Skiers: Newsletter Challenge (09/26/06)

I wasn't aware that skydivers were in a speed race?<p>

World record for sking 251.4 km/hr 156 MPH<p>

After all, does not the skydivers terminal falling velocity depend on their body positioning ? Their 'normal' position being with the hands and arms out to increase their wind resistance. To emulate the skier, they would need to seek to fall vertically instead of horizontally to increase the wind resistance. So the sky diver could exceed the skiers speed simply by tucking in their arms and legs and either diving head first or feet first in a knife like fasion. Performance could be further improved by the appropriate bits of kit to further reduce resistance.<p>

See the Wiki: http://en.wikipedia.org/wiki/Terminal_velocity<p>

Normal skydiver speed 195 km/hr or 120 MPH.<p>

Peregrine Falcon dive 320 km/hr or 200 MPH. or skydiver pulling in arms and legs. <p>

"I wasn't aware that skydivers were in a speed race?"

Just like good coffee. skydivers are good to the last drop.

Not sure how true this is but seems that the record free fall speed is 614 mph or 988 km/h (see link below).

http://www.aerospaceweb.org/question/aerodynamics/q0243.shtml

I am a skydiving instructor.

Typical skydivers can adjust their freefall speed over an almost 2:1 range from about 100 mph to over 200 mph by changing body position.

With newer "wing suits" freefall speeds can be reduced to as slow 50 mph. There also speed contests using slick suits and fairings where speeds over 300 mph are possible!

One of the big challeges (and safety risk) is managing your speed relative to others in freefall.

TomW

Quoting Skydiving Instructor: "With newer "wing suits" freefall speeds can be reduced to as slow 50 mph. There also speed contests using slick suits and fairings where speeds over 300 mph are possible!"

Very interesting. I suppose, if a person in one of those "slick suits" jumps out of a balloon at 100 000 ft, with oxygen, I presume, the rarified air would quickly allow a supersonic fall.

Some record like this has been reported in a previous post. Do you have any idea what the drag coefficient for a typical slick suit is?

The fastest freefall speed is in a head-down dive with your arms at your side. I can usually get up to 200 mph with my normal equipment. The sensation is a little like standing on your head on the floor. Most of your weight is supported by your head neck and shoulders, and keeping your balance requires some practice. There is not much sensation of airflow on your torso and a little on your legs.

I don't think the slick suits worn by speed fallers are a major contributor to the drag they experience. These guys are usually wearing streamlined helmets that create, what feels like, a hole in the air for their body to follow. These jumps are made at "normal" skydiving altitudes.

If we assume the same body configuration at high altitude and that speed goes as the square root of density we get:

Assuming:

d = 1.21exp(h/8000) from simple atmospheric model (valid up to 30000m?)

h = 3000m, d = 0.891kg/m3, v = 300 mph

At 30000m, d = 0.0235kg/m3 then v = 1850 mph!

Extreme altitude jumps require an amazing amount of planning, training and equipment. A fully pressurized space suit and life support equipment are necessary! Unfortunately, a few have died due to equipment failure or stability problems, and they were only going for altitude records, not speed.

TomW

Thanks Tom, very interesting values! You wrote: "If we assume the same body configuration at high altitude and that speed goes as the square root of density we get:

Assuming:

d = 1.21exp(h/8000) from simple atmospheric model (valid up to 30000m?)

h = 3000m, d = 0.891kg/m3, v = 300 mph

At 30000m, d = 0.0235kg/m3 then v = 1850 mph!"

I was the instigator of that little table in post #7, where I used a Cd of about 20% of the normal skydiver's drag and an average air density of about 50% of ground level, which correlates well with the average density between ground and yours at 30000m. The answer, as you can check was some 1130 km/h (about 700 mph).

I actually think the value will be between yours and mine, but perhaps closer to yours! The air will become denser exponentially, but then, the speed will build up very quickly in the rarified air, almost like a vacuum fall.

Somebody may want to program this into a spreadsheet and let us know!

Increase in air density buildup, in a free fall in a vertical line will be faster that the density buildup on a diagonal line acting as "air-break". I don't know the exact relations, but this can easily be calculated, and an optimum point can be found.

Wangito

Wangito,

This thread is dead. The answer has already been published by CR4 and yours is found severely lacking: too little, too late, and not making much sense.

If by "increase in air density buildup" you mean the opposing air friction that leads to a terminal velocity, you are on the right track, but the fact that the "build up" is slower because it is not on a diagonal vector has really nothing to do with the reason a skiier can reach a greater maximum velocity than a skydiver.

Go to the CR4 home page and read the answer in the newsletter. If you read further on in this thread you will find many right answers and also some very wrong ones as well.

Why don't you try one of the newer challenges?

As compared to the usual free skydiving free-fall position, a skier's tuck reduces frontal area by as much as 50%, and lowers the coefficient of drag, as well (probably from about .8 down to .5) for a total aero drag of perhaps 35% that of the skydiver at the same velocity. Thus, on a 45 degree slope, with about .7 times the g force, there is still a significant advantage for the skier. Ski friction is low, and its curve is very flat, so we can darn near ignore it.

Imagine how fast a nicely faired human body could go in free fall: head first, packed into an airfoil shape spun into a body of rotation, the Cd would be about .06. A couple of fins at the back to keep you stable, and with a small fraction of the skydiver's frontal area, you could really get ripping!

It is a question of will, grasshopper. The sky diver wills his fall to take longer and the skier wills his trip to end quickly.

It is the force, Luke. The diver uses the Force to slow himself and the skier has the Force at his back.

Waxed skis on snow have less friction than booted feet on air.

Sky divers have parachutes. Let's see a skier get some speed up with a canopy dragging behind him.

Skiers use poles to propel themselves downward so in addition to gravity they have the force of their poles.

The skydiver is slowed by the air below him. The skier has no air below him to slow him down.

Wind, for the most part moves horizontally (except during thunderstorms and such) so that must mean that air is slightly crystalline making it easier to move through it horizontally than vertically. The skier has a horizontal component to his motion and that allows him easier movement through the air.

That's why cars are faster than people and animals - because when people or animals run they also bound up and down and the vertical component slows them down. This works with aircraft, too, as they slow down when they go straight up and move very fast while moving horizontally.

