 So, much about gliding, now let us go to climbing. Climbing flight is a flight, so in the throttle of the aircraft you have a position called as a climb position, this is a throttle of the aircraft, just to give you some idea these two on the right and the left are basically the trimming wheels, they are used to trim the aircraft so that the pilot can fly hands free, so they are just the trim tabs and other things to ensure that the net moment is 0 and these two are the throttles, so throttles you have, you can see there is a reverse position which is marked in yellow color which is back and then you have climb position then you have cruise position etc etc, okay. So, that means this is the aircraft A320, so we have to be careful, first thing you have to be is that some people say oh climbing is basically reverse of gliding, in gliding you are coming down, in climbing you are going up but that is not true, that is not true because in one case gravity is acting in your favor, in the other case you are going against gravity, so you require thrust force to overcome, so thrust comes into play when you go into climbing, yeah that is the important thing and for different aircraft there are different climb speeds and different climb positions, okay. You can see the picture you have a hang glider and you have a normal aircraft and you see there are differences in the way they are climbing, so it depends upon the engine type, okay. So, when you fly an aircraft actually there are four possible ratings, okay, so the first one is called as the MTT and that is basically the maximum thrust that the engine can deliver for 5 minutes, that is the max thrust condition, it is called as the max thrust condition. During this particular condition you are actually creating a huge amount of thrust, so therefore there is a time limit, after that the engine life will be reduced, then you have maximum continuous rating, max continuous, this you can give for as much as time as you want, the engine is certified to work nonstop for many many hours at that rating, then you have what is called as a max climb rating, okay, so certified for en route climb, now climb also is many types we will see that and then you have max cruise rating, that is the thrust allowable for the unlimited fly duration at the design altitude, the MCT is at any altitude but MCR is at the cruising altitude, so these are the four ratings of the engine, let us see the equations of motions, we first have a reference line and then we have this climb, so obviously we have thrust and drag along the flight path, we have weight normal I mean towards the earth center, resolving you get lift and if you have climb angle 5, then you can look at the four forces, so here we have a very interesting observation but before that let me ask you, the aircraft is climbing, so do you think lift is more than weight, it is climbing, it is going up, okay, so you think lift is more than weight, that is wrong, that is a misconception, actually lift will be less than weight during climbing, so why is that so? Because there is thrust which gives you the upward force, not lift, in fact if you have lift, drag, thrust and weight are all balanced, what you see here is of course a simplified representation of the main forces that are in equilibrium, this one we know, this is in level flight, in a steady climb the aeroplane is also in the state of equilibrium, thrust and drag act in line with the relative air flow along the aeroplane's flight path, whereas lift acts at right angle to the relative air flow, weight acts down towards the centre of the earth, the common misconception is that lift increases in a climb, in a steady climb where the forces are in equilibrium, the component of weight points backwards, so weight may be resolved into two vectors, the weight component that opposes lift and the rear weight component, lift is slightly reduced because the opposing weight component is also reduced at the expense of the rear weight component, the rear weight component acts in the same direction as drag, therefore it contributes to drag, so to maintain the equilibrium and steady climb thrust must increase, this is called excess thrust, are you still not convinced that lift is smaller in a climb, imagine that this aeroplane is capable of climbing at the ultimate 90 degree angle of climb, now you can see how it becomes about the excess thrust, not lift, an aeroplane will achieve its best angle of climb when excess thrust is the greatest, this curve represents thrust available against airspeed for straight and level flight, the faster you wish to fly the less effective the propeller is so the less thrust it's able to generate, the thrust required curve suggests that generally you need more thrust if you wish to fly faster, comparing the two curves the greatest difference between the thrust required and thrust available is the maximum excess thrust which happens to be your best angle of climb airspeed, okay so remember vx is a speed which is the best angle of climb speed, so vx is the best angle of climb speed that corresponds to the location where you have maximum gap between thrust available and thrust required, okay, so therefore interestingly lift is going to be less than weight in climb contrary to what we normally expect, l will be w cos phi and phi being non-zero small number but non-zero means l is going to be less than w and t will be more than d because that excess thrust has to be