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Road Cycling “It is by riding a bicycle that you learn the contours of a country best, since you have to sweat up the hills and coast down them. Thus you remember them as they actually are, while in a motor car only a high hill impresses you, and you have no such accurate remembrance of country you have driven through as you gain by riding a bicycle.” -- Ernest Hemingway

5% grade for 1 mile - whats your approach?

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Old 12-09-12, 09:57 AM
  #126  
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Originally Posted by RChung
Possibly one of these?
https://www.ncbi.nlm.nih.gov/pubmed/9268969
https://www.ncbi.nlm.nih.gov/pubmed/11083127
https://www.ncbi.nlm.nih.gov/pubmed/17497402

The bottom line: only when conditions are constant is constant power time-minimizing.
Yes those for my first point, and also something similar to this https://www.move.vu.nl/wp-content/upl...obFos_1999.pdf for the second point (even under constant conditions).
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Old 12-09-12, 06:04 PM
  #127  
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Originally Posted by Brian Ratliff
Here's another example.

1 mile hill, the first half at 8% and the second at 3%. Say the first half is done at 10mph and the second at 15mph under constant power. This gives you 3 minutes for the first half and 2 minutes for the second half for a total time of 5 minutes. If you increase power by 10% on the first half and decrease it by 10% in the second half, you get 2.73 minutes for the first half and 2.22 minutes for the second half for a total time of 4.95 minutes. Not a huge decrease, but in general, it shows it is always better to push on sections where you are going slower and recover on sections where you are going faster.
I agree. However let me put some of my numbers to that example and see what actually happens.

The maximum average power I have recorded in the last year for 5 minutes is 380 watts. That was done under a steady effort in pefect conditions when I was well rested, had eaten well and everything was perfect. It resulted in me unclipping at the end and collapsing over my handlebars, it was a massive effort that I can only do if everything is perfect and I ride as smooth as possible.

Another fact is that the highest power I have ever held for 2.5 minutes is 420 watts, I was utterly shot to bits after this effort, that small extra 40 watts creates significant extra fatigue. Again, to do this everything needs to be perfect

Your suggestion of riding with 10% extra power for the first half of the 5 minute effort (420 watts if the target average is my best 380) would result in me blowing up massively at half way. The suggestion that its ok because I can then recover at 10% less power than my target average (in this case 340 watts) is simply impossible, Id be lucky to stay on the bike and be able to keep it over 100 watts for the next minute or so. I would have blown completely.

Similarly going to more of an extreme lets add 20% for the first half, thats around 460 watts and would see me blow completely in less than 2 minutes, the idea that I can finish the 5 minute segment at 300 watts is crazy - thats my threshold power and theres no way im going to hit that after 2 mins at 460 watts!

This is my point, I know the maths works but the reality is different becasue the relationship between power output and time isnt linear, thats why its plotted on a log scale on the MMP curve. And to add to that, everyone will be different. My power profile slopes up to the right, if yours slopes up to the left maybe you would see different results as you are stronger over the shorter intervals.

I could proportion my effort as you say, but to do it I would need to lower my average power by probably 50 watts or so, and in the case in question, that would give a slower time than the small gains would cover

Last edited by lazerzxr; 12-09-12 at 06:46 PM.
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Old 12-09-12, 06:56 PM
  #128  
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Man, this 5 minute hill is taking a freaking long time.
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Old 12-09-12, 06:56 PM
  #129  
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Originally Posted by wphamilton
Yes those for my first point, and also something similar to this https://www.move.vu.nl/wp-content/upl...obFos_1999.pdf for the second point (even under constant conditions).
Quote from link:
The fastest time on the 4000 m pursuit was achieved with an 'all-out' start
at a high level of initial power output, followed by a constant anaerobic power output
after 12 seconds,

sounds right, a rolling start with a fixed gear track bike needs a massive initial output to get speed up as quick as possible, then after 12 seconds of going nuts at it to get up to speed, level off to a constant power for the rest of the effort. A very specific example that doesnt apply here as you can roll in to the segment already up to speed if you like.

