in: Orienteering; Training & Technique;
| # Posted 2008-02-23 18:03:39 | |
| Sswede: | I found this article today about the fastest way to climb hills, and it got me thinking. I tend to go straight, thinking it's faster, but this article says it's not? What do others do...do you zigzag or go straight up a steep hill?
Here's a snippet, link to full length is below: A straight line may be the shortest distance between two points, but on a steep slope, a zigzagging path is the fastest way to go, a new study confirms. On flat terrain, a straight line is typically still the best way to get from point A to point B. But climbing up a steep hill is a whole different ballgame; the mechanics and energy costs of walking up a hill alter the way we negotiate the landscape. "You would expect a similar process on any landscape, but when you have changes in elevation it makes things more complicated," said study author Marcos Llobera of the University of Washington. "There is a point, or critical slope, where it becomes metabolically too costly to go straight ahead, so people move at an angle, cutting into the slope. Eventually they need to go back toward the direction they were originally headed and this creates zigzags. The steeper the slope, the more important it is that you tackle it at the right angle." Llobera and co-author T.J. Sluckin of the University of Southampton in the U.K. developed a simple mathematical model showing that a zigzagging course is in fact the most efficient way to go up or down a steep slope. http://news.yahoo.com/s/livescience/20080222/sc_li... |
| # Posted 2008-02-23 18:52:57 | |
| Kat: | Depends on the hill, but I've definitely found myself zigzagging on steep climbs before! This seems similar to switching to a lower gear on a bike - although it will result in more steps taken, it is nonetheless usually more efficient. |
| # Posted 2008-02-23 19:43:37 | |
| gail: | I've certainly zigzagged, but I thought it was because I was out of shape and it was the only way to keep moving. |
| # Posted 2008-02-23 20:02:56 | |
| Jagge: | I zigzag also on flat terrain, especially near controls. |
| # Posted 2008-02-23 20:15:35 | |
| rambo: | The author quotes the article as saying that zig-zagging is "the most efficient" way to get up a hill, and seems to assume that this means fastest. Whilst cycling up a hill in a low gear might be the most efficient way, it certainly isn't the fastest, and I guess the same goes for running. |
| # Posted 2008-02-23 22:07:38 | |
| simon: | Catching Features got it right after all |
| # Posted 2008-02-24 11:29:10 | |
| Kat: | Hmm. But when cyclists switch to a lower gear on a hill during a race, they must be doing it in order to achieve a faster time overall, right? Why else would they do it? I always assumed that even if they stayed in the higher gear and managed to make it up the hill (which would indeed mean having got up the hill faster), they would probably be so tired from the effort that they would be slower later on in the race. Unless of course these particular cyclists are strong enough that they can get away with that. (And the equivalent would be having really strong runners that can run straight up a hill and then keep running strongly the rest of the race.)
But you know a lot more about bikes than I do, Amber, so I'm willing to take your word for it! |
| # Posted 2008-02-24 18:09:25 | |
| ebuckley: | I tend to go straight on hills, even if it means slowing to a walk because I can use that time to read the map. I will, of course, go off line to take advangtage of terrain features that give an easier climb (such as following a spur rather than cutting through reentrants.
