Watts encompasses the components of torque.

Person who puts down more foot/lb for a given frequency has a higher energy expenditure (watts).

The 300W @60rpm vs 300W @90rpm, torque is higher, but they're pedaling slower, working out to the same energetic output.

WKO and GC give you QA plots which will show up your 60 v 90 rpm examples.

I don't think, for the same power, that different cadences produce different training stress or stress the body more/less.

No two people of the same mass can go the same speed at a 30% difference in watts.

But a 73 kg person at 220 watts will go the same speed as a 100 kg person at 300 watts depending on some course and weather variables.

Hence they have the same watts / kg.

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Technique will always last longer then energy production. Improve biomechanics, improve performance.
http://Www.anthonytoth.ca, triathletetoth@twitter

Watts are proportional to ft-lb/s. Imperial units, sue me.

Remember Physics class? Energy/work is a force moved a distance - pound-feet. Power is work per time - ft-lb/s. Watts are a unit of power, so we're doing work for some amount of time. ...and this is all people really want to know, normalized energy output to gauge fitness.

Unfortunately, torque is also a force acting at an eccentric distance - ft-lb. You can do the same work/power calculation in angular terms but we'll find that just because the units work out Power != Torque / time. Unfortunately, nobody tends to keep radians in units so to make the equation work we need to add an angle. Naturally you need the torque applied to the rear hub and angular rotation of the rear wheel which means you have to know the gear ratio to scale the rider input torque - so much effort in calculation and data input.
see the following link for more information on work in Cartesian and angular coordinates.
http://spiff.rit.edu/classes/phys211/lectures/rotke/rotke_all.html


so what is important, is decoupling the meaning of the measurement from how it is measured (in this case). Whether the power meter measures torque and converts or measures force and converts is completely irrelevant. Your power meter is saying: given conditions x, you output y Watts. In this, and all, cases, Watts need to be interpreted by the user for applicability. More simply, given the same setup - you on a bike connected to a machine, you could move xxx pounds, yyy feet, in zzz seconds. Whether you do that at 30 RPM and a huge force/torque input or 90 RPM and a smaller force/torque input (assuming constant time) the work performed and power output is [ignoring realism factors] identical. The same person, doing the same work, using different cadences (withing reason, ignoring realism factors) should be equally capable to perform additional work at a later time - identical stress score.


Of course, in your example things have been taken past the extreme - 30 RPM and 90 RPM. A lot of people don't ride at 30 RPM. If your question was more reasonable 80 vs. 90 or 90 vs. 100 would we expect an appreciable difference in TSS? Probably. But we'll notice the source of that difference is due to biomechanical adaption rather than the work being performed. Given a course, person, bike (all the forces which need to be overcome to complete a course of Distance - F*d) and a goal, say, 3600 seconds. There is a known amount of work that needs to be performed, which has a corresponding power output required. Of course, all those factors cannot be know and the competition has very different forces to overcome so that makes racing exciting.


Power meters use torque to calibrate because everyone can just about nail torque in the comfort of their home. Putting xx lbs on a 175mm crank creates a very accurate torque input which the internal sensors can use to establish a baseline, or an offset to a baseline.

You will have done 30rpm more for the same wattage at 90rpm compared to 60rpm.

Sit on your turbo, disconnect the chain and ride at 30 rpm for an hour - easy but it does burn energy.

There will be less force at 90rpm though but you can't ignore the effort required just to turn the pedals. The muscles used to lift the leg and move the feet round the stroke use energy even when they are not delivering power.

Heart rate will invariably be higher for the same power at higher cadence, a response to the increased oxygen use.

Same TSS though.

You've trotted that analogy out before. I ride the bike with the chain intact so I don't think your thought experiment is applicable. It certainly doesn't prove that training stress is greater at higher cadence given the same power outputs.

How much do you believe a cadence difference of 30 (60rpm to 90rpm) increases the training stress? 1%, 5%, 10%?

Do you deny it takes energy to turn the pedals at 30 times more often each minute?

A better example might be to compare 80rpm to 110rpm at say 200 watts over 20 minutes. Compare RPE and heart rate. Or you could go the whole hog and measure everything using a metabolic cart.

