These pages provide the backdrop of scientific research relating to strength and power measurements as they relate to specific biological processes and measurements (i.e. Vo2 Max, body mass, surface area, etc.).

Through reading it, you will discover the need for future research in the sport of nordic skiing in using allometric scaling in measurements of strength/body mass to more accurately predict performance. While this has been done in the sport of cycling, it is more of a novel concept in skiing. This will explain that and also provide a defense for looking specifically at UB strength/mass and LB strength/mass measurements in the double pole technique on flat and inclined terrain.

I present to you the final 1/3 of my literature review…

Dig in if you dare….

Free chocolate candy if you prove to me that you read it…

**Body Mass and Performance**

*Allometric scaling in endurance sports*

Three primary models are typically used to express power as a performance variable: absolute expressions, simple ratio-standard scaling, and allometric scaling.

In the context of the current research, an absolute expression of power poses a problem when comparing subjects because it does not take body mass into account. Simple ratio-standard scaling (W/kg) assumes a linear relationship between body mass and performance (Jaric, 2005), and has been used to effectively predict sprinting performance better than absolute measures (Hansen et al., 2003). More recently, the use of allometric models have proven to more accurately predict performance involving the relationship between body mass and power in cycling (Jobson et al., 2008; Heil, 1998; Nevill, 2006; Lamberts et al., 2014), running (Svedenhag, 1995), rowing (Neville et al., 2010), soccer (Nevill et al., 2004), rugby, (Nevill et al., 2005), and weightlifting (Cormie, 2007; Comfort et al., 2014). Allometric scaling is potentially more effective in normalizing athlete performance as it takes into account the ratio at which increases in body mass impact power increases (Comfort et al., 2014). It is based on the theory of geometric symmetry, which suggests power increases with body mass to the power of .67 (Nevill et al., 1992; Jaric, 2005).

In cycling, early research using an absolute expression of power showed a correlation between 1-h lab and 40km time-trial (TT) performance on the road (r = .88) (Coyle, 1991). Swain (1994) analyzed the differences between flat and uphill cycling, where air resistance is the primary force to overcome in the former, and gravity in the latter. On the flats, air resistance scales as body mass to about the ⅓ power (.32), giving large cyclists an advantage over smaller cyclists, since the relative (to body mass) frontal drag for smaller cyclists is much greater than it is for large cyclists (Swain, 1994). Padilla et al (1999) used this mass exponent (.32) developed by Swain (1994) in conjunction with the data of Coyle (1991) to more accurately correlate 1-h lab performance and 40km TT on the road (r = .94), early evidence of the preference of allometric scaling.

The mass exponent produced in the work of Swain (1994) for uphill cycling was 0.79, which, because it is greater than that for O2 max (.66), predicts small cyclists to have an advantage in climbing, which is supported by field data. Heil (1998), Nevill et al. (2006), and Svedenhag (1995) found comparable body mass exponents of .89, .91, and .75 to best predict uphill cycling and running performance, respectively.

Padilla (1999) utilized the exponents recommended by Swain (.32 for frontal area – used in flat terrain, and .79 for body mass – for uphill terrain) to further demonstrate the importance of allometric scaling over either absolute or simple ratio expressions in an analysis of 24 members of a pro cycling team. Members were divided into four groups based on their morphotype dependent speciality: uphill (UH), flat (FT), all terrain (AT), and time trial (TT) and underwent incremental lab tests to assess max power output (Wmax), maximal oxygen uptake (VO2max), lactate threshold (LT), and onset of blood lacate accumulation (OBLA). FT had the highest absolute Wmax (481 +/-18 W) while UH had the highest Wmax relative to BM (6.47W/kg). WLT and WOBLA values were significantly higher in FT and TT than in UH cyclists; however, when scaled relative to frontal area (FA) and body mass (BM) exponents .32 and .79, group differences were minimized and the hierarchy shifted (Padilla et al., 1999). TT showed a performance advantage over FT, AT, and UH in all cycling terrains and conditions, including uphill cycling (Padilla et al., 1999).

In discussing these results, Padilla (1999) notes that during uphill cycling, the submax intensities are often close to LT and OBLA, and therefore, scaling mechanical power output at these submax intensities may “be necessary to appreciate performance potential during uphill cycling.” It was also mentioned that TT bikers often excel in uphill sections, though field results tend to show UH cyclists, due to their low body mass, are able to accelerate more efficiently than larger cyclists, and thus show the best performance in field tests. Therefore, Padilla et al (1999) concluded that an exponent of 1 (as opposed to .79) should be used to evaluate uphill cycling ability, but suggest that WLT/kg and WOBLA/kg, figures which TT and UH cyclists share similar values, could contribute to their uphill ability.

While the crossover of these findings is likely obvious to those experienced in nordic ski racing and research, and will be discussed at greater length later, it is worthy of mention in this section as well. In relation to cross country skiing, where dominant male skiers fit a similar morphotype as TT cyclists, it is possible that WLT/kg and WOBLA/kg is another mechanism which could explain why larger male skiers excel more so than lighter skiers in long distance classical ski races despite long stretches of uphill double poling sections, as the majority of these uphill sections within the Visma Classics are raced at those intensities. In World Cup sprints and relays, max power as expressed absolutely might be more beneficial to performance, as steeper, shorter hills and strategic placement and race strategy require skiers to put out “supra-aerobic” efforts wherein they exceed their peak VO2 power (110-160% according to Komi, 1987; Sandbakk et al., 2011; Karlsson et al., 2018). This theory would fall in line with the findings of Padilla et al (1999) in cycling, as he recommends absolute Wmax values for predicting performance in short events, but WLT and WOBLA in longer time trials and uphill cycling.