although I did post earlier that a peak power at the start and a sprint finish would be beneficial, the bit in the middle is constant.
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Old 12-09-12, 07:01 PM
  #130  
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personally, i would ride my bike up it by pedal'in
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Old 12-09-12, 07:42 PM
  #131  
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Originally Posted by lazerzxr
Quote from link:
The fastest time on the 4000 m pursuit was achieved with an 'all-out' start
at a high level of initial power output, followed by a constant anaerobic power output
after 12 seconds,

sounds right, a rolling start with a fixed gear track bike needs a massive initial output to get speed up as quick as possible, then after 12 seconds of going nuts at it to get up to speed, level off to a constant power for the rest of the effort. A very specific example that doesnt apply here as you can roll in to the segment already up to speed if you like.

although I did post earlier that a peak power at the start and a sprint finish would be beneficial, the bit in the middle is constant.
It is one example, but your interpretation is suspect. There is no indication that the improved performance is due to simply accelerating more quickly - in fact there isn't that much gain in time. But assuming you're right about that for the sake of argument, it would follow that a series of accelerations, just like the initial one would be more effective than the same power expended in a steady effort.
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Old 12-09-12, 07:57 PM
  #132  
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Originally Posted by lazerzxr
A very specific example that doesnt apply here as you can roll in to the segment already up to speed if you like.
Let's face it, there are no examples or scientific studies that will exactly replicate the hill under question. The idea of scientific study is to understand the underlying physics and physiology and apply it to a variety of situations.

Now you are accepting that uniform power is not optimum for some short 4 min TTs but not all. Incidentally, the reason you go all out at the beginning of a short TT is exactly the same as going harder on steeper sections of a hill.
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Old 12-09-12, 08:51 PM
  #133  
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Originally Posted by gregf83
Let's face it, there are no examples or scientific studies that will exactly replicate the hill under question. The idea of scientific study is to understand the underlying physics and physiology and apply it to a variety of situations.

Now you are accepting that uniform power is not optimum for some short 4 min TTs but not all. Incidentally, the reason you go all out at the beginning of a short TT is exactly the same as going harder on steeper sections of a hill.
The track TT example is hopeless, they are on single speed track bikes, extremely high geared, and the only way to get them moving is to put out huge watts. Getting moving takes enormous power, even a leasurely start from a set of lights will routinely exceed 300 watts for a few seconds even for an untrained cyclist due to the large resistance to overcome - in fact its difficult not to hit 300 watts ( I'm sure greg knows this with his reported 2 powermeters ). I mentioned earlier in post 101 paragraph 3 that constant power wont work if your target power is insufficient to turn the pedals. If they could roll over the start line already up to speed you can bet your life they wouldn't dump huge watts to start with, they would simply target a slightly higher average wattage and aim to blow up right before the line.

Another example. I can avarage 600 watts for 1 minute absolutely maxxed out. if the first half of the minute was up hill and the second half downhill, does that mean I should just pump out 1200 watts for 30 seconds and then freewheel to the line. NO it does not. Yes I can produce 1200 watts, but i'll blow big time after 5 seconds. You cant just proportion power like that, we are people, not machines. (let me just be clear that due to the downhill in this example I dont advocate constant power either) Large efforts are like shorting out a battery, they do more damage than the energy released suggests.

Last edited by lazerzxr; 12-09-12 at 09:04 PM.
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Old 12-09-12, 09:34 PM
  #134  
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Originally Posted by lazerzxr
I agree. However let me put some of my numbers to that example and see what actually happens.

The maximum average power I have recorded in the last year for 5 minutes is 380 watts. That was done under a steady effort in pefect conditions when I was well rested, had eaten well and everything was perfect. It resulted in me unclipping at the end and collapsing over my handlebars, it was a massive effort that I can only do if everything is perfect and I ride as smooth as possible.

Another fact is that the highest power I have ever held for 2.5 minutes is 420 watts, I was utterly shot to bits after this effort, that small extra 40 watts creates significant extra fatigue. Again, to do this everything needs to be perfect

Your suggestion of riding with 10% extra power for the first half of the 5 minute effort (420 watts if the target average is my best 380) would result in me blowing up massively at half way. The suggestion that its ok because I can then recover at 10% less power than my target average (in this case 340 watts) is simply impossible, Id be lucky to stay on the bike and be able to keep it over 100 watts for the next minute or so. I would have blown completely.

Similarly going to more of an extreme lets add 20% for the first half, thats around 460 watts and would see me blow completely in less than 2 minutes, the idea that I can finish the 5 minute segment at 300 watts is crazy - thats my threshold power and theres no way im going to hit that after 2 mins at 460 watts!