I'm not advocating deliberately choosing a lower cadence than is comfortable or self selected just pointing out that there is an extra energy cost to higher cadence which isn't shown in the watts output and because the watts are the same TSS will be the same.

https://www.physics.uoguelph.ca/.../Q.torque.intro.html

http://www.slowtwitch.com/..._Meter_101_3643.html

At the same wattage, lower rpm stresses your muscular system more, higher rpm stresses your cardio vascular system. Is this a big mystery / discussion point?

You're not taking into account CdA.

There is also the stress caused to ligaments, tendons and joints at high cadence, which is a different sort of stress to the stresses from high force.

I find that on a turbo, I assume it's due to the different inertia I can't generate and sustain the same wattage at my usual road cadence. I need to up the cadence. This higher cadence and no doubt the lack of the same amount of cooling as on the road, pushes my heart rate up, and I find I'm breathing more heavily indoors than outdoors.

For a 20 minute test I would be naturally selecting 85rpm to 90rpm outdoors but 100 to 110 on a turbo indoors. I'm still 30 watts down indoors though.

http://www.ncbi.nlm.nih.gov/pubmed/22648142

Although I don't see a cadence as low as 60rpm is practicable this study shows the effect of higher cadence on efficiency and economy.

http://www.researchgate.net/...ensity_cycling_trial

This study shows 80rpm more efficient than 100rpm.

Now look at the total energy costs.

100rpm 15.2 kcal.min / 19.1 kcal.min
80rpm. 14.3 kcal.min / 18.3 kcal.min

That is 5% less kcal.min for the same wattage - thus the same TSS.

When they did maximal tests at self selected cadence after 80 rpm power was higher at 362 watts compared to 327 watts after 100rpm.

Clear evidence that the training stress was greater at 100rpm than 80rpm.

Note that Heart Rate, VO2 and blood lactate were higher at 100rpm.

Heart rate reflected the increased oxygen consumption. TSS based on wattage would not track the increase in training stress.

So much for cadence being a red herring and heart rate being redundant when you know power.

Yes they can. Just because they have the same mass doesn't mean they are exactly the same size.
Some people have short legs and long body which has less drag than long legs short body.

jaretj

Score, I guess I can't be a model, but at least I can be a cyclist.

You still haven't shown that increasing cadence at the same power also increases training stress. Metabolic/energy costs yes, but training stress no.

If the metabolic energy cost is greater, heart rate, VO2 consumption and blood lactate is higher, then the physiological cost is higher and TSS is supposed to measure physiological cost.

Note how NP which is used to calculate TSS is an estimate of the power you could have maintained for the same physiological cost if the
Power had been constant.

Quoted from TrainingPeaks
"What is TSS?Training Stress Score (TSS) is a composite number that takes into account the duration and intensity of a workout to arrive at a single estimate of the overall training load and physiological stress created by that training session. It is conceptually modeled after the heart rate-based training impulse (TRIMP). By definition, one hour spent at Functional Threshold Power (FTP) is equal to 100 points.
Normalized Power (NP): An estimate of the power that you could have maintained for the same physiological "cost" if your power had been perfectly constant, such as on an ergometer, instead of variable power output. NP is used to calculate TSS."

Note how the subjects performed better in the Max test after 80 rpm, this rather proved the training stress at 100rpm was greater because it knackered them more.

A watt is 1J/sec so in this papers analysis the wattage cannot possibly be the same and since efficiency intra-individual won't change then for arguments sake Kcals/min at same would *should* be same. Statistically you may well see inter-individual differences in efficiency.

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David T-D
http://www.tilburydavis.com

Just re read it they were cycling at the same power but different rpm.

80 rpm was lower heart rate lower VO2 and lower blood lactate for the same power.


http://www.researchgate.net/...ensity_cycling_trial


From the results.

Effects of Cadence: During the 190 min exercise period at the higher power output, lactate concentrations were 18.8% greater at the 100 rpm cadence than those seen at the 80 rpm cadence (Table 2). Regardless of power output, heart rate (3-4%), VO2 (4%), and EE (4-6%) were higher at 100 vs. 80 rpm (Table 2). However, at both the low and high exercise intensities, gross efficiencies were 4-7% less at 100 vs. 80 rpm (Table 1.). Glucose concentrations, RER and RPE were not altered by cadence (Table 2).

