Student Name: Scott Axel Block: A Graduation Project—Informative Research Product Organizer Hook/Grabber: The benefit of shaped skis can be proven scientifically. Focusing Statement: The increased sidecut decreases the necessary force required to perform a pure carved turn, and better materials are used to allow for stronger skis. Essential Background information: Sidecut on a traditional straight ski ranges from 0 to 4 mm in most cases. The composition of skis started out as brittle wood. Then they transitioned to bendable hickory, then on to wood/metal composites, then to solid metal (aluminum or titanium). Each of these skis increased only a few millimeters in sidecut, so that by the time the first modern competitive ski came out they ranged from 7-14mm sidecut. Now skis are metal/fiberglass composites and there are countless customizable settings that can make a ski perform ideally for each user. Topic 1: Construction and composition of skis – composite metal alloys and fiberglass skis ensure durability and flexibility Subtopic: The Core: modern composite vs. wood/metal composite Details/Evidence/Quotes: “Traditionally constructed skis are made of wood cores and contain fiberglass and metals…The layered Carbon Fiber used in all GOODE Skis has twice the strength of fiberglass (3.5 times the strength of aluminum) while weighing half as much. That is a four times (4X) Strength to Weight Ratio.” (http://www.goode.com/skiconstruction.htm) “Völkl is well known for producing the highest quality wood core skis. Our engineers believe that wood cores provide the ultimate smoothness, power, stability, and durability for high performance skiing. Völkl uses two different types of wood core configurations.” (http://www.volkl.com/ski_05/ski_tech.html) Subtopic: metal edges vs. no edges Details/Evidence/Quotes: “In 1930, an Austrian Rudolph Lettner put metal edges on his wooden skis for protection and found that they turned much better.” (http://www.vermontskimuseum.org/exhibit09.htm) “1949: Howard Head's plywood-core, pressure-bonded aluminum Head Standard with continuous integral steel edge began its journey toward becoming the most commercially successful early metal ski.” (http://skiinghistory.org/skishistory.html) Subtopic: tip and tail composition/design Details/Evidence/Quotes: “Additional mass at the tip and tail, combined with improved edge contact through the turn, meant that the new 180cm skis could be as stable as the old straight 205s. Another design change proved essential: the ski had to be stronger and stiffer through the center to prevent the wider tip “hinging” upward in bumps and deep snow.” (http://www.skiinghistory.org/sidecut.html) “Capped construction at tip and tail = increased torsional rigidity for higher performance, increased durability and tolerance for edge abuse.” (http://www.genuineguidegear.com/sites/default/files/learningcentre/downloads/2009-2010-G3SkiManual_0.pdf)
“Powder Specific Tip Design The widest point of this tip is the forward contact point as opposed to 7cm in front of it like most of our shaped skis. This design makes the ski more stable and predictable because it won’t hook or grab erratically in windblown snow and other variable conditions that you’re likely to encounter in the backcountry.” (http://k2skis.com/technology/skis)
Topic 2: camber and rocker – a totally new technology that has revolutionized the shaped ski, it allows for different types of shaped skis Subtopic: What a camber is Details/Evidence/Quotes: “Camber describes the minor upward bend commonly found between the tip and tail on a ski, a curve that peaks beneath the binding, and becomes increasingly visible when a pair of ski bases are pressed together. The purpose of this design is to allow for greater edge control, and greater acceleration when initiating a turn. The skier's body weight naturally forces the bend into a flattened position, and the skier is hardly the wiser.” (http://www.theskichannel.com/news/skinews/20091117/New-ski-technology-blending-the-old-with-the-new-) “With proper edging and the aid of the side camber or curve built into the ski, a turn may be started with very little movement” (Ski magazine) Subtopic: What a rocker is Details/Evidence/Quotes: “All-Terrain Rocker Featuring an elevated tip for variable and soft snow performance and camber underfoot