## NATHAN CHEN wins Gold but Figure Skating Scores can be BAD MATH

February 10, 2022

Nathan Chen, 22, USA, wins GOLD in the Men’s Figure skating with 5 brilliant, soaring quadruple jumps executed to perfection to Elton John’s “Goodbye Yellow Brick Road” and “Rocket Man.”

## Nathan Chen’s Winning Performance on You tube HERE.

According to the fab  nine Figure Skating judges score competitors for the complexity of each element (eg. Triple axel or triple spin jump) and the quality of the performance producing a score out of ten.

## Tessa Virtue and Scott Moir(Above) GOLD Medal performance at Pyeongchang 2018 here.

Kailani Craine, Australia

This is a typical figure skating score card for one competitor.

The final score, however, is based  on the average for only 5 of these scores. Two are eliminated by random selection (Red Brackets). Then the top and bottom scores are removed and the remaining five scores averaged.

Screen grab NBC Mathletes

# Skater A:

Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them)

# Skater B:

Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them). But this time the random selector eliminates two low scores.

The average:

## =  35.25/ 5 = 7.05

Same score cards but Skater B gets a higher average score than Skater A.

Skater A is, in fact, beaten by a random number selector!!!!

February 1, 2022

# The Parabola Must Be Obeyed!!!!

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

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

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.

Rocky Maloney Winter X Games Aspen

## Winter Olympics: Bad Math of Figure Skating Scores

February 22, 2018

According to the fab  nine Figure Skating judges score competitors for the complexity of each element (eg. Triple axel or triple spin jump) and the quality of the performance producing a score out of ten.

Tessa Virtue and Scott Moir win GOLD at Pyeong Chang 2018

Kailani Craine, Australia

This is a typical figure skating score card for one competitor.

The final score, however, is based  on the average for only 5 of these scores. Two are eliminated by random selection (Red Brackets). Then the top and bottom scores are removed and the remaining five scores averaged.

Screen grab NBC Mathletes

# Skater A:

Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them)

# Skater B:

Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them). But this time the random selector eliminates two low scores.

The average:

## =  35.25/ 5 = 7.05

Same score cards but Skater B gets a higher average score than Skater A.

Skater A is, in fact, beaten by a random number selector!!!!

## 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

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

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.

Rocky Maloney Winter X Games Aspen

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 :  vr = 308 RPM

Other spins include:

## Triple Axel spin vr = 220 – 280 RPM

……………………………………………………………………………………………..

## Maximum Triple Axel spin vr = 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 vr = 90 RPM

Kim Yuna, South Korea

# REASON 2:

## a camel spin into a very fast standing spin?

Now, mathspiggies, you must separate Linear Velocity (v1 ) from Angular Velocity (vr ). 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.

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 vr = 90 RPM

…………………………………………………………………………………

## 2. One Rule Aerial Skiers Cannot Break

January 23, 2014

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

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

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.

Rocky Maloney Winter X Games Aspen

## 4. Why the best figure skater doesn’t always win

January 23, 2014

According to the fab NBC video, Mathletes,  nine Figure Skating judges score competitors for the complexity of each element (eg. Triple axel or triple spin jump) and the quality of the performance producing a score out of ten.

Joannie Rochette

Brendan Kerry Australia…..

This is a typical figure skating score card for one competitor.

The final score, however, is based  on the average for only 5 of these scores. Two are eliminated by random selection (Red Brackets). Then the top and bottom scores are removed and the remaining five scores averaged.

Screen grab NBC Mathletes

# Skater A:

Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them)

# Skater B:

Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them). But this time the random selector eliminates two low scores.

The average:

## =  35.25/ 5 = 7.05

Same score cards but Skater B gets a higher average score than Skater A.

Skater A is, in fact, beaten by a random number selector!!!!