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 of flight and start climbing descending and turning well let's find out [Music] 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 uh camera 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 low 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 um 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 see the 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 a drag and this additional component of weight so thrust is larger than drag in a climb in a claim lift is also less than weight which does seem a bit odd basically the lift now instead having to account for um in normal flight it has to account for the full amount of weight but now it only has to account for a 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 processor 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 weak points Let's uh 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 track 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 left beat low is the same as lift 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 this for minimum drag or v m d the bottom of that total graph drag curve and as you can see from the equation here there's no mention of weight it's not of all 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 that more of that induced drag and that means that the ratio of drag to left or left to drag doesn't actually change it's the same ratio so therefore we have the same angle um of Glide depending it 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 back the aircraft over we're using of the 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 left that means that if we had the same amount of lift for the turn as during the turn then we'd suddenly you 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 and by using the load factor which is the ratio of lift to weight so let's start with um 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 the weight over lift equals cosine Theta and then we can inverse this and get lift over weight equals 1 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 back to third is I'm going to use 60 because it uses 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 two what does that actually mean though well remember it's lift over weight four we start at 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 2 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 2 for example two over one is two so that means that in this term with a six degree angle 60 degree angle of bank we would need to increase the amount of lift we have by a factor of two we need to double the amount of lift that we have and how do we do that well basically we can't we're not going to be taking Flaps in the middle of turns and stuff like that otherwise we'd be 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 flight series if you want a bit more detail but uh 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 with those components now we have to balance out the appropriate components depending on the maneuver 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 this down slope and also the wait 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's 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 left equal to W cosine Theta again left 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 T 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'd 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 a minimum drag in a turn we use a component of a 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 see that the leftover weight is equal to one 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 left we'd suddenly lose L sine theta's worth of lift and we wouldn't be able to maintain level flight