National Airlines 102 which I'll link down below. What happened in this flight is a bit of cargo came loose and moved aft during takeoff and it moved the centre of gravity so far aft that the centre of gravity was then outside the limits. This became a problem when it caused a pitch moment that was unrecoverable.

It caused a nose up pitch moment that led to the stalling of the aircraft and led to a disaster. Now a nose up pitch moment that I just talked about. about would be a nose up movement around this center of gravity.

A moment is something that causes rotation and it is expressed as a force times by the distance from the fulcrum or in the case of aviation it would be our center of gravity. There are a few methods for measuring the distance on aircraft, such as from a datum point or referring to certain parts of the aircraft as stations, but all calculations are the same. It's simply a force times the distance.

We just have to find the distance in different ways. If we have two people exactly the same weight on either side of a seesaw it will not move unless they push with additional force. This is because by pushing they are making the moments no longer equal and therefore it causes a rotation.

For example Mike weighs 70 kilograms and is sat two meters away from the center of the seesaw. Jenny is on the other side of the seesaw and weighs 50 kilograms. How far back will she have to sit to make the seesaw balanced? Now In all maths and balance questions to do with moments, you should draw the picture.

Draw the effing picture. I always say it, said it during my exams that I sat myself, draw the effing picture. Never try and do these things in your head. Doesn't have to be exact, just rough.

So we're thinking about a seesaw, here we go. Mike weighing 70 kilograms sat two meters away and we know Jenny is weighing 50 kilograms sat somewhere along here. Okay so we said that to calculate moments we have to do force times distance.

We have a mass here which is not a force but because we're converting both to the same thing It isn't really necessary to bother with that conversion. We can just use force times mass because we're going to end up with the same proportions and same scaling of the values. So if we take our clockwise moments, so clockwise, they're considered positive. and we'll do our force times our distance but we're not going to bother with the conversion because it's unnecessary in this case.

We'll do 70 times 2 and come up with a value of 140. That would be our moment for this direction. We know that if we want the anti-clockwise negative moments we have to have 50 kilograms times some distance. For this to be balanced the moments have to be equal so therefore positive moments equal the negative moments.

So we have 140 equal to 50x. We solve for x, we'll end up with 2.8. So for this seesaw to be balanced, Jenny must sit 2.8 meters away all the way out here. If we apply this principle of moments to an aircraft, we can see this diagram. So thrust acts forward from the engines.

and the weight acts downwards from our centre of gravity. Lift and drag both act through something called the centre of pressure. This is a point on the wing where the lift caused by the wing is averaged out as the amount of lift over the wing is not even over the whole surface. This is covered a lot more in Principles of Flight. The drag is also a byproduct of lift, something called induced drag, so this is thought to act through the center of pressure as well.

You may have noticed that the center of gravity and the center of pressure are not in the same position. This is due to the aircraft design and therefore the design of the ...wing being fixed, so the centre of pressure remains relatively fixed, but the mass of an aircraft changes. So the centre of gravity changes position either forward or aft.

The difference in position between the centre of pressure and centre of gravity causes rotation. Remember, the centre of gravity is where the aircraft rotates around, and if the centre of pressure is placed somewhere other than directly on top of the centre of gravity, it will cause a moment, a rotational moment. The moments will therefore need to be balanced out if the aircraft is not to rotate. This is best shown through an example.

An aircraft of mass 10,000 kgs lift 98,100 newtons, thrust 100,000 kilonewtons and drag 50,000 newtons. Center pressure 2 meter math. Okay let's stop. Draw the f-ing picture.

So here we go. I've drawn the picture out it makes it so much easier to understand. We have aircraft mass 10,000 kilograms.

So we've got our centre of gravity acting straight down through that as our aircraft mass of 10,000 kg. We've converted it into weight for this case so we've timed it by 9.81, 98,100 newtons. Our lift is acting through our centre of pressure which is two meters aft of the C of G.

