1 00:00:00,000 --> 00:00:15,560 Hi, I'm Danica McKellar. 2 00:00:15,560 --> 00:00:20,160 When I was your age, I played a character named Winnie Cooper on a television show called 3 00:00:20,160 --> 00:00:21,160 The Wonder Years. 4 00:00:21,160 --> 00:00:25,280 You may be wondering what an actor like me knows about math and science. 5 00:00:25,280 --> 00:00:30,480 Well, in fact, I love science so much that I majored in mathematics at UCLA. 6 00:00:30,480 --> 00:00:36,000 On today's episode of NASA Connect, you will discover how ratios, proportions, and mathematics 7 00:00:36,000 --> 00:00:39,960 are found in nature, in our bodies, and in things we create. 8 00:00:39,960 --> 00:00:44,880 We'll also see how, in the near future, you may be taking driver's ed and flyer's ed at 9 00:00:44,880 --> 00:00:46,320 the same time. 10 00:00:46,320 --> 00:00:50,440 So prepare for takeoff as hosts Van Hughes and Jennifer Pulley pilot you through this 11 00:00:50,440 --> 00:00:52,600 episode of NASA Connect. 12 00:01:20,600 --> 00:01:25,600 Hey guys, welcome to NASA Connect, the show that connects you to the world of math, science, 13 00:01:25,600 --> 00:01:27,600 technology, and NASA. 14 00:01:27,600 --> 00:01:28,600 He's Van Hughes. 15 00:01:28,600 --> 00:01:29,600 And she's Jennifer Pulley. 16 00:01:29,600 --> 00:01:32,800 We're your hosts, along with Norbert. 17 00:01:32,800 --> 00:01:36,040 He's going to help us take you through another awesome episode of NASA Connect. 18 00:01:36,040 --> 00:01:40,800 Right, every time Norbert appears, have your cue cards and your brain ready to look for 19 00:01:40,800 --> 00:01:43,360 answers to the questions he gives you. 20 00:01:43,360 --> 00:01:48,480 And teachers, when Norbert appears with a remote, that's your cue to pause the video 21 00:01:48,520 --> 00:01:50,520 and think about the problems he gives you. 22 00:01:50,520 --> 00:01:51,520 Got it? 23 00:01:51,520 --> 00:01:53,240 Oh yeah, I got it. 24 00:01:53,240 --> 00:01:55,160 Today we're in Kitty Hawk, North Carolina. 25 00:01:55,160 --> 00:02:00,480 This is where the Wright Brothers took the very first controlled, powered flight in 1903. 26 00:02:00,480 --> 00:02:01,480 And guess what? 27 00:02:01,480 --> 00:02:02,480 What? 28 00:02:02,480 --> 00:02:04,680 They used mathematics, like ratios. 29 00:02:04,680 --> 00:02:05,680 What is a ratio? 30 00:02:05,680 --> 00:02:06,680 Good question. 31 00:02:06,680 --> 00:02:13,760 A ratio is a pair of numbers that is used to make comparisons, and ratios are everywhere. 32 00:02:13,760 --> 00:02:14,760 Like this. 33 00:02:14,760 --> 00:02:19,520 Before the Wright Brothers flew planes, they were experts in one of the most revolutionary 34 00:02:19,520 --> 00:02:23,200 means of travel since the wheel, the bicycle. 35 00:02:23,200 --> 00:02:28,560 So in memory of the Wright Brothers' pre-flight days, let's use this bike as an example of 36 00:02:28,560 --> 00:02:29,560 a ratio. 37 00:02:29,560 --> 00:02:30,560 Good idea, Van. 38 00:02:30,560 --> 00:02:36,960 Let's say we want to compare the number of revolutions, or complete circles, that one 39 00:02:36,960 --> 00:02:41,040 tire makes to the distance that the bike travels. 40 00:02:41,040 --> 00:02:45,320 Pretend this wheel measures 76 centimeters, or 30 inches. 41 00:02:45,320 --> 00:02:50,880 By measuring the distance that the wheel rolled after one revolution, you can set up a ratio. 42 00:02:50,880 --> 00:02:53,880 One revolution to 239 centimeters. 43 00:02:53,880 --> 00:02:54,880 Right. 44 00:02:54,880 --> 00:02:57,640 When you find ratios, you're also using proportions. 45 00:02:57,640 --> 00:03:03,040 A proportion is a number sentence or equation that states that two ratios are equal. 46 00:03:03,040 --> 00:03:07,400 How could you use ratios and proportions to determine how far your bike would travel if 47 00:03:07,400 --> 00:03:09,560 the wheel made five revolutions? 48 00:03:09,560 --> 00:03:10,640 Simple. 49 00:03:10,640 --> 00:03:13,240 Set up a proportion like this. 50 00:03:13,240 --> 00:03:21,120 One revolution to 239 centimeters equals five revolutions to X, which is the unknown distance. 51 00:03:21,120 --> 00:03:28,720 Now, by cross-multiplying, we can see that the wheel would roll 1,195 centimeters in 52 00:03:28,720 --> 00:03:30,320 five revolutions. 53 00:03:30,320 --> 00:03:32,920 Notice that the fraction ratios are equivalent. 54 00:03:32,920 --> 00:03:36,000 Hey, here's another problem for you to try. 55 00:03:36,000 --> 00:03:42,280 If your bike wheel makes one revolution and travels 239 centimeters, how many revolutions 56 00:03:42,280 --> 00:03:47,840 would your wheel make if you traveled 2,352.3 inches? 57 00:03:47,840 --> 00:03:50,040 Be sure to watch your units. 58 00:03:50,040 --> 00:03:54,040 So now that you have a better understanding of ratios and proportions, let's get back 59 00:03:54,040 --> 00:04:00,320 to the Wright Brothers. 60 00:04:00,320 --> 00:04:05,560 How did mathematics and ratios help the Wright Brothers test and design their glider? 61 00:04:05,800 --> 00:04:09,040 Before Flyer One, the Wright Brothers worked on bicycles. 62 00:04:09,040 --> 00:04:13,320 As young men, Orville and Wilbur started a bicycle manufacturing and repair company in 63 00:04:13,320 --> 00:04:15,560 their hometown of Dayton, Ohio. 64 00:04:15,560 --> 00:04:20,040 The Wright Brothers used the money they made to finance their interest in aviation. 65 00:04:20,040 --> 00:04:24,440 In the winter of 1901, Orville and Wilbur Wright used their knowledge of math to build 66 00:04:24,440 --> 00:04:27,800 a wind tunnel in order to study how to control an aircraft. 