for power, energy and edge-hold in firmer conditions.” (http://k2skis.com/technology/skis) “Rocker opens up a whole new spectrum of angles on take-offs and butters, while variable side-cut ensures plenty of stability on landing and between features” (http://www.theskichannel.com/news/skinews/20091117/New-ski-technology-blending-the-old-with-the-new-) Subtopic: Different camber/rocker combinations vs. straight skis Details/Evidence/Quotes: “Camber has been built into skis to give them a lively and playful feel on snow. Until recently very few companies attempted to modify the standard camber to give the skis additional performance advantages in different snow conditions or terrain. Standard Camber The FCP and ACP are the first two locations that come in contact with the snow when the ski is placed on a flat surface. This type of camber is still the most versatile camber to keep a ski lively and versatile in all types or terrain or conditions. We use a traditional camber on certain models in all three categories of skis” (http://www.golfskiwarehouse.com/pdf/tech_k2skis.pdf) “The downside of wood is that they lose their camber and spring, they have to be rather thick and do not turn well in soft snow.” (http://www.vermontskimuseum.org/exhibit09.htm) Topic 3: The sidecut technology and the sidecut of modern skis Subtopic: What a carved turn is Details/Evidence/Quotes: "The skier senses the moment when the edge of the outside ski takes over the powering of the turn. He consciously surrenders to its external force. The result is a feeling that the skis are literally carving the turn for you." (ski magazine) “The new ski conformed more easily to the actual arc required to carve a clean turn in the racecourse. For any given turn, the racer needed less edge angle, and could therefore stand on a straighter, stronger leg. Folks on the World Cup circuit woke up.” (http://www.skiinghistory.org/sidecut.html) Subtopic: What a sidecut is Details/Evidence/Quotes: “The new shaped skis…the tip and the tail are much wider than the waist of the ski…it creates an hourglass shape…added weight creates an arc effect which creates a natural turn” (http://www.youtube.com/watch_popup?v=hugIvXY6xAo&vq=medium#t=12) “An original Völkl technology, Dimension-3 sidecuts are an important reason that our skis perform so well. Völkl engineers design Dimension-3 sidecuts using computer models of the ski in a flexed condition - simulating a ski turn. The result is a more natural, elongated sidecut shape which, when engaged, contacts the snow with exceptionally even pressure. The result is a smoothness and precision that no non-Dimension-3 ski can equal.” (http://www.volkl.com/ski_05/ski_tech.html) Subtopic: The math behind it all Details/Evidence/Quotes: “Assuming
The ski edge forms the arc of the circle in the wedge.
The contact line is the line running from the widest point on the tip of the ski to the widest point on the tail of the ski.
The sidecut depth of the ski is the maximum height of the ski edge measured from the contact line.
define the variables
L = length of the contact line
d = sidecut depth
Rsc = sidecut radius
then the sidecut radius is
Rsc = (L^2/4 + d^2) / (2*d)
The variables are:
phi = angle swept out by the sidecut of the ski, i.e. Rsc*phi is the length of the edge from the widest point on the tip to the widest point on the tail.
d_rc = reverse camber distance, distance from the flat ski to the edge when the ski is pushed into the snow
alpha = inclination angle of the skiers leg.
theta = inclination angle of the slope.
Rcyl = cylinder radius.
Rturn = turn radius
Here is the result
d = Rsc * (1-cos(phi/2))
d_rc = d * cot(alpha-theta)
Rcyl = (L^2 + 4*d_rc^2)/(8*d_rc)
Rturn = Rcyl * sin(alpha+theta)
This formula is messy, but the interpretation of the formula is interesting and easily understood. It explains, mathematically, how a deep side cut ski carves easily. To understand this, I'll make a comparison between two different skis.” (http://www.math.utah.edu/~eyre/rsbfaq/physics.html).
Conclusion: The point in any scientific endeavour is to prove something; often times, only a theory is made. Shaped skis can be proven to be physically more durable, stronger, carve easier, require less force, and cut cleaner. There is mathematical, testimonial, and countless first hand data to back this up.
