While air resistance has little impact on aerial skiers (above) it is a significant factor used by ski jumpers to increase their jump distance.
The significant maths for ski jumpers is therefore X-section area.
Here is the jump at Sochi. Just imagine going down that at top speed!!!
Sochi Ski Jump 2014 by blogger Melbourneer
Ski jumpers increase their speed going down the ramp by reducing their X-section area:
Lindsey Van, USA, practicing in a wind tunnel
Once they leave the ramp, ski jumpers try to increase their X-section area like Ski Divers to slow their vertical fall. But they have to land safely so they keep their skis at a minimum angle.
Abby Hughes going down jump:
Abby Hughes, USA, practicing in a wind tunnel.
Abby Hughes, USA, in the air
Here are the X-section areas for Abby Hughes*:
Here is the formula for Air Resistance of Drag:
D = ½CApv2
Where C is the drag coefficient or constant, which depends on the shape and spin of an object. It is found by testing the object in a wind tunnel.
As Abby Hughes has tripled here X-section area in the air she will
have tripled the vertical drag during her jump. This will slow here decent.
*Mathspig calculated the X-section area by the old fashioned method of counting squares and rounding off the final count. Mathspig sized the two pics of Abby Huges so that her head was the same size in both pictures.
K = Coefficient of Exposure = 0.5 (Engineers use standard tables for K)
v = Wind velocity = 72 kph = 20 m/sec
A = area of X-section exposed to the wind
Now, we’re going to be tricky. A 1 kg weight (eg. a litre of milk) exerts a force of 9.8 N or 1 kgf = 9.8 N on your hand. If we divide the above formulae by 10 we end up with a unit we know …. kgf.
F = Kv2A/10 kgf
If the wind force is 9,560 kgf in a storm it can easily pick up a 600kg duck. In fact, if you do the calcs, it is only in a normal wind ( 20 kph or 5 m/sec) that the duck would stay put (F = 597 kgf).
So WATCH OUT!!!!!
If that duck is not tethered to a building or pontoon it could take off and it could easily take out a school!!!!!
Skills:Geometry, measurement, cylinders, area, symmetry and creativity.
Year Level: Year 4 – whatever
Ask students to build their own cardboard armour and helmet. Give prizes in the category of Scariest, most Mathematically-Complex, Star Wars Potential, Most Historical, Most Creative and any other category that crops up. You can source cardboard from your nearest Self-Storage Warehouse.
Mathspig was at Womadelaide Music Festival 2013 and saw the Box Wars at work. The Box Wars guys, Joss, Josh and Hoss, started in Melbourne and now travel to Music Festivals around Australia. Boxwars builds sculptures, armour, props and sets and airplanes , tanks, cannons and the rest.
They stage battles of destruction … but destruction isn’t always the outcome.
If you want to interest kids especially boys 8 – 12 years of age in maths, get them building armour.
Mathspig saw dozens of them at WOMAD and they so loved their armour they wouldn’t take it off in 39Cº.
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Sometimes it is just lots and lots of fun. Here is a recently staged BOX WARS in Canberra. You only need watch a few minutes of the video to get the idea.
Or search topics on Youtube eg. Introduction to Conics Khan
Why Does Mathspig like The Kahn Academy? Because it’s:
1. Free.
2. Quick
3. Clear
4. Low-key
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Salman gives digital chalk-and-talk tutes like a teacher. He hand draws the equations and graphs. He uses a calculator from time to time, but he tends not to use whizz bang spreadsheet graphs or perfectly presented textbook equations. It’s a bit wobbly and it’s all coming from Salman’s head.
And students like this approach. It makes maths look do-able.
The tutes on Maths Online are produced by Aussie Maths teachers and they are very good. Mathspig, of course, imagined the quadratic function tutes might look something like this:
Graffiti pic found @ imfunny blog.