67 00:04:27,800 --> 00:04:30,920 It was then that they realized the importance of ratios. 68 00:04:30,920 --> 00:04:31,920 Right. 69 00:04:31,920 --> 00:04:35,260 The Wright Brothers used something called the aspect ratio. 70 00:04:35,260 --> 00:04:39,460 That is the ratio of the wing's length to the wing's width. 71 00:04:39,460 --> 00:04:44,380 By increasing the length of the wing and at the same time decreasing the width of the 72 00:04:44,380 --> 00:04:49,220 wing, the Wright Brothers cut the drag they experienced in their wind tunnel by half. 73 00:04:49,220 --> 00:04:53,300 Immediately, they began designing a better working glider. 74 00:04:53,300 --> 00:04:58,020 In 1903, after adding a rudder, an engine, and a propeller to their aircraft, the Wright 75 00:04:58,020 --> 00:05:02,620 Brothers achieved the first self-propelled flight of an airplane and began the era of 76 00:05:02,700 --> 00:05:03,700 powered flight. 77 00:05:11,700 --> 00:05:15,220 Describe the girth of transportation since the early 1900s. 78 00:05:15,220 --> 00:05:17,660 What is mathematical about its girth? 79 00:05:17,660 --> 00:05:23,620 Hi, I'm Ardeth Williams, pilot and air traffic controller with the Federal Aviation Administration. 80 00:05:23,620 --> 00:05:26,460 Back in 1903, there was only one aircraft. 81 00:05:26,460 --> 00:05:28,940 Not much need for us to have an air traffic control system. 82 00:05:29,260 --> 00:05:34,620 However, by 1960, there were over 78,000 commercial and general aviation aircraft. 83 00:05:34,620 --> 00:05:40,100 And in 10 years, by the year 2010, we believe there will be almost 228,000. 84 00:05:40,100 --> 00:05:41,900 Air traffic is growing and growing. 85 00:05:41,900 --> 00:05:46,940 We anticipate by the year 2010, almost 1 billion people will be traveling by air. 86 00:05:46,940 --> 00:05:50,300 The year 2003 begins century number two of aviation. 87 00:05:50,300 --> 00:05:53,980 I hope in 10 years or so, you will be one of the visionaries that will ensure my safe 88 00:05:53,980 --> 00:05:59,860 and efficient flight by designing, building, maintaining, controlling, or flying the aircraft. 89 00:05:59,860 --> 00:06:02,500 The future of aviation is in your hands. 90 00:06:02,500 --> 00:06:05,980 You know, Ardeth is right. 91 00:06:05,980 --> 00:06:09,980 Mathematical concepts are everywhere and they help us explain the world we live in using 92 00:06:09,980 --> 00:06:10,980 a system of numbers. 93 00:06:10,980 --> 00:06:15,420 For example, remember when Ardeth used a bar graph to explain the growth in the number 94 00:06:15,420 --> 00:06:17,420 of airplanes since the Wright Brothers? 95 00:06:17,420 --> 00:06:19,000 Well, get this. 96 00:06:19,000 --> 00:06:24,000 We can also create a graph to show the growth of all types of transportation, from cars 97 00:06:24,000 --> 00:06:27,680 to planes to jets to future aircraft. 98 00:06:27,680 --> 00:06:29,360 Look closely at this graph. 99 00:06:29,360 --> 00:06:31,840 Can you see a pattern? 100 00:06:31,840 --> 00:06:35,400 Patterns like the growth of transportation are everywhere. 101 00:06:35,400 --> 00:06:39,320 You just have to look around. 102 00:06:39,320 --> 00:06:45,080 Speaking of patterns, a man by the name of Fibonacci discovered a very famous pattern 103 00:06:45,080 --> 00:06:48,640 of numbers a long time ago in Italy. 104 00:06:48,640 --> 00:06:55,100 This pattern of numbers is called the Fibonacci sequence and the ratio of certain numbers 105 00:06:55,100 --> 00:06:59,400 in this sequence is so special it's called the golden ratio. 106 00:06:59,400 --> 00:07:03,360 Hey, how would you like to meet an expert on Fibonacci? 107 00:07:03,360 --> 00:07:05,200 He's also a poet. 108 00:07:05,200 --> 00:07:09,000 Hi everybody, this is Bud Brown talking to you from the Math Emporium at Virginia Tech 109 00:07:09,000 --> 00:07:10,600 in Blacksburg, Virginia. 110 00:07:10,600 --> 00:07:15,600 The Emporium is a large room with over 500 computers where students can come day or night 111 00:07:15,600 --> 00:07:17,280 to learn about math. 112 00:07:17,280 --> 00:07:22,240 And speaking of learning, here's a little verse I've written about a man called Fibonacci. 113 00:07:22,240 --> 00:07:24,240 How many ancestors do we have? 114 00:07:24,240 --> 00:07:26,280 That number is easily found. 115 00:07:26,280 --> 00:07:31,480 For we all have two parents, four grands and eight greats, just double the previous round. 116 00:07:31,480 --> 00:07:35,300 But the family tree of the honeybee is not like any other. 117 00:07:35,300 --> 00:07:40,800 The girls, good and bad, have a mom and a dad, but each boy has only a mother. 118 00:07:40,800 --> 00:07:45,720 It's true, each drone has a mom alone, but each female has parents too. 119 00:07:45,720 --> 00:07:51,420 In addition, you see, she has grandparents three, one fewer than me or you. 120 00:07:51,420 --> 00:07:56,760 And sakes alive, great grandparents five, that's even true for the queen. 121 00:07:56,760 --> 00:07:59,300 And next, twice great, that number is eight. 122 00:07:59,300 --> 00:08:02,360 And of thrice greats, she has 13. 123 00:08:02,360 --> 00:08:06,580 Now she's asking us, don't make a fuss, to do this calculation. 124 00:08:06,580 --> 00:08:10,400 How many ancestors does she have in every generation? 125 00:08:10,400 --> 00:08:13,360 So hop to it folks, let's crack no jokes. 126 00:08:13,360 --> 00:08:15,760 Don't stop for meals or for slumber. 