created to overcome the rearward weight component, alright, so when you say steady climb again we mean constant speed, okay and what else? No change in the angle of climb, so it's a constant angle constant speed that is the called as a steady climb, so there will be no dv by dt, no acceleration along the plot, so resolving the forces you can get a very simple idea that the rate of climb will be actually the dh by dt the vertical component of tas and that will be a function of the climb angle that will be sin phi, so t minus d by w, so if you want to have a better phi other things remaining same either you have more thrust less drag lower weight, so weight is something which is fixed, so we cannot touch it that much, you cannot throw passengers away or you cannot say I will dump half the fuel and climb better, maybe you can in an emergency but in general w is constant, d will be a function of the aircraft configuration, yeah it changes with flaps and landing gear etc, so mostly what you can do is control t minus d, okay, so the rate of climb will be basically the true air speed into sin phi that will be the dh by dt, so remember ROC or Ryc will be dh by dt will be v sin phi where v is the speed during climb, okay, so let's see, so r by c by definition is basically the true air speed into t minus d by w, so the rate of climb will increase when either tas increases that means if you fly at a faster speed and you go into a climb you will be able to go into a better speed or if you have more excess thrust or if you have lower weight, it's very obvious, now this already we have seen in the video, this is how the drag which is equal to thrust in case of level flight, here drag is going to be less than the thrust, thrust has to be excess, so you can say that this is a drag of the aircraft, there is one velocity at which drag is minimum and that corresponds to if you remember CD0 is equal to CDi when the two powers are equal, okay, the thrust for jet engine remains almost constant, actually it changes slightly but you can assume it to be constant, so therefore and for piston engine aircraft it is going to come down, so the red line is true for both the aircraft the numerical value may be different but that does not depend upon aircraft type, the shape is the same, the shape of the thrust with the jet or thrust with the piston changes, okay, so therefore the shortest time to climb is where the, now here we come to power because now we are looking at time, that was rate, now this is time, so if you want to go for time to height then you look at the power available versus power required which is nothing but P into V, okay, so now the way in which a transport aircraft climb is a very different from what you think, it does not go straight up, it follows a particular sequence, okay, so the first step is called as a constant IAS climb and then you have a constant Mach climb, let us see, so up to a particular Mach number typically 0.8 or so the pilot is requested to climb at a constant indicated air speed and then once you reach that Mach number then the pilot is asked to maintain a constant Mach number and change the speed accordingly, so for a Airbus A320 this is a given time, climb profile 250 knots, 300 knots 0.78, so 250 knots is below flight level 100 or below 10000 feet because of the air traffic control restrictions, you are asked to fly at a constant speed of 250 knots, above flight level 100 till you reach the height at which your Mach number reading is 0.78, you are allowed to fly at 300 knots and then when you reach M equal to 0.78 you are asked to maintain same Mach number till you reach the end of the climb or you reach the cruising altitude, so this is the climb profile, now why do we do it because of the atmosphere, so on the left hand side we have a curve which is power available versus true air speed and it follows this particular sequence due to the change in the temperature and there is a effect on the thrust, on the right hand side we have two lines, one is the red line which is the theoretical line for the rate of the climb and then we have a green line which is the real aircraft rate of climb or the actual ROC, so typically what we do is up to that particular kink altitude you fly at a constant speed and then you proceed to a constant Mach number, so first part of the climb constant IAS, second part TAS reduces it is a constant Mach number climb, now many people ask a question that why is it so that aircraft fly at a particular height, for example if you look at helicopters we do not normally go beyond 10,000 feet unless you have a special requirement like operating in sea a chin or any other high altitude requirement, piston engines aircraft generally do not go beyond 25,000 feet, turboprops 41,000, jets can go to higher they do not normally go beyond 36,000 40,000 but they can go up to 51,000 if required, so why is it so that they fly at different altitudes, so that is explained in this short video okay, very fast after all it is a jet aircraft, so he wants to go at high speed, so let us break down what he says into bits and pieces which we can understand, first thing he says is planes fly at a high altitude because the density of air is less, so therefore at a given speed it will encounter lower drag and therefore if thrust can be produced the amount of thrust needed will be less, but as you go higher up even the thrust available will also change because the same mechanism also comes