The skier is paid more if he/she goes faster and the skydiver pays more for a longer fall. Money makes the world go 'round.

Aerodynamics! The sky diver has less air above him than below him so he is being held up just like they tell us an aircraft wing works. The skier, again, has no air below him so there is no lifting component.

It's the 'flat side - round side effect'. If an aircraft were designed to fly flat with it's control sufaces neutral, and then it turned over it would come down quickly. This is because the push is on the flat side of the wing and the pull is on the round side. People are the same, and the skier's flat side is behind him with a rounded tummy. The effect doesn't work on the sky diver because his parachute pack makes him round on both sides. If you put a large ball on skis, it would go slower as well.

Sailboats do this as well - with the push on the concave side of the sail and the pull on the convex side. Amusingly enough this one is almost close to right because two identical single masted sail boats, one using a flying jib for a sail and one using a ball presenting an identical profile to the wind will result in the ball boat being slower.

I really hope you are joking with most of your answers, which are totally absurd! The other fellows above are basically correct. The only reason which makes any practical difference is air friction, which is less for a skier in "tuck" position with a tight skisuit and aerodynamic headgear and more for a skydiver with outstretched arms and legs wearing a baggy "jumpsuit". Ever watch skydivers who do tricks? They move extremely fast when they "tuck" their arms and legs together and fall feet first instead of the normal face down prone position.

"People are the same, and the skier's flat side is behind him with a rounded tummy."

ROFL

that's pretty funny

I also like your explanation of why air must be crystalline

I watched a program on these lunatics that try for the world speed record on skis and the first thing that I noticed was the slope was almost vertical at the start. The also go to enormous lengths to reduce drag by wearing Very smooth and shiny clothing that will allow for laminar air flow along with fitting fairings to the back of their legs and tips of their stocks. The also use specially designed helmets and practice in wind tunnels to develop the best possible stance to reduce wind resistance.

The upshot of it is that the skier goes faster due to reduced drag as a result of the aerodynamic measures that are taken.

As an aside the record speed for a person in free fall is held by J Kittinger. He bailed out of a balloon at 102,800 feet and claims to have broken the sound barrier on the way down. In any case he reached a speed of around 1,000 Km/h on the way down. If you really went to go to town as suggested earlier and streamlined your body with fins and things you could probably achieve speed close to that of a streamlined bomb designed by Barns Wallace back in World War II. It came in two sizes, 12,000 Lb (5,400Kg) and 22,000 Lb (10,000Kg) , and when dropped from the designed altitude of 30,000 feet would exceed the speed of sound on the way down. The armored nose would allow the bomb to bury itself in the ground and when it went off it would cause a small earthquake in the surrounding aria.

Free fallers wear bulky clothes, and equipment. Also they try to lengthen their fall to enjoy it more. If they were trying to be streamlined, and didn't mind going without a parachute etc. they would be the faster. Skiers are trying to go as fast as possible, and are dressed for it.

I doubt your premise though.

All the best,

Ron Wagner

For fun, and using the terminal velocity equation from Wikipedia, I calculated rough values for some scenarios. I played around with frontal area (A) and drag coefficient (Cd) to get values near what was reported in this thread so far.

For the "Speed Skier" I used 70% of g (roughly 45 deg. slope) and for the "Speed Dive" I used half the air density (average) because of the extreme altitude. All the parameters were rounded and are obviously open to debate...

I like your chart. I think the frontal area of the skydiver is much too high, however, and the Cd is much too low. If you imagine a person standing with feet together, and ignore arms and head, there is pretty good fit with a trapezoid of .4M (ribs) x .2M (ankles) x 1.5M. That's only .45M². Adding arms, neck and head gets you to around .7M^2. Given the terminal velocity, which is known, then Cd would have to be .685, to fit. This is a still a bit lower than the .9 - 1 often quoted for the human form, but it may be that the relatively loose clothing becomes somewhat teardrop shaped behind the person, or at least interferes with propagation of longitudinal eddies.

To put Cd into perspective, a really clean production car, the Prius, has a Cd of .29. Outstandingly clean concept cars, like the Daihatsu UFE, have Cd's around .2 or just under. Those sleek looking (to the untrained eye) crotch-rocket motorcycles are actually attrocious, with Cd's around .55-.65. A flat plate is the reference with a Cd of 1. Tractor-trailer trucks can actually exceed that value, because they act like one flat plate following another. So I think your skier and ball areas are high and Cd's low, but I am picking nits. The concepts are right, and it's neat to see it in tabular form.

Lemme see... at the speeds attainable with the Speed Dive configuration, even very tiny wings would provide the ability to level off before touchdown. Given somewhere like the Bonneville Salt Flats, one could slide to a stop within a couple miles. Granted the capsule would be red hot afterwards, but wouldn't that be part of the attraction? Any takers?

The explanation is similar to the explanation of how a sailboat can go faster than the driving breeze: They accelerate in the vertical direction, but that is only one part of the real velocity. The vertical portion of their speed does not reach free-fall, but the overall component does.Think about vector sums. First semester physics at a good school. (Lawrence Tech.)

William Ketel

Mr. Ketel,

Sorry to say, but you are all wet. Better go back to school and take that second semester physics course if that is the one where they teach you about aerodynamic drag and air resistance. The only similarity between this problem and one of sailboats is where sailboats (and boats and ships in general) have what is known as their "hull speed", which is the fastest speed the hull can be pushed through the water (at a given water-line point of course) no matter how much power is pushing it, because of the size and shape of the hull (hydrodynamics in this case) which limits speed due to the pressure of the water the hull must displace as it pushes through it and the turbulence which is created off the sides and back of the hull (drag). That is why fast sailboats have such graceful designs, because they are trying to get every knot out of the hull they can.

"They accelerate in the vertical direction, but that is only one part of the real velocity." OK, I will buy that. The acceleration of gravity is vertical. Therefore the acceleration of the skier in the plane (angle) of the hill must be less than that because the vertical acceleration is the vector sum of the forces parallel and normal to the plane. The normal force is what causes friction, but with the low co-efficient of friction of skiis on snow there is very little drag and the normal force keeps the skiier on the hill, otherwise they would fly off into space.

Rookie mistake, you drew your vectors so that vertical and horizontal were components which added to equal the vector parallel to the hill. This cannot be so, because what is that horizontal force? Where does it come from? It does not exist, you made it up! Try drawing the vertical vector first, then look at ITS components!