Recall that allometric scaling assumes geometric symmetry in mammals, suggesting power increases with body mass to the power of .67 (Nevill et al., 1992; Jaric, 2005). The work of Nevill and colleagues (2004a, 2004b, 2005) challenged this assumption, reorienting the direction of research to consider the size of muscles which are being used, and developing mass exponents based off girth measurements. In a cross-sectional study of 119 professional soccer players, Nevill et al (2004b) confirmed the inflated mass exponent used in the power function relationship between metabolic rate and body mass to be to .75 as opposed to the anticipated surface area exponent when applying the law of geometric symmetry of .67 (Nevill et al., 1992). In addition to this finding, a biological explanation explaining these inflated exponents was proposed and confirmed – larger individuals grow disproportionately more muscle mass in the arms and legs. Indeed, results showed, when using calf and thigh muscle girths rather than body mass as predictor variables, the analysis explained more variance in the VO2 max than when using body mass predictor variables (Nevill et al., 2004b).

The fitted mass exponents for calf and thigh were .43 and .39 respectively, above the .33 rate predicted by geometric similarity, but in accordance with later findings using a muscle girth measurement on a general population (Nevill et al., 2004a). In the latter study involving 478 subjects split into exercising and non-exercising groups, thigh and calf values for non-exercisers were .46 and .37 respectively. The work of Jobson (2008) found thigh girth to increase as mass to the power 0.42 in cyclists.

This extension by Jobson (2008) of the research challenging the geometric similarity principle, was the first of its kind in cycling, and served to combine Nevill’s (2004a, 2004b, 2005) research on general populations and soccer players with Nevill et al (2006) research on the differences between uphill and flat cycling.

In that research, Nevill et al (2006) hoped to establish whether or not the reported oxygen-to-mass ratios used to predict flat and hill climbing performance (Swain, 1994; Heil, 1998; et al) would extend to similar power-to-mass ratios using convenient labratory measures of power output (maximum aerobic power (W MAP), power output at ventilatory threshold (W VT), and average power output (W AVE) during a 1 hour test). His findings challenged the mass exponent of (.32) proposed by Swain (1994), as it was found that exponent values of 0.54 (W MAP), 0.46 (W VT), and 0.58 (W AVE) explained 69.3, 59.1, and 96.3% of the variance in cycling speeds. In uphill climbing at 6 and 12% grades, speeds, the optimal model to predict cycling speeds had a mass exponent of 0.91 (cycling speeds were proportional to W MAP m^-0.91)0.66), a value that is similar to previous research (Swain, 1994; Heil, 1998; Padilla, 1999) and approaches the recommended value of 1 proposed by Padilla (1999) to align specifically with the field results of hill-climbing specialists.

The work of Jobson (2008) confirmed the girth centered body mass exponent in measuring uphill and flat cycling performance, furthering the overall research of Nevill (2004a, 2004b, 2005, 2006). Using a 5.3 km hill climb TT with mean course gradient of 5.4%, the goal was to verify the importance of mass in uphill cycling, validate laboratory findings in the field, and determine if power-to-mass ratios are affected by a lack of geometric similarities in cyclists, as they were shown to be in football players (Nevill, 2005). It was found that a field test raised the mass exponents used in the allometric model for power to 1.24; however, when using maximal ramp minute power (highest mean power output over a 60-second period (RMPmax)), similar to Nevill et al (2006), this value decreased to 1.04. This value still exceeded previous research: .79 (Swain, 1994), .89 (Heil, 1998), and .91 (Nevill, 2006), however, when using thigh girth measurements, which were found to increase as mass to the power of .42 (a value similar to the .439 found by Nevill et al., (2004a) in pro soccer players), the girth derived body mass exponent equaled 0.86 (Jobson, 2008). This brought the overall results of Jobson (2008) closer to those of Heil (1998) and Nevill et al (2006) (Jobson, 2008).

Taking into account the curvilinear relationship between cycling speed and energy expenditure, which was found to be .54-.59 on uphill compared to .41 on the flat (Nevill, 2005), it was concluded in the case of a cyclist weighing 73.1kg with a VO2max of 4.67 L/min, an increase of 10kg in body weight would result in speed decrease of 1.7km/h, whereas a reduction of 10kg of body weight would lead to an increase in uphill TT speed of 2.15 km/hr (Jobson, 2008). Though this postulation is technically only applicable to the exact course used in the study, its findings speak to the enormous potential contribution of body mass to uphill cycling performance.

Lamberts (2014) replicated the study design of Coyle (1991), adjusting for body mass using the exponents suggested by Swain (1994) of 0.32 for flats, with the intention of discovering whether or not peak power output adjusted for body mass accurately predicted flat 40km TT performance in women the same as had been found previously in men. The allometric relationship between these cycling parameters was found to differ between genders, while the absolute expressions were not dependent on gender (Lamberts, 2014). Thus, gender specific regression equations should be used when predicting relative cycling performance parameters.

When considering the work of Nevill and colleagues (2004a, 2004b, 2005) and Jobson (2008), which showed that muscle girth measurements should be used to scale body mass more accurately, in concert with the understanding of the differences in muscle size in men and women in the major muscles utilized in the DP motion, it becomes apparent just how many potential factors ought to be considered in this sphere of research. Though it may fall outside of the present study’s focus, the advancements in allometric scaling in cycling to involve the measurements of primary muscle groups, gender specific adjustments to prevailing models, and other considerations should be reflected on in the interpretation of the results and perhaps postponed as the primary focus for future research in cross country skiing specifically.

Nevill and colleagues (2010) have more recently shown the value of allometric scaling in another endurance sport, rowing, by investigating whether or not performance on a Concept II rowing ergometer accurately reflects rowing on water. When comparing a 2000m time trial using a Concept II model C rower to a 2000m single scull open water test, water speed was found to be 3.66 m/s, lab speed was found to be 4.96 m/s, and the relationship between the two performances was 28.9% (r = .538). However, when applying the optimal allometric model (ergometer speed x m(-.23)(1.87)), the relationship increased from 28.2% to 59.2% (Nevill et a., 2010). The resulting power-to-weight ratio equation, which exemplified the significant drag effect on water rowing speed, “improves the ability of the Concept II rowing performance to reflect rowing on water,” (Nevill et al., 2010).

