SkinTrack

Vertical climbing speed: Ski mountaineering vs Uphill running vs Slope angle (vs Gear weight)

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How does vertical speed compare between different mountain sports?
And how does slope angle affect that speed?

vertical-speed-ilustrationThese are very interesting questions to which no one has an absolute answer for. I am going to take a shot at it while relying on my knowledge and experience in both ski mountaineering (skimo) and uphill running.

Here is a summary of conclusions from my “study”, but if you have 20min then read on, it’s worth it. Also, share your opinion in the comments below, thus we can all learn even more.

The most efficient angle for:

  • skinning for guided clients is believed to be 12 degrees.

  • skinning for trained athletes is 13-16 degrees.

  • skimo and uphill running isn’t the same.

  • skinning is lower than the one for uphill running.

Why this topic? Why now?

Kilian Jornet Burgada
Kilian Jornet Burgada
I was always interested about this topic and what made me to research it now even more is that, these days, we are fortunate to have a single athlete who is arguably the best in the world at both disciplines. This fact makes things easier as we can “forget” about some variables that are very different between individuals such as body weight, years of training, etc..

The athlete’s name is Kilian Jornet Burgada. He is a 21-year-old phenomenon from Catalonia (Spain) that wins races over any distance, from 30min bursts to 30h mountain marathons, whether on skis or in running shoes. If he is a new name for you then check out his results on Wikipedia – Kilian Jornet Burgada.

The second athlete I will be talking about is Sebastian Selas. I will introduce him further down.

Comparison data – raw race facts

The races (performances) I am going to use for my comparison are:

  • 2009 vertical race at European Ski Mountaineering Championships (Italy)

  • 2007 1km vertical uphill running race (Switzerland)

  • 2009 Grouse Grind Mountain Run (Canada)

The conclusions I am going to draw (or not) in this article come from pure facts I could find and know about these races and athletes, and from my personal experience.

I chose the three races/two athletes for couple of reasons:

  • two of the races were raced by the same athlete in two different disciplines

  • all three races are of very similar vertical gain

  • times at two races stand as course records

  • all three races take place at an arguably low altitude (not going over 2000m)

  • both athletes seem to be quite gifted in terms of vertical racing

  • both athletes are about the same age, 21 and 22

Vertical race at European Ski Mountaineering Championships 2009 (Feb 20, 2009 – Alepago, Italy)

Elevation gain: 835m
Distance: 3800m
Course altitude: 980m – 1815m
Time: 35min 51sec
Winner: Kilian Jornet Burgada
Website: Alpago 2009

“Vertical kilometre” race 2007 (Oct 27, 2007 – Fully, Switzerland)

Elevation gain: 1000m
Distance: 1920m
Course altitude: 500m – 1500m
Time: 31min 52sec (course record – unofficial world record for one vertical km)
Winner: Kilian Jornet Burgada
Website: Team La Trace

Grouse Grind race 2009 (Sep 20, 2009 – Vancouver, BC, Canada)

Elevation gain: 853m
Distance: 2900m
Course altitude: 270m – 1120m
Time: 25min 24sec (course record)
Winner: Sebastian Selas
Website: Grouse Grind

Ski mountaineering vs uphill running

Since we have the same athlete winning in both disciplines we will go straight to differences between the two mountain sports.

Obvious disadvantage in skimo racing versus trail running is gear weight, especially the weight an athlete carries on his feet as that restricts his leg speed (frequency) the most. Of course, we can compare the clothing and pack weight as well, but I am not going to do it as I don’t believe that weight (about 1.5-2kg difference in this case) affects us as much as what’s on our feet.