This is my point, I know the maths works but the reality is different becasue the relationship between power output and time isnt linear, thats why its plotted on a log scale on the MMP curve. And to add to that, everyone will be different. My power profile slopes up to the right, if yours slopes up to the left maybe you would see different results as you are stronger over the shorter intervals.

I could proportion my effort as you say, but to do it I would need to lower my average power by probably 50 watts or so, and in the case in question, that would give a slower time than the small gains would cover
So do the math at 5% or 2.5%. The numbers for time saved differ, but the trend remains the same. Your power band is very narrow, for instance; 10% over pushes you almost completely into anaerobic. My power band, for instance, is broader; I might manage 440W for a couple minutes and finish at 360 for the next three. Everyone is different, and of course, if you push yourself too deeply into anaerobic, you might screw yourself, but the trend of faster times with harder efforts on slower sections holds.
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Old 12-09-12, 10:07 PM
  #135  
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Originally Posted by lazerzxr
The track TT example is hopeless, they are on single speed track bikes, extremely high geared, and the only way to get them moving is to put out huge watts. Getting moving takes enormous power, even a leasurely start from a set of lights will routinely exceed 300 watts for a few seconds even for an untrained cyclist due to the large resistance to overcome - in fact its difficult not to hit 300 watts ( I'm sure greg knows this with his reported 2 powermeters ). I mentioned earlier in post 101 paragraph 3 that constant power wont work if your target power is insufficient to turn the pedals. If they could roll over the start line already up to speed you can bet your life they wouldn't dump huge watts to start with, they would simply target a slightly higher average wattage and aim to blow up right before the line.

Another example. I can avarage 600 watts for 1 minute absolutely maxxed out. if the first half of the minute was up hill and the second half downhill, does that mean I should just pump out 1200 watts for 30 seconds and then freewheel to the line. NO it does not. Yes I can produce 1200 watts, but i'll blow big time after 5 seconds. You cant just proportion power like that, we are people, not machines. (let me just be clear that due to the downhill in this example I dont advocate constant power either) Large efforts are like shorting out a battery, they do more damage than the energy released suggests.
Just because you are in a large gear doesn't mean you need huge power to get it moving. The reason why you hit the start hard is because you are going slow and you are trying to get up to speed as fast as possible. Which, of course, is the same reason why you put your hardest efforts on the slowest sections of a time trial course. If you've ever done a track pursuit or kilo time trial effort, you'll know that the start takes a huge amount out of you and seriously impairs your ability to finish strong. Many a track time trial has been messed up by a start done too hard. As always, there is a fine line between our max efforts and your ability to recover. You'll have faster times if you put more power into the slow sections of the course, but you have to balance those efforts with your ability to recover.

FWIW, I've had a little success in the kilo with a huge start (maybe 1200W), floating on the pedals at speed for a half lap or so to recover from the start, and then picking up the power to the finish.
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Old 12-09-12, 10:16 PM
  #136  
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There is a Strava segment climb almost exactly like this one where I live - 1.14 miles, 4.9% with as constant a grade as you'll ever see in the real world. I've done it over 50 times and I've actually gotten my best times on it by using the 39t ring and concentrating on keeping a reasonably high and very smooth cadence, starting in 39 x 19 and shifting up from there in the final minute or thereabouts. I've done it in the big ring a lot, too, but I'm a spinner and not a masher (and prefer to negative-split my efforts), so it's all about getting that sweet spot rhythm where the cadence is constant and there's just enough pressure to the pedals to avoid a "just spinning the wheels" feeling (which can actually be simultaneously slower and even more fatiguing under some circumstances). Plus I recover much faster doing it this way, and this particular road false flats for almost 2 miles after the main climb, so it's essential to avoid getting way in the hurt box for very long to keep a decent overall ride speed.

If I just wanted to hit a segment like that as a stand-alone, with no concern for keeping a decent speed after it, I might gear up even more in the last 30 seconds or so and stand & crank it. But it would still be a constant cadence early with a harder finish. On a completely even grade, I don't like shifting up and down and up and down in the middle and early parts of the hill unless somebody blows by me and I want to try to latch on. I'll definitely alternate shifting up and standing with shifting down and spinning during the early and middle portions of long climbs with uneven grades, since standing with a good rocking rhythm is sometimes more comfortable and helps maintain focus, but the idea is still to keep out of real trouble early, just barely touching the red zone if I have to during a steep pitch, but only enough that it's possible to recover extremely quickly with spinning on the easier grade.

