Posts Tagged ‘2018’

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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

           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, practicing in a wind tunnel.

Abby Hughes, USA, in the air

          Abby Hughes, USA, in the air

Here are the X-section areas for Abby Hughes*:

Abby Hughes X-section

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.

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Winter Olympics: Beaten by 0.001 seconds

February 14, 2018

 

In 2014 Winter Olympics Annette Gerristen (below) lost the Gold Medal in the 1000 m Women’s speed skate competition by 0.02 seconds.

Annette Gerritsen fromthe Netherlands

Annette Gerritsen fromthe Netherlands

What are the speed skating times for women?

Women’s Speed Skating Calulations:

Here are the speed calcs for Yara Van Kerkhof of the Netherlands in the 2018 Winter Olympics:

If Yara lost the Gold Medal by 0.02 secs (2 hundredths of a second) what would the distance be between the Gold and Silver place getters?

When 1st and 2nd place are separated by 0.02 seconds, they are travelling at almost the same speed. So the second place contestant is:

23.8 cm behind the Gold Medalist

The 2018 Olympic Gold Medalist in the 500m Women’s Speed Skating was Arianna Fontana.

Italy’s Arianna Fontana wins the 500 m Speed Skating 2018 Olympic Gold Medal in 42.569 seconds ahead of Yara van Kerkhof of the Netherlands and Kim Boutin of Canada. 

Men’s Speed Skating:

At longer distances the men’s speed skating speed is similar to the women’s speed above.

If you lose by  0.001 secs…………

Apollo Ono (below) competed in the 1500m men’s speed skating. He has won 8 Olympic Medals.

If a speed skater lost the Gold Medal by 0.001 seconds, the smallest measured time segment at the Olympics, they would be:

1.19 cm

behind the winner. That is less than the length of a small fingernail.

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WINTER OLYMPICS: One Rule Aerial Skiers Cannot Break

February 10, 2018

Aerial skiers aim for height rather than length. Their aerial flight times are much smaller than ski jumpers so air resistance has minimal impact.

In fact, there is one law the aerial skiers cannot break. It is the law of gravity.

Here is an equation for  projectile motion from Wired magazine.

Screen grab from Wired Magazine

Screen grab from Wired Magazine

The equation for projectile motion also applies to Motorbike Jumps and Longbow Arrows.

Here is the x-y graph for different launch angles.

trajectory wired magazine

trajectory wired magazine

 

You can go to this page for complete calculations. Aerial skiers twist and turn but their CENTRE OF GRAVITY must follow this graph. More on centre of Gravity at The Great Back Pack Attack ie.

The centre of gravity of Aerial Skiers must follow a

parabolic curve.

Aerial Parabola final 2

Rocky Maloney Winter X Games Aspen

Rocky Maloney Winter X Games Aspen