Saturday, January 21, 2017

Actionable Intelligence for Running Part 2 : Effect of Step frequency on Leg Spring Characteristics for Treadmill Running

In Part 1, I reviewed research literature on the relationship of inverse ground contact time, 1/tc, to the metabolic cost of running. Further, because the leg stores and reuses elastic energy, spring mass models have been used quite extensively since the 1960's to describe it's spring characteristics. 

In this installment, I will investigate the relationships between leg spring characteristics against variable step frequency and variable ground contact time in two tests. I will use two wearable electronics - a Polar V800 and a Stryd gen 2 footpod - along with a treadmill and an Android phone. Force plates, kinematic arms or 3D motion capture systems were not used.   

A point to note is that the human leg is not a pure linear spring due to various muscoskeletal complexities, therefore the estimated stiffness variables will be preceded with the word "effective" in this writeup while device native metrics are called as is. 

Lastly, as the test was done on myself, there could be an effect of human error and testing inexperience shown in this study. When possible, I've tried to introduce randomization in the test protocol to equalize the effect of external factors not accounted for in the experimental design. You are free to mail me pointing out any flaws in understanding.

Commentary to the findings (or the "intelligence") is highlighted in blue. 

Abbreviations Used

Calculations Used

Read Part 1. Or ask.

Subject and Equipment Used

Test Protocol

1. 5 min warmup at 2.8 m/s pace.
2. 2 min run at 3.3 m/s pace to determine fcSF. 
3. Calculate 6 test SF values from 30% reduction to 30% increase in 10% increments : 0.7fcSF, 0.8fcSF, 0.9fcSF, +1.1fcSF, +1.2fcSF, +1.3fcSF.
They also also called SF-30% ,SF-20% , SF-10% ,SF10% ,SF20% & SF30%
4. Part A (Variable GCT - Variable SF test) : Randomize the order of the above and complete 6 trials of 2 min each at 3.33 m/s. 2 min recovery in between. 
5. Practice a running motion for self-imposing short GCT and long GCT. 
6. Part B (Variable GCT - Fixed SF test) : Complete 2 x 3 min randomized trials strictly at fcSF and at a pace of 3.33 m/s, one with short GCT and one with long GCT.
7. Consolidate data for post processing within a statistical computer package.

Note : 3.33 m/s corresponds to 12 kph on the treadmill and 8 min/mile. A cadence of 180 SPM corresponds to 3 Hz. 

I. Results of Test Part A 

The fcSF during the initial 2 min trial run was 177 SPM which is 2.95 Hz. 
Corresponding GCT was 235.5 ms. 
LSS at fcSF = 10.2 kN/m.

Calculated values of SF for the 6 trial runs were as follows :

626 data points were consolidated from this test. 

Data is plotted below.

Fig.1 ; Spread in data for Part A for each of the 6 SFs.

FIG 1 : Box plots of FT and GCT at the 6 different SF's are shown relative to fcSF (marked with a dotted reference line). 

The data corresponding to 2.065 Hz or
SF-30% has a large spread because I had difficulty trying to main such a low cadence, having to hold the sides of the treadmill for support at times. This plot has been made after cleaning up a lot of null values within the SF-30% dataset. Inspite of this, there still is great spread relative to data at other SFs.

The general takeaway is that ground contact times fall steadily with increase in step rate and rises with decrease in step rate. One would expect aerial times to be high in the low cadence region, but the data seems to show an inflection point at fcSF of 2.95Hz. In the increasing cadence region, FT tends to decrease.  

Fig.2 : Scatter plot showing % change in LSS vs % change in GCT during 
the variable GCT - variable SF test.

Fig.3 : Scatter plot showing % change in LSS vs % change in SF during 
the variable GCT - variable SF test.

FIGS 2 & 3 :  Decreasing changes in GCT obtained from the variable SF test correspond to positive changes in LSS. A simple linear regression shows R^2 value is 0.79. The Pearson correlation test of both yields -0.889 (P < 0.05).  