"The vertical portion of their speed does not reach free-fall, but the overall component does.Think about vector sums."

I am thinking...I am thinking...No, I just don't see it. I think you have confused the velocity and acceleration vectors. Yes, there is a horizontal and vertical component of velocity, which together as a vector sum equals the velocity along the plane. Yes, the vertical component is less than the component in the plane. But you have the tail wagging the dog. The planar velocity is not fast because vertical velocity is slower (than "free-fall"?), but the vertical velocity is slower because the planar velocity is slowed by friction (air and the slight sliding friction of the skiis, which can be thought of as negligible)

"First semester physics at a good school. (Lawrence Tech.)"

You never REALLY studied, did you? Oh, don't get me started on what is a GOOD school. Because I can, and will. My BS in engineering was earned at the University of Missouri-Rolla. UMR started as the MU School of Mines and Metallurgy in 1870. Lawrence Tech? According to the website, 1932 was the first year they started a four-year program, what was it before that? And LTU has 4 ABET-accredited Engineering programs, UMR has 13. In the US News National University rankings, UMR was #112 out of 248 4-year schools ranked, both public and private, putting it into the top 50% or first tier. LTU did not appear in the rankings.

Extending Mr Ketel's logic: If instead of the usual steep ski slope of 45 degrees or so, we could use a 5.7 degree slope (1:10 slope): then the skier would have to go ten times as fast as a normal free faller! Imagine how fast he could go on the level: infinitely fast! Hmmm. Does that seem plausible? I fear this is not first semester physics. It is at the easy end of high school physics.

The ski wax has less friction than the skydiver. Having done both, I speak from experience!

Skydivers can have different terminal velocities depending on dress and equipment, as well as change their terminal velocity while in flight via body position.

Ski wax, if properly applied, is designed to be slick!

The sky driver is falling straight down with gravity. The skier is falling at an angle to gravity. The velocity of the skydiver is equal to the rate of descent. The velocity of the skier is measured by the direction of his or her travel, which could be much faster than the skier's rate of descent.

I think that the sky diver can attain quite a bit of angle and end up far from where the vertical drop would be. Would appreciate info from sky divers.

C'mon, folks. Mr. Fry answered the question well and, except for the optional discussion of clothing, accurately. Otherwise I would not have submitted my rather facetious answer so early.

The motive force is gravity, the resistance to it is primarily air, and a little bit the ski-snow friction. The free-faller (as a rule) is maximizing his/her resistance through both position and material, the ski racer is always minimizing resistance through position, and if wealthy enough, fancy materials.

Dressed the same and presenting the identical profiles to the air, in the direction of motion, the free-faller would win by the tiny difference of the ski-snow resistance.

"Speed skiers on steep slopes, like Les Arcs in the French Alps, routinely exceed the normal free fall terminal velocity of skydivers. This is despite the fact that skiers are moving at an angle to the vertical, thus decreasing the g-force in the forward direction. How is this possible?"

One could 'drive this question into the ground' considering laminar flow effects described by Maurice Frederic Alfred Couette in the 19th century or using simple trig to easily establish a 'greater than' result.

Intuitively and by observation however, I would expect the effective g-force in the tangential direction, rather than the 'forward direction', upon a speed skier would be increased; similarly, as is the thrust applied to a sail boat when the sail boat 'quarters' the wind.

Interestingly, space vehicles take advantage of this effective g-force increase when 'sling-shotting' around planets.

If the question is indeed about the skydiver's 'terminal velocity' then it does not require a speed skier, in that the skydiver's 'terminal velocity' is 0. A person walking along a street would also exceed the skydiver's 'terminal velocity'.

This question rather than being mathematical may indeed be grammatical.

Cheers,

Bob

P.S.

Cute! It took three reads, but then it's after a big meal and I'm fatigued. (Also dumb.)

Yeah ya'll beat this subject into the ground. Seems like some of us have more of a god complex than others. I especially like the guy who researched the guests alma mater to degrade him over a high school physics ponderance. He even had the best answer. I suspect a formal answer is more of a general college physics or dynamics question. All of you seem formally educated and thats very appealing. This is my first post and I look foward to some more challenging questions and discussions.

Brian

Brian,

While I agree this subject has been beat into the ground, I take issue with some of your comments.

"Seems like some of us have more of a god complex than others. I especially like the guy who researched the guests alma mater to degrade him over a high school physics ponderance."

Obviously, you are referring to me and my posting, and I resent your saying that I have a "god complex". I only researched Mr. Ketel's Alma Mater because he laid down a challenge by giving an erroneous answer to the question, then claiming that his answer must be correct because it was "first semester physics" which he learned (implied) at a "good school. (Lawrence Tech)", also implying that others who disagreed with him must not have gone to such a "good school", so I was merely comparing our two schools. It seemed fair enough to me to answer such a challenge and I would ask others here if it was a reasonable reply, not merely an attempt to "degrade him over a high school physics ponderance".

"He even had the best answer." Who had the best answer, Mr. Ketel? If you think that you had better go and reread the 90% or so of posters who came up with a different answer.

I never claim to be right 100% of the time (that would be a 'god complex') but it is hard to just sit there and read someone claim an authority for a wrong answer based on their schooling, with the implication being that they were somehow more right than others because of it, especially when their logic was exactly backwards!

BTW, thanks to Mr. Fry for his follow-up comments!

STL:

You're welcome. I, too, found it rather grating that Ketel presented his reversed logic as the definitive answer, while implying that his schooling was in some way better than that of the others here.

I was just amused by your passion is all. Personally I do have a god complex and have struggled with it for 30 plus years. Over the years I learned not to read so much into what other people say and really take comments with a grain of salt. I think the guy was implying the answer was simple and anyone with a decent education would get it. I also think he was proud of his education. The challenge was your creation not his, thats the amuzing part. I apologize for the off topic comments. Please don't be offended by the personal stuff, I think you're probably a hell of an engineer.

Brian

OK, Brian. No harm, no foul. But see, I wasn't the only one who thought there was a "challenge" implied. Read Ken's post just above your last one!

No need to introduce unstated factors, meteorological anomalies, vector resolutions, and other such minutiae with this one; or even aerodynamic profundities. We can, moreover, leave off with skydiving and skiing techniques—and sporty fashion apparel as well.