127 00:08:15,760 --> 00:08:20,160 Just work your mind, the answer you'll find is a Fibonacci number. 128 00:08:20,160 --> 00:08:24,320 And now, to help you learn more about Fibonacci numbers, here's Jennifer. 129 00:08:24,320 --> 00:08:28,800 Before we begin the student activity, let's learn a little more about the golden ratio 130 00:08:28,800 --> 00:08:29,800 and Fibonacci. 131 00:08:29,800 --> 00:08:30,800 Fib-a-who? 132 00:08:30,800 --> 00:08:38,520 Fibonacci was a 13th century Italian mathematician who was studying a rabbit problem. 133 00:08:39,240 --> 00:08:43,320 He wanted to know how many rabbits he would have at the end of the year if he started 134 00:08:43,320 --> 00:08:47,720 with only one pair of newborn rabbits. 135 00:08:47,720 --> 00:08:53,600 Fibonacci knew that newborns are able to breed after one month, then every month after, if 136 00:08:53,600 --> 00:08:55,400 the conditions were right. 137 00:08:55,400 --> 00:09:05,160 He found that the sequence 1, 1, 2, 3, 5, 8, 13, and so on, demonstrated the total number 138 00:09:05,160 --> 00:09:08,380 of rabbit pairs at the end of each month. 139 00:09:08,420 --> 00:09:12,460 So at the end of the first month you have the original pair of newborn rabbits. 140 00:09:12,460 --> 00:09:16,700 At the end of the second month you still have the original pair because it took a month 141 00:09:16,700 --> 00:09:19,400 for them to become old enough to breed. 142 00:09:19,400 --> 00:09:22,400 At the end of the third month you will have two pairs of rabbits. 143 00:09:22,400 --> 00:09:24,940 The original pair and their newborn pair. 144 00:09:24,940 --> 00:09:29,500 At the end of the fourth month you have the original pair, their first pair born the third 145 00:09:29,500 --> 00:09:32,760 month and their newborn pair born the fourth month. 146 00:09:33,120 --> 00:09:39,840 Following this sequence, at the end of month 12 you will have 144 pairs of rabbits. 147 00:09:39,840 --> 00:09:45,080 Fibonacci and others soon found this sequence occurring in many other things in nature. 148 00:09:45,080 --> 00:09:50,160 By counting the spirals of pine cones, pineapples and sunflower seed heads for example, you 149 00:09:50,160 --> 00:09:53,720 can find neighboring pairs of Fibonacci numbers. 150 00:09:53,720 --> 00:09:59,200 The way in which leaves are arranged on a stem also displays a Fibonacci relationship. 151 00:09:59,200 --> 00:10:02,240 So do the spirals found in seashells. 152 00:10:02,240 --> 00:10:06,160 Now Fibonacci wasn't the only one who was fascinated with these numbers. 153 00:10:06,160 --> 00:10:11,840 The ratio obtained by successive terms in the sequence was thought by the ancient Egyptians 154 00:10:11,840 --> 00:10:13,560 and Greeks to be special. 155 00:10:13,560 --> 00:10:19,800 It was so pleasing that they used this special ratio to design their pyramids, their temples 156 00:10:19,800 --> 00:10:20,800 and buildings. 157 00:10:20,800 --> 00:10:22,720 You know the Parthenon? 158 00:10:22,720 --> 00:10:28,440 That's a great example of what has come to be known as the golden ratio or golden proportion. 159 00:10:28,440 --> 00:10:30,040 Here's the Fibonacci sequence. 160 00:10:30,040 --> 00:10:35,400 Let's see if you can determine the operation used and find the next four terms. 161 00:10:35,400 --> 00:10:45,480 1, 1, 2, 3, 5, 8, 13. 162 00:10:45,480 --> 00:10:52,920 If you guessed 21, 34, 55 and 89 are the next four terms, you're right. 163 00:10:52,920 --> 00:10:54,340 How did you get it? 164 00:10:54,340 --> 00:10:59,000 The ratio of certain pairs of numbers in the Fibonacci sequence is used to describe things 165 00:10:59,000 --> 00:11:00,000 in nature. 166 00:11:00,000 --> 00:11:13,080 1 to 1, 1 to 2, 2 to 3, 3 to 5, 5 to 8, 8 to 13, 13 to 21. 167 00:11:13,080 --> 00:11:19,320 If you divide the denominator of each ratio by its numerator, the results look like this. 168 00:11:19,320 --> 00:11:24,800 The ratios begin to get close to the rounded number 1.62. 169 00:11:24,800 --> 00:11:27,600 What if you divide the small number in the pair by the large number? 170 00:11:27,600 --> 00:11:30,720 Well, you'll get .62 rounded. 171 00:11:30,720 --> 00:11:35,280 If something in nature can be described using the ratios in the Fibonacci sequence, well 172 00:11:35,280 --> 00:11:37,280 then it's said to be golden. 173 00:11:37,280 --> 00:11:44,000 For more Fibonacci fun, let's visit Fairview Elementary in Dayton, Ohio and Roosevelt Middle 174 00:11:44,000 --> 00:11:46,080 School in Springfield, Ohio. 175 00:11:46,080 --> 00:11:48,080 These students are in the SEMA program. 176 00:11:48,080 --> 00:11:53,080 Hi, we're from Fairview Maths Academy, Dayton, Ohio. 177 00:11:53,080 --> 00:11:55,080 We're SEMA students. 178 00:11:55,560 --> 00:12:00,560 Hi, we're from Roosevelt Middle School in Springfield, Ohio. 179 00:12:00,560 --> 00:12:02,560 We're SEMA students. 180 00:12:02,560 --> 00:12:05,560 NASA Connect asked us to help you learn this lesson. 181 00:12:05,560 --> 00:12:10,920 There are many ways to divide the class up to check for the Fibonacci ratio in the objects 182 00:12:10,920 --> 00:12:15,240 you've collected, but we've decided to have three groups. 183 00:12:15,240 --> 00:12:18,480 The first group will measure natural objects. 184 00:12:18,480 --> 00:12:21,720 First count the number of sides of the unpeeled banana. 185 00:12:21,720 --> 00:12:24,200 Write this number on the worksheet. 186 00:12:24,200 --> 00:12:29,320 On the pineapple, count the number of squares in two adjacent spirals. 