That's just how I do it. People have different climbing techniques that suit their physical characteristics and their temperaments. If the gradient is that constant on the whole hill, try repeats at goal speed on the first quarter mile of it (coast down between reps) and tinker about with different gears and climbing styles.
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Old 12-10-12, 12:47 AM
  #137  
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Originally Posted by lazerzxr
The track TT example is hopeless, they are on single speed track bikes, extremely high geared, and the only way to get them moving is to put out huge watts. Getting moving takes enormous power, even a leasurely start from a set of lights will routinely exceed 300 watts for a few seconds even for an untrained cyclist due to the large resistance to overcome - in fact its difficult not to hit 300 watts ( I'm sure greg knows this with his reported 2 powermeters ). I mentioned earlier in post 101 paragraph 3 that constant power wont work if your target power is insufficient to turn the pedals.
None of what you said here makes sense. The power required to get moving has nothing to do with the gearing. They don't need to start a 4k pursuit at 1200W. They could just as easily start at their target power and keep it constant which is exactly what you've been advocating. They would be slower but it is perfectly feasible to do it on a fixed or geared bike. The gearing makes no difference in this example.

Keep digging...
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Old 12-10-12, 10:30 AM
  #138  
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Originally Posted by rdtompki
nothing gets you from point A to point B faster than a friendly competition.

Angry bear > friendly competition
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Old 12-10-12, 02:00 PM
  #139  
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Would weight have any correlation to power output?
What I mean is in terms of speed - a larger rider would need lots of power to move a heavier weight and the lighter rider would not necessarily need the same amount of power because he's propelling less weight, hence maybe less power but same speed.

I'm just a curious noob. Great discussions though, I'm definitely learning alot.
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Old 12-10-12, 02:49 PM
  #140  
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Originally Posted by ianGP
Would weight have any correlation to power output?
What I mean is in terms of speed - a larger rider would need lots of power to move a heavier weight and the lighter rider would not necessarily need the same amount of power because he's propelling less weight, hence maybe less power but same speed.

I'm just a curious noob. Great discussions though, I'm definitely learning alot.
going uphill weight matters, the deciding element for speed on inclines is W/kg or power-to-weight ratio. on flats aerodynamics are the principle opposing force and W/CdA is the deciding factor for speed. CdA is a factor that determines how aero someone is (has to do with surface area and streamline) so on the flats size / weight doesn't matter nearly as much because CdA doesn't vary much if at all wether you are 85 kg or 75 kg. so on flats absolute watts is more important and on hills w/kg is more important. Hence good time trial riders are generally larger bulkier riders than climbers.
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Old 12-10-12, 04:29 PM
  #141  
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Originally Posted by ianGP
Would weight have any correlation to power output?
What I mean is in terms of speed - a larger rider would need lots of power to move a heavier weight and the lighter rider would not necessarily need the same amount of power because he's propelling less weight, hence maybe less power but same speed.

I'm just a curious noob. Great discussions though, I'm definitely learning alot.
You are touching on an important point here. I know you can pedal a large gear from standstill with low power and accellerate slowly but again the practicalities often mean this doesnt happen. If i have a large gear i dont sit there at 10rpm and turn it slowly, thats knee breaking. I would stand and turn it slowly if thats what i wanted to do. In this case a heavy rider with all that resistance just putting their weight on the pedals will produce a lot more power than a light rider.

Greg im not being funny but im not the one digging, you came on here saying that the theory is clear - you should aim to maintain contstant speed on a segment. You said that, it is utterly wrong - no one else has argued that is the way to go. Followed by telling us you had 2 power meters. From every single ting you have written about power, I dont believe for a second you have ever seen your power output or have any idea what your power does during a ride. And if the theory that mainaining constant speed is correct as you suggest then what on earth did you spend 5k on powermeters for when a 10 dollar speedo would do the job? Answer.....you didnt.
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Old 12-10-12, 04:49 PM
  #142  
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Originally Posted by Brian Ratliff
So do the math at 5% or 2.5%. The numbers for time saved differ, but the trend remains the same. Your power band is very narrow, for instance; 10% over pushes you almost completely into anaerobic. My power band, for instance, is broader; I might manage 440W for a couple minutes and finish at 360 for the next three. Everyone is different, and of course, if you push yourself too deeply into anaerobic, you might screw yourself, but the trend of faster times with harder efforts on slower sections holds.