The solution to (or, rather, the logical discrediting of) the challenge lies simply with discerning the apples-oranges nature of the challenge; that the challenge has posited a seemingly valid comparison—but one which, in truth, is a fallacious comparison predicated on a false premise—that it's a trick question—that it's seeming logic rests upon confounding the reader as to the definition of terminal velocity. Uncover the fallacy and you've defeated the challenge.

By definition, terminal velocity is always the maximum speed attainable by a free-falling object that, theretofore, had been accelerating toward Earth's center of gravity—the speed at which (without outside impetus other than gravity) headwind (upward moving wind by virtue of the falling object's movement downward through the atmosphere) becomes so great as to prevent any further acceleration (either by the falling body or, relatively speaking, by the upwind). Sideslip velocity—its earthbound analogy being the skier's ground speed—is irrelevant: it can be zero or any amount; terminal (i.e., downward) velocity is unaffected.

In contrast, terminal velocity can never apply to an object moving on the surface—it is undefined for an object not in free fall—and if it cannot apply, it cannot be a limiting factor. An object on the surface cannot fall (or even be propelled) downward through the atmosphere—as least not for so far a distance that it would be possible to reach a velocity that could not be exceeded—until, that is, it was stopped from further downward motion by the earth's surface. The challenge attempts to confuse the issue by introducing the notion (the false comparison) that the skier is moving downhill under the influence of gravity. However, the skier is not moving directly downward; nor (in contrast with the free faller) is the skier losing altitude at the velocity (the ground speed) at which the skier is traveling. Neither can there be a virtual headwind issuing (as it were) directly upward from the surface to limit the skier's acceleration—or rate of loss of altitude. The skier has two "facilities" by which to increase ground speed: the pull of gravity (the vertical component) and the ability to increase speed by pushing backwards against the snow pack (the lateral component). Thus the skier can accumulate ground speed (virtually) indefinitely. By the same token, the free falling body has resort only to gravity for downward impetus. There is nothing…against which to push backward and, even if there was, its speed is also limited to terminal velocity—pushing against it would only slow it down—momentarily--until it again attained terminal velocity—but was no longer available to push against. So, the only way that a skier can be limited by terminal velocity would be for the skier to be free falling—to ski overboard from an airborne platform at sufficient altitude to permit gravity-induced acceleration downward until terminal velocity was reached.

I am surprised at the number of people that don't understand vector analysis, the equations:

Kinetic Energy = ½ m v²

Potential Energy = m g h

and the Law of Conservation of Energy. This implies that two identical bodies falling through the same vertical distance will have the same velocity.

What some have said with their faulty vector analysis is that the skier going down the slope will travel faster than a skydiver falling vertically through the same distance. For this to be true then the skier would have greater kinetic energy than the sky diver and bingo we could build a perpetual motion machine. This is of course nonsense.

As was displayed earlier in the table that one writer posted the coefficient of friction is the controlling factor. The table takes a known equation, inserts some roughly known parameters into these equations and comes up with the results we already have of the skier, skydiver and aerodynamic body.

Keep in mind the KISS rule. Keep It Simple Stupid

masu wrote: "This implies that two identical bodies falling through the same vertical distance will have the same velocity."

Correct for vacuum, where the object on a frictionless slope will take longer to travel the distance than the free-fall one, but they will have the same final velocities for the same initial and final heights, as you stated. So what can one learn from this for the case in the air?

I think it says that for the same mass and drag coefficients, the object on the slope will lose more energy because it takes the longer route through the air, so it will achieve a lower final speed. However, reduce the drag of the object on the slope enough and it may lose less energy and win the top speed title.

My 'tuppence' worth, without math.

CowAnon, in fairness to the challenge, it said nothing about terminal velocity of speed skiers. It said "Speed skiers …. routinely exceed the normal free fall terminal velocity of skydivers". Talking about "No need to introduce unstated factors…". Ok, I guess the OP could have stated it as: "the speed of speed skiers … routinely exceed…"

I must say your post contains some good points, like the use of equipment to increase speed. Unfortunately, due to the above oversight, most of the lengthy reply seems, to me at least, irrelevant.

There also appears to be a bit of confusion in the post about the effect of air resistance (drag) on a speed skier - I think it is ultimately what determines the top "ground speed" for a given slope. At 200+ km/h, further 'pushing himself on' is probably near impossible, so the only real propulsion is the vector component of "g" in the forward, downhill direction. The limiting factor is the drag, plus a little friction on the ice, which I believe is fairly velocity independent.

The calculation of top ski speed should be exactly the same as for terminal velocity, just with slightly different constants, e.g., 6 m/s² for "g" instead of 9.8m/s².

I suppose it is okay to dispute in the margins, but "fairness to the challenge" is not a thing at issue. It is not something to which the challenge might, if it could, take umbrage to say that it was premised upon a fallacy (or reliant upon the challengee's acquiescence in a fallacious proposition); or to say that the challenge, when seen for what it was, was to spot the fallacy--the scenario being nothing more than a diversion--a kind of slight of hand (as in a magician's misdirection), but with words and well contrived mental images. Such is the nature of challenges at times--riddles if you please--to state a proposition which seems--but only seems--well reasoned... but whose only valid resolution lies in discerning (exposing if you will) the faulty reasoning and then examiniing the competing outcomes (skiers vs. skydivers) from a validly reasoned perspective. The challenge did not, as you imply, suggest any kind of qualification of the term, terminal velocity...because that would have exposed the fallacy implicit in the challenge, don't you see. So, to say that we might make a special case kind of "terminal velocity," one that could be conjured for, say, the breeze that blows the skiers hair, or makes it difficult for him to add an increment of ground speed, does not actually touch on what the challenge was asking us to discover. (It would only be using a red herring to logically counter a red herring; a fallacy of reasoning to disprove another fallacy of reasoning.) It would be, therefore, something extraneous to the actual issues posed by or implicit in the challenge; and, therefore, not something that would (or could) unravel the challenge or provide the "solution" (the "discrediting") that the challenge was actually seeking: which, simply put, was no more than to realize that the same terminal velocity (we'll accept your special case terminal velocity--albeit that it would be very difficult to define) applying to the freefaller does not apply to, or limit in the same way, the person moving laterally and downward on the surface. Therefore the posting with which you take issue is the "solution" (without extraneous points that are neither needed or evoked by the challenge)...all the "solution" that is required (but with some points of elaboration and illustration so as to be more easily understood), nothing more, nothing less.