Here, just out of curiosity, are the weights per foot:

  • super light running shoe is about 200g

  • super light ski, bidding and a ski boot combination is about 1350g

  • a difference of 1100g

  • pole weight doesn’t matter since Kilian used poles at both races

Skimo vertical race analysis

Based on the raw race facts Kilian’s average vertical speed for the vertical European Skimo Championships was:

23.29 m/m (metres per minute) = 1397.4 m/h (metres per hour)

Click on the image to see a bigger version.
Click on the image to see a bigger version.
The skimo race course contained a boot-pack section where racers attach their skis to their packs and hike up a preset boot-pack track. This section was only 95m vertical according to organizers.

A super fast boot-pack bottom transition takes around 15-20s and the top one about the same.

According to summary articles of that race Kilian had troubles with his boot-pack bottom transition, so it took him longer than usual, and almost lost a race there.

Kilian’s winning time over the 835m was 35min 51sec but after deducting transitions times I feel comfortable at settling with a time of 35min flat.

That would mean his actual average vertical speed when he was moving was:

23.86 m/m (metres per minute) = 1431.4 m/h (metres per hour)

1. This means it would take him 41min 55sec to skin up 1000m (vertical) if the course would continue and he would keep the same speed.

2. Kilian’s pace in this race was 9min 13sec per kilometre. This is a pace road runners calculate, so it is not a vertical kilometre but a normal one.

Since the 23.86 m/m is the “unbiased” speed (without transitions) we can compare it with his running race as there are no transitions in that discipline.

Uphill running 1km vertical race analysis

Again, based on the raw race facts Kilian’s average vertical speed for the vertical kilometre race in Switzerland was:

31.38 m/m (metres per minute) = 1882.8 m/h (metres per hour)

Click on the image to see a bigger version.
Click on the image to see a bigger version.
1. Since the race was over 1 vertical kilometre, his time to climb 1000m – 31min 52sec – was the same as his overall time.

2. Kilian’s pace in this race was 16min 35sec per kilometre which is much slower than in the skimo race.

In the race, he had to pass a couple of slower competitors, but I don’t think this affects the comparison of the two disciplines too much.

The uphill run was done as a time trial and the skimo vertical race had a mass start. So passing few racers versus fighting in the mass start cancels the factors out.

Comparison – vertical skimo and uphill running races

Here is a conclusion to the first question, “How does vertical speed compare between different mountain sports?”:

We can clearly see that Kilian’s vertical uphill running speed is way faster than the one reached at a ski mountaineering race. This should be no surprise as equipment weight plays an important role. Therefore, of course, this is a bit of comparing apples to oranges, yet it is still interesting to see the numbers.

Also, there is a fact of two years between the two races. In that time Kilian got faster for sure as he proved it at many ski mountaineering races. However, he is running virtually the same time over the vertical kilometer race (at the same venue) past three years, between 2006 and 2008.

Therefore, I consider his record the best time in the world over one vertical kilometre that is not getting any faster at the moment. The vertical kilometre race is still due this year, so we shall see (Oct 24, 2009).

Another factor to consider and compare is the slope angle, which we will get a better comparison lower down when comparing running with running:

The skimo vertical race gained 835m over 3800m which means a slope of 12.69 degrees or 22.52%. Compare this to the uphill run and a 1000m gain over 1920m which means a slope of 31.39 degrees or 61.01%.

Two interesting facts to compare are Kilian’s vertical speeds and his paces per kilometre as they go in the opposite dirrection – smaller vertical speed with faster pace versus  higher vertical speed with slower pace.

Skimo race:

  • vertical speed is 1431.4 m/h

  • pace is 9min 13sec / normal kilometre

Uphill run:

  • vertical speed is 1882.8 m/h

  • pace is 16min 35sec / normal kilometre

Vertical speed and slope angle – running vs running

To answer the second question, “How does slope angle affect vertical speed?”, I didn’t use the same athlete as I couldn’t find enough facts about other Kilian’s vertical races. Instead, I opted to use a race that I know the course of very well; therefore, allowing me for somewhat “accurate conclusions”.

Also, the follow up question should be: “Which incline angle is the most efficient and the fastest to climb at?”. I’ll take a stab at this too, for now lets go back to the second uphill running race.