On the somewhat related subject of gears on a bike, keep in mind that by lowering the gear, you are not increasing the distance traveled, you are merely changing the ratio of internal (leg) to external (bike) motion. Clearly, it is in the interest of both efficiency and speed to keep the internal (leg) motion at an optimal rate if the total work is not increased. There is a slight increase in total work since your leg motion is not 100% efficient, but when running a zigzag, you are also adding the real work of covering more distance to the work of climbing, which will be the same regardless of what path you take. Although it rarely happens, elite cyclists do "run out of gear" from time to time. When a hill is so steep that a good cadence can't be maintained even in the lowest gear, riders will "tack" up the road to effectively lower the gear. This is both more efficient and faster than trying to grind out too big of a gear. The proper way to do this is to turn the front wheel just before the top of the stroke so the gear is lowered during the dead portion of the stroke and then you're pointing straight up the hill again during the power portion (when the cranks are closer to horizontal). If you're so far out of your gears that such small adjustements on each stroke aren't enough, you're better off walking (yes, even pros will do this when necessary - several of the spring classics have cobbled climbs where hopping off is the fast way up). Keep in mind though that a runner can always lower the "gear" without zigzagging by simply taking shorter steps. Finally, the optimal cadence for climbing is not a single fixed number. It varies on individual, grade, length, and power output. I would expect this is true for running as well, although I have no hard data to support that assertion. |
| # Posted 2008-02-25 04:34:05 | |
| ebone: | It seems like training (specificity) must come into play. A runner/walker who is better trained for steep hill climbing might do better going straight up a given slope while those less specially skilled/trained might do better zig-zagging. |
| # Posted 2008-02-25 18:00:45 | |
| chitownclark: | Well, I think the cited article has it correct...zig-zagging is still faster.
After all, you could argue that a staircase represents everyday zig-zagging. A sloping incline would actually be a shorter distance up. But you seldom see sloping inclines designed into anything beyond a mild climb. |
| # Posted 2008-02-25 18:23:29 | |
| ebuckley: | No, a staircase serves to provide a flat footplant. There is no reduction in the grade. (I'm not quibbling with the conclusion about zig-zagging). Also, while stairs are generally preferred by builders, they aren't always faster. At the Pere Marquette Trail Run (AKA, The Toughest Run in the Midwest) the final climb has stairs, but those who have the legs to run at that point (probably less than 30 of the 600 entrants) will run to the side so they can use a shorter stride. |
| # Posted 2008-02-25 19:15:35 | |
| ndobbs: | or longer... the problem with steps is you only have a small choice (typically one or two) of stride-lengths... whereas slopes are continuous. My guess is that slopes are also more efficient than flat stairs (at least when running) because one can stay on one's toes without using the calves so much, but this may be rubbish.
Incidentally, playing with my new hr monitor recently, discovered that slow-jogging or even walking up a fairly steep hill, my hr was significantly higher than running fast downhill... a little surprised |
| # Posted 2008-02-25 19:21:18 | |
| j-man: | I've often wondered about the walk/run uphill decision, straight or not.
Assuming you are going straight up (not zigzagging) there is a point when running is impossible. Stairs make steeper slopes possible to run? Are there times when you should be walking? I find prolonged running on my toes to be difficult; it feels unnatural. Is this something that should be trained? |
| # Posted 2008-02-25 19:38:22 | |
| jeffw: | If the speed difference between walking and running up hill isn't much, might as well walk and study the map. You could more than make up the difference finding a good route choice later in the race. |
| # Posted 2008-02-25 21:51:45 | |
| stevegregg: | This perhaps does not apply so much to orienteering, but in a cross-country race, clearly there is a point at which you should go into a "power walk", even when it is possible to keep running. Exactly where that point is, in terms of steepness of slope, depends on one's fitness level.
The idea is that even though running may still be marginally faster, it uses up SO much more energy than walking that it makes no sense to needlessly drain your energy reserves by continuing to run. The few seconds the runners gain on you going uphill will be more than made up for later in the race, when you will be fresher and more able to run strongly to the finish. I coach cross-country, and one of our league 5K courses has a brutally steep hill halfway through. I hear some coaches instruct their runners to "keep running no matter what--don't walk!" I guess it's a macho thing, as in terms of maximal race performance, it makes no sense. |
| # Posted 2008-02-25 23:01:06 | |
| boyle: | Racing cross-country, I would run (rather than walk) the steep incline so that those trying to catch me got the (false) impression that I still had lots in the tank. Coach always said: attack the hills.
