Tips for Flatlanders training for Backcountry skiing
 and snowboarding

Ken Roberts

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Feb-06 : using indoor exercise bicycle trainer to simulate ski mountaineering climbing.

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Feb-2006: using indoor bicycle trainer

On using an indoor bicycle trainer to simulate ski mountaineering climbing.

Key Points

training goals for ski mountaineering climbing:

  • speed goal of training: 300-400 vertical meters per hour -- little need to go faster to complete a single-day tour (except competition).

  • power goal: 120-160 Watts in good climbing conditions, 140-200 Watts for broader range.

  • cadence: likely somewhere in the range of 25-40 rpm (50-80 steps per minute)

  • steepness of climbing track: 30%-50% grade. Vertical range-of-motion per step 8-12 cm, Horizontal 25-39 cm.

  • specific muscle moves: In addition to the main push of the skier up and forward, also need to move a heavy ski while recovering the leg up and forward.

bicycling on indoor trainer:

  • bicycling could train all the specific muscle mores used for ski-climbing.

  • but not if use the obvious common bicycling techniques -- many people would need to learn and practice more how to engage all four kinds of muscle moves used for ski climbing.

  • many fluid-mechanism indoor trainers do not supply sufficient resistance power at low cadence. (nor does outdoor bicycling on flat smooth pavement)

  • many magnetic-mechanism indoor trainers can supply sufficient resistance at 40 rpm, perhaps barely sufficient at 30 rpm.

  • bicycling offers sufficient Vertical range-of-motion to simulate ski-climbing, but not sufficient Horizontal range-of-motion. Ski climbing is more "elliptical" than bicycling.

Characteristics of Ski Mountaineering climbing

Pace

Guidebook pace is 300 vertical meters per hour (1000 ft/hr), but with rests probably need to climb at 360 m/hr in order to achieve that pace. Faster skiers can sustain 450 m/hr -- or even 600 m/hr or more. There are very few single-day tours longer than 1830 meters of climbing (6000 vertical ft), and very very few tours longer than 3000 meters (10000 vertical ft). Long tours are usually done in later season (after the equinox), so there is 12 hours of daylight, so even with time for breaks and downhill runs, it is reasonable to assume 8 hours for climbing (with the possibility of a pre-dawn start).

  • 300 m/hr is enough to climb 1830 meters (6000 ft) in 6 hours. With a 5:00am start and 1.5 hour of rests, that puts us on the summit at 12:30pm

  • 400 m/hr is enough to climb 3000 meters (10000 ft) in 7.5 hours. With a 3:30am start and 2 hour of rests, that puts us on the summit at 1:00pm

  • 400 m/hr is enough to climb 2000 meters (6500 ft) in 5 hours. With a 6:30am start and 1 hour of rests, that puts us on the summit at 12:30pm.

So there's really no need for more than 400 m/hr for single-day touring requirements (as opposed to racing).

Power

Assuming no wind (and no trail-breaking), about 10% losses in moving the skis forward along the ground up a slope of 19% grade, the muscular power required for ski mountaineering climbing for a 65kg person with 15kg of equipment and clothing and pack (143 lb + 33 lb = 176 lb) is around:

100 Watts for 300 m/hr (1000 ft/hr)

133 Watts for 400 m/hr

200 Watts for 600 m/hr (2000 ft/hr)

Calculation

Upward_Velocity = 300 m/hr = 0.0833 m/sec

Forward_Velocity = 0.0833 / 19% = 0.4386 m/sec

Power against gravity = Force * Velocity = Mass * Gravity * Upward_Velocity

= 80 kg * 9.8 gravity * 0.0833 m/sec = 65.4 Watts

Resistance of skis moving forward = 10% * Mass * Gravity * Forward_Velocity

= 10% * 80 kg * 9.8 * 0.4386 m/sec = 34.4 Watts

Total Power = 65.4 + 34.4 = 100 Watts

Skiers with larger or smaller weights of body or equipment or clothing or pack can adjust those calculations proportionally.

Compare power to other motions

100 Watts is about the same power output for cycling at 16 mph (or 26 km/hr) in low-crouch position on a drop-handlebar road bicycle with no wind on a flat road -- a typical pace for an athletic non-racer. 200 Watts on a drop-handlebar road bicycle is about 21 mph -- which is pretty fast.

100 Watts is about the same power output for jogging or fast walking at around 4.5 mph or (7 km/hr). A typical speed for an athletic runner is more like 6 mph (10 minutes per mile, or 4 hours and 20 minutes for a marathon of 26 miles or 42km), and 7 mph is not unusual for an adult runner who trains seriously. 200 Watts for a runner is about a 41:20 time for 10km -- which is pretty good.