187 00:12:29,320 --> 00:12:33,280 Are the adjacent numbers in the Fibonacci sequence? 188 00:12:33,280 --> 00:12:35,840 Count the segments of the halved grapefruit. 189 00:12:35,840 --> 00:12:38,600 Is the grapefruit golden? 190 00:12:38,600 --> 00:12:44,120 Examine the pine cone for the number of spirals that go to the right and compare that number 191 00:12:44,120 --> 00:12:47,720 to the number of spirals that go to the left. 192 00:12:47,720 --> 00:12:49,440 Look at the daisy. 193 00:12:49,440 --> 00:12:54,360 Compare the number of petals that grow in a clockwise direction to the number that grow 194 00:12:54,360 --> 00:12:57,240 in a counterclockwise direction. 195 00:12:57,240 --> 00:12:59,680 Is your daisy golden? 196 00:12:59,680 --> 00:13:04,640 Now check any other natural objects that you have brought to class. 197 00:13:04,640 --> 00:13:10,200 The second group uses body measurements that approximate the golden ratio. 198 00:13:10,200 --> 00:13:15,960 Write the ratio of finger segments in one finger to the number of fingers on one hand. 199 00:13:15,960 --> 00:13:17,840 Is your hand golden? 200 00:13:17,840 --> 00:13:22,360 Now measure each student's height and record the results on the worksheet. 201 00:13:22,360 --> 00:13:26,320 Measure each student from the top of their head to the top of the middle finger of the 202 00:13:26,320 --> 00:13:28,120 outstretched arm. 203 00:13:28,120 --> 00:13:29,560 Record the results. 204 00:13:29,560 --> 00:13:33,960 What is the ratio of the height to the measure of the length from the top of the head to 205 00:13:33,960 --> 00:13:36,200 the end of the outstretched arm? 206 00:13:36,200 --> 00:13:39,740 Does it approximate the golden ratio? 207 00:13:39,740 --> 00:13:44,160 Measure the height of each student and the navel to floor height of each. 208 00:13:44,160 --> 00:13:49,080 Write the result as a ratio of body height to navel to floor height. 209 00:13:49,080 --> 00:13:52,440 Is the result close to the golden ratio? 210 00:13:52,440 --> 00:13:56,280 Measure each student's arm length and fingertip to the elbow. 211 00:13:56,280 --> 00:13:58,120 Write the result as a ratio. 212 00:13:58,120 --> 00:14:00,120 Is it golden? 213 00:14:00,120 --> 00:14:03,160 Group three measures man-made objects. 214 00:14:03,160 --> 00:14:09,520 Verify the Fibonacci numbers by measuring the length and width of an index card. 215 00:14:09,520 --> 00:14:12,040 Try this with an ID card. 216 00:14:12,040 --> 00:14:15,800 Measure other objects in the classroom or brought to class. 217 00:14:15,800 --> 00:14:20,760 When all groups finish with their explorations, they could summarize their findings and report 218 00:14:20,760 --> 00:14:22,760 to the rest of the class. 219 00:14:22,760 --> 00:14:28,800 Special thanks to our AIAA student mentors from the University of Cincinnati. 220 00:14:28,800 --> 00:14:29,800 Great job, guys. 221 00:14:29,800 --> 00:14:34,400 After you've completed the activity on the golden ratio, you should analyze your observations 222 00:14:34,400 --> 00:14:37,920 and respond to the following. 223 00:14:37,920 --> 00:14:44,200 In four sentences, describe the activity you just completed. 224 00:14:44,200 --> 00:14:48,760 Was everything you examined golden? 225 00:14:48,760 --> 00:14:52,240 How do you determine if an object is golden? 226 00:14:52,240 --> 00:14:59,640 Do you think that there is another special ratio, like the golden ratio, that exists 227 00:14:59,640 --> 00:15:01,200 in nature? 228 00:15:01,200 --> 00:15:02,200 Why? 229 00:15:02,480 --> 00:15:06,480 Teachers, check out our NASA Connect website. 230 00:15:10,480 --> 00:15:15,480 How are NASA engineers using Fibonacci sequence and the golden ratio to research, design, 231 00:15:15,480 --> 00:15:17,480 and develop airplanes? 232 00:15:17,480 --> 00:15:22,480 When NASA engineers are designing airplanes, they want to be sure that all their airplanes 233 00:15:22,480 --> 00:15:23,480 handle the same way. 234 00:15:23,480 --> 00:15:26,480 It's kind of like driving a car or a truck. 235 00:15:26,480 --> 00:15:29,480 Whatever car or truck you drive should perform the same way. 236 00:15:29,760 --> 00:15:35,760 Anyway, let's say engineers have designed a new airplane with a larger wing than a previous 237 00:15:35,760 --> 00:15:36,760 design. 238 00:15:36,760 --> 00:15:41,760 They have to use ratios to scale or size parts like the ailerons to fit the new wing. 239 00:15:41,760 --> 00:15:45,760 Ailerons are the movable parts of airplane wings that control roll. 240 00:15:45,760 --> 00:15:50,760 If the ailerons are not the correct size for the new wing size, the plane might not fly 241 00:15:50,760 --> 00:15:51,760 the way it should. 242 00:15:51,760 --> 00:15:56,760 So you see, the golden ratio helps designers determine the geometric relationships needed 243 00:15:57,040 --> 00:16:00,040 to keep the plane flying the same. 244 00:16:00,040 --> 00:16:02,040 Hey guys, meet Bruce Holmes. 245 00:16:02,040 --> 00:16:07,040 He's an aeronautical engineer at NASA Langley Research Center in Hampton, Virginia. 246 00:16:07,040 --> 00:16:10,040 So Bruce, let us know what you're working on here at NASA. 247 00:16:10,040 --> 00:16:16,040 Well, as Ardith told you, our transportation demand in this country will soar beyond supply 248 00:16:16,040 --> 00:16:19,040 in the new century, the 21st century. 249 00:16:19,040 --> 00:16:25,040 And we have just got to figure out how to make more places available to more people 250 00:16:25,040 --> 00:16:26,040 in less time. 251 00:16:26,320 --> 00:16:31,320 And so we're working with smaller airports and smaller aircraft that fly ever faster 252 00:16:31,320 --> 00:16:35,320 and ever safer than before to meet this 21st century demand. 