In power sports, Comfort (2014) justifies allometric scaling, but ultimately argues for the practicality and simplicity of simple ratio-standard scaling. Using 15 pro rugby players, it was found that heavier athletes had higher absolute values of power during the squat jump, but when using allometric scaling modeling, there were no differences (Comfort, 2014). In 1RM performance, the lighter group was significantly stronger when using ratio and allometric methods (2.1 vs. 1.9 kg/kg and 10.42 vs. 9.87 kg/kg(.28)) (Comfort, 2014). In analyzing the effectiveness of ratio and allometrically scaled power cleans and back squat to 5 m, 10m and 20m sprint performance, it was found that ratio and allometrically scaled power cleans correlated with 5m sprints, allometrically scaled power cleans and back squat correlated with 10m sprint, and ratio and allometrically scaled power cleans inversely correlated with 20m sprints (Comfort, 2014). When scaling squat jump power by either method (allometric or linear scaling), higher correlations with jump height were observed compared to using absolute power and jump height.

This combined with the fact that sprint times for different distances, as measured above, were correlated with both methods of scaled strength and power regardless of the method, led Comfort (2014) to conclude that for practicality purposes, strength and conditioning coaches can opt for simple ratio scaling in favor of complex allometric scaling. This opinion differs from the prevailing research involving endurance sports mentioned previously. This may suggest in explosive power sports, relationships between body mass and power are equally quantified using a simple ratio-standard scaling. It is possible, however, this statement stems from the practical application goal held by Comfort (2014), seeking to assist coaches who may not be as adept at the complexity of allometric scaling, in which case simple ratio-standard scaling can suffice.

*Body Mass, Body Composition, and Measures of Power and Performance in Cross Country Skiing*

While it may be true that in power/speed sports, this is a more approachable method for coaches and athletes, the prevailing research suggests endurance sports, which mix anaerobic and aerobic energy systems, and particularly those which consist of an uphill performance dynamic, wherein gravity is the key resistance, should use appropriate allometric models to scale for body mass and specific performance variables (VO2 max, power, and/or strength). The preceding review of the literature clearly demonstrates the warranted attention on the relative importance of body mass to uphill and flat performance in endurance sports which involve both mechanical and gravitational resistive forces. While many concepts addressed in this research are directly transferable to skiing, the quadrupedal nature of cross country skiing, a key source of its complex metabolic, biomechanic, and technical nature, are perhaps reasons why it lags behind other endurance sports in this area of study.

Thus, while the necessity of the usage of allometric scaling in the measurement of performance variables normalized for body mass in nordic skiing can be thoroughly defended, a proper understanding of the background of early research in the sport in regards to body mass, composition, and its relationship to performance parameters is also justified.

Early Research (1970-1992)

Recall that the mechanical forces acting against skiing speed are gravity, friction, and air resistance (Frederick, 1992). Ski speed is the product of cycle length and cycle rate, variables which are increased by factors important to force production (e.g. aerobic and anaerobic power; upper and lower body strength, and technical skill/ability). Thus, the ratio of the effect of body mass on these factors (force production/mechanical forces) should theoretically explain the overall impact of mass to performance (Bergh, 1987).

One of the earliest studies on body mass examined this ratio in part, using dimensional analysis of the ratio (R) between body mass impact on factors of importance to power production (in this case: VO2 max and acceleration of gravity) and braking powers (friction and air resistance) in 39 male and 18 female Olympic athletes (Bergh, 1987). R was found to be less than unity for rather steep uphills (a benefit for lighter skiers) and greater than unity for moderate uphills, flats, and downhills (a benefit for heavier skiers) (Bergh, 1987). This is due to 1) the increased cost of lifting the center of mass (COM) during uphill skiing, 2) the accelerating force of gravity in downhill skiing being directly proportional to body mass, and 3) the friction between skis and snow being inversely related to body mass to the magnitude of 1%/kg of body weight (Bergh, 1987). Thus, the heavier skier is favored in downhills because while the accelerating force increases proportionally to mass, the braking forces grow less than proportional to mass.

In terms of VO2 max, an increased body mass would induce smaller increments in the maximal aerobic power than the power needed to elevate the COM, lending to a benefit for smaller skier in uphill sections (Bergh, 1987). Bergh’s (1987) finding that the energy cost per kilogram of transported weight decreased as body mass increased was in line with earlier research by Stattin and Lindahl (1973), though their research should not be considered due to the fact that they altered mass through a weighted vest without switching skis, neglecting to compensate camber stiffness with the increased skier weight (thus, increasing ski-snow friction).

Though early researchers did not fail to account for the influence of technical ability, recall from the section on the history and development of skiing that this time frame (1970s and 1980s) was characterized by some of the most transformational developments in technique, training, and equipment. Even during this time period, before many of these rapid advancements, energy transfer was recognized as a critical ingredient in the skill matrix, as exemplified by Bergh (1987), who while explaining 1) when transforming muscle energy into potential energy, a low body mass is favorable, since the quotient between these two is W^-⅓; and 2) when transforming potential energy into kinetic energy, the opposite is true, due to the equation being W^⅓, says,

“this should not, be confused with the fact that energy transfer can be an important constituent of skill which is a dimensionless factor.”