Problematic, however, is the fit of SF variation with LSS. Some of the noise in the left hand side is most likely due to the improperly executed low cadence test at SF-30%. If you consider just the right hand side of Fig 3, there seems to be a +ve to +ve relationship between higher SFs (SF10%, SF20% ,SF30% ) and LSS. The Pearson correlation between SF and LSS yields -0.421 (P < 0.05). 

Takeaway here is that GCT maybe a better predictor of LSS. Test Part B will prove if this is correct.

II. Results of Test Part B 

With some time given to practice, I was able to achieve a short and long GCT as follows :

Short GCT   226.6 ms
Long GCT   246 ms

The short GCT was obtained by conscious fore foot landing close to vertical line passing through COM and quick leg swings. The long GCT resulted from an exaggerated rolling motion of the feet, almost to the point of heel first first landing. Point of contact was farther away from the vertical line passing through COM. 

326 datapoints were consolidated from this test. 

Plots of data are presented below. 

Fig 4. Scatter plot showing % change LSS vs % change GCT during 
the variable GCT - fixed SF test.

Fig 4 :   Almost 96% of the variation in LSS was explained by variation in GCT. Further, the Pearson correlation between variable GCT and variable LSS was 0.98 (P < 0.05). The plot shows that variations in GCT in a variable GCT test - fixed SF test are more strongly related to LSS than in a variable GCT - variable SF test. This plot shows the LSS - SF relationship for both tests A and B making it clear the stronger regression in Test B (orange markers).

Takeaway is that lesser ground contact times are correlated with higher leg stiffnesses. (whether one causes is the other cannot be proved here. Also, that there maybe an injury limited stiffness value beyond which it is futile to stiffen the leg is also impossible to show here, since both tests rarely exceeded 12 kph. Theoretically, it seems possible that to generate high leg stiffnesses, the body may have to exaggerate dorsiflexion in the feet. But stiffness could also be a function of knee and hip torques so I refrain from digressing.)

III. Other Results 

A. Variation of Estimated Ground Reaction Force with Change in SF

Fig 5. Scatter plot showing peak nGRF expressed as N/kg with % variation in SF.

Fig 5 An expression for GRF was obtained from sinusoidal approximations given in Blum and verified with an older paper by Morin et. al. Using temporal variables measured by Stryd, the calculated GRF was then normalized by my body weight. This is shown in Fig.5.

The takeaway here is that nGRF decreases with increased SF, seemingly stabilizing between 
SF20%. and SF30%. Above the preferred step frequency, peak ground force decreases. This finding agrees with literature. The behavior at lower SFs could be a product of high COM elevation or aerial time. It tends to agree with certain reality that drastically reducing cadence at the same high running speed makes loud landing sounds in the gym. High force = high loading = high noise! This observation points to a flaw in the finding in Fig 1 that aerial time reduces with decreasing step frequency, infact I believe it should be the opposite. 

B. Variation of Rate of Force Production with Change in SF

Having seen in Part 1 that metabolic cost is directly linked to the inverse of GCT, it's interesting to inspect the behavior of this variable from the variable SF test data from Part A.

Fig 6. Scatter plot showing rate of force production vs % change in SF.

Fig 6 : There seems to be a distinct bow to the shape of this curve corresponding to the line of fcSF. Below and above this line at SF-30% ,SF-20% ,SF-10% ,SF10% ,SF20% & SF30% , inverse GCT shows increase. 

While data is limited to 626 samples and there is still some noisy data at the extreme low cadence, this graph generally agrees with literature. The surrogate data here suggests that there is a global minimum in metabolic cost at my freely chosen cadence of 177 SPM at 3.33 m/s pace. Intuitively, faster cadence means lesser GCTs. Muscle firing must be fast to produce ground force. Faster muscle firing has an oxygen penalty. Lesser cadence than preferred cadence at the same running speed also doesn't look optimal, as leg loading increases (Fig 5).

C. Vertical and Leg Spring Stiffness

One of Stryd's developers told me recently that they had not decided to release the math used to calculate leg spring stiffness (LSS) just yet. Curious as I am, I investigated how my own estimated values of ELS and Δy(COM) compare with Stryd's LSS and VO. 

EVS is the ratio of peak GRF and the vertical change in COM. ELS is the ratio of peak GRF and change in resting leg length. Both can be estimated from temporal variables and some high school math. 