into play for thrust production, you need more air, you need more oxygen therefore you need more air, so if you have a rarer air molecules you have rarer oxygen, so there is a sweet spot there is a place something like 36,000 feet to 45,000 feet wherein it is the most optimal, the drag reduction and the thrust availability are in sync and that is the kind of altitude at which most aircraft powered with jet engine would like to fly, turboprop and piston props are worse hit with density change, so therefore they would like to fly at a lower altitude, their optimum altitude tends to be 25,000 to 40,000 feet, so one reason is they said jokingly that if you are at a high altitude then you can have a longer glide if the engines fail, but that is not the reason why they glide so high, so it is basically a function of what is optimal from the point of view of fuel consumption and efficiency, alright, so similarly now let us look at the climb speeds, so this is a slightly interesting part there are various types of speeds in climb one of them is what we have seen that is the vx, okay, the other is the rate of climb, so one of them corresponds to what is the best angle for you to climb, the other is the one that gives you the best rate of climb dh by dt and these speeds are called as vx and vy and then we have a normal or cruise climb, okay, so you can see now max angle of climb, so this is basically here you are interested in knowing what would be the rate of climb, so you are concerned about dh by dt here, the other thing that you are interested in knowing is what would be the angle at which I should climb, so that I can have a best angle of climb, so they are both different and there is a reasoning for that, so if you want to clear the obstacle height at a smallest possible distance, you need to fly at maximum angle speed because you want to reach a height at the shortest horizontal distance but if you want to reach the altitude of your intention in the shortest possible time then you have to go at the speed which corresponds to the maximum rate of climb, so let us see vx versus vy on the chart which shows the rate of climb versus the true airspeed, so the rate of climb actually varies like this with true airspeed, it increases below a particular speed you cannot climb, at some speed you have ROC equal to 0 that means just lift equal to where that is the stalling speed, after that you have excess power, so you are able to climb but the excess of t minus d is small, so therefore the ROC is small, so the point where the line is tangent to the r by c line would be the best angle speed and the point where it would be maxima, the r by c will be maximum that would be the maximum r by c speed, notice that vx is always less than y, how do you remember because x comes before y, so therefore vx is less than vy, you have to remember these things right in some manner otherwise it will be difficult when you are given only 15, 30 seconds in the quiz and when it is more than one can be correct then you have to remember these tricks to remember the answer. So if you want to look at the constant IIS climb, you can notice that the percentage climb capability that means how much of the energy can be used for climb, it also changes with the altitude or the height to which you want to go, so as an aircraft climbs it is true airspeed increases therefore drag will increase because drag is a function of true airspeed not indicated airspeed and if the drag increases then t minus d will reduce, so therefore the r by c r by c also will reduce, so that means slowly if you start increasing your speed continuously you will get lower and lower r over c, at some time you will have 0 r over c, so that is why it is very important for us to know the difference between the power available and the power required, so the minimum power for piston engine will be at a tangent, at a horizontal tangent to this line, so that will be at a speed called vxp, p stands for power propeller engine aircraft vx is the minimum speed and the maximum difference between the power available and power required will be at a higher speed vy and that is called as vyp, again y is the symbol for max roc speed and p for turbo prop piston prop, on the same graph if I want to now show power available for a jet engine aircraft it is t into v, t is almost constant for a turbo jet engine aircraft, so 2 into v will be a straight line proportional to v, so here you find that you have vxj and vyj at a slightly different values, so looking at the graph what do we see, we see that vx is always less than vy which we have already seen before and also we have seen that typically vxp and vyp vxj and vyj also have the same relationship, so here are the important points for you to remember always vx is more than vy for jets it is higher than piston both for x and y because these intersections take place at a slightly larger velocity, now what happens to these values with the altitude, they do not remain the same, so they also change with the altitude. Hello folks my name is Rob Machado and I want to thank you for attending my aviation learning center, I have a question for you have you ever wondered why vx and vy the best angle of climb speed and the best rate of climb speed respectively change with altitude, well perhaps I can offer you a different angle from which to look at this particular question, I want you to take a look at these three rate of climb curves, there's one for