Up and Down Acceleration

[Mike King]

Paging @Jamt and @François Pugh to the white telephone. I've seen @Jamt's discussions of up and down acceleration and I've come to believe there is something very important there, but I just do not understand what it is. I have the unfortunate disability in that I never took physics, but I am somewhat mathematically competent. So, for this simpleton, can you guys help me to sort out what you are talking about? And help me to understand why it is important?

Let's start with the post you had explaining this concept in the edge angles thread. You said:

​

What I mean with up and down acceleration is the acceleration of the CoM from or towards the snow surface.​

​

This would seem to imply that the sign of the acceleration would be associated with the direction of the CoM wrt the surface of the snow, but you later seem to contradict this by stating:

​

Just a point about movement and acceleration. Acceleration is the rate of change of velocity. This means that in a turn the up acceleration starts while the CoM is still moving down, and is usually maximal when the CoM is closest to the ground.​

​

Can you help me understand then what is the difference between "up" and "down" acceleration then?

​

As you know in physics there is always a cause and effect and the acceleration of the CoM towards the surface is directly given by the force on your skis that is perpendicular to the snow surface and your weight (gravity).​

​

For example: if you are jumping up and down continually on a flat surface the acceleration is -1g when you are in the air (no force from the surface)​

​

Now if you spend half the time in the air and half the time on the ground the average contact force while contacting the surface is 2g, because on average it must be 1g.​

If we translate this to skiing and assume you spend half the time with little "up" force and half the time with a lot of "up" force it means that in the belly of the turn, where the up force is maximal it is like some invisible helper is pushing your skis down into the snow. The amount of grip you get from this is just amazing, it is like you cannot lose the grip.​

​

Is this "up" force simply the leverage over the ski that's caused by moving from an inclined position to an angulated one?

​

There are studies on WC skiers measuring all forces and with little exception when they have a good turn this up force is in the order of 2 g's or larger (and the total force can be up to 4-5 g and often above 3g).​

​

Compare this with a static turn, where you have the CoM on the same distance from the snow all the time and no acceleration or no extra helping force to get the skis to grip. If you are static on a difficult surface like ice there is a very high risk that the skis slip after the fall line. Sure enough most people that struggle on ice do this because they tense up and become static, the exact opposite of what you need to do. Same thing for other hard conditions like chicken heads etc.​

​

Just a point about movement and acceleration. Acceleration is the rate of change of velocity. This means that in a turn the up acceleration starts while the CoM is still moving down, and is usually maximal when the CoM is closest to the ground.​

​

When we see pictures of high edge angle skiing it is just a snapshot in time, in a good dynamic turn this high edge angle is held for a very short time. I think this is very important to have a clear picture in your mind. If you ride around and think that you should hold the same high angle throughout the turn you make it so much more difficult, in particular on other surfaces than hero snow.​

​

This is something that even WC skiers struggle with. Just watch the WC in Kranjska Gora where skiers like Marta Bassino skied with a very fluent dynamic and seemed to have very little problems with grip, whereas other top 15 skiers ended up in static positions and struggled a lot.​

​

This may be slightly off topic but not so much. IMO the lack dynamics of up and down acceleration is what keeps many from achieving high edge angles and good skiing in general. If I look around my local ski resort I'd say that 95-99% of people ski too statically. They hurry the transition and then park and ride.​

​

Please feel free to ask for clarification. I would really like to have a understandable version of this text and I know it is a difficult concept to grasp.​

 

[François Pugh]

For the direction thing:
Since F=ma and your mass isn't changing, you can think about the the force instead of the acceleration. The force is the push. The push will have the same direction as the acceleration.

If your are driving your car at 60 mph towards a brick wall and decide not to hit that wall, you will put on the brakes. The brakes and tires will "push" your car backwards, even though your car is still going forwards (towards the wall). Lets say you get stopped before the wall, and decide to back up quickly because it's about to fall on your car. You stick it in reverse, and floor it. Now the the engine transmission and tires will push your car backwards as your car moves backwards (away from the wall). It the same thing with you going up and down, the push up happens when you're going down and continues after you start going up.

More later; I gotta go work.