C.1  Variation of Stryd Reported ELS vs % Change in SF

Fig 7. Scatter plot showing change in Stryd reported LSS and estimated VO with % change in SF.

Fig 7 : For lack of a metric to compare Stryd's LSS, I plotted it against the measured VO. The data suggests there's a curvilinear relation in both the variables with variable SF. LSS appears convex shaped against SF. The lowest VO corresponds to the highest SF's (and vice versa) whereas in leg spring stiffness, there appears to be a global minima between fcSF and SF10%.

The takeaway is that oscillation of a fixed point on my COM decreases with increasing step frequency. This agrees with the decreasing trend of FT and GCT at high SF's from Fig 1. Spring stiffness also increases with step frequencies. Both these findings tend to agree with literature.

C.2  Variation of estimated EVS vs % Change in SF

Fig 8. Scatter plot showing change in estimated EVS and estimated Δy(COM) with % change in SF.

Fig 8 : The change in estimated EVS is convex shaped with % change in SF whereas that of Δy(COM) is concave shaped. The data seems to suggest that global minima in EVS is somewhere between fcSF and SF10% and much higher in both directions from this point. Global minima in Δy(COM) is closer to the highest SFs and maxima is clustered around the lowest SFs. The magnitude of estimated EVS seems smaller than I expected compared against literature reported values.

The estimated value of vertical stiffness agrees with Stryd's LSS trend (Fig. 7) - both are convex shaped in SF and there appears to be a global minima between preferred cadence and SF10%

Variation of estimated ELS vs % Change in SF

Fig 9. Scatter plot showing change in estimated ELS and estimated ΔL with % change in SF. Note that ELS calculation corrects for the translation in point of foot contact, therefore it is a POFT corrected spring stiffness, yielding higher magnitudes than those calculated without POFT correction. 

The change in estimated ELS is convex shaped with % change in SF whereas that of ΔL is concave shaped. The data seems to suggest that global minima in ELS is somewhere around SF10% and much higher in both directions from this point. Global minima in ΔL is hard to tell, there seems to be two local minimas instead at the lowest and highest SFs each. The magnitude of estimated ELS also seems smaller than I expected compared against literature reported values. 

Comparing Figs. 8 and 9, the increase in effective vertical stiffness is more pronounced than effective leg spring stiffness at higher SFs. The magnitude of effective vertical stiffness is also higher than that of effective leg spring stiffness. This is in direct agreement with observed trends in literature (duh, most are using the same mathematics!)

Estimated ELS Compared to Stryd's Leg Spring Stiffness

Fig. 10.  Scatter and median value of bias magnitude between estimated Δy (COM) and VO reported by Stryd. Bias =  [Δy (COM) - VO ].

Fig 11. Scatter and median value of bias between estimated ELS and Stryd reported LSS.  
Bias =  ELS - LSS.

Figs. 10 & 11 : The last two plots show the difference in Stryd's metrics of VO and LSS vs estimated Δy(COM) and ELS respectively. 

The bias in estimated Δy(COM) and VO each is lowest around SF-30% and SF-20% and progressively increases with increasing SF. At SF10% and beyond, there is an average of 0.1m of difference.   

The bias (or delta) in estimated ELS is approximately 5 KN/m less than Stryd's LSS between SF-20%  and SF20%. At lower and higher SF's, the bias seems to get larger, with the highest bias of 10 kN/m at SF-30%

I'm not able to justify this difference, especially since ELS was estimated from Stryd's GCT and speed. The bias may result from a misunderstanding of how Stryd is calculating it's LSS. It could be possible that the GRFs measured by Stryd, if it does at all, are much higher than estimated GRFs from the spring mass model and they are using some inhouse fudge factors to agree with their test data. An explanation of these differences would be nice actually. However, what I have proven is that in the absense of any LSS data, just being able to use speed and a footpod that measures GCT will help you estimate ELS and EVS as surrogate data to measured LSS. I suppose trends are as instrucive as specific values.