The skill concept was laid earlier by Norman, Caldwell, and Komi (1985), and it is for this reason that Bergh (1987) is also critical of the work in this area by Wehilin et al (1970), as the subjects were quite heterogeneous in regard to skiing experience. Though the goal of Bergh (1987) was not to establish an appropriate model for allometric scaling, but rather is interested in the effect of mechanical factors in relation to body mass, it is mentioned in the study design that the “dimensional analysis was performed on the assumptions that skiers are geometrically uniform and qualitatively equal (skill).” This approach, assuming the laws of geometric symmetry, is sensible when considering the prior review of endurance sports and body mass, wherein during this period (late 80’s and early 90’s), this law had not yet been challenged by Nevill et al (2004).

A final consideration to take from this seminal piece of literature which should be regarded in the interpretation of more recent research is this: unlike other endurance sports, the measurement of body mass on mechanical forces in skiing is uniquely complex, as snow conditions in combination with ski type and wax selection play a pivotal role in the influence of body weight on the coefficient of friction, making on-snow research very difficult. Thus, tests using rollerskis are sometimes favored for their control and reliability, but they contain different mechanical properties in terms of rolling resistance and friction (Hoffman, 1990), which will be discussed later.

Bergh (1992) expounded upon his earlier research by using theoretical analysis and experimental data from Hoffman (1990), Norman et al (1985), Bergh (1987), and Nilsson (1984) to show that max aerobic power (VO2 max) and the power needed to sustain various energy transfers and external resistances (submax oxygen uptake) increase at a rate proportionally less than body mass. This analysis could be considered the first forray of cross country ski research into the consideration of allometric scaling in examining the relationship between body mass and markers of performance. Theoretical analysis showed the best results when max aerobic power scaled with mass to the ⅔ power, while the submax exponent value ranged from ⅓ to 1; both lending an advantage to heavier skiers (Bergh, 1992). The finding that VO2 max expressed as mlxmin^-1xkg^-⅔ power reflects differences in performance capability among elite skiers better than an mlxkg^-1xmin^-1 was supported later on by Ingjer (2007).

The experimental data supported this theoretical analysis, with max aerobic power scaling with mass ^.07 and submax to mass ^ .04 (Bergh, 1992). Results comparing the 10 lightest with the 10 heaviest members of the Swedish Ski team from 1970 until the time of Bergh (1992) confirm the advantage of heavier skiers over lighter skiers in males, though this was not the case with female skiers. It is possible that recent research pointing to male performance on the flats (where heavier skiers are favored) (citation from “incline” section) and female performance on the uphills (an advantage for lighter skiers) (citation from “incline” section) as being the deciding metric for overall performance has its foundation in these early findings.

The novelty of this type of analysis is evidenced by Bergh’s (1992) own admission that the mass exponent, especially for inclines is far from established, and “the data are limited, especially for uphill skiing, and thus it is too early to propose values for the mass exponent that will equalize heavy and light skiers.” Indeed, data from Bergh (1987) and Nillsen (1984) showed a mass exponent of (.89). However, using the data from high speed films taken during competition with world-class skiers, a mass exponent of 1.4 to 1.9 was shown for uphill skiing (Norman et al., 1985). Overall, the data was higher than that obtained from level skiing (.38), but it is evidence of the early stages of scaling body mass to performance measures in the realm of cross country ski research.

At this point, it is critical to be reminded of the assumption made by Bergh (1987, 1992) that “metabolic power production is originating from aerobic power production, while the anaerobic power supply is disregarded.” Thus, these findings comparing uphill terrain to flat terrain and their relation to body mass and scaling are not taking into account measures of force (watts), but rather, the scaling of body mass to VO2 max and submax oxygen uptake (Bergh, 1987, 1992). While in the 80s and 90s, it is true that the ski performance was dictated relatively more so by the aerobic energy supply than today, where “supra-aerobic” (110-160% of VO2 max) efforts forced on by strategy, pacing habits, and the physiological make-up of skiers currently on the World Cup force athletes to blend and balance aerobic and anaerboic energy systems perfectly, it should remain obvious, particularly in the DP sub-technique, to consider force production in terms of anaerobic power in modern research concerning body mass and performance.

Hoffman (1990) also demonstrated that metabolic power expense does not increase in direct proportion to body mass using rollerskis. A key difference between these two studies was that Hoffman (1990) conducted his research using rollerskis while the work of Bergh (1987, 1992) was conducted on snow, and though the cost of oxygen, expressed relative to transported mass, decreased similar amounts in both studies (1% in Hoffman and 0.8-1.2% in Bergh), the power cost of overcoming friction on rollerskis painted a different story than snow. Bergh (1987) showed this to be proportional to body mass to the ⅓ power based on theoretical analysis, and .14 based on experimental analysis (on snow). These findings, which indicate that as body mass is increased there is a smaller proportional increase in the power cost of overcoming friction, suggest a benefit for larger skiers on flat terrain from the standpoint of overcoming friction. On rollerskis, it was experimentally determined to be proportional to body mass raised to a factor of 1.4, which would suggest a benefit for the lighter skier (at least on flat terrain) (Hoffman, 1990). Yet, because the power cost of overcoming friction is a small component of the total mechanical power cost for roller skiing, the heavier skier still has a lower power cost relative to body mass for rollerskiing on flat terrain. Thus, when looking at the theoretical effect of body mass on mechanical power cost of cross country skiing relative to its effect on maximal aerobic capacity, the lighter skier should benefit on flat terrain on rollerskis and the heavier skier should have a slight advantage when skiing on flat snow, an implication when considering study design (on snow vs. rollerski).

Upper body power (UBP)

Many studies have demonstrated the importance of upper body power (UBP) as a determinant of cross country ski performance in high school athletes (Gaskill et al., 1999), NCAA athletes (Alsbrook, Heil, 2009; Jacobson, 2008; Heil et al., 2004; Whitham, 2016) and national and international level athletes (Staib et al., 2000). However, the scaling approach by each of these studies involved either absolute expressions of UBP or simple ratio standard expressions of UBP (W/kg).

