 Now we come to endurance, basically endurance is how much time you spend in the air. So this is again another small graphic which shows from climb at the end of climb till before descents, whatever time you spend that is called as the, so let us see a short film about an aircraft that. This is the Voyager, holder of the last major first in atmospheric flight. In just over nine days in December 1986, it flew around the world non-stop and unrefueled. It was the brainchild of brilliant California aircraft designer Burt Rutan and was built and flown by his brother Dick and Gina Jaeger. It was a unique design, extremely light with vast fuel capacity. For the first part of the flight it ran with two engines and then when enough fuel was burnt off to reduce the weight, the front engine was shut down. The story of Voyager is a story of great courage, ingenuity and determination. It's a story of three people and their friends, setting out to do what had never been done before in the face of immense difficulty. They noticed they flew non-stop for nine days. So they were so particular regarding reducing weight that the toothbrush that they took, they broke it off and said that we do not need the rear portion or the toothbrush, we can hold it with our fingers. My question is why toothbrush? So that is a different situation. So many IT Bombay students are champions in reducing weight. Now one very interesting thing happened when they were trying to take off and that is the wing actually hit the ground because 76% of the aircraft was fuel. In a typical aircraft approximately 20% of the aircraft is fuel and remaining is W1. In Voyager it is the opposite, 76% of the aircraft is fuel. So the wings were like this during takeoff, just a few inches above the ground and only during the, so I'll show you a very short video, we don't have time, this is a very long video but it's an amazing video. So the designer is Bert Rutan. He is sitting in an aircraft and shooting this film and he is going to take off and follow them for the first 4 hours. And you just listen to the conversation, it is amazing. Bert Rutan knows that this aircraft is safe after 61 knots, that is the lift of speed. So he tells the pilot, I just want to hear 61 knots because that means you are going to be airborne. The takeoff roll begins. Takeoff speed is around 90 knots and the speed of 100 knots is critical for Voyager to climb with the full fuel load. Gina Jaeger caused off the speed and the distance covered down the runway. As the airplane started to move down the runway, I didn't know if it was controllable, I didn't know for sure whether it could get off in that much runway, I didn't know whether the landing gear would take the banging of the ruts in the concrete at that weight. At first everything is fine, but then the fuel laden wingtips begin to literally fly downwards and scrape on the runway surface. Listen to her, I need to hear her. I need to hear 61 knots there, how are we doing? What do you say, I need to hear 61 knots. There is confusion. Neither Dick nor Gina realize what is happening to the wingtips. I don't want to ever thought that it would drive itself down into the ground like it did and it was terrifying watching the wings grind away, knowing there was fuel right at the wingtips almost. It was so frightening and hearing Gina's voice come out, she was counting for 100 yards as they were going and it was just this real steady, almost monotone voice that I was thinking to myself, how can she do this, unbelievable. You can see the lift on the wings, now lifting the wing literally. See the flexing of the wing. The thrill of seeing the wings finally lift and then finally bend and then lift off, wow. And then the magic 100 knots is reached. All right, so that is again for you the record on Voyager, but then of course it has been broken by so many other people. Now let's look at another very recent record on endurance. This is on UAV now. This is the research UAV from ETH Zurich. So again, in the interest of time, I am just going to show you. Look at that, this is the hours. This was in 2015. The aircraft has been flying nonstop for 12 hours 40 minutes. The battery is 89 percent. Now they enter the night flight, coming into land autonomously. So this is a world record for an aircraft less than 50 kilograms of weight, flew for more than 81 hours nonstop on autonomous flight. So that is the current world record for endurance. So just like we have the range equation, we have the endurance equation which is also very similar. Again DT is equal to DWF by C transpose T. But now we do not bring in RV infinity into that. We just go to this T integrated. Then there are some conditions which I will leave you for self-study that talk about. This is not the interesting part. This is the TDS calculation part. But look at the endurance equation. It has eta P cl3 by 2 by CD. We have always been saying that the propeller aircraft has a maximum endurance when cl3 by 2 by CD is maximum. This is the proof of that in the calculations. So to maximize of course, just maximize these things and minimize the thing on the bottom. So condition comes for propeller aircraft. I am going to rush through this. This also you know because we have already derived it. For jet engine aircraft, it is a simple equation. 1 by C L by D log of weight ratio. So the same expression. So the expression for maximum range for turboprops is similar to the equation for maximum endurance for turbojet system. So same conditions are applicable. And finally if you look at the comparison, there are these four speeds. There is one speed, number one at which power is minimum. Therefore endurance is maximum for a prop. There is another speed at which drag is minimum. That will give you the maximum range for props and maximum endurance for jets. Point number 3 is the same. Point number 4 will be the range for jets to be maximum. Okay. Now wind is going to make a big difference. So let us see effect of wind. So the conditions are the same. Same equations are there. But now you have to replace the value of V with ground speed. So if there is a headwind, okay, then the ground speed will be the actual speed plus the tailwind. If there is a tailwind, sorry. And if there is a headwind, then it will be the opposite. So the ground speed is going to be true airspeed plus tailwind or true airspeed minus headwind. Minus because it is opposite direction. So that is it. You just replace the equations and you will get the expressions. So this will be the same range expression but Vg will now be V plus Vt. Similarly for turboprops and piston props. So tailwind is going to always give you an increase in the range. That is what we saw in the picture also earlier where you can get much more range because of tailwind. So this is a summary. So in summary L by D maximum CL root CL by CD maximum, L by D maximum for endurance, L by D maximum for range and CL 3 by 2 by CD. So there are three conditions. L by D max CL root CL by CD max and CL power 3 by 2 by CD max. So L by D max gives you maximum endurance for jet maximum range for props. CL 3 by 2 by CD max gives you the value of maximum range for maximum endurance for propeller aircraft. And root CL by CD gives you maximum range for the jet aircraft. So this is a summary. Again the same thing I have shown here. So in the next class we are going to look at takeoff and landing.