 

[LiquidFeet]

^^Finally. That is a very good explanation. This clarifies some of what has been tripping me up.

 

[Mike King]

For the direction thing:
Since F=ma and your mass isn't changing, you can think about the the force instead of the acceleration. The force is the push. The push will have the same direction as the acceleration.

If your are driving your car at 60 mph towards a brick wall and decide not to hit that wall, you will put on the brakes. The brakes and tires will "push" your car backwards, even though your car is still going forwards (towards the wall). Lets say you get stopped before the wall, and decide to back up quickly because it's about to fall on your car. You stick it in reverse, and floor it. Now the the engine transmission and tires will push your car backwards as your car moves backwards (away from the wall). It the same thing with you going up and down, the push up happens when you're going down and continues after you start going up.

More later; I gotta go work.

Ok, let's try it with some simple calculus. Acceleration is the derivative of velocity, right? So wouldn't the sign of acceleration in your car example be negative until the direction of travel of the car changed?

 

[scott43]

There is also angular acceleration. Si even if your velocity is constant you can still be accelerating.

 

[Erik Timmerman]

There is also angular acceleration. Si even if your velocity is constant you can still be accelerating.

I’m no physics expert but you can’t be accelerating without a change in velocity. Velocity is a vector so your speed might stay constant while experiencing acceleration but not your velocity.

 

[graham418]

I’m no physics expert but you can’t be accelerating without a change in velocity. Velocity is a vector so your speed might stay constant while experiencing acceleration but not your velocity.

A change in direction is a change in velocity, and therefore an acceleration

 

[mdf]

Ok, let's try it with some simple calculus. Acceleration is the derivative of velocity, right? So wouldn't the sign of acceleration in your car example be negative until the direction of travel of the car changed?

Even after the direction changes, the velocity continues to get smaller is a signed sense.
It goes from big positive, to small positive, to zero, to small negative to big negative.

The signed value gets less all the time, so the acceleration continues to be negative even when the direction of the velocity switches.
I think you might be getting the magnitude of the velocity and the signed value of the velocity mixed up.

 

[Jamt]

inline:

Paging @Jamt and @François Pugh to the white telephone. I've seen @Jamt's discussions of up and down acceleration and I've come to believe there is something very important there, but I just do not understand what it is. I have the unfortunate disability in that I never took physics, but I am somewhat mathematically competent. So, for this simpleton, can you guys help me to sort out what you are talking about? And help me to understand why it is important?

Let's start with the post you had explaining this concept in the edge angles thread. You said:

​

What I mean with up and down acceleration is the acceleration of the CoM from or towards the snow surface.​

​

This would seem to imply that the sign of the acceleration would be associated with the direction of the CoM wrt the surface of the snow, but you later seem to contradict this by stating:

​

Just a point about movement and acceleration. Acceleration is the rate of change of velocity. This means that in a turn the up acceleration starts while the CoM is still moving down, and is usually maximal when the CoM is closest to the ground.​

​

​

Can you help me understand then what is the difference between "up" and "down" acceleration then?

No contradiction. If your have been light an are moving back towards the snow, you will first continue to accelerate towards the snow, then for an very short time the acceleration will be zero and this is when the up force from the snow is equal to your weight (times g). At this time you are still moving down with considerably speed. Then the force becomes larger than your weight and you start to accelerate up, but still moving down. You will keep moving down for sometime untill the accleration has pushed the velocity to zero.
Then you start moving up and the acceleration and velocity is now in the same direction

​

As you know in physics there is always a cause and effect and the acceleration of the CoM towards the surface is directly given by the force on your skis that is perpendicular to the snow surface and your weight (gravity).​

​

For example: if you are jumping up and down continually on a flat surface the acceleration is -1g when you are in the air (no force from the surface)​

​

Now if you spend half the time in the air and half the time on the ground the average contact force while contacting the surface is 2g, because on average it must be 1g.​

If we translate this to skiing and assume you spend half the time with little "up" force and half the time with a lot of "up" force it means that in the belly of the turn, where the up force is maximal it is like some invisible helper is pushing your skis down into the snow. The amount of grip you get from this is just amazing, it is like you cannot lose the grip.​

​

Is this "up" force simply the leverage over the ski that's caused by moving from an inclined position to an angulated one?