Gaskill et al (1999) explored the relationship between max UBP and ski skating performance using a cross sectional representation of high school and adult cross country skiers, with the dual purpose of comparing UBP of skiers with distance runners. UBP was determined using a Street Arm Ergometer, and a correlation was found between absolute UBP and race velocity (RV) in men (r = .845) and women (r = .843) and also between relative UBP (W/kg) in men (r = .884) and women (r= .884) (Gaskill et al., 1999). Staib et al (2000) would also find a correlation between UBP and FIS rank in international level athletes, though not as high (r = -.68). The high correlations in the work of Gaskill et al (1999) likely stem from the wide range of race velocity, an occurrence more probable in high school aged athletes, where technical proficiency and experience varies considerably. As such, when athletes were grouped by ability, correlations decreased. Thus, it is likely that UBP is a stronger predictor of race performance for developing athletes, but for typically homogeneous elite athletes, it may not be the case.

Using similar methods to determine absolute and relative peak power (Freestyle Arm Ergometer), Staib et al (2000) advanced the work of Gaskill et al (1999) by also looking at upper body endurance, investigating the relationship between DP aerobic and anaerobic power and cross country ski race performance in elite athletes. DP aerobic power was determined using a DP VO2 peak test on a treadmill beginning at 7% incline with increasing speeds every 2 minutes. Absolute UBP correlated more with FIS rank in points (r = -.68) than relative UBP (W/kg) (r = -.48) (Staib et al, 2000). The highest correlations with FIS rank in points was DP time to exhaustion (TTE) (r = -.80) and DP VO2 peak (r=-.74), which was measured using ml/kg^⅔, scaling for body mass as recommended by Bergh (1992) and later justified by Ingjer (2007). Furthermore, 75% of variance in FIS could be accounted for by DP VO2 peak and UBP, but DP VO2 peak exhibited the highest beta (Staib et al., 2000).

While these findings point to aerobic DP fitness as being more effective at describing ski performance than lower body peak VO2 values and DP peak UBP (W and W/kg), Staib et al (2000) also hints at the interdependency of the aerobic and anaerobic components of UBP, as a critical level of UB anaerobic power as necessary to maximize UB aerobic power. Higher maximal power output in the DP as a mechanism for improved economy, which could improve long duration DP as well because of a lower relative intensity, is a suggestion supported by more recent research (Alsbrook & Heil, 2009; Osteras et al., 2002; Hoff et al., 2002). Of note is the gender dependent contradiction to these findings made by Osteras et al (2016), which showed the relative importance of UB strength and lean mass in predicting DP power production and overall cross country performance to decline with distance in sample of 13 elite female athletes, while VO2 max shows the opposite tendency (i.e. increasing in influence with distance).

Alsbrook and Heil (2009) investigated the relationship between short (10s and 60s) and long duration (4-12 min TTE) measures of upper body power and mass start classical ski performance using a modified ski ergometer (for measures of UBP) and an on snow competition (performance). UBP10s (r=.93), UBP60s (r =.92), and UBPpeak (r = .94), and VO2 peak (r=.88) all correlated with 10km classical race performance. Measurements of UBP for all three tests (10s, 60s, and TTE) were given in absolute and relative (W/kg) expressions .

It is worth noting that in women, the correlation coefficients for UBP10s and UBP60s (W/kg) was much higher than in men (r = .96 to .53 and .94 to .52 respectively) (Alsbrook and Heil, 2009). In previous work using similar tests and subjects, Alsbrook (2005) showed a similar result. There, UBP expressed relative to body mass (W/kg) showed women to have higher correlation coefficients in 10s and 60s tests as well (.96 to .42 and .99 to .14, respectively) (Alsbrook, 2005, 2009). Thus, it seems likely that upper body power relative to body mass might play more of a role in women than in men, at least in the DP technique. The higher numbers in the earlier study are due, however, to the low number of subjects (3), which prevented the calculation of confidence intervals (Alsbrook, 2005). The latter research contained only 5 women versus 10 men, which may also explain these differences (Alsbrook and Heil, 2009).

It is the opinion of the current researcher that it was an interesting choice for Alsbrook and Heil (2009) to not elect to use allometric scaling when expressing relative upper body power, since Heil (1998) had conducted similar research in cycling. It is perhaps why he mentions that the “theoretical advantage of absolute over relative UBP measures in predicting classical race performance was not clearly established by the present study” (Alsbrook & Heil, 2009). Thus, Alsbrook and Heil (2009) could only surmise that heavier skiers with higher absolute power measurements held an advantage on the flat sections of the course, while they may have struggled on uphills. Alsbrook and Heil (2009) indeed postulate that the best skiers were those who likely had the highest absolute UBP to maintain high speed on flat terrain, complemented by the ability to generate enough relative whole body power to not sacrifice performance on uphills.

A noteworthy final recommendation of the group, which has implications on the current study, was to organize future research involving either entirely uphill or entirely flat terrain to identify the role of absolute versus relative UBP in various sections of a classical race course (Alsbrook & Heil, 2009). Later research by T. Carlsson (2013) pushes this suggestion further by introducing the idea of using allometric scaling to quantify relative UBP. Of importance in the work of Alsbrook & Heil (2009) is the fact that race performance was determined using a mass start set-up, promoting strategy and positioning more so than a time trial. Also, because this study was conducted on snow, control of wax and ski selection should have been a key constant, but the lack of this element is discussed as a limitation (Alsbrook and Heil, 2009).