It is a value of 98,100 newtons up there. Our thrust is acting through our engines which are one meter below the C of G and the value of a hundred thousand or a hundred kilonewtons. And our drag also acts through the center of pressure and it has a value of 50 kilonewtons. 50,000 units. So much easier to understand, draw the effing picture.

So let's calculate the moments. Let's first look at our positive moments, our clockwise moments. So Our weight acts straight down through the center of gravity, there is no rotation caused by that. The only thing causing rotation clockwise is our thrust due to our engines being below the center of gravity.

This is going to cause clockwise positive rotation. So again we can just take our force times our distance, we've got 100,000 multiplied by one and we end up with a value of 100,000 and this is going to be Newton meters. Next up we'll calculate our negative anti-clockwise moments. Drag is acting straight back through the centre of gravity, not causing any rotation.

Our lift acting through the centre of pressure, two metres away, that is going to cause a rotation around. So we've got force times distance 98,100 times two. which gives us a value of 196,200 Newton meters.

So we can see these are not balanced. We have a larger negative anti-clockwise moment than we do positive clockwise moment. So in this case our aircraft will be pitching down, we'll be pitching nose down.

How do we solve this problem? Either we just have to reduce the lift or increase the thrust and that will balance out this motion. But if we are flying at this weight we need this much lift and if we're flying at this speed we need this much thrust.

So how do we solve this problem? We need a counter moment. We get this counter moment from the tail of the aircraft out here. As we can see, in this case we need a counter moment, counter positive moment.

of 96,200 newton meters because that's the difference between these two. How do we make it a positive moment from the tail? It must have to come down so we need this value here to be 96,200 newton meters and our tail is located seven meters back from our Centre of gravity. So this is our moment, this is our distance, what force is the tail having to apply?

We know moments are equal to force times distance. So we have our moment of 96,200 equal to our force, we don't know, times our distance 7. So we take this 96,200 divided by 7 to find out what force we need from our tail. And in this case it would be 13,742.86 N worth of force from the tail.

The distance of this counter moment tool known as the tail is fixed by nature of its design and therefore it can only produce a certain amount of downforce. This is why the center of gravity position being in a fixed range becomes so important. Let's take the example of the National Airlines flight from before. The center of gravity moved afterwards because the weight distribution changed, therefore making the center of gravity move backwards and the moment arm became shorter for the tail. So short in fact that the force produced by the tail at maximum force was not great enough to overcome that moment caused by the loose cargo and the changing centre of gravity position.

This caused the aircraft to stall, which means losing sufficient airflow over the wings to cause lift. And by the time the pilots recovered that stall, it was too late and they were crashed into the ground. Other implications of a moving center of gravity follow the same principle of the balance arm changing length.

For example, a forward CFG means that the balance arm is going to be longer, meaning tail is... way more effective at very low deflections. Therefore any change, any ripple in the air for instance, the tail is going to recover it really fast because it has much more of a moment due to the longer balance arm. Or in a more simple explanation, the longitudinal stability of the aircraft has increased.

If the centre of gravity is too far forward however, it can lead to the tail and elevator needing to be displaced to the opposite direction throughout the whole flight to counteract the rotation that is caused by this forward CFG. The displacement of the tail and elevator can cause extra drag leading to an increase in fuel burn, lower speeds and a reduced range. To summarise, we have our cargo loading limitations which are max load, max linear and max area. Max load is the max load. Max linear, max per unit distance.

Max area, max per unit area. Centre of gravity position. is in between a fixed range.

If it moves too far forward we can get too far of a nose down motion and if it's too far backwards we can see that National Airlines flight disaster unfold. Moments. Positive is clockwise, negative is anti-clockwise and a moment is expressed as a force times a distance. For something to be balanced, the moments have to be balanced.

If they are unbalanced, it will cause a rotation in that direction. The centre of gravity and centre of pressure are not located in the same location. So therefore, in normal aircraft there is an implicit rotation, an implicit moment that we counteract with the tail.

Transcript for:Understanding Mass and Balance in Aviation

Transcript for:
Understanding Mass and Balance in Aviation