Photo cropped from The Province photo.
Sebastian Selas. (Cropped from The Province photo.)

The Grouse Grind Mountain Run in North Vancouver in BC, Canada is a very popular uphill race that is regularly attended by very strong athletes; however, no European speedsters have came to check it out yet.

This year (2009) the record was set to an incredible 25min 24sec for gaining 853m over 2900m.

The winner was a 22-year-old local Vancouverite, Sebastian Selas, who is an amateur triathlete and cyclist. Judging by his time, I believe Sebastian would be a serious match to Kilian’s climbing abilities.

But lets look at some numbers, to see how a different angle affects the vertical speed and pace.

Sebastian’s average vertical speed when climbing Grouse Grind trail was:

33.58 m/m (metres per minute) = 2014.8 m/h (metres per hour)

Sebastian’s pace in this race was 8min 46sec per kilometre which is 27sec faster than Kilian’s skimo race pace and 8min faster than his vertical kilometre race pace.

The Grouse Grind race starts in waves that are seeded based on runners’ honest expected time estimates. It starts and finishes with a bit of a flat, around 150-200m in total which should account for about 25-30sec in total. So if we subtract 24sec (which gives us a time of 25min flat) we arrive at an average vertical speeds of:

34.12 m/m (metres per minute) = 2047.2 m/h (metres per hour)

1. Based on the second speed, it would take Sebastian 29min 19sec to run up 1000m (vertical) if the Grouse Grind trail (race course) would continue and he would keep the same speed.

2. Sebastian’s pace in this race was 8min 46sec per kilometre. Using 2.9km here and not sub-subtracting the 150-200m since I am calculating runners pace.

Even though we are not comparing the two athletes on those two specific courses, I think, it is very safe to assume that they are both world class uphill runners for efforts of up to 30-35min, and likely even longer.

Now, lets take a look at the slope angles of the two uphill running races:

Kilian’s vertical kilometer race average slope angle was 31.39 degrees (61.01%), compared to the Grouse Grind’s trail average angle of 18.07 degrees (32.63%) – instead of 2900m, I used 2750m as the actual course length due to the flat start (even downhill) and finish sections to calculate the angle.

The Swiss 1km vertical kilometer race is run straight up, doesn’t let up a bit; whereas the Grind has some switchbacks with low angle incline that allow for some recovery, or at least allow to pick up leg speed again.

One last thing to note here is that Sebastian did not use poles for his run and Kilian did. I believe, both knew what they were doing and picked the right tools for the slope angle they were facing or technique they are using.

Conclusion and an example – slope angles, speed and efficiency

Based on this “study” of mountain uphill running and skimo climbing, and my experience in both disciplines, I am comfortable to say that steeper doesn’t mean faster. However, the more important question is: “Which incline angle is the most efficient and the fastest to climb at?”

To answer that, I can only speculate based on my experience, as would most likely anyone else based on his. But we can clearly see that Sebastian was able to produce an average vertical speed of about 150 m/h (metres per hour) higher than Kilian in his race. This is about 8-9% faster than Kilian’s vertical running speed.

Also, Sebastian’s pace (time per kilometre) values are much more faster than Kilian’s. Sebastian was doing 8min 46sec per KM versus Kilian’s 16min 35sec per KM; that is almost 90% faster pace.

That leads me to say that Grouse Grind’s slope angle is more efficient (18.07 degrees) than the one in Switzerland (31.39 degrees). And that the most efficient angle is somewhere in between the angles of the two courses, while personally leaning more towards the incline values of the Grouse Grind.

But since the techniques of climbing (due to terrain and equipment) in ski mountaineering and uphill running are quite different we should not assume that the most efficient angle for both disciplines is the same.

Based on my experience, I would speculate that the most efficient and the fastest angle for skinning is lower than the one for uphill running.