These days, racers walk right past me while I'm running up the same hill. |
| # Posted 2008-02-26 02:03:58 | |
| jjcote: | One of my orienteering mentors (who may well be smarter than the authors of this study) presented me with several rules of thumb. One of these is that once the slope becomes significant, the dominant factor is that you are raising your body weight, and lateral motion has little effect. His point was that, in climbing a hill, you should go diagonally toward your destination if it isn't directly above you, rather than climbing straight up and then contouring to the desination (or running along the bottom and then climbing straight up), since the climbing portion will take the same amount of time whether you go straight up or diagonally. If this rule of thumb is correct, then it suggests that there would be little difference between climbing straight and zigzagging, and you can let other considerations dominate. |
| # Posted 2008-02-26 04:08:03 | |
| Nikolay: | This rule of tumb is true because of the fact that going diagonally towards your destination is the shortest route, and should be faster, than running on the flat turning 90 degrees and then running uphill.
If footing and terrain surface is not a problem running diagonally up would make sence no matter the incline. |
| # Posted 2008-02-26 04:12:53 | |
| Samantha: | After reading this Saturday night, I zigzaged up the hills on Sunday. Maybe it helped! |
| # Posted 2008-02-26 05:29:03 | |
| jjcote: | going diagonally towards your destination is the shortest route, and should be faster
But the rule says more than that. It says that no matter where you reach the top, you'll reach it at the same time. So even though it's a greater distance to go diagonally than it is to go straight up, you'll arrive at the top with the same elapsed time, and then if you went straight you'll have the entire sideways distance left to cover, not just part of it. Your rate of ascent is a constant, no matter whether you're moving sideways or not. |
| # Posted 2008-02-26 05:51:42 | |
| cedarcreek: | Just thought I'd throw in some simplistic physics:
I don't have my copy of Bicycling Science handy, but I recall that reasonably fit athletes can sustain 0.2-0.3 horsepower (hp), and peak out a little over 1hp for short periods. Elite athletes can do 0.4-0.5hp for maybe an hour. (??) 1 hp = 550 ft-lb/sec This units can be rearranged to lbs * ft/sec, which is a weight being raised vertically at a velocity--- 550 pounds at 1 ft/sec or 275 pounds at 2 ft/sec, or 1 G at 4ft/sec (with an optimistic G value of 137.5): Power = Weight x vertical velocity [Professors of Physics would probably start with: Work = Change in Potential Energy Work = mgh = Wh (where h = the change in height) dWork/dt = Wdh/ht * h dW/dt (where W is weight) but dW/dt (change in weight wrt time) = 0, and dh/dt = vertical velocity, and dWork/dt is "Power" so Power = Weight* vertical velocity] For power in hp, you would use: HP = (Weight*vertical velocity)/550, where weight is in pounds, and vertical velocity in feet per second. (This might be fun if you find a big hill with known height and time yourself up it.) Up to this point, the math shows no preference for zigzagging or going straight. The physics (without any human issues) would probably work out that there are additional (small) losses by zigzagging. To reconcile the study with the physics, you need to add what ebuckley mentioned: efficiency. I'd propose that there are two obvious topics for further study here: 1. Optimum use of muscle groups and range of motion. If the steepness of the slope prevents you from a normal leg motion, it's probably suboptimal. 2. Optimum vertical velocity to achieve a desired power output. If you can maintain 0.3 hp for the climb, this should translate to a specific vertical velocity. Obviously the two biggest factors are the weight and the ability to sustain power output. For long climbs you could probably use a HRM or just go for a certain level of burn. As a less-than-fit athlete, I often zigzag so I can move my legs in a fuller motion than straight up, and so I can reduce the exertion to tolerable levels. Sometimes, I just go really slow straight up. Has anyone read the journal article? |
| # Posted 2008-02-26 07:13:35 | |
| levitin: | Triathlete wisdom is to spin the hills in order to save the leg muscles for the run. I've never done an IM, and my last Half IM was 5 years ago, but I have to think this is correct advice.