I accept your numbers Brian, and its nice to talk to someone with experience rather than the theory people here. However the practicalities of doing what you say are not that easy. 2.5% for example is less than the standard deviation of my output anyway and only marginally more than the accuracy of the powermeter. If im going that hard, im going to struggle to be that accurate, we're talking about roughly 8 watts on my local 10 minute climb.

On that climb the switchbacks ramp up steep for 10 seconds or so before the grade continues as normal, doing everything I can to maintain constant power will see me rise by more than 8 watts anyway, probably 20 watts. By the time i have reacted to bring it down again the steeper section is over.

for those non powermeter users here, it is very difficult to maintain constant power, impossible in fact, you simply target constant power but you will never achieve it. You achieve it as a trend of constant power over the time in question but at any given point your actual output will be maybe +-15 watts or so. If the grade changes your power will rise and fall until you correct it, that takes practice. In a sense the numbers rarely indicate you should work harder as the grade goes up, they normally indicate you should slow down, if the grade goes up and you dont react, your power will climb naturally over your target by as much as 100 watts without you even realising (until its too late)

I could try varying the output by 5% Brian but I think that would lower the average overall. You are right I do have a narrow powerband, I am working on it.

My point to all of this is that the KOM guys graph does not show a rider on his limit. And if you tell someone without a powermeter to work harder on the steep sections, the chances ae they will well over cook it. If you tell them to maintain constant output, they will probably put out more power when it gets steep without even knowing.
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Old 12-10-12, 06:29 PM
  #143  
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Originally Posted by lazerzxr
Greg im not being funny but im not the one digging, you came on here saying that the theory is clear - you should aim to maintain contstant speed on a segment. You said that, it is utterly wrong - no one else has argued that is the way to go. Followed by telling us you had 2 power meters. From every single ting you have written about power, I dont believe for a second you have ever seen your power output or have any idea what your power does during a ride. And if the theory that mainaining constant speed is correct as you suggest then what on earth did you spend 5k on powermeters for when a 10 dollar speedo would do the job? Answer.....you didnt.
Hmmm. Here's a simple example for you. Assume a 1 km long hill, first 500 meters 5%, last 500 meters 6%. Let's say the rider and bike total 80 kg, rho=1.2, Crr=.005, and CdA=.3. Compare two trials:

1. Constant speed at 20 km/h. The hill is 1 km long so that should take 1/20th of an hour, or 3 minutes. Calculate average power over the entire hill. Call that W*.

2. Constant power at W*. Calculate total time for the hill. Is it greater than or less than 3 minutes?
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Old 12-10-12, 06:51 PM
  #144  
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Originally Posted by lazerzxr
Greg im not being funny but im not the one digging, you came on here saying that the theory is clear - you should aim to maintain contstant speed on a segment. You said that, it is utterly wrong - no one else has argued that is the way to go.
What I said consistently is that you should push harder on the steeper sections and ease a little on flatter sections. This is well supported by anyone who has studied it and has the net effect of bringing your speed closer to the average for any particular segment. Obviously the speed won't end up being constant but it will have less variation.

I suspect part of the problem may be that you have a very flat power profile. You said your 5min power was 10% less than your 2.5m power. My 2.5 min power is 25% higher than 5min so perhaps I have a bit more headroom for hard efforts.

I don't normally go for KOMs. My biggest power numbers generally come during group rides when I can attack a hill without worrying about blowing up. Here is my best power for a little over 3min. It is a hill with an initial steep section that I stand up on and once I'm over the steep bit I sit and push as hard as I can. When I'm doing this hill I'm trying to get to the top first so I go hard initially to make sure no ones on my wheel. I suppose I could try doing a 3min effort at 425W but I don't think I'd make it unless I had someone on my wheel. I need the motivation as these efforts hurt
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Old 12-10-12, 06:53 PM
  #145  
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Originally Posted by gregf83
I suspect part of the problem may be that you have a very flat power profile.
Perhaps. But I suspect the other part of the problem has nothing to do with his power profile.
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Old 12-10-12, 08:26 PM
  #146  
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Originally Posted by RChung
Hmmm. Here's a simple example for you. Assume a 1 km long hill, first 500 meters 5%, last 500 meters 6%. Let's say the rider and bike total 80 kg, rho=1.2, Crr=.005, and CdA=.3. Compare two trials:

1. Constant speed at 20 km/h. The hill is 1 km long so that should take 1/20th of an hour, or 3 minutes. Calculate average power over the entire hill. Call that W*.