I believe that in uphill running you can sustain your most efficient leg speed on a steeper slope over a longer period of time than while climbing on skis. This has very much to do with equipment weight and leg speed (and technique).

In fact, you can see this if we compare the paces per KM and vertical speeds:

Kilian went at a slower pace (9min 13sec / KM) and at a slower vertical speed (1431.4 m/h) on a lower angle course (12.69 degrees) when compared to Sebastian’s 8min 46sec / KM, 2047.2 m/h speed, and 18.07 degrees angle slope.

To demonstrate this without calculations here is an example:

Imagine running on a flat ground wearing a 400g pair of shoes (200g per foot). You run for 1km flat-out and record your time and you count your steps.

Now you do the same with a 2700g pair of shoes (1350g per foot). Your time will be slower and you will most likely (absolutely sure about this) do more steps. If you manage to keep the same number of steps you will be even slower.

Without going in more detail about step frequency (because it’s a very individual thing) the example demonstrates you had a lower average speed while running with heavier shoes.

Translating this onto a 20 or 30 degree slope would show at least the same difference. Running with heavier shoes at the same vertical speed, with the same leg turn-over (leg speed) would tire you way faster than lighter shoes.

Subsequently, if you would want to keep the same vertical speed on the same incline you would have to change something – and that is either a faster leg turn-over or have lighter shoes (equipment).

If you don’t trust my example, go and try it out, but before you run around your house in ski boots make sure your neighbors know about the experiment, otherwise they might call for help 😉 and hopefully you don’t think I am crazy for writing all this 🙂

As for ski mountaineering skin track angles, mountain guides are thought to set about 12 degree tracks for their clients, so it must be believed by the experienced ones this angle to be the most efficient angle for most of the clients. The slope angle of Kilian’s skimo vertical race was just over 12 degrees as well.

However, I believe that trained athletes have their most efficient and the fastest skinning angle a bit steeper than average Joe. I would estimated it at about 13-16 degrees.

Now, what’s left to do is to either get Kilian run the Grouse Grind next year or get Sebastian to go to Switzerland for this years race (Oct 24, 2009), so we can truly compare the two machines and have more consistent data.

I hope you enjoyed this article and you are welcome to share your opinion on this topic in the comments below.

Reader Interactions

Comments

  1. Hi Graham,
    While that could perhaps be the required test I find it hard to believe that anyone passes it 🙂
    Are you sure it’s 1000m vertical gain? Because if the trail is 1000m long with up to 400-500m of vertical then that would be doable.
    Just think about it logically – if the fastest and perhaps most talented mountain runner in history cannot even come close to ascend 1000m in 20min (despite training 24/7 since very young age) then it is highly unlikely that there is even single pre-teenage boy passing the test even once in 100 years. VO2max required for such effort could be calculated and it might be a decent number even for a husky dog, never mind an undeveloped human 😉

  2. hate to burst your bubble! ..but young shaolin temple recruits in china (average about 12 to 14 yrs old) are required to ascend a 1000 meter mountain trail in no more than 20 minutes if they wish to continue their training. I didn’t buy it, but checks out.

  3. after a little perusing:
    The race covers a vertical distance of 1,050 feet (320 m) and takes in 1,576 steps. The record time is 9 minutes and 33 seconds, achieved by Australian professional cyclist Paul Crake in 2003,[73][74] at a climbing rate of 6,593 ft (2,010 m) per hour.
    this is for the eiffel tower which looking at your numbers are the same.
    Various sources, including the building’s owners, give the height of Taipei 101 as 508.0 m (1,667 ft), roof height and top floor height as 448.0 m (1,470 ft) and 438.0 m (1,437 ft).
    The tai pei race only covered 91 of the floors. The 438 m refers to all 101 floors, that is roughly 4.3 m/floor. consider 91 floors of that we have 391.3 m. paul’s record is in 10:29 so that is 37.3 m/min and about 2240 m/hr. which is much more realistic considering 2900 m/hr >> 2021 m/hr and they were set by the same person. my numbers may still be a little off as well. 37.3 m/min is fast, very impressive.