In the next installment, I'll be continuing to stick with leg spring characteristics but with a changes in running speed. I will also hope to compare treadmill running with outdoor running to see what real world conditions impose on the metrics. 

Sunday, January 15, 2017

Actionable Intelligence for Running Part 1 : Ground Contact & Leg Spring Characteristics

This is what I hope will be a multiple part series on my lab efforts to study running characteristics and extract what I call 'actionable intelligence'. I hope it will be an enjoyable read. Readers are encouraged to submit findings of flaws to my email.  

The cost of transport is the average energy required for an animal to travel a unit distance and is composed of the mechanical power to :

1. Accelerate limbs with respect to center of mass during each stride. This is a change in kinetic energy

2. Raise and re-accelerate the center of mass against gravity during each stride. This is a change in potential energy.

3. Move against resistance in the environment by virtue of opposing effect of the medium, such as air resistance, friction or viscosity. This is resistive work. 

4. In the legs of larger animals, where both the front and hind legs can be used for braking and accelerating, muscles store elastic energy lost from potential and return some of this energy again on takeoff. It's a convenient way to preserve and recycle effort. So there is a change in elastic energy. 

The energy and power to supply the above are delivered by positive work (shortening) of some groups of muscles in conjunction with the negative work (lengthening) of some other groups of muscles.  The net energy equation then is :

Perspective is nice to have. Robert McNeil Alexander, the father of animal locomotion research, stated in the first chapter of his book on locomotion that it takes 15 Joules of energy for a human to increase the sum of kinetic and potential work in the course of a single step.

Running Metabolic Cost and Rate of Force Transfer

In a landmark paper by Kram and Taylor, metabolic rate of running was hypothesized to be proportional to the cost of supporting the animals' weight and the energy used by each gram of active muscle used in running. 

Observations established ground contact time, or the time available for each foot to generate this running force on the ground, to be inversely proportional to energy used by active muscle. Volume of active muscle was established to be proportional to body weight across a range of species and body sizes.

It became simple to describe metabolic rate of running. If Wb is body weight and ground contact time tc, the mass specific power can be established with a proportionality factor, c :

            EQ. 1

This spectacularly simple model explains 70-80% of the metabolic cost in both two legged and four legged vertebrates. 

A graph in that paper revealed the linear relationship of mass specific metabolic cost and ground contact time with speed. It showed the remarkable differences in running cost across a range of species of different sizes. Also shown is the largely speed independent co-efficient c, which is the ratio between mass specific metabolic cost and tc in EQ. 1. 

An important concept was the influence of body mass on energy cost mainly through rate of force transfer, or the reciprocal of ground contact time tc (1/tc).

If I were a rabbit escaping from a big dog straight out of hell, the rate of force generation I would need would be higher (greater 1/tc) than that of the dog because I need faster steps to cover the same ground (due to decreased step length), which involves lesser ground contact time, faster muscle firing and rapid rates of actin-myosin cross bridge cycling. 

Faster muscle firing means recruiting more energy intensive muscles. Conclusion : the metabolic rate expressed per kg of body weight would be higher for smaller animals than larger ones. This has been proven in animal locomotion research beyond any doubt.

Rate of force transfer, 1/tc, was shown to be a power function of running speed. But not on speed alone said a paper by Hoyt Those researchers displayed an intuitive plot of tc vs relative running speed, defined as running speed divided by leg length and explained that relative speed accounted for 97% of the variability in ground contact time tc. 

Running Economy and Ground Contact Time

Aerobic capacity, has been a subject of hot debate. Research found that athletes with similar maximal aerobic capacity values don't necessarily perform equally in distance running. Figure below shows two athletes with different running economies but similar VO2-dot-max values.

The opposite also seems to be true. Santos-Concejero showed that less efficient RE at velocity eliciting 10-km race pace in North African runners implies that their outstanding performance on the track at international athletic events appears not to be linked to running efficiency. It is possible that less efficient runners might be making up at world events by displaying greater VO2-dot-maxes.

The factors for describing running economy itself are complex. Investigating a few out of this bunch of variables give insight but leaving out the rest is problematic. This is why papers like that of Saunders make for good reading for a review of influencing factors of running economy.

