 Okay, now we come to V1, the same. Okay, let's look at V1. Imagine yourself in the cockpit of your plane and applying takeoff thrust to your engine and as you gently accelerate down the runway, you come to a point where you reach V1. So by the book, V1 is defined as the speed beyond which the takeoff should no longer be aborted, meaning that in case you experience any trouble with your plane before reaching V1, the classic example would be an engine failure, you would immediately abort your takeoff and would apply all necessary matters to bring the aircraft to a stop. Although the use of full reverse thrust is not mandatory. I'll come back to that in a second. So in this video here, this Airbus A319 applied takeoff thrust and due to a technical malfunction had to abort the takeoff prior reaching V1. Just listen to the sound of the engines. The system comes active and immediately applies pressure to the brake cylinders, the ground spoilers are deployed so are the reverses and the plane and crew come to a safe stop on the runway. The smoke you can see here is coming from the brakes as they are the primary force slowing down the aircraft. Now let's say there were to be an engine failure so one of the reverses would be inoperative and therefore full reverse thrust can't be added to the braking measures as mentioned before. Because V1 needs to be calculated prior every takeoff taking into account airplane weight, runway length, wing flap setting, engine thrust used, runway surface contamination and environmental factors and even the aircraft brakes to assure yourself that any given failure prior reaching V1 you'll have enough runway left over to come to a complete stop. Now if it's just a minor failure you can continue to take off but that's a whole another video about the stop or go decision-making. And besides that this is one of the reasons why the captain keeps his hands on the throttle until the pilot monitoring calls out V1 and then he moves his hands away from the throttle to not inadvertently abort the takeoff after V1 in case of a failure. So in case you experience any serious malfunction after V1 you would have to commit yourself to continue to take off otherwise a takeoff abort will lead to a runway over. Okay so do you understand now why it is called decision speed? Because during takeoff if the malfunction, engine failure, any problem is observed before V1 what is your decision? What would you do as a pilot? 100% right abort the takeoff. Do not be a hero or don't try to be hero you can say I'll take it no. Decision is before V1 you have to abort. Okay now if for some reason engine failure occurs now in this case that we saw an example the problem was thrust loss it was rejected before V1 so the pilot applied full brakes you saw the brakes were fuming okay so there were so but then suppose a decision suppose the failure is recorded after you cross V1 what is the decision to be taken? Even though there is an engine failure you will continue takeoff. I admire your guts you have two engines and one engine has failed it has failed after you cross V1 why will you continue takeoff? Yeah let me ask this captain why would you continue takeoff after V1? Correct so the numerical value of V1 is decided based on this calculation that if you abort takeoff after you have crossed V1 you may still be on the ground but if you abort after V1 then the accelerate stop distance it is called from start to the end accelerate and then break that will exceed the safe runway available now this safe runway is a very big word I'll have to explain to you in an airport you just don't have a runway you have a runway you have a clearway you have a stopway apart from taxiways and aprons so a runway is basically the hard surface which is designed to take the impact of the aircraft when it comes into land okay the stopway is an additional part of the runway may not be as hard as a runway to take impact because you don't land on that but you may exceed runway and go to the stopway for a accelerate stop distance and the clearway is nothing but an area under the control of the aerodrome during which obstacle height can be cleared by the aircraft so clearway can be ground it need not be even paved it may be grass but it is a area which is under the no construction is permitted beyond a particular height in fact nothing is allowed to be there except required by function some instruments for navigation some antenna some wall lights etc okay but otherwise clearway is supposed to be clear of all obstacles fine so therefore if the problem is detected just beyond V1 you are not supposed to about your takeoff under any circumstances what happens if the problem is deducted at V1 now what would you do before V1 it is clear after we when it is clear but suppose it is at V1 most pilots will about but you can do both it's the intersection point so you will not be charged if you continue takeoff at V1 but most pilots will not they will discontinue okay so now let's go to VR VR you know is a V rotation speed the speed at which the aircraft can be rotated for takeoff the call out is VR or better known as rotate by the book VR is defined as the speed at which the pilot begins to apply control inputs to cause the aircraft knows to pitch up after which it will leave the ground again VR is also calculated prior takeoff in accordance with aircraft weight environmental factors etc and it's the point where the generated lift over the wings becomes higher than the aircraft weight keeping it on the ground easiest way to memorize VR is the point where the nose wheel leaves the ground and vortexes are created at the wing tips which rotate behind the aircraft and the point where the main gear leaves the ground that's the point where you have reached the loft the lift okay so we rotate is when the nose wheel has left the ground and we lift off or we love is there the main wheel leaves the ground then we have VMU minimum unstick speed okay this is the point at which the aircraft could take off if the maximum possible rotation angle were reached remember there is something called a stalling angle so when you rotate you cannot exceed alpha stall