So a "guidebook pace" for ski mountaineering climbing of 300 vertical meters per hour (1000 ft/hr) is a Power output which is reasonably achievable for a "normally athletic" adult -- provided that their method for training that power trains the same muscles in similar ways.

Specific Muscles used

The power to move the hips and upper body up and forward comes mainly from the hip extension and knee flexion muscles, with help from several arm and shoulder (and perhaps abdomen and back) muscles for pole-pushing.

The power to move the mass of the skis and boots and lower legs up the hill comes mainly from the hip flexion and knee extension muscles.

Trail-breaking adds to the total power, but tends to focus on a different proportion of muscles: mainly hip flexion and knee extension muscles.

Cadence / Turnover Frequency

By "cadence" I mean the frequency per minute of complete two-leg strides. Which is not the same as the count of "steps" per minute often used for analyzing walking. The rationale for my definition of "cadence" is that the body must must go through a complete cycle of motion that bring the body back into exactly the same configuration as it started the cycle -- so it is prepared to immediately start the next cycle. This concept of a complete stroke-cycle is critical for analyzing propulsive motion which is going to be repeated over any significant distance or time.

So there are two steps, one with the right foot and one with the left foot, for each stride-cycle for measuring cadence. If someone counts 80 steps in one minute, 40 right-foot steps and 40 left-foot steps, then by my definition their "cadence" is 40 rpm. ("rpm" = "repetitions per minute")

Typical cadences for other motions:

  • Walking on flat ground: 35 rpm to 60 rpm

  • Running on flat ground: 60 rpm to 90 rpm

  • Bicycle pedaling sitting: 80-90 rpm for skilled athletic riders. Racing sprinters can go up to 140-160 rpm. Less skilled riders tend to use much lower cadences.

  • Bicycle pedaling standing: 60-75 rpm for skilled riders (though it's possible for skilled riders to go higher). Less skilled riders tend to use lower cadences.

Ski climbing: I'm not sure, but it makes sense that it should be slower than walking, since skis and boots are heavier. I counted my own cadence in ideal climbing conditions on a slope of 30-45% steepness grade as 35 rpm (but that was at a climbing rate of around 600 meters per hour, much faster than the goal pace for ski touring).  I'd guess the range is 25 rpm to 35 rpm -- perhaps 40 rpm for climbing speeds significantly higher than 400 meters per hour.

Range-of-Motion

A typical climbing track with "gentle" switchbacks (as set by a guide for clients) might be around 16 degrees (slope grade 29%). Athletic skiers sometimes climb straight up a 25 degree slope (steepness grade 47%). It takes unusually good snow conditions to be able to climb straight without switchbacks up more than 30 degrees (steepness grade 58%). So let's use 16.7 degrees (grade 30%) and 26.565 degrees (grade 50%) as our key points for analysis.

16.7 at 300 m/hr at cadence 30 rpm =

8.33 cm vertical per step (3.28 inch vertical per step)

29.0 cm per step along ground surface (11.4 inch) = 8.33cm / sin(16.7)

16.7 at 400 m/hr at cadence 40 rpm =

8.33 cm vertical per step (3.28 inch vertical per step)

29.0 cm per step along ground surface (11.4 inch) = 8.33cm / sin(16.7)

16.7 at 300 m/hr at cadence 25 rpm =

10.0 cm vertical per step (3.94 inch vertical per step)

34.8 cm per step along ground surface (13.7 inch) = 10cm / sin(16.7)

16.7 400 m/hr at cadence 25 rpm =

13.33 cm vertical per step (5.25 inch vertical per step)

46.4 cm per step along ground surface (18.3 inch) = 13.33cm / sin(16.7)

26.6 at 400 m/hr at cadence 25 rpm =

13.33 cm vertical per step (5.25 inch vertical per step)

29.8 cm per step along ground surface (11.7 inch) = 13.33cm / sin(26.565)

A typical length of a Men's ski boot is around 30 cm or 12 inches (Men's Euro size 44)

So the stride length results for 25-30 rpm are looking reasonable to me. But the stride length results for 40 rpm are seeming too short based on my experience -- which leads me to suspect that a cadence of 40 rpm is used only for speeds higher than the touring goal range of 300-400 meters per hour.

Bicycling on Indoor Trainer

Power

The range of 100 - 200 Watts is easily handled by most indoor bicycle trainers.

The problem is whether that resistance Power can delivered at a cadence appropriate for ski climbing.

Specific Muscles used

If we divide the pedaling cycle into four phases, we can make this correspondence to ski climbing:

  1. main down-push = move the weight of the body vertically up against gravity.

  2. pull foot back under = drive the skier's mass forward parallel to the ground surface.

  3. lift foot up behind = lift the ski off the ground.

  4. push the foot forward over the top = recover the ski forward for the next push, and with greater force required for breaking trail in soft snow.