A cycling reporter once asked Tyler Hamilton (I think) whether he ascended steep hills by mashing a high gear (applying high force to a high mechanical advantage gear with a low cadence) or spinning a low gear (applying comparatively less force to a lower mechanical advantage gear with a higher cadence). His reply? Mash a high gear. |
| # Posted 2008-02-26 07:57:19 | |
| ebuckley: | Bernard Hinault and Eddy Mercx would have approved. On the other hand, Miguel Indurain and Lance Armstrong were spinners, especially when attacking. So, even among the greatest riders ever, it really is a very personal thing.
When running, the full range of motion is key. The point of being airborne between footplants is that you have a "glide" portion to your stride. The extra effort to lift yourself in the air is offset by the fact that "flying" is lower resistance than moving your weight along the ground. If you're moving so slow that this just becomes hopping up and down with no considerable forward progress, you're better off keeping one foot on the ground at all times. My guess is that this is the basis for the the result. By zigzagging, you get your running stride back which is faster than walking a shorter distance. Finally, I generally have no problem walking when the situation calls for it, but at Pere Marquette I always run the last hill simply because to do otherwise risks giving up at a very crucial point in the race (45 minutes into a 1-hour effort). I believe the psychological aspects of continuing to run outweigh any physical gains in situations like this. This might be another thing to recommend zig-zagging. You can keep your running stride going and this just "feels" like you're more in the game. There is universal agreement among pro cyclists that handling mountains is predominantly mental. Keeping yourself motivated counts for a lot. |
| # Posted 2008-02-26 08:41:41 | |
| stevegregg: | Obviously, at some point JJs rule of thumb breaks down, and it would be interesting to find out where this happens. If your destination is 20 meters uphill from your current location and 1 kilometer away, clearly it will take far less time to go straight uphill for 20 meters than it will to include the 1 km sideways distance as well.
Perhaps the direction of travel needs to be at an angle of 45 degrees or less from the straight uphill direction of travel? I'd be willing to believe the rule of thumb in that case. |
| # Posted 2008-02-26 08:47:32 | |
| jjcote: | When presented to me, it was only claimed to be applicable to typical orienteering hill climbing situations. |
| # Posted 2008-02-26 10:00:30 | |
| danf: | I guess that wouldn't include BAOC meets then. |
| # Posted 2008-02-26 16:05:53 | |
| simmo: | Great - now I can match my zig-zag gps routes!
Seriously, has anyone run this past a real mountain runner - like Scotty from Canberra? Is anyone on speaking terms with Jos Naylor? I tried it up a short (50m) but very steep hill on my normal 8km run today. I seemed to go faster (maybe 30%), but then was it fast enough to compensate for the extra distance. It was too hot (35C at 6pm!) to repeat the hill. I did feel fresher at the top however, and maybe this would be an advantage for orienteering. |
| # Posted 2008-02-26 16:30:13 | |
| gordhun: | There is one advantage sometimes available to orienteers when hill climbing but never available to cross country runners or cyclists. That is the use of our arms. Some time ago I found I would have extra energy available in my arm muscles when the legs were nearly spent. By grabbing (solid looking) trees I am able to pull myself up a significant part of most steep hills thus taking critical stress off the legs.
Yes, one has to find a way to deal with the map and sometimes the compass but the advantage of having an extra set of fresh muscles at critical time overcomes that small challenge. Also, whether one zig zags, pulls or goes straight up the hill a critical factor to remember is to carrry through that energy output through your first seven or so strides after you top the hill. Thus the momentum will carry forward and running speed is rebuilt more quickly. |
| # Posted 2008-02-26 16:35:15 | |
| candyman: | Any thought to the fact that by going diagonally uphill you could well be increasing your chances of making a mistake? Generally it is much easier to find a control successfully by either attacking it from a point directly above or below or on the same contour.
