Understanding Forces in Flight Dynamics

In the previous class we established some basic principles for level flight. We need thrust equal to drag, we need lift equal to weight. But what happens when we move away from this level flight and start climbing, descending and turning? Well, let's find out. Hi, I'm Grant and welcome to the third class in the performance series. Today we're going to be taking a look at the physics and forces involved in climbing, descending, turning and gliding. This is another sort of refresher topic from principles of flight that we need to understand before we move on to more complicated performance based stuff. If you're looking for a bit more information on the topics covered in today's video I'd recommend going back and watching the principles of flight. I can't remember what episodes they are but basically they're called flying physics 1 and flying physics 2 which talk about these maneuvers in a bit more detail should you need that extra bit of help. So our baseline for all these maneuvers is steady level flight. We're not changing our altitude or direction and this is where our four forces of the aircraft are all in balance. We've got thrust equal to drag and lift equal to weight. As soon as we move away from this steady level flight load things change. In a climb for example we still have the four forces acting on our aircraft lift, weight, thrust and drag. but the weight is always pulling us straight down rather than the other three forces that continue to act in the normal directions relative to the aircraft. The weight of the aircraft can therefore be broken down into two elements using some trigonometry. We have the force that is acting down the slope which is the weight times sine of the theta which is the angle of the slope because these angles are equal. The other side of the triangle is the weight times cosine theta and that is the force acting into the slope. For us to be in a steady climb then the forces again have to be balanced out but for the components of the weight not the total weight. If we take a look at the thrust for example we can see that it now has to counteract the drag plus the weight sine theta component that is pulling us down the slope. So if we want to be in a steady climb we can say that thrust equals drag plus w sine theta. The other weight component, the weight acting into the slope, the cosine theta element, has to be balanced out by the lift. So we can say that lift equals w cosine theta. This means that we can see some interesting things about a steady climb. Thrust basically has to be more than drag because now thrust has to account for drag and this additional component of weight. So thrust is larger than drag in a climb. In a climb lift is also less than weight which does seem a bit odd. Basically the lift now instead having to account for in normal flight it has to account for the full amount of weight but now it only has to account proportion of this weight because the thrust is dealing with the other proportion of the weight. So therefore the lift is lower. So in a climb lift is less than the weight which does seem a bit weird. Another way to think of it would be that thrust could be broken up into two components. You would have like a horizontal and a vertical and some of the vertical component of the thrust is helping with the weight. That might be another easier way to think of it. If we reverse the process of climbing into descending steadily then we see a change around and a few values. We still have our weight split into the two components the w cosine theta acting into the slope and w sine theta acting down the slope. We see again that the lift only has to balance out the w cosine theta so we can make that assumption again that lift would have to be less than weight in a descent as well as in a climb. The other component of the weight is now acting along with the thrust to pull us down the slope and the drag is resisting that. So for a balanced descent thrust plus w sine theta has to equal drag and that means now that the drag has to be larger than the thrust because it's got to account for the thrust and this element of the weight. So we can say that in a descent drag is larger than thrust. which does make sense if we're more draggy we're going to start descending if we've got more thrust we might start climbing gliding is very similar to descending but we have no thrust to account for so again Our lift is only equal to the W cosine theta element, but our component acting down the slope only has to balance out the drag. So our drag is equal to W sine theta. There's no thrust to think of because we're gliding. That's what a glide is, a descent without thrust. If we then zoom in on our triangle of weight components, let's draw this out. So let's say it looks something like this. then we know that this element, the w cosine theta element, has to equal lift. So we'll give that the lift marker. And we know that this element here, w sine theta, has to equal drag, because it says so here, drag. And therefore, we have this angle in here, which we can figure out as, use some trigonometry to figure out that tan of this angle equals the opposite over the adjacent which equals drag over lift. The value of this angle theta will be the lowest and therefore shallowest. If you think about this value being really low this triangle will be a very thin like this then this will also be very thin and that means we can glide quite far and that's when this is going to be very low as well. Or in other words we could invert this and say that when the lift drag ratio is up the angle will go down as well. So drag to lift being low is the same as lift to drag being high. So this makes a bit, this makes logical sense to me. If we've got a lot of lift and not a lot of drag we're going to be able to keep ourselves in the air and not get pulled back and spend more time in the air descending down on it. This maximum lift to drag ratio is only occurring at one specific speed which we saw in the previous class and that specific speed would be the speed for minimum drag or VMD, the bottom of that total drag curve. And as you can see from the equation here, there's no mention of weight. It's not involved in the angle of the glide. This is because as weight increases, we also need more lift to take care of that weight. And when we generate more lift, we also generate more drag, more of that induced drag. And that means that