sea level, one for 5,000 feet MSL and one for 10,000 feet MSL, now each curve represents the rate of climb for a typical small general aviation airplane at three different altitudes and the very tip top of each curve represents the maximum rate of climb for that particular altitude, now unless there's been an oxygen shortage in your neighborhood it should be pretty apparent to you that is altitude increases the maximum rate of climb decreases, but I want you to take notice that the top of each curve shifts to the right slightly as altitude increases, in other words as the maximum rate of climb decreases with altitude the airspeed at which this occurs increases slightly when measured as a true airspeed and this is found by dropping down to the horizontal axis of the graph which is calibrated in terms of true airspeed, by the way the reason I'm using true airspeed on the horizontal axis instead of indicated airspeed is that it allows us to more accurately represent the airplane's performance at various altitudes, since the green dots represent the best rate of climb speed at three different altitudes it's pretty clear that vy does indeed increase with an increase in altitude, now let's create three lines running from the origin of the graph and tangent to each rate of climb curve, the point where the line touches each curve the red dot represents the best angle of climb speed or vx which is similarly found by dropping straight down to the graph's horizontal axis, geometrically speaking the slope of each tangent line running through each red dot represents the maximum vertical gain for a given distance traveled horizontally and we know this to be the classic definition of the best angle of climb speed, the important thing to notice here is that the best angle of climb speed also increases with an increase in altitude but it does so a little bit faster than the best rate of climb speed therefore vx and vy as true air speeds converge on each other as altitude is increased, now here's the plot of vx and vy as true airspeed values on a traditional graph, so ask yourself what airspeed would you need to indicate to achieve each true airspeed value for vx and vy at c level 5000 feet and 10,000 feet msl and the way to find that out is to use your e6b computer and as you can see here at 10,000 feet msl on a standard day we need an indicated airspeed of 65 knots to produce a true now now he goes into the piloting information because he has plotted the graphs in terms of true airspeed but pilots do not know true airspeed normally pilots only know indicated airspeed and you cannot tell the pilot oh vas is equal to as into root of rho, so take a calculator calculate the density at 5000 feet okay 6.5 degree per kilometer Marjaya by that time he will crash so they do not do all these calculations today they have a small computer with them earlier they used to have these slide rule kind of a system so they would inbuilt all these values into these kind of hand held devices where they would enter IAS and get the equivalent airspeed subtract the various errors listed in the placard and then get the value of true airspeed modern day cockpits have a indicator in front of them but that is there only on very advanced aircraft on very small aircraft on GA aircraft you may not actually see always the true airspeed so then you have to do these kind of things to figure out airspeed of 77 knots and an indicated airspeed of 69 knots to produce a true airspeed of 82 knots and when you do this for all the other airspeed values you get these indicated airspeed now let's take our indicated airspeed values for vx and vy and plot how they change with altitude now here's the graph that you're probably more familiar with so why does the best rate of climb line here in other words the vy line tilt to the left while vy the best rate of climb speed increases with altitude as a true airspeed it just doesn't increase that quickly therefore the indicated airspeed value needed to produce any given true airspeed value decreases at a slower rate for vy than vx as altitude increases and that's why the best rate of climb line tilts to the left and converges with the best angle of climb speed line in fact the point at which they converge is the point where the airplane has zero rate of climb also known as its absolute ceiling so there you have it a brief explanation as to why vx and vy converge on each other as true air speeds and as indicated air speeds so so even if you plot if you plot the if you plot the true air speeds then they will be little bit both will be inclined towards the right but they will meet at some point if you plot indicated air speeds then they will actually be like a vertical triangle the vy value will be reduced actually okay and the vx value will still be increased but not at the same rate value decreases at a as indicated this is what you will get now there is something called as optimum climb speed also which is the speed at which the aircraft is actually made to climb this is not driven by either vx or vy this is driven by economics yeah no no wait wait wait what did you say did they do not have a landing gear or an engine do not confuse between landing gear and engine they are two different things they do not have an engine agreed but they have a landing gear yeah yeah they have a landing gear you have seen it it in the shop in that in that super in the video that I showed you it shows in fact the landing gear was