Kind of, compare with a pole vaulter how he/she converts momentum in one plane to acceleration in another

​

There are studies on WC skiers measuring all forces and with little exception when they have a good turn this up force is in the order of 2 g's or larger (and the total force can be up to 4-5 g and often above 3g).​

​

Compare this with a static turn, where you have the CoM on the same distance from the snow all the time and no acceleration or no extra helping force to get the skis to grip. If you are static on a difficult surface like ice there is a very high risk that the skis slip after the fall line. Sure enough most people that struggle on ice do this because they tense up and become static, the exact opposite of what you need to do. Same thing for other hard conditions like chicken heads etc.​

​

Just a point about movement and acceleration. Acceleration is the rate of change of velocity. This means that in a turn the up acceleration starts while the CoM is still moving down, and is usually maximal when the CoM is closest to the ground.​

​

When we see pictures of high edge angle skiing it is just a snapshot in time, in a good dynamic turn this high edge angle is held for a very short time. I think this is very important to have a clear picture in your mind. If you ride around and think that you should hold the same high angle throughout the turn you make it so much more difficult, in particular on other surfaces than hero snow.​

​

This is something that even WC skiers struggle with. Just watch the WC in Kranjska Gora where skiers like Marta Bassino skied with a very fluent dynamic and seemed to have very little problems with grip, whereas other top 15 skiers ended up in static positions and struggled a lot.​

​

This may be slightly off topic but not so much. IMO the lack dynamics of up and down acceleration is what keeps many from achieving high edge angles and good skiing in general. If I look around my local ski resort I'd say that 95-99% of people ski too statically. They hurry the transition and then park and ride.​

​

Please feel free to ask for clarification. I would really like to have a understandable version of this text and I know it is a difficult concept to grasp.​

 

[Jamt]

I’m no physics expert but you can’t be accelerating without a change in velocity. Velocity is a vector so your speed might stay constant while experiencing acceleration but not your velocity.

Yes, but for simplicity we are only considering vectors perpendicular to the snow here, so the direction is just up or down (towards the snow)

 

[Jilly]

For the direction thing:
Since F=ma and your mass isn't changing, you can think about the the force instead of the acceleration. The force is the push. The push will have the same direction as the acceleration.

If your are driving your car at 60 mph towards a brick wall and decide not to hit that wall, you will put on the brakes. The brakes and tires will "push" your car backwards, even though your car is still going forwards (towards the wall). Lets say you get stopped before the wall, and decide to back up quickly because it's about to fall on your car. You stick it in reverse, and floor it. Now the the engine transmission and tires will push your car backwards as your car moves backwards (away from the wall). It the same thing with you going up and down, the push up happens when you're going down and continues after you start going up.

More later; I gotta go work.

Reminds me of the Zoom meeting a few weeks ago. The snow is pushing on you, not you pushing the snow.

 

[scott43]

Reminds me of the Zoom meeting a few weeks ago. The snow is pushing on you, not you pushing the snow.

Frame of reference..

 

[JESinstr]

Reminds me of the Zoom meeting a few weeks ago. The snow is pushing on you, not you pushing the snow.

Or using another car analogy.

You are in the passenger seat of a car doing 50 mph. Suddenly, the driver swerves to the left and your right arm makes contact with the door. Did you move into the door or....did the door move in to you?

 

[Seldomski]

So physics...

Acceleration is time rate of change in velocity. I think the key to understanding here is realizing that redirecting something with mass, that is changing the direction of a traveling particle, is also nonzero acceleration. That means a force was required to make the redirection happen.

Redirection of the velocity of the COM is accomplished through high reaction forces at the ski/snow interface. Skiing with a static stance results in the COM following a jerky path (multiple COM redirections) down the mountain. The COM is redirected uphill at the end of each turn. For large radius turns, the acceleration variations are small. For quick short turns, the acceleration variations are much larger and impact ski grip/snow penetration. Large radius, redirection happens over longer time period. Short radius, redirection is over shorter time period.