Researchers have reported a 20-30% range in running economy among age, gender and performance matched groups of trained distance runners. Therefore, it was only natural that deeper interest would go into the structural characteristics of running motion to explain differences in metabolic demand and performance.

A paper by Weyand showed that in 36 healthy subjects, the rate of force transfer (inverse of ground contact time) was strongly related to maximal aerobic power across a range of steady speeds on a treadmill. 

Regression analysis showed 98.5% of the within-subject variation in mass specific maximal aerobic power was accounted for by 1/tc. 


Santos-Concejero, linked to earlier, also showed ground contact variables as having strongest correlations to the poor economy in North African runners vs European counterparts.

Similarly, Nummela showed that ground contact time was the only stride variable showing significant correlation with both running economy and maximal running speed in young well-trained endurance athletes, but wasn't sufficient by itself to explain running economy in the most economical runners.

Below is a graph showing the decrease in ground contact times (black dots) and aerial times (white dots) with increase in speed in Nummela's study.

Again, correlation is not causation. But short contact time, according to the Nummela paper, seemed logically beneficial for both running economy and maximal running speed since the critical point in maximal sprint running and economical running is the speed lost during the braking phase of a run.

Leg Spring Characteristics

A staple in engineering science, the mass spring elastic model came to fantastic help to analyze running motion. Several researchers have used the spring loaded inverted pendulum (SLIP) model (without damping) to accurately describe locomotion, whether that be trotting, hopping, or running, in a range of body sizes across 3 orders of magnitude. 

It turns out that whole-body center of-mass motion during running is similar to a pogo-stick (spring-mass) model where the leg can be represented effectively as a spring. So forget the complex neuromuscular stuff going on within the body. You can describe leg physiology quite nearly as the real thing with a linear spring model. 

A direct result of the linear spring is that the calculated work rate in the spring must equal the work rate in the center of mass.  If the leg cannot be assumed as a linear spring, this equivalence is flawed. 

The mass specific work rate of the leg spring, Pspring or mechanical power output, is established as reciprocal of leg spring stiffness multiplied by the product of the square of spring force (F), step frequency (f) and body mass M. 

In biomechanical research, there appears to be several calculation techniques to estimate leg spring stiffness. To derive each of these secondary factors would be pedantic, but one paper by Blum et. al nicely summed up the "difference in the math"  : 

The authors suggest that independent of low and high speed running regimes, method E is a simple and robust technique to estimate leg spring stiffness based on the spring model. In the low speed regime, a simpler calculation method such as A was found to suffice.

Another point of contention arises with the assumption in the SLIP model that the foot's point of the contact with the ground does not move. In reality, this is not true. When humans walk or run they tend to make initial ground contact with the heel or the middle part of the foot, and then to roll the foot forwards and lift off from the toe. This moves the point of contact. The SLIP model was modified with the point of force translation model (POFT) to portray this reality, first in this paper by Bullimore and associates. 

The difference in the two representations are shown below, showing how choice of methodology can affect the calculated value of leg spring stiffness :


L = initial leg length
ΔL = leg length variation (compression) during contact in the classical SLIP model
ΔL' = leg length variation (compression) during contact in the POFT model
Δy = vertical downward peak displacement of the center of mass during contact
tc = ground contact time
Fmax = peak ground reaction force
d = point of force translation distance
v = forward running velocity

One words of caution. Different calculation techniques to estimate the compression of the leg while deriving leg spring stiffness can influence overall findings, sometimes even misguide. 

Papers written in the early 90's like this were stating that leg spring stiffness was observed to be constant across forward running speeds. Later, some papers like this one stated that leg spring stiffness could change dramatically with different stride frequencies at the same speed although leg spring stiffness was constant across running speeds. Most of these papers were using a calculation method advanced by McMahon and Cheng

Arampatzis corrected that leg spring stiffness is influenced by running velocity and influenced by the increase in knee spring stiffness rather than ankle spring stiffness. They also stated that older methods such as those of McMahon and Cheng overestimated the change in leg length in the spring mass model causing leg spring stiffness to be constant across velocities.