  5. John, This would be very interesting to test and information.
    The way to test would be to have couple of run full out for about 6-10min at 10, 15, 20, 25%. Few days apart for the various angles to make sure they are again at their best but not long enough to benefit much from training. Anyways, there are protocols that could be followed for the most objective comparison.
    However, I don’t know whether any treadmill goes to 25%.

  6. Does anybody know what the best inclined performances are on a treadmill ,saY at 15%,20% and 25%(over a vertical kilometer ideally).
    I realise that different brands of treadmill may have varying levels of accuracy.Any thank you very much for your interesting article.

  7. Interesting thanks for all the info! I have problems with tailors bunions when ever I wear stiff boots especially w/ Dynafit boots and so far the only boot with a wide enough toe box for me is the F1. I have felt the weight of Grants XP and I must say its unbelievable and if I had an extra 1200 Euros I would buy a pair and use them just for races. As we all know this science is still far from complete and with all these new boots it will be really interesting to see which ones preform this year!

  8. Your vertical climbing story has been well and truly hijacked Stano!
    I spent 2008 in France and and think, then, across the board it was pretty even on the XP/F1 mix. Amongst the French team XP more or less all the way. Same in Switzerland. Italy was different, they are pretty proud of Scarpa I think and Pierre struggles to sell boots there, thats why he started to sell them on the Crazy Idea site.
    Would racers use the XP no strings attached? I would say yes, with out a doubt. For example, 1 Scarpa sponsored athlete payed for and then painted his XP green. It gets better, I heard another guy disguised his XP’s by racing with a F1 shell over the top, all to keep the sponsors happy! There were few people that owned XP, but didn’t use them because of scarpa contacts.
    That was a few years ago and looking now at photos for the 2009 season, I think there are a lot more of the top racers using the XP.
    The DyNA is a great little boot, but it is still to heavy for real serious racers. I think it wouldn’t make a lot of difference in results for me if I used my XP or DyNA, but for those guys that cut the matches………
    the way I see it, XP or DyNA, if you can get our hands on them!
    I will take some photos some time and send them to Stano of the 2 boots for a comparison. Sorry, no F1 photos, I sold them to some poor sucker in France………
    Don’t worry, do relies I will probability get my ass kicked by a bunch of F1 wearing Canadians in Andorra!

  9. Good introduction with the DyNA boot Alex.
    One more thing with F1s bending while skiing: once you have skis mounted with a low heel, like ATK, the boot is so low above the ski when skiing that you need only a very thin (thus light) shim to compensate for the bellows bending. So I no longer consider any issue skiing in F1s. However, you can catch an edge like mentioned above by me and Alex.

  11. James, I had the Dynafit DyNA boot in my hands this weekend but not much time to check it out as I was in a rush. I think it flexes about 1/3 of the F1. Looks very slim, which I find great, because on the skinny skis I tend to catch a “boot edge” when skiing steep hard pack or just carving too much.
    I will send an email to Grant to poke him to comment on your post. I am interested too.

  12. Grant, it sounds like you have a lot of experience with bellows vs no bellows. So what it the draw of the F1? How does the current market share break down between the F1 and XP in the European race community? (50/50) Are you saying that if all the racers that use the F1 could switch to a stiff boot (no strings) that they would? Does anyone know how much the DyNA flexes? I looked at a demo shell last spring that had the carbon cap taken off. By the look of the cut-away inside, it looked like the toe was meant to flex. However, nowhere near as much as a bellow would. This is very interesting because we are just now gaining access to many of the new race boots here is Canada. I mean, it’s still hard to get them all but…. not for long hopefully!