UBP expressions in analyzing equipment

We see the usage of absolute and ratio standard (W/kg) expressions in literature analyzing the influence of equipment on UBP output in cross country skiing as well (Heil, Engen, & Higginson, 2004; Jacobson, 2008), though the absence of allometric scaling here is acceptable due to the nature of the tests. In the case of Heil et al (2004), the influence of ski pole grip on peak UBP output in 9 men and 2 female regional, national, and international level skiers using a modified ski ergometer, peak UBP was expressed absolutely and relatively (W/kg). Using an integrated strap system, skier’s produced 2.3W/kg in peak UBP, defined as the highest 5s average power output during the last 10s of each of the three 15s tests. Because the nature of this test was not looking at power and body mass relationships and a performance variable, but rather an independent variable (grip) on power, it was appropriate to utilize absolute and relative expressions. This should provide a sufficient explanation to the observant reader who noticed Heil (1998) being involved as an early proponent of allometric scaling in endurance cycling research as mentioned earlier in this literature review.

Similarly to Heil (2004), Jacobsen (2008) wished to analyze an equipment aspect (pole stiffness) on upper body power output in NCAA skiers, and thus elected to utilize an absolute expression of power (W).

Research involving body composition and body dimensions

Research has also probed relationships between body composition, body dimensions, and peak speed in cross country skiing in both collegiate and senior elite athletes (Larsson & Henriksson-Larsen, 2008; Stoggl et al., 2010; Andersson, 2010; Osteras et al., 2016; Whitham, 2016). The motivation for this research area likely stems from evidence of lower BMI, total body weight, and higher amounts of lean mass correlating with improved performance as athletes progress towards a “peak” phase at the end of the competition calendar (Polat, 2018, Grzebisz, 2016; Losnegard, 2013).

In 15 FIS athletes tested at 3 points (July, October, and February) during a cross country season, a reduction in body fat and total weight and an increase of lean body mass coincided with increases in VO2 max and VO2 at lactate threshold, allowing for higher loads of training and increased performance in races (Grzebisz, 2016). In regards to VO2 max and gas exchange threshold, Polat (2018) showed different results to Grzebisz (2016), but BMI and body weight were also lower at the end of the year, when performance was at its highest in an examination of athletes at 3 different time points in the year.

Larsson & Henriksson-Larsen (2008) showed that total body weight and absolute lean body mass were significantly related to final time (r = -.721 and -.830 respectively) for collegiate male skiers in a 5.6 km on snow time trial. Furthermore, absolute lean arm mass was negatively correlated to final time (r = .648) and relative lean arm was significantly related to speed, mainly in uphill sections (r = .636 – .867). Thus, large amounts of lean body mass, especially in the arms, would appear to enhance performance, especially in the uphills (Larson, 2008). These findings, coupled with the findings of Alsbrook and Heil (2009), further support the need to use a more accurate scaling of body mass with the isolated testing of both flat and uphill only sections in order to identify how relative power impacts DP performance specifically.

In contrast to Larsson et al (2008), Andersson (2010) found only a correlation between the skier’s absolute values of lean body mass and performance in the starting section (r = .78) and DP max velocity (r = no value is given). The importance of body mass for acceleration from standing still and DP max velocity is also supported by Stoggl et al (2010), who showed the advantage of a high absolute trunk mass together with high amounts of total lean mass. Osteras et al (2016) found similar findings, with the two best predictions of 30-second DP power being lean UB mass and max UB strength (r = .84 and .81 respectively). In NCAA skiers, lean mass predicted DP performance (r = -.72), but power and max strength were not significantly correlated with DP performance (r = -.55, p value = .10; r = .06, p-value = .87) (Whitham, 2016), though the latter findings may have been skewed due to a lack of participants and the use of strength tests which were potentially not as important to DP technique (bench press, trunk flexion, tricep extension).

Stoggl et al (2010) also looked at how body dimensions and composition influence performance in nordic skiing, furthering the work of Larsson et al (2008) by examining elite skiers within the classical technique. Absolute values of mass, lean body mass, and anthropometric measurements of limbs as measurements of peak speed were looked at, and thus, scaling body mass to a performance variable was not involved in the approach. Lean trunk mass (r = .75), BMI (r = .66), total lean mass (r = .60), and body mass (r = .57) were positively correlated with DP peak speed, body height showed no relation to peak speed, and shorter arm length aided in DIA stride peak speed (Stoggl et al., 2010). When considering the results, it is important to note the nature of the DP protocol, which was on a flat grade, where higher absolute power expressions, regardless of body mass, could be advantageous (Bergh, 1992).

One reason high values of lean mass (LM) is advantageous to performance is because increased muscle volume is linked to a larger anaerobic capacity and thus, ability to develop force. This explains why larger skiers produce higher speeds in the flat sections of races and also demonstrate a more positive pacing approach (T, Carlsson, 2015a). This is further supported by the work of M. Carlsson et al (2014), who showed that absolute expressions of whole body LM, upper body LM, and lower body LM were significant predictors of sprint prologue performance in both males and females, and distance race performance in females. Between sexes, males have more LM in the body segments which contribute to propulsive forces than females (Carlsson et al 2014). The findings of this research also point to the importance of both UB LM and LB LM to improve competitive performance capability, which, when coupled with previously mentioned findings of increased involvement of the lower body in the DP technique as incline increases (Rud et al., 2014; …. ), illuminate the need for further research analyzing both LB and UB power in relation to body mass at both flat and uphill inclines, which will be addressed in the present study.

Losnegard et al (2014) examined exercise economy in V2 skating, DP, and uphill running in elite male cross country skiers to see if they were affected by body height, body mass, and VO2 peak. Though it was found that those intrinsic factors could only partly explain variations in exercise economy in the three techniques, it is worth noting that DP exercise economy correlated with body mass (r = -.46) and body height (r = -.11).

