Topography, aerodynamics, and HACE/HAPE..

Post general questions and discuss issues related to climbing.
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Yeti

 
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Topography, aerodynamics, and HACE/HAPE..

by Yeti » Sat Jun 09, 2012 4:37 am

This struck as I was going to bed tonight... it stewed to the point that I had to come write it down.

I'd recently read an account of two strong climbers that had been pinned down by wind at 14,000ft. One was tragically claimed by HACE while they waited out the winds. It stuck me as odd that they he had done so well over two strenuous days, only to have it hit suddenly while stationary and a somewhat mild altitude.

I moonlight in motorsport, and have taken an interest in aerodynamics over the years. Oversimplified; the area on the leading edge (windward) of a surface experiences high pressure, the area on the trailing edge (leeward) experiences low pressure. The air density in areas protected form the wind is lower.

At altitude, it's not that there is less O2 in the air, there is less of everything, less air altogether. The pressure drops as you distance yourself from the earths core, hence the popping of ears while flying.

When you are pinned down by wind, and you seek shelter in the on the leeward side of a rock or ridge, the localized pressure in that area is lower than it is on the windward side. By how much depends on the speed of the wind: The higher the wind, the lower the pressure.... and the less air density you have. Being pinned down implies wind of excessive speed, has anyone ever mention the pressure differentials?

Could the low pressure area on the leeward side of rock in a wind storm produce O2 levels lower than would be expected for a given altitude?

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Re: Topography, aerodynamics, and HACE/HAPE..

by dadndave » Sat Jun 09, 2012 6:52 am

That's an interesting question, and you seem to have partially answered it yourself. Under lower pressure, there's less of every gas, including oxygen. I imagine that a complete answer would be pretty complex because (among other things that I probably haven't thought of) the actual pressure drop would depend on the shape of the object to the windward.

Mythbusters did a series of experiments in relation to tailgating large trucks (I forget what you call tailgating over there, but you know what I mean - following a speeding truck to get the slipstream effect) They gave figures for the effect at various speeds but I can't remember the details. Obviously the effect would be much smaller if the windward object is a more streamlined shape with the air departing the rear of the object "cleanly". I suppose there would be barely any slipstream effect at all a couple of metres behind an aircraft wing, but to state the bleeding obvious the pressure differential between the upper and lower surface of an aircraft wing is enough to lift the weight of the plane.

Come to think of it, when I lost tiles off my roof in a gale some years ago, much to my surprise at the time, the tiles stripped off the leeward rather than the windward side of the roof. After scratching my head for a while I realised that this is what I should have expected because of the negative pressure caused by the airstream over the roof crest - much like the upper surface of an aircraft wing.
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Re: Topography, aerodynamics, and HACE/HAPE..

by Enkidu » Sat Jun 09, 2012 7:14 am

This is a very interesting thought. The effects of wind on man-made structures has been studied extensively at many universities and "pocket vacuums" are a well documented occurrence on the leeward side of buildings. A rock large enough to block the wind would likely have a similar effect. Whether the pressure drop would be significant enough to exacerbate things beyond normal for a given altitude is a good question. Probably a great thesis project idea for some grad student.
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Re: Topography, aerodynamics, and HACE/HAPE..

by coldfoot » Sat Jun 09, 2012 7:40 am

To first order I think this effect turns out to be negligible.

I'm going to calculate the pressure increase on the windward side of a rock because that's pretty easy to make a model. The pressure decrease on the leeward side should be the same or less. You can think of the pressure decrease as being due to air blowing away from the leeward side.

Suppose the air molecules just blow right into a bluff body, like the rock, and decelerate to zero, exerting a pressure on the rock. (This overestimates the pressure somewhat since the air isn't fully decelerated.) If the air density is rho and the wind speed is v, the mass hitting the rock per area per time is rho*v, and the force per area (change in momentum per area) is rho*v^2. Force/area is pressure, so the pressure increase is rho*v^2. (I can't really explain this more clearly without drawing pictures, but if you work through the unit dimensions you'll see that is correct.)

At sea level and 20 C the air density is about 1.2 kg/m^3 and the pressure is 1 atm = 101 kiloPa (Pa = Pascal = 1 Newton/m^2). At 14000 ft the air density is about 0.65 sea level and the pressure about 0.6 sea level for a standard atmosphere.

Suppose we're talking about a 100 mph wind = 44 m/s. At sea level, the pressure increase on the face of the bluff body is about 1.2 * 44^2 = 2.3 kPa, compare to ambient pressure 101 kPa. At 14000 ft, the pressure increase is 1.5 kPa and the ambient pressure is 61 kPa. Again, I think the pressure decrease on the leeward side is similar or less.

So this is a few percent effect at most. Basically 1 atmosphere is really an enormous amount of pressure. We just don't notice it because it's balanced out, except when you change altitude quickly and your ears pop, or your half-empty water bottle is squished while driving down the mountain.