Student Name: Scott Axel Block: A
Graduation Project—Informative Research Product Organizer
Hook/Grabber: The benefit of shaped skis can be proven scientifically.
Focusing Statement: The increased sidecut decreases the necessary force required to perform a pure carved turn, and better materials are used to allow for stronger skis.
Essential Background information: Sidecut on a traditional straight ski ranges from 0 to 4 mm in most cases. The composition of skis started out as brittle wood. Then they transitioned to bendable hickory, then on to wood/metal composites, then to solid metal (aluminum or titanium). Each of these skis increased only a few millimeters in sidecut, so that by the time the first modern competitive ski came out they ranged from 7-14mm sidecut. Now skis are metal/fiberglass composites and there are countless customizable settings that can make a ski perform ideally for each user.
Topic 1: Construction and composition of skis – composite metal alloys and fiberglass skis ensure durability and flexibility
Subtopic: The Core: modern composite vs. wood/metal composite
Details/Evidence/Quotes: “Traditionally constructed skis are made of wood cores and contain fiberglass and metals…The layered Carbon Fiber used in all GOODE Skis has twice the strength of fiberglass (3.5 times the strength of aluminum) while weighing half as much. That is a four times (4X) Strength to Weight Ratio.” (http://www.goode.com/skiconstruction.htm)
“Völkl is well known for producing the highest quality wood core skis. Our engineers believe that wood cores provide the ultimate smoothness, power, stability, and durability for high performance skiing. Völkl uses two different types of wood core configurations.” (http://www.volkl.com/ski_05/ski_tech.html)
Subtopic: metal edges vs. no edges
Details/Evidence/Quotes: “In 1930, an Austrian Rudolph Lettner put metal edges on his wooden skis for protection and found that they turned much better.” (http://www.vermontskimuseum.org/exhibit09.htm)
“1949: Howard Head's plywood-core, pressure-bonded aluminum Head Standard with continuous integral steel edge began its journey toward becoming the most commercially successful early metal ski.” (http://skiinghistory.org/skishistory.html)
Subtopic: tip and tail composition/design
Details/Evidence/Quotes: “Additional mass at the tip and tail, combined with improved edge contact through the turn, meant that the new 180cm skis could be as stable as the old straight 205s. Another design change proved essential: the ski had to be stronger and stiffer through the center to prevent the wider tip “hinging” upward in bumps and deep snow.” (http://www.skiinghistory.org/sidecut.html)
“Capped construction at tip and tail = increased torsional rigidity for higher performance, increased durability and tolerance for edge abuse.” (http://www.genuineguidegear.com/sites/default/files/learningcentre/downloads/2009-2010-G3SkiManual_0.pdf)
“Powder Specific Tip Design
The widest point of this tip is the forward contact point as opposed to 7cm in front of it like most of our shaped skis. This design makes the ski more stable and predictable because it won’t hook or grab erratically in windblown snow and other variable conditions that you’re likely to encounter in the backcountry.” (http://k2skis.com/technology/skis)
Topic 2: camber and rocker – a totally new technology that has revolutionized the shaped ski, it allows for different types of shaped skis
Subtopic: What a camber is
Details/Evidence/Quotes: “Camber describes the minor upward bend commonly found between the tip and tail on a ski, a curve that peaks beneath the binding, and becomes increasingly visible when a pair of ski bases are pressed together. The purpose of this design is to allow for greater edge control, and greater acceleration when initiating a turn. The skier's body weight naturally forces the bend into a flattened position, and the skier is hardly the wiser.” (http://www.theskichannel.com/news/skinews/20091117/New-ski-technology-blending-the-old-with-the-new-)
“With proper edging and the aid of the side camber or curve built into the ski, a turn may be started with very little movement” (Ski magazine)
Subtopic: What a rocker is
Details/Evidence/Quotes: “All-Terrain Rocker
Featuring an elevated tip for variable and soft snow performance and camber underfoot for power, energy and edge-hold in firmer conditions.” (http://k2skis.com/technology/skis)
“Rocker opens up a whole new spectrum of angles on take-offs and butters, while variable side-cut ensures plenty of stability on landing and between features” (http://www.theskichannel.com/news/skinews/20091117/New-ski-technology-blending-the-old-with-the-new-)
Subtopic: Different camber/rocker combinations vs. straight skis
Details/Evidence/Quotes: “Camber has been built into skis to give them a lively and playful feel on snow. Until recently very few companies attempted to modify the standard camber to give the skis additional performance advantages in different snow conditions or terrain.