2. Constant power at W*. Calculate total time for the hill. Is it greater than or less than 3 minutes?
I dont care becasue if I rode that the average power for the segment would be different in both examples with the constant power average being higher resulting in a faster time.

I am pleased to see that you are starting to accept that maths is only par of the story and that an individuals output chartachteristics are different and will effect the result significantly. If I produced a graph as Greg just posted I guarantee that id be able to go back, smooth out the output and probably level off at a constant 440 watts ish (if id produced those numbers). My output is clearly different from his which is my point.

All the studies and maths i have seen assume that between one method of pacing and another the average power remains constant, even now you are posting examples which assume this. I have found however through riding my local hills literally hundreds of times that if I employ peaky tactics that have sustained periods of higher and lower affort, the average power changes significantly. By deliberately smoothing out my effort I have taken minutes off all my local hills by bringing the average power up to a maximum.

I have stated all along you can forget this approach if downhills are present, changing head/tail wind standinng starts and any time you run out of gear ratios but on a steady or wobbly grade, provided it remains up hill, constant power for me will trump any other method by a long way. Maybe its just a charachteristic of my output or maybe others would find the same if they tried.

At the same time I have spent the last 6 months improving my sprint so maybe I will start to see trends change, who knows. Im not saying i cant ride like you say, but i'll lose overall time if I do. Its more fun, and if your racing, you have to ride like this, but if a stava time is what im after, constant power will get it for me
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Old 12-10-12, 08:29 PM
  #147  
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Originally Posted by gregf83
The principle is the same. It's better to attempt to maintain constant speed than constant power.
since you spent ages going on about sections with uphill and dowhill elements I have no idea why you post this
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Old 12-10-12, 08:53 PM
  #148  
RChung
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Originally Posted by lazerzxr
I dont care becasue if I rode that the average power for the segment would be different in both examples with the constant power average being higher resulting in a faster time.

I am pleased to see that you are starting to accept that maths is only par of the story and that an individuals output chartachteristics are different and will effect the result significantly. If I produced a graph as Greg just posted I guarantee that id be able to go back, smooth out the output and probably level off at a constant 440 watts ish (if id produced those numbers). My output is clearly different from his which is my point.

All the studies and maths i have seen assume that between one method of pacing and another the average power remains constant, even now you are posting examples which assume this. I have found however through riding my local hills literally hundreds of times that if I employ peaky tactics that have sustained periods of higher and lower affort, the average power changes significantly. By deliberately smoothing out my effort I have taken minutes off all my local hills by bringing the average power up to a maximum.

I have stated all along you can forget this approach if downhills are present, changing head/tail wind standinng starts and any time you run out of gear ratios but on a steady or wobbly grade, provided it remains up hill, constant power for me will trump any other method by a long way. Maybe its just a charachteristic of my output or maybe others would find the same if they tried.

At the same time I have spent the last 6 months improving my sprint so maybe I will start to see trends change, who knows. Im not saying i cant ride like you say, but i'll lose overall time if I do. Its more fun, and if your racing, you have to ride like this, but if a stava time is what im after, constant power will get it for me
I don't really have a comment to make on this. I'm just responding so I'll have a marker on your post. It makes it easier to find whenever I want to come back and laugh at it.
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Old 12-10-12, 09:09 PM
  #149  
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Originally Posted by lazerzxr
I dont care becasue if I rode that the average power for the segment would be different in both examples with the constant power average being higher resulting in a faster time.
...
You've said this a couple of times, that your maximal steady power will necessarily drop if you peak and recover. I've disregarded it because in expressing my first opinion I said "if your legs and lungs can handle it", which I thought fairly covered that particular situation. I find the opposite, that peaking above and recovering near the threshold increases the amount of overall power. In his example, the first trial wins.

I don't claim to be an expert climber but I have nothing but hills here and I ride a lot of miles, about average for this forum. An unavoidable but mercifully short 5 degree hill every time I hit the road. You probably owe some apologies for the remark implying that those of us expressing theories have no experience ...
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