Gloersen et al (2018) used allometric scaling to determine the frontal area variable in analyzing propulsive power in cross country skiing. The exponent used was from Bergh (1987), at mass to the ⅔ power. The main priority of this study was to obtain accurate measurements of propulsive power throughout an entire cross country race, which would in theory give insight to endurance sports characterized by “supra-aerobic” efforts sprinkled in between bouts of recovery, as is the case in ski races, where athletes exceed their peak VO2 power (110-160% according to Sandbakk et al, 2011 and Karlsson et al., 2018) when ascending steep uphills, using downhills to recover. Though it falls out of the scope of this particular research, it is perhaps worth noting that propulsive power was normalized to body mass using a simple ratio standard approach (W/kg).

*Allometric Scaling in Cross Country Skiing*

Although the literature clearly establishes the influence of body mass, body composition, and upper and lower body power to double poling performance, there has been little research which has employed allometric scaling to express power/body mass relationships and cross country ski performance, as is the case in cycling (Nevill et al 2006; Jobson, 2008), rowing (Nevill et al., 2010), and running (Svedenhag, 1995), and none which express strength/body mass relationships using allometric scaling.

Bergh (1992) established a 0.67 body mass exponent for VO2 max to evaluate performance in cc skiing, but recall that this exponent might be lower and higher for level and uphill skiing, respectively. Also, ski speed has been shown to be positively related to body mass (Bergh, 1992; others), and thus, in order to explain performance, the influence of VO2 max and body mass needs to be considered, which is possible using the allometric models which form the basis of the doctoral research of T, Carlsson (2015a) who summarizes four studies highlighting the importance of body mass exponent optimization for the evaluation of performance capability in cross country skiing.

The first study aimed to establish an optimal body mass exponent for VO2 max to indicate 15km performance in elite male cross country skiers (T, Carlsson, 2013a). Models using VO2 max divided by body mass raised to the 0.48 explained 68% of the variance in mean skiing speed and the 95% confidence intervals for the body mass exponents used here and in later work by the same group did not include either 0 or 1 (T, Carlsson et al, 2013a; T, Carlsson et al 2015b). The second study validated this approach, as an exponent value of 0.53 explained 69% of the variance in race speed in a 15km performance by elite male skiers.

Furthermore, T. Carlsson et al (2013) found that the body mass exponent increased with incline, validating an earlier suggestion by Bergh (1992) that the 0.67 body mass exponent for VO2 max might be lower for flat terrain and higher for uphill terrain, while T. Carlsson et al (2015b) found the body mass exponent for VO2 max increased with distance, which corresponds to Heil et al (2013) who advocated for a relationship between distance performance and body mass raised to the power of .26.

The reason for an increase in the exponent due to incline, as expressed by the equation -(0.38 + 0.03 x &) where & is the incline of the section, is likely due to the larger proportion of the total resistive force related to the net increase in potential energy, which is supported by the previous studies mentioned in cycling. Compared to level cycling, uphill cycling utilizes a higher body mass exponent for VO2 max (Swain, 1994; Padilla, 1999; Nevill, 2006). Together, this may suggest that lighter skiers have an advantage over heavier skiers on steep uphill sections, whereas heavier skiers are favored everywhere else, which is supported by previous research (Bergh, 1987, 1992).

The equation which shows the influence of distance on the body mass exponent related to VO2 max was -(0.49 + 0.019 x lap), and indicated a more pronounced positive pacing profile by heavier skiers (T, Carlsson et al., 2015b). This can be explained by larger skiers having higher amounts lean muscle, which enables them to have an edge in utilizing anaerobic processes to generate high skiing speeds at the beginning of the race. This increases the concentration of metabolites related to fatigue, which leads them to the more positive pacing (T. Carlsson et al., 2015b)

In regards to VO2 max, there is a considerable amount of debate as to what is the appropriate exponent value, as the surface law indicates 0.67, and 0.75 is based on the theory of elasticity, which suggests that the absorption and release of energy from the body’s structures can influence the relationship between body mass and metabolic rate (Jensen, Johansen, & Secher, 2001). The model proposed by T, Carlsson et al (2015b) arrives at a value of 0.76. T, Carlsson (2015a), in considering this debate, offers up the suggestion of an exponent of .67 or .75 if the goal is to compare the physiological capability of an individual against a standard or to compare groups on the basis of VO2 max, but if the goal is to evaluate an elite male skier’s performance capability in 15km classical technique skiing, then the 0.5 exponent value is proven to be superior based off of his present research.

This group’s most recent research (not a part of the dissertation) looked to fill in the gap regarding power function modeling by investigating the optimal expression for VO2 max and lean mass to indicate sprint performance among elite female skiers (T, Carlsson, 2016), as opposed to male skiers in a 15km race (T, Carlsson et al., 2013a), and found some noteworthy differences. Body mass didn’t contribute to the model (explained by the strong intercorrelation between VO2 max and body mass) and thus, evaluation of sprint performance capability among elite female skiers should be based on Vo2 max expressed absolutely (L/min^1), a contrast from our summary above, which suggests mass expressed to the 0.5 power exponent for male skiers (T. Carlsson et al., 2013a).

The reason for this could be tied to the findings on the influence of distance on the relationship between body mass and performance (Heil et al., 2013; T. Carlsson et al., 2013a) as well as the effect of lean mass on sprint performance (M. Carlsson, 2014). As mentioned before, Heil et al (2013) found that race speed in distance competitions was related to body mass raised to the power of 0.26, while speed in a 1km freestyle time trial is proportional to body mass raised to the 0.43 power. According to T. Carlsson (2016), power function modeling showed that the absolute expression of LM should be used to predict sprint performance over LM as expressed as a percentage of body mass. Coupled with the findings of M. Carlsson (2014) that high volumes of lean body mass aid in anaerobic energy production and thus, force generation, both of which are more critical in sprint racing compared to distance racing, it is sensible to assume an absolute expression of LM will be more accurate in predicting sprint performance than a relative LM expression.

