Posts Tagged ‘Olympic Maths’

WINTER OLYMPICS: How ski Jumpers Use Math to Increase their Jump Length

February 16, 2018

While air resistance has little impact on aerial skiers 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 Pyeong Chang, 2018. Just imagine going down that at top speed!!!

A ski jumper is set to jump in Pyeongchang.

Casey Larson USA Pyeong chang 2018

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, 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.

A is the X-section Area,

p is the density of the air and

v the velocity of the object.

More here.

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.

Posted in algebra, Area, Winter Olympics Maths, Year 7 mathspig, Year 9 Mathspig | Tagged 2018, air resistance, area, calculations, crouch down?, drag, drag formula, lean forwards?, Middle school, Olympic Jump, Olympic Maths, pyeong Chang, Ski Jump, Why do ski jumpers, X-section | Leave a Comment »

1. The Real REASON why figure skaters can spin so fast

January 23, 2014

REASON 1:

Well, mathspiggies, the girl in this video is right. Angular momentum remains constant unless external forces are applied.

L = mvr

L = angular momentum

v = linear velocity

r = separation of object

Louisa Barama, USA

Let’s have a look at this equation:

The fastest spin on ice skates was achieved by Natalia Kanounnikova (Russia) with a maximum rotational velocity of 308 RPM (rotations per minute) at Rockefeller Centre Ice Rink, New York, USA on 27 March 2006. See Guinness Book of Records.

Record spin : v_r = 308 RPM

Other spins include:

Mao Asada, Japan, triple Axel

Triple Axel spin v_r = 220 – 280 RPM

……………………………………………………………………………………………..

Maximum Triple Axel spin v_r = 402 RPM

Skaters can spin faster during a triple axel jump because there is no friction from the ice slowing their spin.

To complete a quad axel, it’s estimated that the skater would have to rotate in the air at:

540 rpm.

…………………………………………………………………………………

Camel spin v_r = 90 RPM

More info here.

Kim Yuna, South Korea

…………………………………………….

REASON 2:

How can a figure skater move from

a camel spin into a very fast standing spin?

Now, mathspiggies, you must separate Linear Velocity (v₁ ) from Angular Velocity (v_r ). Linear Velocity is measured in m/sec ie. it is the speed of, say, a skaters foot around the circle. Angular Velocity is measured in either RPM (Revolutions Per Minute) or degrees or Radians per minute. Ie. It is the rate of spin. We can’t judge how many m/sec a skaters foot is moving in a circle. We can only see how fast they spin. In other words, we see their Angular Velocity. When a skaters foot is in the Camel position that foot travels in a very big circle.

But when that same foot is in a Triple Axel postion it moves in a very, very small circle.

Patrick Chan, Canada, Camel Spin

Patrick Chan, Canada, Triple Axel

By halving the radius, firstly, a skater’s Linear Velocity doubles due to the conservation of angular momentum.

Then, secondly, by halving the radius the circumference of the circle moved by , say, the skaters foot is halved.

Overall, by doubling the velocity around the circle and halving the circumference a skater increases their rotational velocity by a factor of 4.

Look at the numbers:

Camel spin v_r = 90 RPM

…………………………………………………………………………………

Triple Axel spin v_r = 4 x 90 RPM = 360 RPM

That’s about right.

Posted in algebra, Middle School, Senior School, units speed, Winter Olympics Maths, Year 7 mathspig, Year 9 Mathspig | Tagged Amo Asada, Angular Velocity, Camel, Fastest figure skater spin, Figure skating, How fast do figure skaters spin?, Kim Yuna, Linear Velocity, Olympic Maths, Patrick Chan, Quadruple Axel, Record Spin, RPM, Sochi, Triple Axel, What is RPM?, Winter Olympic Math, Winter Olympics, World Record spin | 5 Comments »

3. How maths rules ski jumping

January 23, 2014

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