Why does a spoon get pulled into a tap stream?
Tonight's idea
Dangle a spoon by the tip of its handle and bring its rounded back up to a thin stream from the tap. It is pulled in, not pushed away.
The water clings to the curved back and follows it round, so it leaves heading off to the spoon's side. The spoon has turned the water sideways, and the water pulls the spoon the other way: into the stream.
Flowing water and air tend to follow a gently curved surface. Turn a fluid one way and it pushes you the other way.
A wing turns passing air downward, and the air pushes the wing up. That push is lift. Air over the top of a lifting wing also moves faster, and its pressure is lower. "Faster flow, lower pressure" is Bernoulli's principle. It is exact only for an ideal fluid, one with no friction that cannot be squeezed, flowing steadily. For a wing at ordinary speeds, real air comes close.
One measure of a wing is its glide ratio: metres travelled forward for each metre of height lost.
Watch one: a paper plane's glide ratio
A paper plane is let go 2 m above the floor and lands 10 m away, measured along the floor.
\[\text{glide ratio} = \text{distance forward} \div \text{height lost} = 10 \div 2 = 5\]
The plane goes 5 m forward for every 1 m it drops. This is a model: it assumes a steady glide in still air, at the same slope all the way down. A real throw wobbles at the start. In the model, the same plane let go from 3 m keeps the same slope and lands \(3 \times 5 = 15\) m away.
Your turn
Use the model every time: a steady glide in still air. All the test results are made up.
- Find each plane's glide ratio. Dart: let go from 2.5 m, landed 10 m away. Wide: from 1.5 m, landed 9 m away. Stubby: from 2 m, landed 5 m away. Which flew furthest? Which has the best ratio?
- How far would each of the three planes glide if it were let go from 3 m?
- A real glider with no engine can have a glide ratio of 40. (a) It is 500 m above flat ground. How far can it glide, in km? (b) An airfield is 30 km away. How high must the glider be to just reach it? (c) Why would a careful pilot want more?
- Kim lets four versions of one paper plane go from 2 m. Plane A, the plain one, lands 7 m away. B is A with wider wings: 9 m. C is A with its back edges bent sharply down: 4 m. D is B with a paper clip on the nose: 10 m. (a) Find the four glide ratios. (b) Which changes made the ratio better, and which worse? (c) Do these tests show that a clip would help plane A?
- True or false? Give a reason. (a) "The air over the top of a wing must reach the back at the same moment as the air underneath." (b) "A plane with glide ratio 5 always lands 5 m away." (c) "A wing that is giving lift is turning air downward."
Stretch: why gliders have long, thin wings
Two rectangular wings, seen from above. Wing P is 15 m from tip to tip and 0.6 m from front to back. Wing Q is 6 m from tip to tip and 1.5 m from front to back. (a) Find each area. (b) For each wing, work out tip-to-tip length \(\div\) front-to-back width. (c) Under a lifting wing the pressure is higher than on top, so at each tip some air slips round the end and trails off in a swirl. Swirls waste energy. Which wing has less tip for its size? (d) With wing P a glider has glide ratio 40, with Q only 16 (made up). From 1000 m up, how much further does P take it?
Answers
- Dart: \(10 \div 2.5 = 4\). Wide: \(9 \div 1.5 = 6\). Stubby: \(5 \div 2 = 2.5\). Dart flew furthest (10 m), but only because it started highest. Wide has the best glide ratio, 6: it gets the most distance out of each metre of height.
- Multiply 3 m by each ratio. Dart: \(3 \times 4 = 12\) m. Wide: \(3 \times 6 = 18\) m. Stubby: \(3 \times 2.5 = 7.5\) m. From the same height, the order of the distances is the order of the glide ratios.
- (a) \(500 \times 40 = 20\,000\) m, which is 20 km. (b) 30 km is 30 000 m, and \(30\,000 \div 40 = 750\), so 750 m. (c) The 750 m is for still air and a perfect steady glide. Wind blowing against the glider, or air that is sinking, means less ground covered for each metre lost. The pilot also needs height left over to line up and land.
- (a) Divide each distance by 2. A: 3.5. B: 4.5. C: 2. D: 5. (b) Wider wings made it better (3.5 to 4.5). Bending the back edges sharply down made it worse (3.5 to 2). The paper clip made the wide plane a little better (4.5 to 5). (c) No. The clip was only tried on the wide-winged plane. To know about plane A, test A with a clip and nothing else changed. One throw each is also thin evidence: Kim should repeat every throw several times.
- (a) False. Nothing forces the two streams to meet up again. In wind tunnel films, the air over the top of a lifting wing reaches the back first. (b) False. The ratio is forward distance for each metre dropped. From 2 m it lands 10 m away, and from 1 m it lands 5 m away. (c) True. The air pushes the wing up, and the wing pushes the air down.
Stretch. (a) P: \(15 \times 0.6 = 9\) square metres. Q: \(6 \times 1.5 = 9\) square metres. The same. (b) P: \(15 \div 0.6 = 25\). Q: \(6 \div 1.5 = 4\). This number is called the aspect ratio. (c) P. Its tips are only 0.6 m wide on a 15 m wing, and Q's are 1.5 m wide on a 6 m wing. For the same lift at the same speed, a longer wing loses less to the swirls, and keeping it thin stops the area growing. (d) P: \(1000 \times 40 = 40\,000\) m, or 40 km. Q: \(1000 \times 16 = 16\,000\) m, or 16 km. P goes 24 km further. In a steady glide, less wasted energy means a flatter slope, which is a bigger glide ratio.