253 00:16:35,320 --> 00:16:39,320 You're telling me smaller airplanes, you mean like smaller, like this smaller right here. 254 00:16:39,320 --> 00:16:41,320 How is that going to happen, Bruce? 255 00:16:41,320 --> 00:16:47,320 Well, many people don't know that the ratio of the total number of airports in the country 256 00:16:47,320 --> 00:16:51,320 to the number that have hub and spoke airline service is about 10 to 1. 257 00:16:51,600 --> 00:16:55,600 And so we can go 10 times as many places and save time for people 258 00:16:55,600 --> 00:16:59,600 if we can figure out how to use these smaller airplanes and smaller airports. 259 00:16:59,600 --> 00:17:02,600 I mean, there are several ratios that aircraft designers use 260 00:17:02,600 --> 00:17:06,600 to sort of score themselves with the design of the airplane. 261 00:17:06,600 --> 00:17:11,600 Wing loading, for example, is where you take the whole weight of the airplane 262 00:17:11,600 --> 00:17:15,600 and divide by the wing area that you see out here. 263 00:17:15,880 --> 00:17:21,880 And that gives you a sense of the relationship between the weight of the vehicle 264 00:17:21,880 --> 00:17:24,880 to how much area is supporting it. 265 00:17:24,880 --> 00:17:31,880 Another ratio that's very useful is the total lift efficiency or lift capability 266 00:17:31,880 --> 00:17:33,880 of the wing divided by the weight of the airplane. 267 00:17:33,880 --> 00:17:37,880 And that tells you how efficient of a lifting device the airplane is. 268 00:17:37,880 --> 00:17:39,880 And it also tells you how long the runway needs to be 269 00:17:39,880 --> 00:17:42,880 because it tells you how slowly you can land the airplane. 270 00:17:42,880 --> 00:17:44,880 Very important ratio. 271 00:17:45,160 --> 00:17:49,160 So I guess what you're saying is that smaller airplanes mean smaller runways. 272 00:17:49,160 --> 00:17:50,160 Much smaller runways. 273 00:17:50,160 --> 00:17:56,160 You know, big runways at big airports can be 10,000 feet, 12,000 feet, 15,000 feet long. 274 00:17:56,160 --> 00:18:02,160 And yet you can use a runway that's only about 2,000 feet, about one-fifth the length. 275 00:18:02,160 --> 00:18:04,160 Okay, Bruce, this plane already exists, obviously. 276 00:18:04,160 --> 00:18:06,160 I mean, you fly this thing around. 277 00:18:06,160 --> 00:18:11,160 How are you and how is NASA going to use an airplane like this to help travel in the future? 278 00:18:11,440 --> 00:18:14,440 The Small Aircraft Transportation System, 279 00:18:14,440 --> 00:18:18,440 which is using smaller aircraft and smaller airports 280 00:18:18,440 --> 00:18:22,440 as a means by which we can move more people to more places. 281 00:18:22,440 --> 00:18:24,440 And you're working on this right now at NASA. 282 00:18:24,440 --> 00:18:29,440 What we want to do with SATS is make it possible for people to have another choice 283 00:18:29,440 --> 00:18:36,440 for intercity travel in the 21st century, a bypass around hub lock and a bypass around gridlock. 284 00:18:36,440 --> 00:18:40,440 If you want to be in those systems for other reasons, that's fine. 285 00:18:40,720 --> 00:18:42,720 We'd like to give people an alternative. 286 00:18:42,720 --> 00:18:45,720 We're proposing to make these smaller airports all across the country 287 00:18:45,720 --> 00:18:48,720 more accessible in virtually all weather conditions 288 00:18:48,720 --> 00:18:51,720 with airplanes that are as easy to use as cars 289 00:18:51,720 --> 00:18:55,720 and cost about the same as a car trip for long trips. 290 00:18:55,720 --> 00:18:57,720 And about as small as this? 291 00:18:57,720 --> 00:18:59,720 Well, the airplanes will be a little bit bigger than this. 292 00:18:59,720 --> 00:19:02,720 I mean, you'll be surprised, actually, at how big they'll seem once you get in. 293 00:19:02,720 --> 00:19:05,720 They'll seem more like minivans and things like that. 294 00:19:05,720 --> 00:19:09,720 So if you think about one of the other ratios or proportions that's interesting 295 00:19:10,000 --> 00:19:14,000 is how much power you have in the airplane relative to the weight of the airplane. 296 00:19:14,000 --> 00:19:17,000 We call it power loading or thrust to weight ratio. 297 00:19:17,000 --> 00:19:22,000 And the people at NASA's Glenn Research Center are working on how to get more efficiency 298 00:19:22,000 --> 00:19:27,000 and more thrust out of less weight in engines. 299 00:19:27,000 --> 00:19:29,000 This is like our little map here of telling us how to go. 300 00:19:29,000 --> 00:19:30,000 Let's plan a trip. 301 00:19:30,000 --> 00:19:32,000 Are we there yet? 302 00:19:32,000 --> 00:19:35,000 Well, here's how we find out. 303 00:19:35,280 --> 00:19:37,280 When you navigate, you pull out the map 304 00:19:37,280 --> 00:19:39,280 and you just kind of look at your route of flight, 305 00:19:39,280 --> 00:19:42,280 figure out where you're starting from, where you want to go to. 306 00:19:42,280 --> 00:19:44,280 And this is kind of a big mess. 307 00:19:44,280 --> 00:19:49,280 The more you got into it, the more involved this whole thing became. 308 00:19:49,280 --> 00:19:50,280 Oh, yeah. 309 00:19:50,280 --> 00:19:52,280 And then you peek over here and make sure everything's still going. 310 00:19:52,280 --> 00:19:53,280 All right. 