I would never expect such a line of thought from an engineer. Verbal slight of hand and such. I thought engineers were straightforward, and logical. Left brained types. What is more logical than challenging the premise, on an engineering site?

And I thought I was long-winded!

There is no discrediting of the challenge, here. The challenge was well-phrased by Jorrie, in the form of a simple question. Data supports his contention that speed skiers exceed the (ordinary) terminal velocity of a sky diver. (Sky divers who intentionally go fast can go faster than a skier, of course.)

There is little in the challenge that is truly apples/oranges. It is very much oranges/oranges. Both a sky diver and skier are powered by gravity. Their maximum speeds for a given body and clothing configuration are determined by the same factors: a simple equilibrium between the force pulling the object along its path and the drag retarding the object along that same path. Given the magnitudes of the drags involved, one can safely ignore ski/snow friction, so all the drag is aerodynamic. In both cases, there is only a headwind, because we can also ignore ground winds for our discussion here: we are not trying to calculate the speed of a skier under a particular set of meteorological conditions, we're simple wanting to say, "Yes, I can see why a skier would be faster."

If one were to simply increase the slope of the skier's hill to vertical, then the two situations would be identical. At 89 degrees of slope the situation does not suddenly change to something entirely different. Nor does it at 70, or 45 degrees (the slope of a moderately steep ski run). Actual speed skiing slopes are often steeper than 45 degrees, especially near the top, but 45 is an easy slope to use because most engineers have memorized the trig functions for angles like 30, 45 and 60. Also 45 is useful because we can then say, "Well, if a certain speed is possible on a 45 degree slope, then even higher speeds would be possible on a 55 degree slope, or an 89 degree slope.

To suggest that the concept of terminal velocity exists at 90 degrees but not at 89.999... or 89.9... or 89... or 70... is naive. The term is used in physics texts and aerodynamic texts and in common parlance for instances precisely like this. (What is the terminal velocity of an airplane diving at 60 degrees nose down, given these aerodynamic characteristics?...) Real world terminal velocity is the velocity at which the component of gravitational force causing the motion is exactly balanced by drag in the direction opposing that motion. For our purposes here, if the ski slope were 80 degrees, the situations are effectively identical (the sine of 80 degrees being .98 or so). At that angle, the normal force on the skis is negligible, so ski friction, already just a couple percent of the normal force) is infinitesimal. The situations becomes somewhat different in the particulars, but identical in concept at 45 degrees. The force pulling the skier down the slope is now 70 percent of his/her weight. Ski friction, now much higher than at 80 degree slope, is still small enough to ignore. At some speed, drag will equal that force, and further acceleration will cease. That speed is very high, because the skier is quite streamlined and small in cross section when viewed from the perspective of the apparent wind, which is straight up the slope. If the sky diver tucked into a similar shape, (and could steer himself into the comparable position vs the apparent wind -- no small feat) he/she would go faster because the force of gravity is closer to being aligned with the sky divers motion. In practice, the sky diver's motion is very unlikely to be straight down, because sky divers fly through the air, whether they want to or not, i.e., they are not perfectly symmetrical. (This effect is taken to extremes in sky surfing, where the sky diver wears a snow board or similar contrivance.)

You say "The skier has two "facilities" by which to increase ground speed: the pull of gravity (the vertical component) and the ability to increase speed by pushing backwards against the snow pack (the lateral component)." This is nonsense. For one, speed skiers do not push against the snow pack. They are going far too fast for that. If they were to do this at the beginning of a run, they would push in a direction aligned with their path, not laterally. And the only useful component of the pull of gravity is that aligned with the skier's motion, not the vertical component, which simply adds ski/snow friction (about 3%).

The skier cannot "accumulate ground speed virtually indefinetly" any more than the skydiver can. Both reach equilibrium (and both reach it fairly quickly, at that).

A good challenge question, most elegantly answered by "guest" in post #7.

First, there is long-winded; and there is comprehensive, but to the point. However, since it is of no concern to me who "wins," (or who is better or more narrowly indoctrinated, or who pisses farthest), and because I am comparatively unpracticed at "proof by ad hominem," I am forced to relent, and humbly accept that your explanation is the one that most authoritatively answers the challenge...leaving nothing except to reconcile the challenge to the explanation. So, in fairness to us both--and leaving rhetorical irrelavencies such syntax, semantics, and reading comprehension aside--I will depart from the fray with at least the self assurance that (even if only to the discerning eye) we have each amplified and reinforced the other's points. It would also be ill-mannered of me not to admit my error in seeing the challenge as a contrived, real-world-inspired dilemma asking to be resolved. For that, apologies are due both to the Challenge, and to any who hold it dear as an immutable (and, therefore, inviolable) sine qua non.

Why not just say, "No lo contendere."?

He probably doesnt understand Spanish. Meybe try again, with nolo contendere.

Ahah!! (The North American version of Eureka!)

... "At that angle, the normal force on the skis is negligible, so skifriction, already just a couple percent of the normal force) isinfinitesimal."

Skiing memories jogged by your comment. Most of the time (I would say in the high 80s of 100) when skiing and falling (also in the high 80's) I would fall on my butt. If the drag on my skis were really negligible, it should be closer to 50%. If the drag on my skis were significant, then I should fall on my face (as I do in most every other endeavour). So...

The drag on skis must be negative!

So you see, CowAnon is sort of right - it's an apples/oranges problem in that the sky diver is only propelled by gravity while the skier has gravity and adds the propulsive effect of negative friction!

(Living in Canada, I experience negative friction seasonally when my car slides backwards down the hill while in dirve.)

I revise my assessment that "guest" (#7 post) had the best answer. Your's is clearly it. For me, skis have a very strong sideways propusive effect, leading to many hip bruises. It is clearly the same sort of negative friction you mentioned but in a different direction. (I'd suspect that the skis are capable of vectoring their anti-friction in any direction, and that they can sense the direction most appropriate for downing any given skier.)