the ratio of drag to lift or lift to drag doesn't actually change, it's the same ratio, so therefore we have the same angle of glide, no matter what weight we are. The only thing that will change is the speed that it takes for us to complete this glide. Basically when we're heavier our VMD occurs at a higher speed so we're therefore going to fly faster and that means that say we've got this distance to glide if we're traveling at a faster speed we're going to cover it quicker so we're flying the same angle but we complete the glide we land on the ground um yeah in a lot less time if we're heavier it has no influence on the angle is what i was trying to illustrate there when we turn in an aircraft we back or roll the aircraft into the turn and this means that the lift now acts at an angle to the normal vertical plane, not too dissimilar to the slope of the aircraft in the previous examples. In turning though we only need to consider two forces, the lift and the weight. So when we bank the aircraft over we are using a component of this lift force to pull us into the turn and rotate the aircraft around. On our diagram we can break the lift down into the vertical and the horizontal component. So we see that weight and lift times cosine of the angle of bank balance out. So weight equals lift cosine theta. And the horizontal component L sine theta isn't balanced down by anything as that's the force that we're using to turn us. Because now some of this lift is being used to turn us, we're taking away L sine theta from the total amount of lift. That means that if we had the same amount of lift before the turn as during the turn, then we'd suddenly lose L sine theta's worth of lift and the aircraft would be unable to maintain steady level flight. We therefore need to increase the amount of lift we have in a turn so that if we lose this horizontal component of lift it means that our vertical component is still sufficient to balance out the weight of this aircraft. We can calculate the amount of lift that we would need extra by using the load factor, which is the ratio of lift to weight. So let's start with... this equation here. So we've got weight equals lift cosine theta. If we do a bit of rearranging and cross multiplying we can get that weight over lift equals cosine theta and then we can inverse this and get lift over weight equals one over cosine theta and lift to weight is the same as the load factor. So if we put a value in for theta we can see how we would use the load factor for our turn. So let's decide how bad our turn is. I'm going to use 60 because it makes the maths really easy. So let's say our load factor is 1 over cosine 60 degrees. Cosine 60 equals 0.5 half. So 1 over 0.5 is 2. So load factor equals 2. What does that actually mean though? Well remember it's lift over weight. Before we started the turn we know that lift is equal to weight. That very first starting point that we started with lift and weight are in balance. So we could say that this is one over one for example. If we then need to increase this to two what we're going to do we're going to have to the weight can't change but the lift can change. We could increase that to two for example. 2 over 1 is 2, so that means that in this turn with a 60 degree angle of bank, we would need to increase the amount of lift we have by a factor of 2. We need to double the amount of lift that we have. And how do we do that? Well, basically, we're not going to be taking flaps in the middle of turns and stuff like that, otherwise every time we turn we'd have to consider flaps. So basically what we do is we increase the angle of attack of our wing. by pulling back and pitching the nose up, increasing our coefficient of lift and our overall lift. So a quick refresher class there. As I said in the intro, look up the videos in the Principles of Flight series if you want a bit more detail, but this is all the essential information we need. So for a climb, the forces are out of whack. We can split the weight into w cosine theta and w sine theta. We can do that for all of the climbing and descending maneuvers. And in the turn we do the same with the lift, we split the lift into lift cosine theta and lift sine theta. And basically those components now have to balance out the appropriate components depending on the manoeuvre. So in a climb we need thrust going up the slope, for a steady climb anyway. Thrust has to be balanced by the drag pulling us down the slope and also the weight times sine theta. So that means that in a climb thrust is larger than drag. The lift now only has to balance out the component that is pulling us into the slope, the w cosine theta, which therefore means the lift is less than weight now, which is a bit weird but you can think of it as the a component of the thrust is now pulling us up the slope, that's what this is telling us really. In a descent it's basically flipped around, the thrust plus the weight pulling us down now has to equal the drag, so our drag has to be larger than thrust and the same applies for the lift and weight balancing. We only have to balance out w cosine theta with the lift so therefore lift is still less than weight. In a glide there's no thrust to consider so we just have drag equal to w sine theta and lift equal to w cosine theta. Again lift would be less than weight in this example. And what we do is we can sort of zoom in on this triangle, say that because drag and weight are equal to w sine theta and w cosine theta, we call this lift and we call this drag. And then to find out the angle, which is equivalent to this angle, we would say tan of the angle is equal to the drag over the lift. And when that value is very small, this value will be very small and that would be a very shallow. descent we'd actually descend quite far and when the drag to lift ratio is low that means that the lift to drag ratio is very high and that happens at the speed for minimum drag. In a turn we use a component of lift to turn it's the l sine theta that is actually used in the turn and the l cosine theta is equal to the weight it's balancing out the weight here. And then through a bit of rearranging we could say that the lift over weight is equal to 1 over cosine theta. That is the load factor and that tells us how much more lift we're going to need in the turn. Because if we didn't add more lift we'd suddenly lose l sine theta's worth of lift and we wouldn't be able to maintain level flight.