I am not qualified to say why a strong climber might succumb to altitude sickness at 14000 feet, but I'd have to guess something about exhaustion and cumulative time at altitude.

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Re: Topography, aerodynamics, and HACE/HAPE..

by byrdrw72 » Sat Jun 09, 2012 4:07 pm

Hi,
Great question and a concern I haven't pondered until now. I am a professional pilot and flight instructor and know a bit about aerodynamics and physiology. I have training related to high altitude exposure and the effects on the human body.

Most people think that O2 content lessens with altitude. This was already mentioned in other post but is simply less pressure which means more space between molecules. The closer to sea level, the closer the molecules and the more that can be absorbed by our bodies tissues. A perfect example is a pressurized aircraft. Pressurized aircraft environmental systems actually use ambient air to provide a life supporting environment. No supplemental O2 is needed for this process. The system compresses the outside ambient air to a lower level atmosphere and the cabin air is circulated and pushed out of the pressurized vessel through an outflow valve to keep the environment properly saturated with O2.

I believe you may have merit in your speculation about lowered air pressure due to airflow over a surface. If this surface is shaped to act as an airfoil, the airflow from wind should produce a low pressure area. Somewhere in this process does a high pressure area have to be produced. The difference has to go somewhere! There is another process that occurs that might relate to this. All airflows over surfaces produce boundary layers which is a thickness layer of air that binds to the surface, caused by surface friction. Maybe this boundary layer of air might be like a pressured aircraft without an outflow valve and the O2 is depleted which induces altitude sickness/ hypoxia. I would say that if wind does lower the air pressure more that it would make a difference on tissue O2 satuaration and could accelerate the effects on the body.

My thoughts!

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Re: Topography, aerodynamics, and HACE/HAPE..

by ExcitableBoy » Sat Jun 09, 2012 4:14 pm

Yeti wrote:I'd recently read an account of two strong climbers that had been pinned down by wind at 14,000ft. One was tragically claimed by HACE while they waited out the winds. It stuck me as odd that they he had done so well over two strenuous days, only to have it hit suddenly while stationary and a somewhat mild altitude.


It takes 5 -7 days of yo-yoing to 14k and sleeping low to fully acclimatize to 14k. There are stories of scientists/climbers spending the night on the summit of Rainier and dying of altitude related illness because they did not take enough time to fully acclimatize. I think all the other factors are negligible compared to this simple fact.

As far as people thinking there is less O2 at altitude, what folks are referring to is the partial pressure of O2. I think most people realize the partial pressures of all atmospheric gasses remain the same at varying altitudes, just fewer molecules are available the farther one gets from the surface of the earth.
Last edited by ExcitableBoy on Sat Jun 09, 2012 8:59 pm, edited 1 time in total.

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Re: Topography, aerodynamics, and HACE/HAPE..

by MoapaPk » Sat Jun 09, 2012 6:44 pm

Start by using the simple formula for laminar flow in a pipe or between two infinite planes, expressed as
average fluid speed as a function of plane separation( or radius), viscosity, and the pressure gradient. It won't take you too long to realize that with air, even at a substantial fluid speed, the pressure change isn't much. That's a gross oversimplification, since you may be in a world of non-laminar flow, but it will give you the 1st-order answer.

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Re: Topography, aerodynamics, and HACE/HAPE..

by stinkydog » Sun Jun 10, 2012 3:16 am

I can't remember enough of my college fluid dynamics to back this up, but I know based on experience: if you're walking directly into the wind with your mouth open, you'll be getting more oxygen than you would be turned the other way. Obviously, the real world is more complicated, but remember: low pressure vortexes really do contain less air pressure.

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Re: Topography, aerodynamics, and HACE/HAPE..

by Damien Gildea » Sun Jun 10, 2012 4:27 am

ExcitableBoy wrote:It takes 5 -7 days of yo-yoing to 14k and sleeping low to fully acclimatize to 14k. There are stories of scientists/climbers spending the night on the summit of Rainier and dying of altitude related illness because they did not take enough time to fully acclimatize. I think all the other factors are negligible compared to this simple fact.


Yep. If you go from sea-level, or even around 2000ft, to 14,000ft in two days you are asking for trouble. It would be rare for a person to do this and not start to feel sick after a few hours at max height. If they stayed there, or got stuck, most would get very sick and some would die.

Driving to the trailhead, going up Shasta and down again, or overnighting at Muir, summiting Rainier, having an hour on top then descending are not the same thing, quite different. Up so fast and staying there is the problem. Your body has a delayed reaction, susceptible to many variables - yet another reason for getting down asap.

In fact, almost no one ever gets fully acclimatised to anywhere very high, they just reach a workable level. If you live in LaPaz or Lhasa or somewhere high (10-11,000ft) it will actually take a couple of months before you are acclimatised to a level where you are just like at home. Climbing big peaks (>6000m) from base camps above 4000m are just exercises in hitting the sweet spot where acclimation turns to deterioration.