Standard Camber
The FCP and ACP are the first two locations that come in contact with the snow when the
ski is placed on a flat surface. This type of camber is still the most versatile camber to
keep a ski lively and versatile in all types or terrain or conditions. We use a traditional
camber on certain models in all three categories of skis” (http://www.golfskiwarehouse.com/pdf/tech_k2skis.pdf)
“The downside of wood is that they lose their camber and spring, they have to be rather thick and do not turn well in soft snow.” (http://www.vermontskimuseum.org/exhibit09.htm)
Topic 3: The sidecut technology and the sidecut of modern skis
Subtopic: What a carved turn is
Details/Evidence/Quotes: "The skier senses the moment when the edge of the outside ski takes over the powering of the turn. He consciously surrenders to its external force. The result is a feeling that the skis are literally carving the turn for you." (ski magazine)
“The new ski conformed more easily to the actual arc required to carve a clean turn in the racecourse. For any given turn, the racer needed less edge angle, and could therefore stand on a straighter, stronger leg. Folks on the World Cup circuit woke up.” (http://www.skiinghistory.org/sidecut.html)
Subtopic: What a sidecut is
Details/Evidence/Quotes: “The new shaped skis…the tip and the tail are much wider than the waist of the ski…it creates an hourglass shape…added weight creates an arc effect which creates a natural turn” (http://www.youtube.com/watch_popup?v=hugIvXY6xAo&vq=medium#t=12)
“An original Völkl technology, Dimension-3 sidecuts are an important reason that our skis perform so well. Völkl engineers design Dimension-3 sidecuts using computer models of the ski in a flexed condition - simulating a ski turn. The result is a more natural, elongated sidecut shape which, when engaged, contacts the snow with exceptionally even pressure. The result is a smoothness and precision that no non-Dimension-3 ski can equal.” (http://www.volkl.com/ski_05/ski_tech.html)
Subtopic: The math behind it all
Details/Evidence/Quotes:
“Assuming
- The ski edge forms the arc of the circle in the wedge.
- The contact line is the line running from the widest point on the tip of the ski to the widest point on the tail of the ski.
- The sidecut depth of the ski is the maximum height of the ski edge measured from the contact line.
define the variables- L = length of the contact line
- d = sidecut depth
- Rsc = sidecut radius
then the sidecut radius is- Rsc = (L^2/4 + d^2) / (2*d)
The variables are:- phi = angle swept out by the sidecut of the ski, i.e. Rsc*phi is the length of the edge from the widest point on the tip to the widest point on the tail.
- d_rc = reverse camber distance, distance from the flat ski to the edge when the ski is pushed into the snow
- alpha = inclination angle of the skiers leg.
- theta = inclination angle of the slope.
- Rcyl = cylinder radius.
- Rturn = turn radius
Here is the result- d = Rsc * (1-cos(phi/2))
- d_rc = d * cot(alpha-theta)
- Rcyl = (L^2 + 4*d_rc^2)/(8*d_rc)
- Rturn = Rcyl * sin(alpha+theta)
This formula is messy, but the interpretation of the formula is interesting and easily understood. It explains, mathematically, how a deep side cut ski carves easily. To understand this, I'll make a comparison between two different skis.” (http://www.math.utah.edu/~eyre/rsbfaq/physics.html).Conclusion:
The point in any scientific endeavour is to prove something; often times, only a theory is made. Shaped skis can be proven to be physically more durable, stronger, carve easier, require less force, and cut cleaner. There is mathematical, testimonial, and countless first hand data to back this up.