Well, let's find out. Hi, I'm Grant and welcome to the third class in the performance series. Today we're going to be taking a look at the physics and forces involved in climbing, descending, turning and gliding.

This is another sort of refresher topic from principles of flight that we need to understand before we move on to more complicated performance based stuff. If you're looking for a bit more information on the topics covered in today's video I'd recommend going back and watching the principles of flight. I can't remember what episodes they are but basically they're called flying physics 1 and flying physics 2 which talk about these maneuvers in a bit more detail should you need that extra bit of help.

So our baseline for all these maneuvers is steady level flight. We're not changing our altitude or direction and this is where our four forces of the aircraft are all in balance. We've got thrust equal to drag and lift equal to weight. As soon as we move away from this steady level flight load things change.

In a climb for example we still have the four forces acting on our aircraft lift, weight, thrust and drag. but the weight is always pulling us straight down rather than the other three forces that continue to act in the normal directions relative to the aircraft. The weight of the aircraft can therefore be broken down into two elements using some trigonometry. We have the force that is acting down the slope which is the weight times sine of the theta which is the angle of the slope because these angles are equal. The other side of the triangle is the weight times cosine theta and that is the force acting into the slope.

For us to be in a steady climb then the forces again have to be balanced out but for the components of the weight not the total weight. If we take a look at the thrust for example we can see that it now has to counteract the drag plus the weight sine theta component that is pulling us down the slope. So if we want to be in a steady climb we can say that thrust equals drag plus w sine theta.

The other weight component, the weight acting into the slope, the cosine theta element, has to be balanced out by the lift. So we can say that lift equals w cosine theta. This means that we can see some interesting things about a steady climb.

Thrust basically has to be more than drag because now thrust has to account for drag and this additional component of weight. So thrust is larger than drag in a climb. In a climb lift is also less than weight which does seem a bit odd. Basically the lift now instead having to account for in normal flight it has to account for the full amount of weight but now it only has to account proportion of this weight because the thrust is dealing with the other proportion of the weight. So therefore the lift is lower.