retractable type with hydraulics they have see there are three ways of launching one way of launching is with the engine that is a motor glider okay but even the normal glider how will it roll on the ground it has a small landing gear it could be fixed in many cases the landing gear of the glider is half the wheel single wheel half outside half inside so that drag is minimum but there is landing gear and then in the nose they have a skid they have a skid skid is basically a small place where you rub on the ground so what they do is they they come they land on the main wheel so they have a landing gear they do not have an engine but they do have a landing gear okay and in some cases landing gear is retractable type because it depends on whether it is going to give you lot of benefit it will because drag will reduce drastically but then there is a complexity issue weight complexity cost so there is a tradeoff there are many gliders in which you have a you have no engine but you have a landing gear which goes inside okay but in most gliders you have a fixed landing gear but a very beautifully shaped one so that the drag is minimum the most common one is a single main wheel one small tail wheel but then when you land on the ground you have very long wings so they will hit the ground this way or this way because it is very difficult to land perfectly like this and then remain like this it will go this way or it will go this way so on the tips they have a small support so that it can rest on the ground okay so the engine is not there but landing gears are there okay so coming back to the optimum climbing speeds so we are looking at efficiency and operating costs when we fly an aircraft for money for commercial purposes so these speeds are usually higher than the best rate of climb speed you are not interested in having only the optimum rate of climb that is just the numerical value what you want is higher efficiency so there are some factors which affect the optimum climb speed when the weight goes up this speed goes up so heavier aircraft climb at a higher rate if the fuel price goes up normally the speed goes down and maintenance and crew costs are higher if OCS is higher so this is something I want you to find out and report on model why is it so and how is it done remember this is not for gliders this is not for sail planes this is for only commercial aircraft in other words I am saying that commercial aircraft do not operate at either vx or vy they operate at OCS optimum climb speed which is slightly higher than vy okay so your job is to find out why and report it on model okay moving on to climb gradients basically a climb gradient is an indication of how much altitude is gained per unit horizontal distance and the unit is basically 100 feet in this case so it is like how much do you gain in 100 feet horizontal distance okay so it can be called as a ratio of the horizontal distance to vertical distance and this is affected by wind and by many many other factors so let us see the factors one is pressure altitude so if you are at a higher altitude and if you are taking off then your climb gradient will go down and therefore the ROC will go down temperature is also very bad and weight obviously so all these three affect the climb performance of an aircraft in a very negative fashion okay this is also something which I do not want to cover I would like you to do it yourself so it is a homework for you to load on model effect of altitude effect of temperature effect of weight on the climb performance why is it so that this climb gradient reduces and the ROC reduces if you go into now this is an interesting concept that remember I told you that as you store as you as you climb up slowly you are consuming fuel and your speed is in your density of the air is decreasing so what will happen is the rate at which you climb is going to become very slow and it is also not permitted okay so why do you think why do you think you are not allowed to continuously climb when you go into a flight what is the problem as a passenger aircraft you are taking off from an airport you want to reach the cruising altitude and then you want to cruise what is the problem the pilot would like to do this because as you are as you are climbing you are consuming fuel so you are becoming lighter so therefore you would like to go continuously up in fact if you want to let us look at a short range flight let us say Mumbai to Pune flight now in Mumbai to Pune flight we have these mountains in between but suppose there was a short distance flight with no mountains and no constraints what would be the best profile to fly what do you think will be the optimum flight profile for a short distance flight so the answer is if you want to fly with minimum fuel consumption you take off from Mumbai and you keep on climbing till you reach a height from where if you descend you will hit Pune this is called as a saw tooth but what is the problem in this what is the problem in saw tooth flight I will change it no problem do not get worried about climb speed I want optimum from fuel consumption so the optimum from fuel consumption is I will keep on adjusting the speed to whatever gives me the minimum fuel consumption and then come and descend so what is the problem not only Mumbai to Pune even if I have to go from Mumbai to New York this is the best trajectory for minimum fuel keep on going up reach cruising altitude above which you do not want to fly