I would say most of this discussion is quite pointless, how should you climb the hill? The best way to find the control! The orienteering is far more important than any minor advantages of going diagonally or zig zagging or anything else which is only likely to make it harder to find the control. |
| # Posted 2008-02-26 17:12:30 | |
| Sswede: | I appreciate hearing other's experiences. Trying to run and/or orienteer with asthma presents some challenges for me. I'm always looking for ways to make it easier. Perhaps this, like so many other variables, could be helpful to some and not others. |
| # Posted 2008-02-26 18:21:55 | |
| RJM: | The original article (M. Llobera, T.J. Sluckin. 2007. Zigzagging: Theoretical insights on climbing strategies. Journal of Theoretical Biology 249:206-217) includes a lot more nuance than the newspaper article. I can't post it here, but look for it in google scholar and you'll at least see an abstract.
A couple of relevant bits. -their equations also predict that zigzagging downhill will be advantageous on steeper slopes (the size of the zigzag depending on the steepness of the slope). -the critical angle (subject, I think, to individual differences in climbing strength and ability) for switching to zigzags is 16degrees for uphill, and 12.4 for downhill). -variable and irregular topography greatly complicates the situation (they did a lot of their mo del on 'mount conicus', a perfectly symmetrical peak). Those complications are not evaluated here -downhillers will prefer to take shortcuts that are not feasible for uphillers (trail 'shotguns'). - the authors clearly and specifically call for field testing of these ideas. I am a big fan of using math to guide thinking, but this last point is an important one. No matter how much we may refine our physical m odels of the system, they are a prelude to, and not a substitute for, field testing. In particular, since individual abilities are a part of the equation, in the end we should each take a stopwatch with us to some hills that vary in steepness, and try this all out ourselves (keeping in mind the many very useful comments above about, for example, using the climb to plan a route, or to demoralize an opponent). |
| # Posted 2008-02-27 04:35:43 | |
| ebuckley: | ... never available to cross country runners or cyclists. That is the use of our arms.
No? I guess you've never heard of a "power bottle." I used to be quite relieved when I'd get sent back to the support vehicle to get bottles on a climb. 2 bottles each for 5 teammates + 2 for me with an allowable exchange of 10 seconds per bottle = 2 minutes of free climbing! Of course, then you had to catch back up with an extra 12 pounds stuffed in your jersey, but it was always worth it. |
| # Posted 2008-02-27 05:16:10 | |
| Eoin: | zigzagging downhill will be advantageous on steeper slopes
To use the Americanism - NO WAY! As Simmo suggests - talk to any hill/fell runner. |
| # Posted 2008-02-27 06:57:50 | |
| boyle: | The day after racing downhill, your knees and quads might say "zigzagging downhill would have been advantageous." With that exception, there is no advantage to zigzagging downhill! |
| # Posted 2008-02-27 07:28:55 | |
| Ricka: | With that approach, I'm sure that many "fell" runners earn the that title :) And are proud of it.
(which is Brit, not American English of course) |
| # Posted 2008-02-27 20:02:12 | |
| Nails: | Downhill eyeballs out straight. I totally agree with candyman though -its pointless thinking about zigzagging if you ain't gonna hit the control ! |
| # Posted 2008-02-27 23:10:59 | |
| jblaisdell: | I think they are measuring total energy expended, not total time. The right downhill analogy might be driving down the mountain, achieving minimal wear on the brakes. Zigzags seem right for that. Orienteering would have a different metric. But once the hill is long enough and steep enough that you reach your maximum tolerable velocity and you need to do some braking with each step, maybe zigzags give you more steps to brake with so you can stay closer to maximum speed more of the time (gravity accelerates you between steps) compensating for a little added distance. |
| # Posted 2008-03-04 10:32:12 | |
| leepback: | I just walk straight or contour around. Who runs on hills anyway? |
| # Posted 2008-03-05 07:30:44 | |
| JaysonR: | I like running on hills. It takes less time for me, and its good exercise for my quads. |
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