  13. Hello Grant,
    Thanks a lot for your opinion. Since you’ve skied both boots (F1 and XP) you have a “legs on” experience, which is the best.
    Grant, the link you posted doesn’t work. Is that review posted somewhere else?
    We went from vertical speed to boots 🙂 But it’s great because that’s ultimately the part of equipment that currently defines our sport the most by allowing changes in technique and speed.
    Thanks all for bringing their thoughts. It makes me think whether to invest in F1 Carbon or go with a w/o a bellow boot.
    But I think I have to defend the bellows a bit having able to compare it to older Dynafit models. Yes, I have F1s and I like it but here is my logic:
    Simply, the bellow provides the most natural movement for your foot, it’s the closest to running in shoes. That means your body (muscles) is naturally “fitted” for such a movement, therefore, you are not redefining nature. That to me is as efficient as it can get. (Uphill runners don’t use “unbendable” sole either.) However, I had to learn with the F1s to not bend the bellow much going steep uphill or when traversing, then my skis/skins don’t hold on the snow as good.
    Ultimately, it comes back to weight. And I believe that if they make the F1 bellow bend about 30-50% less and make the boot even closer to XP weight, it would perform better than the XP. (But I don’t know whether it is technically possible to mach XP weight and keep the bellow.)

  14. sorry guys, the bellows are a joke.
    To compare the F1 to the XP…………….
    The flex is terribly inefficient, and your foot flexs inside the boot cause your heal can lift when the cuff is open away.
    The first time I skinned in the XP I found it horrible with no flex, that lasted about 5 mins..
    250 gr liner? That’s your problem right there.
    Sorry, this is getting away from the discussion at hand (but Jon has posted a good boot review (preview?) here- http://theseskisarewings.blogspot.com/)
    Stano- nice article and great site, keep it up.

  15. I like the bellow although one other downside is the need for a support base under the bellow that can add weight to the overall set-up. I don’t think the stiff boots are that much lighter than the bellowed Scarpa though. Even the Gignoux at a crazy sub-500gr is not that much lighter than the Carbon Scarpa at 840g. Once you add a liner to the Gignoux boot at 250-ish grams it is pretty much on par.
    What I like most about the bellow is the fact that it allows me more range of motion throughout my entire leg. It’s nice to be able to get up on your toes and almost “flick” your ski back with that bellowed movement. When that flex is taken away from my front toes I just feel this sense of fatigue through the calf and an inability to pivot my hip like I want to. I don’t know if its more efficient but it feels better for me at race paces. Just my 2 cents.

  16. Couldn’t help my self to not think about the differences in race boots with or with out a bellow. I heard that stiffer boots are more efficient for steeper angles and boots with a bellow are more efficient for lower angles. The bellow seems to utilize the calf muscle more and because the calf seems to be used more for forward motion it makes sense that the bellowed boots would be faster on a lower angle. Another thing to take into consideration is if the stiff boot skier has there buckles loose then there will probably be quite a bit of movement similar to boots with a bellow. One thing is for certain they are making the stiff boots at about 1/2 the weight of the lightest bellowed boot.

  17. Great thoughts from all of you guys.
    I knew I couldn’t do exact science due to obvious reasons but I believed the article could inspire thinking and a good discussion; I am glad it did 🙂
    Once in Europe this winter, we can ask Kilian (and others) whether they have a preferred angle(s) for skinning, and if they do what the range would be.

  18. With stair climbing, the foot is not on any angle, it is flat. Running up hill, the heel is lowered, this causes way more physical strain in the calf and hamstrings. Whereas, stair running the foot is flat, less strain on the calves, but more on the quads. Because the muscles are smaller in this case (running uphill) oxygen demand is much different than muscles which are larger. Specializing is incredibly important for any athlete going up hill, and training as sport specifically as possible is important, but creates a barrier for us to draw conclusions between the two.
    Running uphill, much like skimo racing, does engage our bodies very similiarly, but with the bootpack thrown in, we’re back into stair climbing mode. Again drawing from the two is difficult.
    The differences are fantastic to think about to build a well rounded training program and build that incredible speed. We can learn alot about what we need to do just from studying these guys.
    Great article mad scientist Stano!