My experience on ice skates mirrors yours on skis. The skates are very clearly driven forward, out from under me, by a force that is bent on causing me injury. Skiing and skating have frozen water in common, so I'd have to assume that your (earlier) mention of crystal orientation has a lot to do with it. As you have no doubt heard, there are those who claim that ice crystals can be changed by your thoughts... I think we're getting somewhere here... just needs a little more work.

I was jus looking at this discussion and your post reminded my of some thing that I read one time. It was that while skating the blades never actually come in contact with ice, the pressure melts so the skate glides on liquid, and refreezes as the skate passes. Apart from gliding on a water lubricated surface seems like it coud be possible that the skate and skater are always going slightly downhill even on level ice? Maybe something like that could also happen with skis? I was also wondring if the the skier might not get extra push from turbulence behind as passes through the air. Or even that the freefaller might encounter lift for a similar reason and be slowed in descent, which the skier would avoid because he isn't falling. Another thing that might help the skier to sometimes go faster is downslope wind on the mountain, depending on the time of day if it was late or evening. Not real familiar with teh topic but maybe this can help anyway.

The little known details of how things work are pretty interesting, aren't they. I think you are right re ice skates traveling on a film of liquid water -- at least I have read the same thing, and have witnessed the effect in iceboating (an interesting area of applied physics). In iceboating, it is customary to push the boat back and forth in light winds to get the runners to work in the way you've described. Otherwise, when you sit on the boat, you just sit there without enough force from the sail (or increasingly, the wing) to overcome static friction. Iceboats and very fast sailboats (those that can sail at multiples of wind speed) have the peculiar ability to "sail on their own wind" (which sounds like a perpetual motion machine, but is not) so that as they accelerate in a constant true wind, the force propelling them forward actually increases (even though the vector alignments become increasingly less advantageous). Thus, on the fastest iceboats (which can sail at up to 8-9 times wind speed), the same boat that just sat there in a light wind, once moving, accelerates like crazy, and ends up sailing in hurricane force winds of its own creation.

As far as the water effect on skis: having done some skiing and a little ski racing, I'd have to think that when the ski is on edge, that the phenomenon might very well occur. On the other hand, when the ski is flat on the snow (when you're going straight), encountering wet snow can slow you so much that you feel like you're going to fall flat on your face.

it was my, perhaps false, impression that powder would be preferred to high-moisture content snow because the latter tends to plow-up under the fronts of the skis, giving that head forward-feet backward effect you talk about. It seems to me that even the flats could cause the melt-refreeze phenomenon, judging by the hard-pack (even shiny) icing conditions in well travelled snow. Seems to me also that downhill racers mostly try to stay in these packed "grooves" laid by previous racers, and avoid fresh/dry snow. On the other hand, slalom-ers and recreational skiers would probably prefer powder where the edges can be put to good use, and without side slippage?? I thought the idea about a skate always going down hill even on level was intriquing. If I understand, the idea is that the front of the skate contacts and liquifies the ice first while the rear of the blade is still (higher) on harder ice. If the same kind of continuous blade front-blade rear falling thing goes on with skis, couldn't that have an extra accelerative effect, aside from slope of the hill??? Just wondering.

You may be right, guest in post 54. I think the water effect in high moisture snow has to do with viscosity effects distributed over a large area. The analogy would be in boat design where one works hard to keep wetted surface low. But I'm not sure. I know the ice on ice friction coeff is about the same as teflon on teflon, and the ice/ice measurement does not rely on the ice skate phenomenon -- which I understand, requires the high pressures of a small surface. So I think that the polished surface of a ski track on a cold day is just from the compaction of a frozen material, with a bunch of flat shiny surfaces pushed into alignment. But I'm not certain.

Although here's a thought: on a nice cold skiing day, those smooth tracks can be easily disrupted -- they don't appear fused. This is in contrast to an icy day, where they are fused so much that when you fall, you don't make the slightest dent.

Then there is corn snow, which is a delight to ski on, because it combines high speed with good control. It is a bunch of rounded pieces of ice that require just the right near freezing temps to form. I think it is fast because the water layer cannot cover a large area of the ski due to the rough texture.

Who knows? Yike's -- I've got to get back to work!

Guys,

Let's not forget snow and ice, being made of water, contain a certain proportion of deuterium, D, and tritium, T, istopes of hydrogen. These isotopes, like standard hydrogen, H, react with Oxygen to form the components of "heavy water". Since the D and T isotopes have more neutrons, D20 and T20 are larger and heavier than H20 and tend to accumulate at the rear of the ski as the water is melted by normal friction, because they cannot keep up with the smaller and lighter H20 molecules, causing the ski to "ride up" in the back, creating the negative friction you described. The same thing happens on ice when the skater goes too fast and the larger, heavier molecules accumulate at the rear of the blade. Accentuating the problem, the Tritium, being radioactive and unstable, releases energy and converts to Helium, He. Since Helium, an inert gas, cannot combine with Oxygen, O2 and He gas are released. By itself Helium, being lighter than air, will create additional lift at the back of the ski or skate, but with the addition of heat energy from the decay of T to He, the He and O2 gases expand, creating high pressure micro-bubbles which lift the rear even further, adding to the negative friction.

Simple first semester chemistry, at a good school!

Some how I doubt you would ever be able to measure the effects of D₂O and T₂O as you have described

The final velocity of the skier sliding down a hill of angle alfa with respect to the vertical and assuming only dry friction on snow would be something like

VSkier =Sqrt ( 2 MassSkier * g * (cos(Alfa) - DryFrictionCoeff * sin(Alfa)) / ( CdwrtFrontalAreaSkier * Airdensity * FrontalAreaSkier) )

The final velocity of the skydiver would be something like:

VSkydivder =Sqrt ( 2 MassSkydivder * g / ( CdwrtFrontalAreaSkydivder * Airdensity * FrontalAreaSkydivder) )

Comparing the two equations we can observe that to have Vskier > Vskydiver,

MassSkier * (cos(Alfa) - DryFrictionCoeff * sin(Alfa)) / ( CdwrtFrontalAreaSkier * FrontalAreaSkier)

must be bigger than

MassSkydivder / ( CdwrtFrontalAreaSkydivder * FrontalAreaSkydivder)

When assuming the same person (Skier = Skydiver), then the mass is identical and only the position this person takes with respect to the incoming air stream in combination with the Hill angle Alfa will make it possible for the Skier to exceed the Skydiver in speed. That is to say if the Skier tucks down as to decrease his FrontalArea and takes the best aerodynamic shape to decrease his friction coefficient CdwrtFrontalArea, only then can he exceed the Skydiver in speed if that one does exactly the opposite, by increasing his FrontalArea and increasing his friction coefficient CdwrtFrontalArea.

