Lockdown Challenge: Beware of the falling teddy bears!

Dang-a-lang-Dang-a-lang-a-Dang-lang-a…! That’s the fire alarm! DON’T PANIC! But hey, what’s this, it’s a rope. Phew! You can relax… but wait a minute, can you climb down a rope safely? If you’re a trained mountaineer, sure. The rest of the us, maybe not. But using the magic of friction and an upward-falling parachute maybe we could all go down safely. Here we see how it would work by making a scaled-down version for your furry friend Edward Bear to safely descend from a height.

People do just parachute from tall buildings but it’s difficult and dangerous. The large size of parachutes is a huge problem. The Drag Equation tells you the force a parachute gives. Cd, the drag coefficient, is the first element; the same Cd you see quoted for cars. Cd is then multiplied by a constant x speed² x area normal to flow. For parachutes, Cd is 1.5, and for a fall speed of 4ms^-1, a ‘chute has got to be a mammoth 10m in diameter.

But if there was some way of amplifying the force, you could use a tiny parachute. And… there is a way! We’ve all seen a sailor looping a rope around a capstan drum or bollard. The sailor uses friction between rope and capstan and can control a pull of many tonnes force on the rope with his hands. The Capstan Equation tells you what is going on. The governed force goes up as the controlling force times the exponential of (friction coefficient x angle of wrap). Wrap a rope once around a capstan and you might get an ‘amplifying factor’ of 10x. But with two wraps you’ll get a 100x, and with three, a whopping 1,000x amplifying factor.

The cunning plan here is to use this effect for a Safe Descender. The escapee dons a harness with a rope that goes around a capstan and down to a small parachute on the ground. The ‘chute falls upward, parallel to the downward-going escapee, and its drag force is amplified to allow a safe descent. Now you could simply wrap the string around the capstan about a turn and a half (540°), but the rope might tangle. So it’s better to use four or five ‘capstans’ none with more than 180° of wrap, but which add up to 540°.

To make a Safe Descender for Edward Bear, first, find a piece of wood that can be used for Teddy’s descent down from the upstairs hall or simply from ceiling height. We used an 80cm length of 7 x 5cm timber diagonally across the corner of the railing at the top of the hall. The string needs to slide smoothly, so use thick bolts with a few cm near the head not threaded, rather than thin nails or screws. Try five bolts with 6-10mm shafts, fitted in two rows, as in the picture. The outer two bolts should be spaced so that the parachute doesn’t get in the way of the escapee. Screwing the bolts into holes in the wood is a good way to fit them. Leave them projecting 2 or 3cm and then glue washers to wood and to the bolt head to stop the string from jumping off. Finally, make a parachute. Try a 40cm-square supermarket bag taped to 50cm strings.

Now fit your descender to the jumping point, connect string to parachute and Bear, loop it around the bolts, and drop the ‘chute, ready to fall upwards. Then… GERONIMO!! (traditional parachutist word), Teddy can leap downwards safely.

Once you’ve got the Upward-Falling Parachute Safe Descender working, try different loads on your parachute or different sizes of parachute. And try wrapping around three, four, or five capstans to see the effect of changing the amplification factor.

If you liked this, you will find lots more fun science stuff in Neil Downie’s books, like ‘The Ultimate Book of Saturday Science’ from Princeton University, and for lots of other things (and a free copy of the ‘Exploding Disk Cannons’ book), visit www.saturdayscience.org

There is the back catalogue of Lockdown Challenges from the past year to choose from if you are looking for more options. The IET also has a host of resources that adults can use to engage children with the world of STEM.