Big problem

The big problem is that the way most unskilled or uncoached riders pedal a bicycle does not use specific muscles to drive all four phases. Instead they focus on the main down-push phase 1, and then let momentum from phase 1 (and lots of help from the other pedal) to carry the foot through the other phases.

But in actual ski-climbing, it doesn't work much to try to use main push by the other leg to recover the weight of the ski up and forward. And sometimes driving the foot and ski forward (phase 4) is the major portion of the work: for trail-breaking in soft snow -- so in ski-climbing you can't just use momentum from some other phase to "carry through" that like on a bicycle.

Therefore:

  • indoor bicycle training can be very specific for ski-climbing

  • but to obtain that specific benefit, must learn the neural control of muscles in all 4 phases

Single-leg pedaling can help a lot in learning the feel of this required neural control.

Because the mass of the ski and boot is so much larger than the foot in walking and running, phase 4 and phase 3 are especially important to focus on improving.

Phase 2 is similar to walking and running, but for skiers who do mostly bicycling in the summer, and not much walking and running, it's important also to work consciously on pulling the foot back and under.

Other problem

Bicycling doesn't do hardly anything to train pole-push muscles -- need to find some completely different way to train those.

Small problem

Although skillful pedaling using specific muscles in all four phases does train all the key leg muscles for ski-climbing, it might not train them in the same proportions they are used in ski-climbing. So even if I am successfully pedaling my bicycle at my desired "ski guidebook pace" of 100 Watts, that does not mean that my leg muscles can actually deliver 100 Watts in actual ski-climbing.

Suppose my power contribution from each muscle move on the bicycle is as follows:

40 W -- Hip-extension
15 W -- Knee-extension
10 W -- Ankle-extension
  5 W -- Hip-flexion
25 W -- Knee-flexion
  5 W -- Ankle-flexion

But suppose the required proportions for ski-climbing are:

35% -- Hip-extension
25% -- Knee-extension
  3% -- Ankle-extension
15% -- Hip-flexion
22% -- Knee-flexion
  0% -- Ankle-flexion

Applying those percentages to my desire 100 Watts, I see that I've trained for extra power in Hip-extension, and especially Ankle-extension and Ankle-flexion. But I'm short on Knee-extension and Hip-flexion. So our of proportions actually needed, my specific muscles are really only capable of delivering:

35 W -- Hip-extension
15 W -- Knee-extension
  3 W -- Ankle-extension
  5 W -- Hip-flexion
22 W -- Knee-flexion
  0 W -- Ankle-flexion

80 Watts total

Shortfall of 20 Watts.

Therefore it makes sense to train for a higher Power output than just the total number, say 20% higher. And it doesn't hurt to throw in another 20% for difficult snow and weather conditions: wind and difficult trail.

Perhaps 140 Watts on an indoor bicycle with good use of specific muscles in all four phases is a reasonable goal for effectively achieving a "ski guidebook pace" of 300 vertical meters an hour out on the snow.

Cadence / Turnover Frequency

For an integrated bicycle trainer (usually seen at fitness clubs), the simplest ways to find out what resistance power it delivers at different cadences are: (a) if the machine has electronic read-outs for Cadence and Power in Watts, try pedaling at different cadences and resistance settings, and see what the Watts is for different settings from cadences from 25 rpm to 40 rpm; or (b) somehow get manufacturer's specifications.

For an "add-on" trainer designed to be used at home with your own bicycle and the rear wheel lifted off the floor, there are some other approaches to calculation. The amount of resistance often depends on the speed of the wheel rolling against the roller of the trainer-mechanism -- which is not the same as your pedaling cadence. So the amount of resistance power is strongly influenced by what gear you pedal in.

Wheel_roll_speed = Wheel_circumference * Gear_ratio * Pedaling_cadence

wheel_circumference = 3.14159 * wheel_diameter

gear_ratio: for high power at low pedaling cadence you usually want a high gear ratio, so gear_ratio = teeth_largest_front_chainring / teeth_smallest_rear_cog

pedaling_cadence = repetitions per minute (but we need to multiply by a factor to get it in terms of "hour", if that's how we measure speed.