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Re: Topography, aerodynamics, and HACE/HAPE..

by ExcitableBoy » Sun Jun 10, 2012 1:56 pm

Thanks for that Damien. Many Seattle based climbers climb Rainier from Seattle and descend in under 24 hrs. They are in effect outrunning altitude sickness. I have done this many times and never felt ill, as well as on other 14k+ mountains. On Denali we took 5 days to move into the 14k camp and I had a variety of minor altitude related maladies; Chyenes-Stokes breathing, mild headache, and general lassitude for a day or two. It was an eye opener.

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Re: Topography, aerodynamics, and HACE/HAPE..

by Yeti » Sun Jun 10, 2012 3:26 pm

Outrunning AMS sounds interesting, but also dangerous. With something like HACE, you won't know you've hit your wall until you're unable to function, and as good as dead without a significant effort from your mates... or a helicopter pilot.

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Re: Topography, aerodynamics, and HACE/HAPE..

by ExcitableBoy » Sun Jun 10, 2012 3:37 pm

Yeti wrote:Outrunning AMS sounds interesting, but also dangerous. With something like HACE, you won't know you've hit your wall until you're unable to function, and as good as dead without a significant effort from your mates... or a helicopter pilot.

Pretty much everyone who climbs Rainier on a two or three day schedule is in effect doing this. Pretty much nobody other than the rangers and guides properly acclimate to 14k+, although many climbers spend a lot of time climbing other peaks which certainly helps. I think most people will experience AMS before HACE sets in, although I don't know this for a fact, and will feel crappy enough to head down. I see the real danger in this is getting pinned down by bad weather and being unable to descend.

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Re: Topography, aerodynamics, and HACE/HAPE..

by Yeti » Sun Jun 10, 2012 4:00 pm

Something that factored into my theory were extreme examples in the other direction, such as the high bivy utilized in "148 Blew Zero". Their snowcave was on the windward side of the mountain, and they spent nearly a week, malnourished and dehydrated, at 18,000 or 19,000ft.

If the the numbers stated above are true; 14,000ft is roughly .65atm. And theoretically, the pressure differential would only be a few percent at most with a triple digit wind speed....
14,000ft represents a 35% drop in air density... a 3% drop in density is akin to being 1200ft higher?

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Re: Topography, aerodynamics, and HACE/HAPE..

by rgg » Sun Jun 10, 2012 4:11 pm

A few weeks ago, I stood on top of Helvellyn in a storm. At times it was impossible to walk in a straight line. The summit is a big plateau, and there was a big cairn as well as a stone pillar, but not quite next to each other. I wondered which one was higher, so I visited both.

My altimeter is an old style one, working on barometric pressure. Normally, when there are multiple summit candidates, I visit them all and rely on my altimeter to tell me which point is higher. I usually stay on each summit for at least a minute before taking an altimeter reading. If the difference between two summits is no more than 1m, I interpret that as inconclusive, otherwise I take it that the one with the higher reading is indeed the summit.

However, the storm on Helvellyn made that impossible. The altimeter readings on the high plateau were simply not stabilizing, whether I was standing on one of the summits, walking between them or sheltering on the leeward side of the big stone structure next to the cairn. I concluded that one of the effects of the storm was that air pressure was fluctuating much more than normal. However, the readings fluctuated only a few meters. From that I'm inclined to conclude that the air pressure variations in a storm are negligible compared to the pressure change due to altitude.

In fact, the effect of a depression on the air pressure is much, much bigger. A strong low pressure system can easily have 3% less pressure than normal (and hence also 3% less oxygen). On a 14000 ft mountain, that would equate to being 700 ft higher (see Air Pressure and Altitude above Sea Level). If you are even reasonably acclimatized to 14k, I wouldn't expect an additional 700ft to be a problem, but if you're poorly acclimatized to begin with, it won't help either.

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Re: Topography, aerodynamics, and HACE/HAPE..

by MoapaPk » Sun Jun 10, 2012 5:17 pm

The best pursed-lip breathing generates only about 1% pressure increase over atmospheric.

Really, the pressure drop over a snow wall is very small, even when the air is whistling by at 20m/s. It's a tiny fraction of an atmosphere. For largely inviscid but laminar flow, the pressure gradient perpendicular to the flow directions is given by Euler's formula,

dP/dR = rho * v^2/R

where R is the radius of curvature, rho is air density, and v is the flow speed over the object. Suppose we have 10 m/s wind blowing over the edge of a round wall top with R= 0.1m. Let's say the air at higher points and lower T was about 1 kg/m^3; we get about 1000 Pa/m, ~0.01 atm over a meter-- and really it would drop back to uniform flow in much less in much less than a meter, so we are talking about < 0.1% of an atmosphere (mea culpa, it's been a long time since I've done this stuff, so check...).

Wings work because the pressure differential, integrated over a large surface, generates forces that are greater than the body to be lifted.

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