There is a third spring analysis method, called the actuated SLIP model with actuation. This method assumes damping and actuation in the leg spring to represent the combined effects of both hip and ankle torque during locomotion. In contrast to the undamped linear spring model of classical SLIP, this method is a non-linear model of running mechanics :  

This extension of the SLIP model with active torque and damping is the simplest established model of legged locomotion that is capable of predicting the mechanical cost of transport. The reason is that by including damping in the leg, the analyst is able to account for the concept of stability in locomotive movement and isolate the non-zero energetic cost to ensure stable motion.

A unique and recent paper written by two mechanical engineers from Purdue, which used the SLIP model with actuation, suggests that when non-dimensionalized for body weight and resting leg length, an optimum "relative leg spring stiffness" was selected by a running organism. This optimum corresponded to the minimize cost of transportation to the organism.

Interestingly, Shen and Siepel found that with the SLIP actuation model, experimental values for leg stiffness in humans matched closely with the simulated relative leg stiffness corresponding to energy minima.

That there could be one, or very narrow range of operational values for leg stiffness, over a range of speeds and leg landing angles is very interesting.  This speed-independent biological preference for optimum leg stiffness also means that all animals prefer to stay somewhere in a narrow range of between 7 and 27 in relative leg stiffness. 

This is a new paper, therefore citations to the work are relatively low in number.  The concept of an energy minima limited leg stiffness makes complete sense and I'm glad that engineers, using analysis tools in dynamical control systems, are lending a multi-disciplinary hand to the whole running biomechanics investigation.  

I effectively stop here in reading papers. The total volume of research in running biomechanics span decades and it is useful not to read every one but establish general principles that research provides.

1) First, that 1/tc, which is the rate of force transfer, is an important running parameter, which explains 70-90% of the energy cost is bipedal organisms.

2) Several factors affect running economy but generally it's been found that ground contact variables, such as tc, have stronger correlations with running economy and maximal speeds.

3) Simplistic linear relationship cannot explain everything going into the energy cost of running. For example, rate of force transfer, is not just related to speed but also factors like leg length.

4) The spring mass model is remarkably powerful to understand running dynamics, inspite of the neuromuscular complexity in the leg. But using incorrect equations to calculate leg spring characteristics result in misguided conclusions about it's relationship with speed.

5)  Leg spring stiffness may or may not be trainable, although there is evidence that this parameter is a strong function of ground contact time.  New research provides evidence of an energy minima limited leg stiffness value when normalized by body weight and resting leg length. 

6) Research is in flux and what was believed 3 decades ago might not be true anymore. Interdisciplinary facets to investigations lend additional insight into the science of running, removing age old myths and misconceptions.

It is important that I get to my own mini-investigations of what ground contact time and leg spring stiffness mean to me as a runner, which will be the subject of part 2.

Friday, January 13, 2017

Cycling Jebal Jais : A Technical Review

Camera shot from behind courtesy G. Pinto.

As the new year unfolded a couple of weeks back, I gave up on alcohol and fireworks related injuries and give some love to the emirate of Ras al Khaimah. The goal was to ride the predominant Jebal Jais and catch a glimpse of the first sun of 2017.

Peaking at 1911m, it is the highest mountain in the country. The call of Jebal Jais is in a stretch of very well maintained mountain road leading to an altitude of 1280m, which makes it roughly 70% to the summit altitude. 

The paved road stops there, beyond which is unpaved territory mainly used by construction crews working to extend the paving by 4km. The actual peak of the mountain lies just across the border in Oman, thereby making the current official stop of the paving just a slope of this local giant. 

Mountain terrain of Ras al Khaimah

Where I typically start this climb from is a non-descript spot near the junction of Wadi Bih and Jebal Jais road at 25° 49' 16.69" N latitude and 56° 6' 46.32'' E longitude. When I arrived at 6:00am, the sky was in transformation, enough to faintly display the outline of the Hajar range around me. At quarter to 7, a friend showed up and we proceeded pedaling our bikes.

About 1.6km from the parking spot, appreciable changes in gradient start to take place. I indicate this spot on the topographic map below. From here it is 4% grade average to the top. 