because it will lead to more consumption then you fly level and then far before just keep descending slowly so what is the problem the problem is you are not alone in the aircraft in the in the sky there are other aircraft flying and who manages them the air traffic controller okay and they will go crazy if there are 100 planes each of them are ascending and descending slowly then how will they keep a track of where they are is very difficult so it is the ATC who says sorry I should know where you are because I have to separate you so one way of separation is by altitude separation 2000 feet gaps you give the aircraft one behind the other in the same direction so the ATC would like you to quickly go to some cruising altitude which they will assign you and they will say maintain that so that I know you are at flight level 280 at so and so time the next aircraft who is coming I have to put it on the same altitude so many minutes behind you or so many nautical miles behind you okay so it is the ATC who is going to complain so the pilots would like to have a continuous increase in the altitude the ATC would like you to fly constant altitude so that they can keep track on you so both of them have a compromise and that is called as a stepped line or a stepped flight so the dotted line is the optimum altitude at which you would like to fly and the red line is the one that ATC gives you so this is also called as cruise climb so you cruise at some altitude and then your weight has reduced now the optimum altitude for cruise is 2000 feet above this to tell the ATC give me a new flight level so for those few minutes 3 4 5 minutes the ATC knows that this guy is climbing you climb and then you again go level then you keep on reducing the fuel you reach another distance where now the fuel is so less that the optimum height is 2000 feet above you so again you stop that is called as a cruise climb so typically from here to New York you may have 3 steps like this in a flight okay the last thing for today is operative ceilings okay so ceiling is very straightforward basically what is meant by a ceiling that is not the ceiling our ceiling is basically to do with altitude at which the rate of climb has reached some minimum value notice it is not zero it is some minimum value so depending on what is the value there are many ceilings there is an absolute ceiling where the value is zero then you have service ceiling you have combat ceiling you have design ceiling and you have propulsion ceiling now this design ceiling and propulsion ceiling normally we do not talk about it that much but the first three are very commonly talked because the first three are actually driven by the rate of climb okay you can numerically decide absolute service and combat ceilings whereas these two are based on the propulsion and the structural properties of the aircraft so let us see what they are absolute ceiling is very simple you just cannot go above it because the power available and power required become exactly matching they are tangential and you can fly only at one speed when you are at that ceiling okay so suppose you reach the absolute ceiling now you can fly only at one particular speed if you fly faster you will fall down if you fly slower you will fall down right now imagine you are flying at that particular altitude and you encounter a mountain so what do you do now the mountain is higher than the value of absolute ceiling okay you can circumvent by turning if you are very near then you cannot do anything because if you go low you will hit it and you cannot go higher that is why it is dangerous for an aircraft to fly at altitudes near absolute ceiling because the reserve capacity is very poor so that is why we define some other ceilings okay so what are these other ceilings the first one is propulsion ceiling that is the altitude at which the thrust provided by the engine allows you to reach above that the thrust available is not going to help you so it is a bit lower than absolute ceiling absolute ceiling is the aerodynamic parameter where the ROCs are matching where the ROC is 0 but before you reach ROC 0 you may reach thrust not available condition then you have service ceiling in service ceiling we want to have a reserve climb capacity of 500 feet per minute it is not meter per second it is feet per minute this is considered to be from safety point of view so that if you have a mountain in front of you at least you can go 100 feet in a minute and avoid it then you have design ceiling a ceiling at which you cannot go because of structure limitations because delta P atmospheric pressure keeps falling pressure inside so the delta P across the structure should not become so much that the structure breaks so the engine is okay but the structure has failed that is design ceiling this we will see later when we study VN diagram also so finally we have these two speeds you can notice the best angle of climb speed and the best rate of climb speed so you have absolute ceiling service ceiling and then you have this cruise ceiling that means you should not cruise at a height higher than the one at which the rate of climb is 300 feet per minute from safety point of view then you have combat ceiling this is for military aircraft so that you do not have you are not a sitting duck target because now you cannot climb okay so these are numbers which are commonly used okay next time when we meet we will take up sustained level turn and pull up