From the abstract.

" The total energy cost while cycling during the 65% and 80% VO2max intervals at 100 rpm (15.2 ± 2.7 and 19.1 ± 2.5 kcal&#8729;min-1, respectively) were higher than at 80 rpm (14.3 ± 2.7 and 18.3± 2.2 kcal&#8729;min-1, respectively) (p < 0.05). Gross efficiency was higher at 80 rpm vs. 100 rpm during both the 65% (22.8 ± 1.0 vs. 21.3 ± 4.5%) and the 80% (23.1 vs. 22.1 ± 0.9%) exercise intensities (P< 0.05). "

I didn't show the -1 after the kcal.min.

Interesting paper whilst it's findings are interesting a few things stand out to me at first pass...

1) Low number of subjects, all of similar age and VO2max
2) Visit 1 protocol..... 40w jumps every 3mins is a huge increase relative to their watts at Vt..... and would certainly influence validity of Pmax findings
3) By testing effort at 80% of VO2max and not % of watts at Vt the W' or anaerobic capacity of each individual (which would have been different) would confound the findings relating to the ensuing max power.

We will only find out a true basis of optimal cadence when a study is done across a wide breadth of subjects (talent-wise), statistics are done firstly looking at intra-subject changes then the pattern of changes across all subjects. Plus a protocol that normalises against critical power and accounts for W' and draws its conclusions by additional biopsies of relevant active muscles to assess mitochrondrial density and fibre type patterns.

And IMHO this will no doubt lead us to conclude that every individual chooses their own optimal cadence based on a variety of factors....

http://forum.slowtwitch.com/...post=5439094#5439094

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David T-D
http://www.tilburydavis.com

,

The subjects cycled at the same wattage at 80rpm as 100rpm.

Energy expenditure, heart rate and blood lactate were higher at 100rpm than 80rpm.

I don't see how you can say the wattage isn't the same. Are we talking at cross purposes?

The total energy cost while cycling during the 65% and 80% VO2max intervals at 100 rpm (15.2 ± 2.7 and 19.1 ± 2.5 kcal&#8729;min-1, respectively) were higher than at 80 rpm (14.3 ± 2.7 and 18.3± 2.2 kcal&#8729;min-1, respectively) (p < 0.05). Gross efficiency was higher at 80 rpm vs. 100 rpm during both the 65% (22.8 ± 1.0 vs. 21.3 ± 4.5%) and the 80% (23.1 vs. 22.1 ± 0.9%) exercise intensities (P< 0.05).

Doesn't mean anything. You want to go fast, not minimize energy expenditure.

Quite possibly. That being said my view is I would be wary of drawing many conclusions from the paper for the reasons I mention above.

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David T-D
http://www.tilburydavis.com

Speed is a function of the rate of energy supply and rate of energy demand. It's not a function of torque.

Our power output tells us the rate of energy supply, but the energy demand factors can vary considerably between different people, even those with the same power output.

They include changes in vertical height/working with or against gravity (which increases with mass), changes in kinetic energy when we accelerate/decelerate (also function of mass and rate of speed change), air resistance (which increases with relative air speed and an individual's aerodynamic properties), rolling resistance of the tyres on the road (varies with speed and the properties of the tyre and road), and some frictional forces in the drive train of the bicycle and wheel bearings.

On flatter terrain the biggest variable is a rider's aerodynamics. e.g. I have a mate who, when we are both fit, weighs the same as me, is the same height and uses similar equipment, and we both have same power output. But his aerodynamic drag coefficient is ~25% less than mine (to do with his body shape vs mine). That means for the same power he gets a LOT more speed than I do.

Same power achieved with higher torque and lower crank rotational velocity does not imply greater stress. The forces involved are still very low, and significantly sub-maximal. It's the power output relative to your capabilities that's the primary determinant of stress.

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http://www.cyclecoach.com
http://www.aerocoach.com.au

these studies showing higher cardio vascular stress on higher rpm is because that is all can measure.... but we are not measuring CNS responses - and on that I dont think there is anything that does.