otherwise it will stall so if you reach alpha equal to alpha max permitted which is below alpha stall then at at this speed or at this minimum speed the aircraft will generate lift more than weight that is the definition of we lift off and this particular angle could be limited not only by aerodynamics but also by geometry for example you may be able to go at a higher angle okay alpha stall may be 15 degrees but alpha for minimum would be 12 degrees because at 12.1 degree the tail will hit the ground because of the geometry of the aircraft so it could be limited by geometry or aerodynamics normally by geometry so basically it is the maximum permitted angle to be given during rotation so what is the minimum speed at which max permittable rotation angle will give you the lift off that is called as the V minimum unstick pilot should know this because the pilot should not try to initiate rotation at a speed below this because at a speed below this if you initiate rotation you will hit the ground before lifting off and then we have we lift off or VLOF we loft then finally we have a speed called V2 take off safety speed but take off safety speed V2 is defined as take off safety speed the speed at which the aircraft may safely climb with one engine in operative okay let's go back to all engines operative now imagine all is normal you take off and someone would measure your height above ground at the end of the runway like in this picture here the height measured is the so-called screen height now let's get back to V2 and our engine failure situation in case one engine fails you need to maintain the speed of V2 in order to leave the runway at a screen height of 35 feet or higher and maintain the climb rate at V2 to be clear of obstacles in the departure sector and you should be able to maintain that speed and climb rate until reaching one engine out acceleration altitude where you then gain speed and retract the slats and flaps and continue with the emergency procedures this video here is a great example for V2 as you can see the Boeing 747 there is a bird which comes in the pot the engine starts getting flamed so engine has flamed out while it's maintained V2 and the respective climb rate retracted the gear and performed all the necessary emergency procedures flew a traffic pattern and landed the airplane safely the reason therefore is when local authorities design departure routes including obstacle avoidance procedures they predict that your aircraft is at least capable of maintaining V2 with one engine and the gear retracted and guarantee obstacle collision protect okay you get the point I'll show you once again you can see this video continue with the emergency procedures this video here is a great example for V2 as you can see the Boeing 757 hit a bird just off the lift off and the engine was severely damaged the pilots maintained V2 and the respective climb rate retracted the gear and performed all the necessary emergency procedures flew a traffic pattern and landed the airplane safely the reason therefore is when local authorities design departure routes including obstacle avoidance procedures they predict that your aircraft is at least capable of maintaining V2 with one engine and the gear retracted and guarantee obstacle collision protect okay so V2 is the takeoff safety speed it is a speed at which with one engine in operational you still are able to maintain climb rate such that you clear the obstacle height at the end of the runway in the example shown the engine failure happened before rotation in the video it was after rotation but in the example in the description it was engine failure to place after V1 but before rotation so obviously when there is only one engine one in the not working you will have less thrust available so the climb rate will be lower so if you have what is the speed at which with landing gear retracted you are able to maintain the required climb that is called the takeoff safety speed okay so these are the speeds which we need to remember during the takeoff run so let us look at the distance and the time covered in the transition phase so during transition phase what is the profile flown by the aircraft is it a straight line is it a curved path is it a concave path or a convex path what do you think what is the flight trajectory during the transition I showed you a figure of an aircraft during takeoff it goes like this and then like this and then it climbs so the climb is straight line ground roll is straight line what about transition it's a curve so is it a convex curve or a concave curve if you are looking from inside it's a concave curve it doesn't go this way it goes this way so to calculate the distance and the time taken during transition you have to assume the thrust is equal to drag plus the kinetic energy that is increasing and the time taken will be average of because speed is V1 and then V2 so the time taken will be the average because speed increases from V1 to V2 so this particular calculation now there is a height that is attained in this phase that height is basically the obstacle height so this is something which I want you to do yourself so I want you to model what you do is I will give you a hint you can model the flight path of the trajectory of the aircraft as a part of a circle okay as a arc of a circle it's an assumption actually it's not arc of a circle but one can assume it to be arc of a circle so from speed V1 at the beginning of the arc of a circle to a speed V2 at the end of the arc of a circle the aircraft is proceeding from a speed from V1 to V2 you have to now calculate what is the height that is traveled so this is homework and I expect you to upload this homework on Moodle okay so once again the first person who uploads is okay the second person should not copy paste or give the same thing the second person should give the same thing in some other way if not don't need to upload so I leave that to you let's look at the climb phase climb phase is very straight forward within the climb phase you are in the straight angle climb so you have a screen height 15 meters 50 feet and you have a climb angle gamma so it's from simple