So in a climb lift is less than the weight which does seem a bit weird. Another way to think of it would be that thrust could be broken up into two components. You would have like a horizontal and a vertical and some of the vertical component of the thrust is helping with the weight. That might be another easier way to think of it.

If we reverse the process of climbing into descending steadily then we see a change around and a few values. We still have our weight split into the two components the w cosine theta acting into the slope and w sine theta acting down the slope. We see again that the lift only has to balance out the w cosine theta so we can make that assumption again that lift would have to be less than weight in a descent as well as in a climb. The other component of the weight is now acting along with the thrust to pull us down the slope and the drag is resisting that.

So for a balanced descent thrust plus w sine theta has to equal drag and that means now that the drag has to be larger than the thrust because it's got to account for the thrust and this element of the weight. So we can say that in a descent drag is larger than thrust. which does make sense if we're more draggy we're going to start descending if we've got more thrust we might start climbing gliding is very similar to descending but we have no thrust to account for so again Our lift is only equal to the W cosine theta element, but our component acting down the slope only has to balance out the drag. So our drag is equal to W sine theta. There's no thrust to think of because we're gliding.

That's what a glide is, a descent without thrust. If we then zoom in on our triangle of weight components, let's draw this out. So let's say it looks something like this.

then we know that this element, the w cosine theta element, has to equal lift. So we'll give that the lift marker. And we know that this element here, w sine theta, has to equal drag, because it says so here, drag.

And therefore, we have this angle in here, which we can figure out as, use some trigonometry to figure out that tan of this angle equals the opposite over the adjacent which equals drag over lift. The value of this angle theta will be the lowest and therefore shallowest. If you think about this value being really low this triangle will be a very thin like this then this will also be very thin and that means we can glide quite far and that's when this is going to be very low as well.

Or in other words we could invert this and say that when the lift drag ratio is up the angle will go down as well. So drag to lift being low is the same as lift to drag being high. So this makes a bit, this makes logical sense to me.

If we've got a lot of lift and not a lot of drag we're going to be able to keep ourselves in the air and not get pulled back and spend more time in the air descending down on it. This maximum lift to drag ratio is only occurring at one specific speed which we saw in the previous class and that specific speed would be the speed for minimum drag or VMD, the bottom of that total drag curve. And as you can see from the equation here, there's no mention of weight.

It's not involved in the angle of the glide. This is because as weight increases, we also need more lift to take care of that weight. And when we generate more lift, we also generate more drag, more of that induced drag. And that means that the ratio of drag to lift or lift to drag doesn't actually change, it's the same ratio, so therefore we have the same angle of glide, no matter what weight we are.

The only thing that will change is the speed that it takes for us to complete this glide. Basically when we're heavier our VMD occurs at a higher speed so we're therefore going to fly faster and that means that say we've got this distance to glide if we're traveling at a faster speed we're going to cover it quicker so we're flying the same angle but we complete the glide we land on the ground um yeah in a lot less time if we're heavier it has no influence on the angle is what i was trying to illustrate there when we turn in an aircraft we back or roll the aircraft into the turn and this means that the lift now acts at an angle to the normal vertical plane, not too dissimilar to the slope of the aircraft in the previous examples. In turning though we only need to consider two forces, the lift and the weight.

So when we bank the aircraft over we are using a component of this lift force to pull us into the turn and rotate the aircraft around. On our diagram we can break the lift down into the vertical and the horizontal component. So we see that weight and lift times cosine of the angle of bank balance out.

So weight equals lift cosine theta. And the horizontal component L sine theta isn't balanced down by anything as that's the force that we're using to turn us. Because now some of this lift is being used to turn us, we're taking away L sine theta from the total amount of lift. That means that if we had the same amount of lift before the turn as during the turn, then we'd suddenly lose L sine theta's worth of lift and the aircraft would be unable to maintain steady level flight.