311 00:19:53,280 --> 00:19:55,280 And we're going to put that away. 312 00:19:55,280 --> 00:19:57,280 Now it's all right here in the computer. 313 00:19:57,280 --> 00:19:58,280 Oh, it's all right here? 314 00:19:58,280 --> 00:19:59,280 Absolutely. 315 00:19:59,280 --> 00:20:00,280 So we can navigate. 316 00:20:00,280 --> 00:20:01,280 We can see where we are. 317 00:20:01,280 --> 00:20:02,280 We can see where the weather is. 318 00:20:02,280 --> 00:20:04,280 We can see where the traffic is. 319 00:20:04,560 --> 00:20:05,560 We can see where we wanted to go. 320 00:20:05,560 --> 00:20:07,560 And we can also have all of the frequencies 321 00:20:07,560 --> 00:20:09,560 and all the information that was on that map 322 00:20:09,560 --> 00:20:10,560 is stored in the computer. 323 00:20:10,560 --> 00:20:11,560 And we don't have to use the map. 324 00:20:11,560 --> 00:20:13,560 So I just push a button and pull it up. 325 00:20:13,560 --> 00:20:14,560 That's the idea. 326 00:20:14,560 --> 00:20:15,560 Wow. 327 00:20:15,560 --> 00:20:18,560 And you put all these technologies into this airplane. 328 00:20:18,560 --> 00:20:21,560 This is an airplane that has many of the SATS technologies. 329 00:20:21,560 --> 00:20:23,560 There are many more to come, 330 00:20:23,560 --> 00:20:25,560 but this is sort of the grandfather of SATS airplanes. 331 00:20:25,560 --> 00:20:28,560 So, Jennifer, Van, what do you say we button up 332 00:20:28,560 --> 00:20:31,560 and fly on over to the Research Triangle Institute 333 00:20:31,560 --> 00:20:33,560 and look at the computerized simulator 334 00:20:33,840 --> 00:20:35,840 so we can put some of this highway-in-the-sky theory 335 00:20:35,840 --> 00:20:36,840 into action? 336 00:20:36,840 --> 00:20:37,840 I love computers. 337 00:20:37,840 --> 00:20:38,840 Let's do it. 338 00:20:38,840 --> 00:20:39,840 That sounds great. 339 00:20:39,840 --> 00:20:40,840 And, you know, speaking of computers, 340 00:20:40,840 --> 00:20:43,840 did you know that the Boeing 777 was the first airplane 341 00:20:43,840 --> 00:20:46,840 ever to be designed completely using a computer? 342 00:20:46,840 --> 00:20:47,840 Isn't that right, Bruce? 343 00:20:47,840 --> 00:20:48,840 That's right. 344 00:20:48,840 --> 00:20:49,840 Yeah, they used computer technology 345 00:20:49,840 --> 00:20:51,840 and it gave engineers immediate feedback 346 00:20:51,840 --> 00:20:53,840 and eliminated the need for building expensive models. 347 00:20:53,840 --> 00:20:55,840 So while Bruce, Van, and I head over 348 00:20:55,840 --> 00:20:57,840 to the Research Triangle Institute, 349 00:20:57,840 --> 00:20:59,840 why don't you go see Dr. Shelley Canright 350 00:20:59,840 --> 00:21:01,840 and design an airplane using your own computer? 351 00:21:02,120 --> 00:21:06,120 Many of you have been a passenger on an airliner 352 00:21:06,120 --> 00:21:08,120 and I'm sure at least all of you have seen one 353 00:21:08,120 --> 00:21:09,120 flying across the sky. 354 00:21:09,120 --> 00:21:12,120 Maybe you've wondered what goes into designing one. 355 00:21:12,120 --> 00:21:15,120 Well, this show's online activity 356 00:21:15,120 --> 00:21:17,120 gives you the opportunity to model 357 00:21:17,120 --> 00:21:19,120 your own future passenger plane. 358 00:21:19,120 --> 00:21:22,120 By choosing different wings, tails, engines, 359 00:21:22,120 --> 00:21:24,120 and fuselage layouts, 360 00:21:24,120 --> 00:21:26,120 you can put together a complete airplane 361 00:21:26,120 --> 00:21:28,120 and see if it will fly. 362 00:21:28,120 --> 00:21:30,120 All of this right on your computer screen. 363 00:21:30,400 --> 00:21:32,400 Aided by computer analysis, 364 00:21:32,400 --> 00:21:34,400 you'll have quick feedback on the effect 365 00:21:34,400 --> 00:21:36,400 of each decision you make. 366 00:21:36,400 --> 00:21:38,400 The program you'll use is called 367 00:21:38,400 --> 00:21:40,400 Airplane Design Workshop 368 00:21:40,400 --> 00:21:42,400 and it will give you an example 369 00:21:42,400 --> 00:21:44,400 of how artificial intelligence may be used 370 00:21:44,400 --> 00:21:46,400 now and in the future to assist engineers 371 00:21:46,400 --> 00:21:48,400 in the modeling and design process. 372 00:21:48,400 --> 00:21:50,400 Let's go to Central Elementary School 373 00:21:50,400 --> 00:21:52,400 in Pleasant Grove, Utah, 374 00:21:52,400 --> 00:21:54,400 where Mr. Bill Schuler's students 375 00:21:54,400 --> 00:21:56,400 will guide you through this activity. 376 00:21:56,400 --> 00:21:58,400 Hello, I'm Bill Schuler, 377 00:21:58,680 --> 00:22:00,680 and we're doing some problem-based education 378 00:22:00,680 --> 00:22:02,680 using Desktop Aero's 379 00:22:02,680 --> 00:22:04,680 aircraft design program. 380 00:22:04,680 --> 00:22:06,680 The students are pretending 381 00:22:06,680 --> 00:22:08,680 they are design engineers 382 00:22:08,680 --> 00:22:10,680 for an aeronautical firm. 383 00:22:10,680 --> 00:22:12,680 They have a contract with an airline 384 00:22:12,680 --> 00:22:14,680 to design an airplane, 385 00:22:14,680 --> 00:22:16,680 and if they design the airplane properly, 386 00:22:16,680 --> 00:22:18,680 they will receive a contract 387 00:22:18,680 --> 00:22:20,680 for the purchase of these airplanes 388 00:22:20,680 --> 00:22:22,680 and construction. 389 00:22:22,680 --> 00:22:24,680 If not, they'll lose the contract 390 00:22:24,680 --> 00:22:26,680 and the company will go bankrupt. 