trigonometry and you can get gamma ST minus V by W that's it no no no screen height is defined by the regulatory body you have 50 feet and 35 feet for landing it is 35 feet and again for military aircraft and transport aircraft there are different numbers but it is 50 feet it's a 6th number it's not it's not a function of the airport no it's it's a regulatory requirement that you should clear 50 feet obstacle okay so the requirement is same for all so if you sum up these three times and sums you will be able to get the takeoff distance in time alright so let's see what parameters influence the takeoff run so the major portion is ground run unless you have a situation of failure or problem so ground run will decrease takeoff run will decrease so if we focus on ground run only because it's a major part for normal takeoff and if you assume that the takeoff speed V1 is 10% higher not 15% 10% this number also varies for defense aircraft it is 10% for civil it is 15% specified by the regulatory body so if you recall that Vs is to W by rho as CL max so therefore S1 is a function of these parameters so you can see it's very straightforward now the S on the bottom I have taken up to put it as W by S and 1W I am keeping it on the denominator so I get T by W D by W and 1 minus L by W so in other words ground roll increases as the wing loading increases so one very important parameter is keep your wing loading low if you want to have a shorter takeoff ground run in fact when you do design not as part of this course when you do learn design you will find that is going to be a requirement or a tendency to keep the wing loading low from low takeoff requirements okay CL max if it is high ground run will be low because it comes in denominator that is why we put flaps during takeoff and density ground roll will increase as the wing density decreases that is why at a hotter airport or at a higher airport where density is low and if you have hot plus high condition can you name a place where you have hot plus high in India high altitude but hot so lay airport is an example during summer lay airport is one of the most difficult airports to operate because of the hot and high conditions in the US people site Denver as an example of an airport which is hot and high so takeoff run also reduces as the accelerating force increases so this is a very interesting thing basically the faster you accelerate that means T minus D minus mu w so how do you increase thrust at takeoff there are many ways of doing it okay the first way is using afterburners afterburner you are familiar what it is I will just show you a nice video this is afterburner normally you do not need to have large plane behind the aircraft the aircraft length and the length of the afterburner plane is almost the same as we can see such afterburners can also cause tremendous problem to the runway over a period of time the runway will start melting we have experienced these problems in HAL when we worked on military aircraft we have to replay relay the concrete okay so some aircraft takeoff with afterburner routinely one more way of doing it is called as jato or rato rocket assisted takeoff or jet assisted takeoff so this is a very interesting mechanism and you can see it in some military aircraft so this is C-130 the one on which you do the assignment you see have been fitted with rockets as the show opener the C-130 demonstrates its short runway jet assisted takeoff or jato capability okay so this is one way this is also possible on nick 21 if needed they have jato facility or rato facility as we used to call it and then okay so that is the catapult so these are the typical ways by which we can increase the thrust okay now this is a situation when you have one engine failure during takeoff so yes you can apply brakes or you can continue to fly so now we have to understand that there has to be a balance in these two so obviously before v1 you will apply option number one after v1 you will apply option number two that decision speed is v1 interestingly at v1 the accelerates top distance will be equal to the total distance needed from start to reach the obstacle height so that is why v1 is called as decision speed and this distance on the ground total distance is called as the balanced field length bfl so do you understand the balance here the balance is that either you go for accelerate at v1 stop or you go for takeoff at v1 continue takeoff is one engine less so you have lower thrust so at a longer distance you will clear the obstacle height you will clear it but at a longer distance the speed v1 is such that these two distances are same so the definition of balance field length is that distance from the point where the aircraft starts rolling to the point where either it comes to an accelerate stop distance or it clears the obstacle height when the engine failure occurs at decision speed and these two are the same that is the balance field length okay so there are many simple formulae available in literature for calculating balance field length but these are all numbers I will not spend too much time on that also remember that when you fly near the ground then the vortex system on the wing is affected by the presence of the ground so the strength of the wingtip water decreases because the wingtip vortex is killed by the ground there is a upward push so the wingtip vortex reduces so therefore induced drag is reduced and therefore you will have some kind of a improvement so the landing distance will be have a issue because in landing you are being cushioned but in takeoff you are benefited so however the effect of ground wash ground effect actually depends on how much high you are from the ground with respect to the wingspan so that is called as a factor phi h over b h is the height above the ground b is the total wingspan so normally it is said that when h is equal to b that means at a height which is equal to one wingspan above the ground above that the ground effect starts becoming almost zero so you can assume to be out of the ground effect below that height you have a factor phi and the drag is reduced and therefore the landing the takeoff will be improved