When assuming different persons, then the mass can help too, because with increasing mass the ratio Surfase/Volume decreases and so CdwrtFrontalArea will decrease. So you could imagine that a very very big Skier would be capable to outrace a very very small Skydiver.

Nice equations by Guest, just hard to read. I had to rewrite them more symbolically to 'see it'. For others like me that do not read the 'programming style' equations easily, here's the inequality condition for the skier to 'beat' the sky diver:

M₂ g₂ (cos a - k sin a) / (Cd₂ rho₂ A₂) > M₁ g₁ / (Cd₁ rho₁ A₁),

with subscripts 1 for the skydiver and 2 for the skier, Cd the drag coefficients, rho air density, A frontal area, a the slope's angle from the vertical and k the dry friction coefficient.

If we take M, g and rho as the same for both sides, the inequality reduces to:

Cd₂ A₂ < Cd₁ A₁ (cos a - k sin a)

Cute!

Good stuff and good answer.

Elegantly simple. I admire your tolerance for doing subscripts, superscripts, etc. on a computer!

Hi Ken, thanks, but it's no big deal.

That x₂ and x² little symbols on the message task-bar make it really simple - try them. You just hi-light what you want to sub/super-script, click one of them and bingo! (Thanks to the new CR4.)

I use Microsoft^® Word^® to do the initial editing and then just cut and paste the entire posting to the CR4 area. It gives you the use of other things like;

Δ π μ ½ º Φ Θ Ω Ø ¼ © ƒ Σ

Plus a lot more and you can use the spell checker as well.

Δ π μ ½ º Φ Θ Ω Ø ¼ © ƒ Σ copied from your text, presumably from MS Word.

Δ π μ ½ º Φ Θ Ω Ø ¼ © ƒ Σ from the CR4 character map on the message toolbar.

Looks the same to me!

Probably are the same...but who's to care. Also is a good idea to use the Word clean-up button on the right on the CR4 toolbar. It will make sure you original page formatting is preserved when yoo paste Word to the board.

It's that button that looks like....a brush maybe? Or nothing in particular?

That's a broom, not a brush! Hovering over the icons tell their story.

Oh, thanks. And right, it was hovering by accident that I found out that the icon was Word cleaner in the first place.

Thanks, Jorrie! I wish I had known what they were when I was writing H2O instead of H₂O ! Now that you have drawn my attention to it, that character map (the Ω icon) is kind of cool too! It even has the division sign! Now maybe if more people use it, it will be easier to follow formulas instead of using all those parentheses and slash-marks!

Anybody figure in wether they ate? I know after a 16oz Prime rib, a bowl of seafood fondue, steak fries, caesar salad, 3 loaves of Saltgrass shiner bock beer bread, and a two fork cheesecake, my drag coefficient is drastically increased... :D

I thought the "downhill" effect on skates was just tongue-in-cheek humor by "jdst" and Blink. "Propulsive effect of negative friction"? Oh, PLEASE! The gravity effect of such a small angle would be almost negligible! I mean, really, "negative friction"? That is why I posted the humorous hypothesis above about "hard water" and "negative friction"!

Of course any "effect" by D₂O or T₂O would be unmeasurable. It would not exist!

I am intrigued by how a sail boat or ice boat can go faster than the constant wind unless it is accelerated by gusts. Making its own wind? Well maybe after the crew eats a lot of beans!

I thought if an object is moving through the air (horizontally, as a sailboat or iceboat, not a glider) with no propulsion of its own, merely being pushed by the wind, once it achieves the same speed as the wind, it would be traveling at zero velocity relative to the air particles and therefore no longer have any force exerted upon it by the air. Right?

Hey STL, nice post, but you seem to forget that the sailboat/iceboat do not move with the wind, but at an angle to it, also when going downwind.

I'm not a sailing man, but somehow, I think the guys have a point. I'm however also doubtful about the 8x wind speed claimed!

I always thought the fastest a sailboat could go was when it was headed directly downwind. Yes, they can travel crosswind by jibeing and tacking and going zig-zag fashion "upwind", but when travelling cross-wind the force exerted on the sail in the direction of travel is one vector force while the remaining vector force (disregarding torque on the mast, which is counteracted by ballast below the waterline and upward force of the water on the bow as it pushes through) is pushing the sail and the boat it is connected to transversely against the water causing friction or drag. Only the keel and rudder keep the boat on the right heading.

I don't see how the boat could travel faster than a constant tailwind pushing it down wind, assuming its ultimate "hull speed" is higher than the windspeed.

I especially don't understand how it "makes its own wind". No one ever explained that, just put it out there as accepted fact!

Isn't that why sailboats use a spinnaker, to take advantage of downwind sailing?

Yes, I understand how the sail also acts as an airfoil in a cross-wind, redirecting the air flow to the rear causing propulsion forward (as well as increasing hull drag), but, still, how can forward speed (which creates an artificial "headwind" of equal speed) ever exceed the speed of the cross-wind. It seems like they would cancel each other out, as the tendency would be increase drag and to collapse the sail, diminishing any aerodynamic lift, as the forward speed appoached the speed of the cross-wind.

What am I missing? (Darn you Bernoulli!)

Nevermind! I just found this website that explains it all! There is also a picture of Albert Einstein at the wheel of a sailboat!

STL:

You'd love this sailing stuff. Especially sailing fast, where the physics get really interesting. Not too long ago, I designed and built a boat to challenge the speed record for sailboats. It's real intent was to be a commercial endeavour, however. I never was able to get the funding to commercialize it, but did manage to sail the prototoype fairly fast a few times. If I were to pick up the project where I left off, I'd simply try to round up sponsorship money, and forget about the commercial aspects. As it is, I am involved in another project for a while... but eventually.