Climb section of the route marked in purple

Regardless of where people consider the climb to start, I afford the mountain it's respect and count the initial stretches as part of the experience. The reason is that trying to keep a constant pace for the first 11km will elevate heart rate output as you gain around 530 ft in altitude. 

Spatial grade change is indicated below. Speed gradient of the ride follows, which shows that I try to keep a constant, but slower speed at the pronounced "knee" of the climb. The sea blue color indicates around 7.2-7.5 mph of average speed. During the descent, the neon green color indicates an average speed of 26 mph.

Gradient change along Jebal Jais road, courtesy Climbbybike.

Speed shading. Blue (climbing speed of 7.5mph ave) and green (descending speed of 25mph ave)

The amusing bit is how different elevational information services can differ in their estimates of the vertical climb. GPS is nice, but it is inaccurate by +/- something. On top of that, the different services apply their own juicing algorithms to give you wide ranging numbers. 

TopoFusion:      3690 ft
Straight GPS:      3697 ft
Maptech:      3110 ft
Strava/Garmin:    3692 ft

3D image of the route

The sun shone through at 7:05am. Whereas I thought that temperatures would dip to a comfortable 8-10 deg C on the slopes, it was around 5-6 degrees warmer. This made for an uncomfortable experience in arm warmers, which I would roll down at some point along the climb. At these temperatures, warm clothing is dangerous. 

First rays of the sun.
More climbing left.

The plot below shows skin temperature (light brown line) rising slowly but steadily from 37 degrees to around 40 degrees at the top. I'm not sure of the uncertainty in the measurement from the V800. Although I would not consider this as core temperatures, it gives an indication of how intensity steadily rises. It points to the challenge of maintaining a certain wattage input as your blood juggles the duty of powering muscles and cooling the core. 

Ride performance graph 1.

Will lighter wheels make a big difference while climbing? It depends.

The energetics of a rolling wheel involves a translational energy component as well as the effort to roll the wheels through it's rolling inertia, however torque to rotate a wheel is largely dependent on it's angular acceleration. Choice of lighter wheels are felt in quicker accelerations as opposed to slower accelerations.

As one sees below, for the my ascent, acceleration (blue) was limited to 0.1 and more or less steady through the effort. In stark contrast, the descent had higher accelerations (2 units at the maximum) as I navigated out of switchbacks and sharp turns.

Ride performance graph 2.

A simple comparison is below, where delta in power between heavier and lighter wheels is more pronounced in higher acceleration scenarios. In this example, a higher acceleration is moving from 10kph to 40 kph in 7 seconds as opposed to 10. 

Comparisons in the reduction of required power based on wheel rolling weight.

Most recreational cyclists climb and descend a hill at low accelerations. The wattage savings pale in comparison to the savings from shedding body weight. As a percentage of overall climbing wattage, the rolling resistance of the tires and the quality of road surface will equate to a larger proportion than less rolling inertia will.

But I also said it depends. A point here is that higher up in altitude one goes, the amount of power as a percentage of sea level power becomes lower due to the reduced partial pressure of oxygen to burn fuel.

At the current altitude of the Jebal Jais road climb, a non-acclimatized individual will, according to this model, see a net 16W drop from from sea level FTP of 250W as the physiological loss is greater than the gain in aerodynamic. An acclimitized individual will on the other hand only see a 9W drop.

This fact may support the idea of carrying less weight and rolling weight to higher altitudes. To performance oriented riders, the "every bit helps" bit makes sense to them when human power is altitude derated to begin with.

Net effect of altitude on cycling power.

My lonely figure descending down this breathtaking mountain. 

The goal on the descent is to keep the head up and brake before the turns using "pumping action" of the brakes. I've never ridden tubulars down this mountain and probably never will, given the hot temperatures and the unknown consequence of heat and glue dynamics. My suggestion is to ride clinchers if you are unsupported.

We liked coming back to the parking lot after 3 hours in the saddle. The morning was celebrated with some chilled coca-cola and the beauty of the mountains around us. A day well spent.

It is rumored that the 4km extension to the mountain climb will be completed this year and opened to the public. I look forward to the opportunity to experience the mountain in it's entirety. We'll have to wait and see how work progresses.