  19. Sports science being so incomplete with all these variables is what makes it so interesting. All you can really do is speculate what the best combo is using the current top athletes. What I find amazing is when athletes like Usain Bolt come out and destroy times with there unstereotypical body type, mentality or style.
    Like Stano says the ultimate apex is basically impossible to find but general conclusions can be drawn.
    Having athletes like Kilian and for example Michael Phelps that are so dominating seem to be illustrating that specializing in just one distance although counter intuitive is not going to produce top times. Dynamic training and competitions seems to keep the body and mind sharp.
    Strength/weight is a really good way to quantify genetics and adaptations like increased capillary s/mitochondira/O2 uptake ext.//

  20. James, I totally agree with the strength/mass ratio. And yes too many variables, but I wanted to know where I can take it despite that.
    Cyclist (climbers) use power to weight ratio as their “holy number”. They count the bike weight (equipment weight) in addition to their weight. When Armstrong was winning TDFs he was around and above 6.5 power/weight. Also, cyclist don’t use the maximum power they can produce for this ratio, but rather a sustainable maximum power, something they can sustain for about 30min. They found that it applies better for their discipline since it’s an endurance sport.

  21. Just way too many variables here to even think about making a comparison. That said, it is an interesting topic and one that all “vetical” racers should ponder during their own training. Probably the most potent variable is each athletes strength/mass ratio. You should email these guys and ask them what they weigh and what their max squat weight is! I think too with all the amazing 24hr skimo records coming out these days (eg 60 000ft) the sport should try and establish a standard for course length and slope angle so that performances can be more accurately compared. One thing is for sure. These are some fast dudes……
    JM

  22. Great note with stairs running! I didn’t think of that. (And your math is correct.)
    The Taipei guy is way faster than Kilian or Sebastian, but the other run (320m) has a speed like Sebastian did. I don’t think he would last at 2901 m/h for 1000m, never the less, the speed is very impressive.
    All these variables (angle, speed…), including stride length, play a role; however, I believe it is a very individual thing. But that doesn’t mean it is impossible to come up with some general guide lines about all these variables.
    The treadmill test, as you suggest, is definitely a great tool to use for comparison as it is equal for any one at any time. Based on experience, I know that lab data doesn’t transfer exactly into the real but it would be the best starting point, I think.

  23. Thanks for sharing this Stano, I was trying to work this out in my head a number of times and its really nice to see it broken down and with so much thought! It would be really interesting to see some one take this to the next level and produce some parabolic curves for efficiencies of up hill travel. Maybe if we are board one day we can do some tests on a treadmill with different angles. Another thing I find really interesting is on more of a micro scale with stride length and what the most efficient stride length ratio would be for both running and rando. I suppose the angle of hill + stride efficiency + genetics and what they are trained for would all combine to produce a fastest time for each individual but like you are trying to determine it would be really interesting to see what the fastest combo is.
    Anyways I looked into stair running and they move up pretty fast as well! However I don’t think they could really have any stair runs at a 1000 meters unless there is a set of stairs up a mountain.
    Here is Thomas Dold’s and Paul Crake’s stair running records up the Taipei 101 and empire state they both crank out a faster vertical per min then Kilian or Sebastian but only for 1/2 the vertical. Can he keep it up for 1000m? If he can he would be doing the 1000 meters in about 21 min!! Even at say 40% the pace he would still beat Kilian’s record.
    508 m in 10:29 min => 48.38 m/min = 2901 meters / hour! http://www.taipei-101.com.tw/runup2009/prepare.asp
    320 m in 9:30 min => 33.68 m/min = 2021 meters/hour
    http://en.wikipedia.org/wiki/Thomas_Dold
    http://en.wikipedia.org/wiki/Paul_Crake
    Correct me if my math is wrong!
    best regards
    Reiner

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