Iceboating can be baffling for wet water sailors. Ordinarily, when you go down wind on a typical sailboat, the apparent wind (what you feel in the boat) comes more or less from behind (just as you'd expect). On an iceboat, it comes from very nearly in front ALL THE TIME... even when you are going generally down wind. Iceboats actually tack downwind at angles that keep the true wind at 45 to either side. But the boat is humming along so fast, that you'd swear you were in a conventional wet water boat going upwind. The Windrocket would do this trick too, if I sailed it just right -- something I was almost never able to do. Had it up to 32 knots, where is was starting to feel about right, and then had to turn to avoid hitting things.

Look up Yellow Pages Endeavour -- they held the record for quite a while, and were recently nudged out by a windsurfer, which can also be very fast, but require more wind (30-40 knots). YPE did about three times windspeed.

I keep intending to post a challenge question about fast sailboats making their own wind. Soon.

BTW Yellow Pages Endeavour is now Macquarie Innovation, which is the first boat on the site I referenced.

Oh -- other weirdness: If I don't post a challenge on blue light mysteriously appearing under water, remind me to do so.

I posted a note to STL re this stuff. You'd like drawing up the vector triangles for this too. If you can find a copy of Marchaj's book the AeroHydrodynamics of Sailing, second edition on page 723 or 751, (I think -- I used to have it memorized because many people would ask me how fast sailboats and iceboats could go faster than the wind) there is a nice vector summary. Many arrows going every which way, but it is a complete summary. On iceboats, (unlike soft water boats where things are much more complicated) you can pretty well ignore surface friction. It turns out, if you draw up the various triangles (representing true wind, apparent wind, boat velocity, aero drag, aero drag vector that actually slows you, etc.) for an ice boat, and then think about it for awhile, you come to the conclusion that an iceboat and a sailplane operate on the same principals... and that in the end, L/D is equal to glide ratio (plane), which is equal to boatspeed/windspeed (iceboat). Turns out that 8 times windspeed is hard to do with a soft sail, but attainable with a wing. (Not becasue a sail can't produce enough lift -- it simply produces too much drag in doing so.) You might wonder: if sailplanes routinely do 50:1, why can't iceboats? I'll put together a challenge question soon... sortof.

Actually, you're right, much of it was tongue in cheek. I enjoyed your response. The negative friction was a jest for both jdst and me. The water under skates and iceboat runners is true.

The slight slope under the blades was posted by someone else, I think, and while it's and interesting idea, the problem is that the blade would create a small hill in front that would exaclty equal the hill behind (in height).

In addition to the g-force, the down hill ski racers use the momentum of their mass to gain acceleration. With streamlined outfits the body experinces minimal drag and friction. Even the occational out flung arms and poles do not interfere with the accelaration process thus making it possible to reach higher speeds than anticipated.

...read the official answer....a new kind of--valid--answer....to an invalid question, invalid and and misleading to boot. If challenges don't have logical groundrules, what's the point...other than just to stimulate inane chatter?

I have a dumb question. If a person in free-fall is traveling head first towards the ground at 1000 km/hr, how are they able to slow down enough to deploy a chute without tearing themselves apart in the process? Just curious.

If a person in free-fall is traveling head first towards the ground at1000 km/hr, how are they able to slow down enough to deploy a chutewithout tearing themselves apart in the process?

Air brakes???

Sorry - the question is not dumb. To slow down they would have to change position. Sky divers do the spread eagle thing to slow down their descent. Not being one I can't say for sure, but I think it would be more to prolong the experience than to make chute deployment easier. Of course, if they could actually get going as fast as 1,000 km/h deployment would likely fail - in the overall context of a good time and a safe landing.

I think someone should dress in a skier suit and try for a free fall flight record - better still try to break the sound barrier.

1000 kph? ...also, chutes do not pop open like umbrellas (as seen in cartoons).

That's really a stupid question to ask, considering the answer. That's like asking "How is it possible that a guy on a bicycle is travelling faster than a a guy driving a car?" Answer: because that guy in the car has his foot on the brake! Duh...

I'm disappointed...

to assuage your disappointment, "stupid" questions can be as worthy of answers as brilliant questions (sometimes moreso): because they only need to be asked once; and because brilliant questions often do not seek increase in knowledge, only display of knowledge relative to others. Also, stupid questions tend to focus not on self, but on the subject at hand. See?

I have actually competed at Les Arcs. The biggest improvement in speed skiing equipment since the 70's has been the materials used for the suits. At about 180 kph the skis actually start to fly and do not contact the snow. Control is maintained by carefully aligning your knees so that the angle of your ski base as it floats on the snow keeps you moving down the fall-line.

So the answer is, not so much any improvement in skiers position as much as less-porous ski-suits made with low coefficient of friction coated stretch fabrics.

I witnesses a documented crash where the competitor crashed just as he reached the first timing section and continued through to the end of the timed section. His speed while sliding on his side was +240 KPH. His suit caught on fire and he received bad burns to his torso. We put the fire out by heaping snow on him. In subsequent races we had fire extinguishers positioned down the run. His speed while crashing was less than one KPH below the world record at the time, and he was making a world record run. He continued to compete for a few years after this horrible crash

This is in reference to the "flame" that appeared as post #79 and was removed (good job moderator!):

its (your grammatical mistake) hilarious how interested you are in the "argueing (your spelling error) over physics on the internet about an obscure and pointless topic" and in making fun of people you don't even know. If people like to discuss "obscure and pointless" (to you, anyway) topics, what's it to you? I will bet that you have plenty of interests that other people would consider "obscure and pointless" and laugh at you as well.

What the heck is a "noob" and what does "sit in spec" mean anyway? Don't you speak plain English?

Please go away and flame someone else. Better yet, if possible, go flame yourself!

How cowardly, to flame someone as a "guest"! At least use a fake name like everyone else! (grin)

And if this gets removed by the moderator also, so be it. No hard feelings.

Aha! I found the definition of "noob" in the Urban Dictionary (See below). Boy, am I insulted! <Grin> Actually, it just shows the intelligence level of the flamer:

"Generally, however, people use 'noob' as an applicable insult for anyone who happens to piss them off. A person will also often use this term to describe people that they feel are beneath them. Many times, during online arguments, players will pull this term out of their asses as an insult when their own 'wit' is running dry. "

How accurate. I think that describes our flamer to a "T" ! Perhaps he should "sit in spec" himself!

That is all.

Carry on, CR4!