We therefore need to increase the amount of lift we have in a turn so that if we lose this horizontal component of lift it means that our vertical component is still sufficient to balance out the weight of this aircraft. We can calculate the amount of lift that we would need extra by using the load factor, which is the ratio of lift to weight. So let's start with...

this equation here. So we've got weight equals lift cosine theta. If we do a bit of rearranging and cross multiplying we can get that weight over lift equals cosine theta and then we can inverse this and get lift over weight equals one over cosine theta and lift to weight is the same as the load factor.

So if we put a value in for theta we can see how we would use the load factor for our turn. So let's decide how bad our turn is. I'm going to use 60 because it makes the maths really easy.

So let's say our load factor is 1 over cosine 60 degrees. Cosine 60 equals 0.5 half. So 1 over 0.5 is 2. So load factor equals 2. What does that actually mean though?

Well remember it's lift over weight. Before we started the turn we know that lift is equal to weight. That very first starting point that we started with lift and weight are in balance. So we could say that this is one over one for example. If we then need to increase this to two what we're going to do we're going to have to the weight can't change but the lift can change.

We could increase that to two for example. 2 over 1 is 2, so that means that in this turn with a 60 degree angle of bank, we would need to increase the amount of lift we have by a factor of 2. We need to double the amount of lift that we have. And how do we do that?

Well, basically, we're not going to be taking flaps in the middle of turns and stuff like that, otherwise every time we turn we'd have to consider flaps. So basically what we do is we increase the angle of attack of our wing. by pulling back and pitching the nose up, increasing our coefficient of lift and our overall lift.

So a quick refresher class there. As I said in the intro, look up the videos in the Principles of Flight series if you want a bit more detail, but this is all the essential information we need. So for a climb, the forces are out of whack.

We can split the weight into w cosine theta and w sine theta. We can do that for all of the climbing and descending maneuvers. And in the turn we do the same with the lift, we split the lift into lift cosine theta and lift sine theta. And basically those components now have to balance out the appropriate components depending on the manoeuvre. So in a climb we need thrust going up the slope, for a steady climb anyway.

Thrust has to be balanced by the drag pulling us down the slope and also the weight times sine theta. So that means that in a climb thrust is larger than drag. The lift now only has to balance out the component that is pulling us into the slope, the w cosine theta, which therefore means the lift is less than weight now, which is a bit weird but you can think of it as the a component of the thrust is now pulling us up the slope, that's what this is telling us really. In a descent it's basically flipped around, the thrust plus the weight pulling us down now has to equal the drag, so our drag has to be larger than thrust and the same applies for the lift and weight balancing. We only have to balance out w cosine theta with the lift so therefore lift is still less than weight.

In a glide there's no thrust to consider so we just have drag equal to w sine theta and lift equal to w cosine theta. Again lift would be less than weight in this example. And what we do is we can sort of zoom in on this triangle, say that because drag and weight are equal to w sine theta and w cosine theta, we call this lift and we call this drag.

And then to find out the angle, which is equivalent to this angle, we would say tan of the angle is equal to the drag over the lift. And when that value is very small, this value will be very small and that would be a very shallow. descent we'd actually descend quite far and when the drag to lift ratio is low that means that the lift to drag ratio is very high and that happens at the speed for minimum drag. In a turn we use a component of lift to turn it's the l sine theta that is actually used in the turn and the l cosine theta is equal to the weight it's balancing out the weight here.

And then through a bit of rearranging we could say that the lift over weight is equal to 1 over cosine theta. That is the load factor and that tells us how much more lift we're going to need in the turn. Because if we didn't add more lift we'd suddenly lose l sine theta's worth of lift and we wouldn't be able to maintain level flight.

Transcript for:Understanding Forces in Flight Dynamics

Transcript for:
Understanding Forces in Flight Dynamics