The movement of the COM up/down away/toward the skis is meant to reduce/eliminate accelerations of the COM back up the hill at turn completion.

Without collapsing toward the skis (ie skiing statically), the COM accelerates at turn finish as the COM velocity is redirected uphill and/or across the slope. This is followed by a brief free falling period with low G at turn initiation. During this free fall period, it is easy to smear/pivot/redirect the skis. Establishing a carve early in the turn is very difficult/impossible to perform since the skis are unloaded.

By flexing as the turn is completed, the body acceleration uphill is reduced. The forces on the ski at turn finish are reduced. The body is not redirected and it moves consistently downhill. The skis are loaded at turn start and can carve the top of the turn. The COM travels closer to a constant velocity down the hill. Grip and forces at the snow/ski interface are more consistent throughout the turn.

Not mentioned, but critically important, is the need to extend at turn apex... this is required to dynamically flex at the end of each turn. Staying flexed throughout the turn is as bad (or worse) than staying tall the entire time. The skier's COM travels toward and away from the skis in each turn.

 

[François Pugh]

Ok, let's try it with some simple calculus. Acceleration is the derivative of velocity, right? So wouldn't the sign of acceleration in your car example be negative until the direction of travel of the car changed?

If your going to keep track of directions mathematically, you need to define a positive direction.

If you define towards the wall or towards the ground as positive, then at the start the velocity is positive and the acceleration is negative as the car approaches the wall (you approach the ground), the acceleration is still negative and so is the velocity as the car backs away from the wall.

If you define away from the wall or up as positive, then at the start the velocity is negative as the car approaches the wall (you approach the ground), and the acceleration is positive and so is the velocity as the car backs away from the wall (you leave the ground).

It might be easier to understand if you keep the directions in your head (up or down) and not worry too much about the negative or positive.

As @Jamt posted, we are only looking at the up and down motion here because we want to concentrate on the up acceleration only (that thing that helps us grip so we can have better motion in the other directions )

BTW when you push down on the Earth the Earth pushes back on you with equal force, only in the opposite direction. Since we don't really care how much you're moving the earth (it's not very much) we will concentrate on the forces that are moving you.

In the vertical direction the forces include gravity (always pulling you down), and the earth pushing you up via ski/snow contact force. Gravity is always acting on you; that's what accelerates you back down to balance up all of your up force/acceleration. It is the net force, gravity pulling you down combined with the earth pushing you back up (even though you feel your legs pushing the earth).

Now onto this averaging thing. It's complicated. I 'll get back to you; I need a bit of time to simplify it.

 

[François Pugh]

Reminds me of the Zoom meeting a few weeks ago. The snow is pushing on you, not you pushing the snow.

Both are happening. Gravity is also pulling you down and pulling the Earth up.
It is very important when analyzing the motion of an object, we only consider the forces ACTING ON THAT OBJECT. It's not too bad to get them confused in a lot of cases, because when two objects interact the forces acting between them are equal in magnitude, but opposite in direction, as stated by Isaac so many years ago. Since you pushing the Earth has the same magnitude as the Earth pushing you, so long as you don't mix up which way you will end up being pushed things often work out.

 

[cantunamunch]

 

[cantunamunch]

Ok, let's try it with some simple calculus. Acceleration is the derivative of velocity, right?

Yes.

So wouldn't the sign of acceleration in your car example be negative until the direction of travel of the car changed?

No. When the direction of travel changes, velocity goes through zero.
If the velocity is a time-periodic function of the form v=Xsin(wt), the derivative is a time periodic function a=Ycos(wt). They are never zero at the same time.
For time-periodic functions, the derivative LEADS in time.

#simplecalculus
#ELItheICEman

 

[scott43]

I’m no physics expert but you can’t be accelerating without a change in velocity. Velocity is a vector so your speed might stay constant while experiencing acceleration but not your velocity.

You are correct sir! Sloppy typing by me!

 

[Jamt]

On a different note, unless you really want to understand the details I think it is enough to have a simpler approach:

-High edge angles require the CoM to be close to the snow. The only way to get the CoM closer to the snow is by having reaction forces smaller than your weight

Or even simpler

-Be light on your skis until you are close to the snow