Example: (in American units) Road bicycle with 27-inch wheels, large chainring 52 teeth, small cog 13 teeth, pedaling cadence of 40 rpm:

speed (miles per hour) =

  (60 minute / hour) *

* [(3.14159 * 27 inch)] / (12 inch_per_ft * 5280 ft_per_mile)]

* (52 teeth / 13 teeth) * (40 cycles_per_minute)

= .08 * (52 teeth / 13 teeth) *  * (40 rpm)

= .32 * 40 = 12.8 mph

Example: (in American units) All-terrain bicycle with 26-inch wheels, large chainring 46 teeth, small cog 12 teeth, pedaling cadence of 25 rpm:

speed (miles per hour) =

  (60 minute / hour) *

* [(3.14159 * 26 inch)] / (12 inch_per_ft * 5280 ft_per_mile)]

* (46 teeth / 12 teeth) * (25 cycles_per_minute)

= .07735 * (46 teeth / 12 teeth) *  * (25 rpm)

= .2965 * 25 = 7.4 mph

Not many manufacturers publish Power versus Speed values for their trainers. Here's some approximate sample values I found in February 2006:

resistance Power in Watts:

Speed (mph) =

  8

10

12.5

15

17

Fluid trainer (popular model)   50   80 110 140 200
Magnetic (popular) (highest setting) 100 130 165 210 235
Magnetic (special) (highest setting) 190 238 300 358

400

Key points:

  • most Magnetic-mechanism trainers show a linear graph of Power versus wheel-roll-speed (resistance Power is proportional Speed) -- while Fluid-mechanism trainers have a highly non-linear Power versus Speed relationship (Power starts low, but increases highly non-proportionally more at higher Speeds, following a "cubic" curve).

  • Popular Fluid-mechanism trainers have lower resistance power than popular Magnetic-mechanism trainers at speeds of 17 mph and under. (but Fluid trainers often have higher resistance than popular Magnetic trainers at speeds over something like 22 mph)

  • Outdoors on flat smooth pavement normally has lower resistance Power at each speed than the numbers shown above for the Fluid trainer.

Fluid trainer: Lowest speed at which it supports 100 Watts resistance is around 12 mph, which for the road bicycle example given above is a minimum cadence of 37.5 rpm. For the all-terrain bicycle example given above, that's a minimum cadence of 40.5 rpm.  Those cadences are higher than seems realistic for guidebook-pace ski mountaineering climbing. Lowest speed at which it supports 140 Watts is around 15 mph, which is at least 47 rpm, much higher than ski climbing.

The fundamental problem with most Fluid trainers is that they're designed to simulate the Power-versus-Speed characteristics of a riding a bicycle outdoors on flat ground -- which also follows a cubic curve.  Now riding a bicycle outdoors on a smooth road at a slow speed really does not take much power (that's why lots of people like bicycling better than walking).  But ski-climbing at a slow speed does require substantial power.

popular Magnetic trainer: Lowest speed at which it supports 100 Watts resistance is around 8 mph, which for the road bicycle example given above is a minimum cadence of 25 rpm. For the all-terrain bicycle example given above, that's a minimum cadence of 27 rpm.  Those cadence seem realistic for guidebook-pace ski mountaineering climbing -- and if you prefer to train at a higher cadence you can easily shift to a lower gear ratio (or switcth the trainer to a lower resistance setting). Lowest speed at which it supports 140 Watts is around 11 mph, which is 34 rpm for the road bicycle example, and 37 rpm for the all-terrain bicycle example -- on the high side, but might be close enough. It want the option of higher-power training at lower cadence, find a trainer with a stronger magnet . . .

special Magnetic trainer: Easily delivers a resistance Power of 100 Watts or 140 Watts anywhere in the 25rpm to 40rpm cadence range, for either the road-bicycle example or the all-terrain-bicycle example above.

Range-of-Motion

The crank-arms for bicycle pedals are usually 165 mm or 170 mm long.

Splitting the pedal cycle into four equal phases, we can calculate the "linear distance" the foot moves in each phase as the "chord length" of a quarter-circle -- which is the square root of 2 multiplied by the radius. So for 170 mm crank-arms, the linear distance in each phase is:

1.414 * 17 cm = 24 cm = 9.5 inch

Comparing with the vertical range-of-motion above for ski-climbing, this range-of-motion for the main down-push phase 1 is more than enough.

But for the along-the-surface range-of-motion, it's shorter than what we calculated above for ski-climbing. It might be argued that maximum horizontal range-of-motion for bicycle pedaling is 2 times the radius:

2 * 17 cm = 34 cm = 13.4 inch

But even that comes in a little short for 25 rpm cadence at 16.7 degrees climbing steepess.

One answer is that "no simulation is perfect", and indoor bicycling is "good enough".

Another answer is that the leg-motion of ski-climbing is inherently elliptical, and pedaling a bicycle is not.

Note that the elliptical chainrings once widely sold for bicycling are shaped in the wrong way for simulating ski-climbing. They were designed to focus the motion more into the vertical phases of the pedaling cycle, but for ski-climbing we need more range-of-motion in the the horizontal phases.

I don't know if modern "elliptical trainers" help with this horizontal range-of-motion -- since I don't know much about elliptical trainers.

I'd be concerned that they have such large fly-wheels that they might make it too easy to "carry through" the horizontal phases of the cycle.

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