It is worth noting the curvilinear relationship in regards to the above statement, as T. Carlsson et al (2016) does:

“..the performance related effect of an increase in anaerobic capacity will be gradually reduced as the LM of the sprint skier increases, a consequence of the square cube law first described by Galileo in 1638. The performance related increase in the force generating capability, linked to a larger muscle volume will eventually be neutralized by the concomitant increase in body mass (i.e. an increase in the counteracting forces.) the optimal muscle mass to body mass ratio a sprint skier should achieve is influenced by their VO2 max and body dimensions – further research should work to clarify the interplay of the physiological characteristics and body dimensions of elite sprint skiers.”

A third study looked to investigate how body mass contributed to the models to predict sprint-prologue performance in the classical technique using oxygen uptake at the onsent of blood lactate (VO2obla), VO2max, and mean upper body oxygen uptake (VO2dp), and it was found that body mass did not contribute to the models based on VO2 max, VO2obla, or VO2dp (M, Carlsson et al., 2014)

A final study, which is perhaps closest in relation to the present research, identified the lack of allometric scaling to investigate the influence of body mass on the performance capacity of cross country skiers based on their upper body power output, and thus set out to establish the most appropriate model to predict mean skiing speed during a DP roller skiing time trial (T, Carlsson et al., 2013b).

45 Swedish junior cross country skiers (27 men and 18 women) of national and international standard partook in a 120-s double poling test on a ski ergometer to determine their mean upper body power output (W), as well as a 2-km DP time trial on an asphalt road with a mean inclination of 1.2 degrees. The purpose of the study was to develop an allometric model to predict mean skiing speed during DP rollerskiing using the scaling of upper body power output (T, Carlsson et al., 2013b)

As expected, both absolute and ratio standard expressions (W/kg) correlated with 2km DP performance (r = .72 and .73, respectively), and explained 52.3% and 53.5% of the variance, respectively (T, Carlsson et al., 2013b). However, the optimal allometric ratio, 1.06 x (2xm^-0.57)^0.56, explained nearly 59% of the variance, evidence of its preference in the prediction of junior cross country skiers’ performance over the absolute expression or the simple ratio-standard scaling of upper-body power output (T, Carlsson, et al., 2013b).

Similar to the findings of Gaskill (1999), who also utilized junior aged skiers as participants, the modeling was not influenced by the sex of the subjects, though a simple ratio standard scaling was used in that work. In accordance with Mahood et al., (2001), DP performance correlated with ski ranking (r = -0.83 for men; r = -0.76 for women), giving further credence to the value of studying the DP technique as a predictor for overall cross country ski performance.

Though groundbreaking in terms of presenting a valid allometric scaling approach to measuring upper-body power and its effect on DP performance in cross country skiing, this study has notable limitations, three of which illuminate the need the present research to fill in the gap in the literature.

First of all, UBP output was defined as the mean power output during the 120s DP test performed on a modified ski ergometer (T, Carlsson, 2013b). The modified ski ergometer has been validated by several other studies (Alsbrook, 2009; Holmberg & Nilsson, 2008), but other groups have determined UPB through shorter tests – 60s and 10s – in the case of Alsbrook & Heil (2009) and Alsbrook (2005), which might give a better idea of true anaerobic upper body power, as 120s is too long for ATP to be produced solely through anaerobic metabolic processes.

In terms of participants, T. Carlsson (2013b) recommends looking at elite level athletes. In a scenario with these subjects, it is likely that researchers and coaches would have access to the necessary devices in order to measure power, some of which are of considerable cost. They also would be equipped to apply the preferred complex allometric equations. However, in terms of being as applicable to typical coaches of youth and junior programs, a simplified allometric equation is provided by T. Carlsson (2013b): (PCtime trial = √(W/√m)). While expensive equipment such as ski ergometers, Thoraxtrainers, or modified ski ergometers such as the one used by T, Carlsson et al (2013b) are not likely accessible for many youth programs, access to general strength and weight room equipment is. Thus, a study which looks to measure upper body strength by general movements, as well as modified, double poling specific movements with equipment found in a typical weight room would be beneficial both to the body of scientific literature and to the coach and athlete community.

Finally, the vast scope of literature on DP points to the involvement of the lower body in performance as well as the upper body, both in terms of energy metabolism and force production. This proponent appears to be accentuated at different inclines. As incline increases, the lower body is more actively involved, both from a metabolic standpoint and a kinetic standpoint. The muslces of the legs are net consumers of lactate, which is produced at the intensities commonly used in the DP at inclines during distance races. This would suggest that an increase in UB mass alone might not necessarily be the sole factor in improved uphill DP performance, and in fact, slender, more aerobically based skiers may benefit as much or more as “top heavy,” powerful, anaerobic/sprinter based skiers. This is evidenced by the top female skier in the world today, who is built more like a distance runner and yet excels in distance classical races, which can not be attributed to her total UB power but must include some aspect of her 32:00 10km running ability, which is mostly LB based. In order to combat the effect of gravity, skiers must use more rapid and shorter cycles to avoid losing speed (Stoggl & Holmberg, 2016). This increase in motion, as well as the “pumping motion” of the legs, would suggest a disadvantage for skiers who are larger, as they would be required to perform more work in repositioning their COM during the poling phase.

- Carlsson et al (2013b) utilizes a DP test of 2km distance at a fixed incline of 1.2 degrees. Alsbrook & Heil (2009) suggest organizing research which is either entirely uphill or entirely flat in order to fully examine the role of absolute versus relative UBP in relation to body mass in various sections of a classical race course.

Thus, in order to fill in a gap in this body of literature, it seems appropriate to design research where two DP trials are run; one which is entirely flat, and one which is at a fixed incline, and examine both UB strength and LB strength (determined by a battery of general and DP specific strength tests), allometrically scaled to body mass, to determine the relative influence of these relationships on variances in performance amongst junior level skiers. This is the direction of the present research.