391 00:22:26,960 --> 00:22:28,960 NASA Connect asks us to show you 392 00:22:28,960 --> 00:22:30,960 the Aircraft Design Workshop 393 00:22:30,960 --> 00:22:32,960 developed by Desktop Aeronautics, Inc. 394 00:22:32,960 --> 00:22:34,960 The main challenge 395 00:22:34,960 --> 00:22:36,960 with this activity is to see 396 00:22:36,960 --> 00:22:38,960 how fast you can fly 397 00:22:38,960 --> 00:22:40,960 and still meet the design requirements. 398 00:22:40,960 --> 00:22:42,960 First, we go to the NASA Connect 399 00:22:42,960 --> 00:22:44,960 website and click on the Norbert's 400 00:22:44,960 --> 00:22:46,960 Lab button to link to the 401 00:22:46,960 --> 00:22:48,960 online activity. 402 00:22:48,960 --> 00:22:50,960 At the top of the screen, 403 00:22:50,960 --> 00:22:52,960 you'll see a line of pictures. 404 00:22:52,960 --> 00:22:54,960 Click on the picture of the wing on the left side. 405 00:22:55,240 --> 00:22:57,240 Here you choose the sweep, 406 00:22:57,240 --> 00:22:59,240 size, and aspect ratio of your wings. 407 00:22:59,240 --> 00:23:01,240 Okay, now 408 00:23:01,240 --> 00:23:03,240 choose the next button which gives you 409 00:23:03,240 --> 00:23:05,240 size, area, and aspect ratio 410 00:23:05,240 --> 00:23:07,240 choices for your tail. 411 00:23:07,240 --> 00:23:09,240 The next button 412 00:23:09,240 --> 00:23:11,240 over lets you choose the type 413 00:23:11,240 --> 00:23:13,240 of jet, amount of thrust, 414 00:23:13,240 --> 00:23:15,240 and number and placement of engines 415 00:23:15,240 --> 00:23:17,240 for your airplane. 416 00:23:17,240 --> 00:23:19,240 Now select the seating arrangement. 417 00:23:19,240 --> 00:23:21,240 This button lets you select the speed, 418 00:23:21,240 --> 00:23:23,240 altitude, and amount of fuel 419 00:23:23,520 --> 00:23:25,520 for your plane. 420 00:23:25,520 --> 00:23:27,520 Now you'll pick a final destination. 421 00:23:27,520 --> 00:23:29,520 All trips will start at Washington, D.C. 422 00:23:29,520 --> 00:23:31,520 With all these choices made, 423 00:23:31,520 --> 00:23:33,520 it's time to have the computer program 424 00:23:33,520 --> 00:23:35,520 analyze your selection. 425 00:23:35,520 --> 00:23:37,520 Click on the last button to 426 00:23:37,520 --> 00:23:39,520 evaluate your airplane. 427 00:23:39,520 --> 00:23:41,520 You'll find out if you're ready to fly. 428 00:23:41,520 --> 00:23:43,520 If not, you can go back to make other choices. 429 00:23:43,520 --> 00:23:45,520 The software program 430 00:23:45,520 --> 00:23:47,520 will suggest how you might improve 431 00:23:47,520 --> 00:23:49,520 your design. 432 00:23:49,520 --> 00:23:51,520 Thanks for watching NASA Connect 433 00:23:51,800 --> 00:23:53,800 Central Elementary 434 00:23:53,800 --> 00:23:55,800 Bye! 435 00:23:55,800 --> 00:23:57,800 We hope you will try your hand with this 436 00:23:57,800 --> 00:23:59,800 online activity. The program offers 437 00:23:59,800 --> 00:24:01,800 a rich foundation for problem solving, 438 00:24:01,800 --> 00:24:03,800 reflection, and analysis. 439 00:24:03,800 --> 00:24:05,800 See what design situations you might create 440 00:24:05,800 --> 00:24:07,800 and then use the software to 441 00:24:07,800 --> 00:24:09,800 solve them. 442 00:24:09,800 --> 00:24:11,800 Hey Bruce, you know, that looks a little familiar. 443 00:24:11,800 --> 00:24:13,800 It looks like Langley. 444 00:24:13,800 --> 00:24:15,800 Well it should. The Fibonacci ratio we're learning about 445 00:24:15,800 --> 00:24:17,800 is also used by simulation engineers 446 00:24:17,800 --> 00:24:19,800 to recreate a very natural, lifelike appearance 447 00:24:20,080 --> 00:24:22,080 for grass, trees, buildings, 448 00:24:22,080 --> 00:24:24,080 skies, clouds. 449 00:24:24,080 --> 00:24:26,080 That's really cool. This is like a big video game. 450 00:24:26,080 --> 00:24:28,080 What is the purpose of this? 451 00:24:28,080 --> 00:24:30,080 Well, this is a simulator. Imagine though 452 00:24:30,080 --> 00:24:32,080 what it would be like if flying an airplane 453 00:24:32,080 --> 00:24:34,080 were a lot like playing a video game. 454 00:24:34,080 --> 00:24:36,080 I'd be flying all the time. 455 00:24:36,080 --> 00:24:38,080 Well, that's what we want to see happen. 456 00:24:38,080 --> 00:24:40,080 So what we do is we try out all the different 457 00:24:40,080 --> 00:24:42,080 kinds of images that 458 00:24:42,080 --> 00:24:44,080 give you a highway in the sky to follow. 459 00:24:44,080 --> 00:24:46,080 I think, Jennifer, you, Van, 460 00:24:46,080 --> 00:24:48,080 should give this a try. 461 00:24:48,360 --> 00:24:50,360 I have confidence in this, Bruce. 462 00:24:50,360 --> 00:24:52,360 Alright, let's try it out. 463 00:24:52,360 --> 00:24:54,360 There you go. Now, when you get up to 464 00:24:54,360 --> 00:24:56,360 about 80 miles an hour, 465 00:24:56,360 --> 00:24:58,360 you're going to gently pull back. 466 00:24:58,360 --> 00:25:00,360 This is so weird. 467 00:25:00,360 --> 00:25:02,360 Okay, now pull back. 468 00:25:02,360 --> 00:25:04,360 I'm flying! 469 00:25:04,360 --> 00:25:06,360 You just left the ground. 470 00:25:06,360 --> 00:25:08,360 Oh, and there's my pathway in the sky! 471 00:25:08,360 --> 00:25:10,360 And there's your highway in the sky. 472 00:25:10,360 --> 00:25:12,360 Now you can steer with the wheel. 473 00:25:12,360 --> 00:25:14,360 Oh, Bruce, this is so neat! 474 00:25:14,360 --> 00:25:16,360 And this is, the bottom of it is like 475 00:25:16,360 --> 00:25:18,360 the floor of the highway, and the top of it is 476 00:25:18,360 --> 00:25:20,360 the roof of the highway. 477 00:25:20,360 --> 00:25:22,360 It's like driving through a tunnel, if you will. 478 00:25:22,360 --> 00:25:24,360 There are no sides to this tunnel. 479 00:25:24,360 --> 00:25:26,360 And that tells you where you need to go. 480 00:25:26,360 --> 00:25:28,360 And it keeps you clear of everything 481 00:25:28,360 --> 00:25:30,360 that would be hazardous to you. 482 00:25:30,360 --> 00:25:32,360 Traffic, bad weather, 483 00:25:32,360 --> 00:25:34,360 obstacles, mountains. 484 00:25:34,360 --> 00:25:36,360 And who else is on this pathway with me? 485 00:25:36,360 --> 00:25:38,360 No one. This is your own pathway. 486 00:25:38,360 --> 00:25:40,360 Your computer created this for you. 487 00:25:40,360 --> 00:25:42,360 Because you told the computer before you got in 488 00:25:42,360 --> 00:25:44,360 where you wanted to go. 489 00:25:44,360 --> 00:25:46,360 This is so easy. I mean, this is great. 490 00:25:46,360 --> 00:25:48,360 I'll be able to fly like this right on to Richmond, won't I? 491 00:25:48,360 --> 00:25:50,360 Well, we hope anybody can do this 492 00:25:50,360 --> 00:25:52,360 with a little bit of practice on a simulator 493 00:25:52,360 --> 00:25:54,360 to be safe. 494 00:25:54,360 --> 00:25:56,360 You said anybody. I mean, you mean anybody like, 495 00:25:56,360 --> 00:25:58,360 even like a van, anybody? 496 00:25:58,360 --> 00:26:00,360 I just got my driver's license. I can do this. 497 00:26:00,360 --> 00:26:02,360 Right, right. You want to take the wheel? 498 00:26:06,360 --> 00:26:08,360 Left, left. 499 00:26:08,360 --> 00:26:10,360 Sorry, sorry. I got it. 500 00:26:10,360 --> 00:26:12,360 While Van tries to take off, 501 00:26:12,360 --> 00:26:14,360 we'd like to thank everyone who helped 502 00:26:14,360 --> 00:26:16,360 make this episode of NASA Connect possible. 503 00:26:16,360 --> 00:26:18,360 Van, Van, keep your eyes on the road. 504 00:26:18,360 --> 00:26:20,360 Sorry, sir. 505 00:26:20,360 --> 00:26:22,360 I mean, on the highway in the sky. 506 00:26:22,360 --> 00:26:24,360 You know, Van and I would love to hear from you 507 00:26:24,360 --> 00:26:26,360 with your comments, your questions, and your suggestions. 508 00:26:26,360 --> 00:26:28,360 So write us at NASA Connect, 509 00:26:28,360 --> 00:26:30,360 NASA Langley Research Center, 510 00:26:30,360 --> 00:26:32,360 Mail Stop 400, Hampton, Virginia, 511 00:26:32,360 --> 00:26:34,360 23681, or email us 512 00:26:34,360 --> 00:26:36,360 at connect 513 00:26:36,360 --> 00:26:38,360 at edu.larc.nasa.gov. 514 00:26:38,360 --> 00:26:40,360 Hey, teachers, 515 00:26:40,360 --> 00:26:42,360 if you would like a videotape copy 516 00:26:42,360 --> 00:26:44,360 of this NASA Connect show 517 00:26:44,360 --> 00:26:46,360 and the Educator's Guide lesson plans, 518 00:26:46,360 --> 00:26:48,360 contact your local NASA Educator Resource Center 519 00:26:48,360 --> 00:26:50,360 or CORE, 520 00:26:50,360 --> 00:26:52,360 the NASA Central Operation of Resources 521 00:26:52,360 --> 00:26:54,360 for Educators. 522 00:26:54,360 --> 00:26:56,360 All this information and more is located 523 00:26:56,360 --> 00:26:58,360 on the NASA Connect website. 524 00:26:58,360 --> 00:27:00,360 Good job, Van, keeping it pretty level. 525 00:27:00,360 --> 00:27:02,360 All right, okay, well, for the NASA Connect series, 526 00:27:02,360 --> 00:27:04,360 I'm Jennifer Pulley. And I'm Van Hughes. 527 00:27:04,360 --> 00:27:06,360 Van, hands on the wheel, please. 528 00:27:06,360 --> 00:27:08,360 Oh, sorry. 529 00:27:08,360 --> 00:27:10,360 And we're closing in on Richmond, 530 00:27:10,360 --> 00:27:12,360 trying to get there. Will we ever get there? 531 00:27:12,360 --> 00:27:14,360 Whoa! 532 00:27:14,360 --> 00:27:16,360 Good question. 533 00:27:16,360 --> 00:27:18,360 A ratio is a... 534 00:27:18,360 --> 00:27:20,360 Good question. 535 00:27:20,360 --> 00:27:22,360 This is where the Wright brothers flew the very... 536 00:27:22,360 --> 00:27:24,360 Talk, talk. 537 00:27:24,360 --> 00:27:26,360 What is a ratio? 538 00:27:26,360 --> 00:27:28,360 Sorry, my fault. 539 00:27:28,360 --> 00:27:30,360 No problem. 540 00:27:30,360 --> 00:27:32,360 Got it. 541 00:27:32,360 --> 00:27:34,360 Okay, here we go again. 542 00:27:34,360 --> 00:27:36,360 Got it. This is... 543 00:27:36,360 --> 00:27:38,360 That's okay. 544 00:27:38,360 --> 00:27:40,360 That's okay. 545 00:27:40,360 --> 00:27:42,360 So, Jennifer, Van, what do you say we button up? 546 00:27:42,360 --> 00:27:44,360 Ha, ha, ha! 547 00:27:44,360 --> 00:27:46,360 Controlled, powered flight 548 00:27:46,360 --> 00:27:48,360 in 1903. 549 00:27:48,360 --> 00:27:50,360 And guess what? 550 00:27:50,360 --> 00:27:52,360 They used mathematics, like ratios. 551 00:27:52,360 --> 00:27:54,360 Pardner? 552 00:27:54,360 --> 00:27:56,360 We're seamless students. 553 00:27:56,360 --> 00:27:58,360 NASA Connect show, 554 00:27:58,360 --> 00:28:00,360 I have to show you how to do this lesson. 555 00:28:00,360 --> 00:28:02,360 A ratio is a pair of numbers 556 00:28:02,360 --> 00:28:04,360 that is used to make... 557 00:28:04,360 --> 00:28:06,360 Comparison. 558 00:28:06,360 --> 00:28:08,360 Lose. 559 00:28:08,360 --> 00:28:10,360 While we fly on over to the Research Institute... 560 00:28:10,360 --> 00:28:12,360 Research... 561 00:28:12,360 --> 00:28:14,360 Research... 562 00:28:14,360 --> 00:28:16,360 Ha, ha! 563 00:28:18,360 --> 00:28:20,360 Thank you for watching NASA Connect. 564 00:28:20,360 --> 00:28:22,360 Be sure to check out my website 565 00:28:22,360 --> 00:28:24,360 at danicanmckeller.com, 566 00:28:24,360 --> 00:28:26,360 where I'll answer all your math questions 567 00:28:26,360 --> 00:28:28,360 and many more.