Re: MRC COVID 19 Climbing Challenge. Ends June 14th!
Posted: Wed Jun 10, 2020 2:20 pm
My jaw dropped when I saw AJs result, it is now dislocated. Well done Pare!
I will update the results tonight.
I will update the results tonight.
https://minutemanroadclub.com/forum/
You can use conservation of energy to see how much energy went to friction. I would have expected to lose more than 3.4 feet worth of potential energy from friction. Plus you didn't include the Kinetic energy at the end of your attempt in the equation (or maybe you did and your post was already long enough haha)pace21 wrote: ↑Wed Jun 10, 2020 1:58 pm I love challenges. Especially when they combine 2 of my favorite things, bikes and physics! I chose Wilbur Wall in RI as the best option that I could ride to from my house, but after 3 attempts at said Wall I came away concluding that 2 false flats in the middle were providing a few precious seconds where I was putting energy into fighting speed (drag) rather than gravity, and gravity is the King Beast to tackle when vertical ascent is the only output we care about.
I took the data from the Wilbur attempts and went back to the maths. I calculated the total energy involved in the full 1 minute ascent by combining 2 terms: the first is the total mechanical energy that I (my body) injected into bike/rider system. That's a relatively straightforward calculation to make if you have a power meter -- just multiply your 1 minute avg Watts by 60 and that will give you the total "physiological" energy you delivered. In my case it was around 40kJ. In addition to that you can add in your kinetic energy, assuming you started the 1 minute effort with some entry speed. You can calculate that by 0.5*m*(v^2) where in this case "m" is the total mass in kilograms of both you and your bike, for me around 82kg. My entry speed into Wilbur Wall was around 23.5mph (10.5meters/sec) which results in a total kinetic energy around 4.5kJ. [interesting to note that a reasonably high entry speed still only accounts for ~10% of the 1 minute "physiological" energy -- humans are pretty good at creating lots of energy really quickly].
So that's all well and good, ~40kJ physiological and ~4.5kJ kinetic. Now what? Well, I know how far I climbed vertically -- 140 feet, or 139 according to some but knowing that the hill gradient wasn't ideal with the false flats I really wanted to know what that effort would have given me on a different hill. Since we know that the total amount of energy (physiological + kinetic) results in raising you vertically by a certain number of feet we can calculate the resulting potential energy of the bike/rider system, which is given by PE=mgh (mass in kg, gravity constant in m/sec^2, and height in meters). Setting those 2 energies equal we can calculate for different constant gradients (5%, 10%, 15%, etc) what the theoretical height number "h" is. At the limit we can simulate theoretically climbing a purely vertical wall from a standstill and get the theoretical height in that scenario. For me it was 159.4 feet. Of course you can't climb a vertical wall and anything less than vertical will detract from your total because of additional air resistance due to increased airspeed, but it's a start.
Armed with that knowledge I started searching for something steeper. Around about that time AJ posted his result, and looking at his hill I got jealous -- super steep and very constant gradient -- perfect! The rules state that we can't copy segments, but lo and behold AJ's hill had a close sibling running exactly parallel up roughly the same gradient. I'm there.
Got out to Arlington early this morning (yay lockdown) and gave it a go. Better result, in between my previous result of 140 (139) and my calculated theoretical max of 159.4 feet. Clocked in at 156 feet. Minus 5 plus 4 yields 155 feet.
https://www.strava.com/activities/35926 ... /1568/1628
Spot on Rees, although I lumped air resistance and rolling resistance into one bucket and essentially ignored it because the gravity term is so dominant. And yes to the final KE being real, although I think it's small. I entered at 23.5mph and finished at less than 5 or so. With the velocity being squared the end speed is even less of a factor.remad wrote: ↑Wed Jun 10, 2020 2:40 pmYou can use conservation of energy to see how much energy went to friction. I would have expected to lose more than 3.4 feet worth of potential energy from friction. Plus you didn't include the Kinetic energy at the end of your attempt in the equation (or maybe you did and your post was already long enough haha)pace21 wrote: ↑Wed Jun 10, 2020 1:58 pm I love challenges. Especially when they combine 2 of my favorite things, bikes and physics! I chose Wilbur Wall in RI as the best option that I could ride to from my house, but after 3 attempts at said Wall I came away concluding that 2 false flats in the middle were providing a few precious seconds where I was putting energy into fighting speed (drag) rather than gravity, and gravity is the King Beast to tackle when vertical ascent is the only output we care about.
I took the data from the Wilbur attempts and went back to the maths. I calculated the total energy involved in the full 1 minute ascent by combining 2 terms: the first is the total mechanical energy that I (my body) injected into bike/rider system. That's a relatively straightforward calculation to make if you have a power meter -- just multiply your 1 minute avg Watts by 60 and that will give you the total "physiological" energy you delivered. In my case it was around 40kJ. In addition to that you can add in your kinetic energy, assuming you started the 1 minute effort with some entry speed. You can calculate that by 0.5*m*(v^2) where in this case "m" is the total mass in kilograms of both you and your bike, for me around 82kg. My entry speed into Wilbur Wall was around 23.5mph (10.5meters/sec) which results in a total kinetic energy around 4.5kJ. [interesting to note that a reasonably high entry speed still only accounts for ~10% of the 1 minute "physiological" energy -- humans are pretty good at creating lots of energy really quickly].
So that's all well and good, ~40kJ physiological and ~4.5kJ kinetic. Now what? Well, I know how far I climbed vertically -- 140 feet, or 139 according to some but knowing that the hill gradient wasn't ideal with the false flats I really wanted to know what that effort would have given me on a different hill. Since we know that the total amount of energy (physiological + kinetic) results in raising you vertically by a certain number of feet we can calculate the resulting potential energy of the bike/rider system, which is given by PE=mgh (mass in kg, gravity constant in m/sec^2, and height in meters). Setting those 2 energies equal we can calculate for different constant gradients (5%, 10%, 15%, etc) what the theoretical height number "h" is. At the limit we can simulate theoretically climbing a purely vertical wall from a standstill and get the theoretical height in that scenario. For me it was 159.4 feet. Of course you can't climb a vertical wall and anything less than vertical will detract from your total because of additional air resistance due to increased airspeed, but it's a start.
Armed with that knowledge I started searching for something steeper. Around about that time AJ posted his result, and looking at his hill I got jealous -- super steep and very constant gradient -- perfect! The rules state that we can't copy segments, but lo and behold AJ's hill had a close sibling running exactly parallel up roughly the same gradient. I'm there.
Got out to Arlington early this morning (yay lockdown) and gave it a go. Better result, in between my previous result of 140 (139) and my calculated theoretical max of 159.4 feet. Clocked in at 156 feet. Minus 5 plus 4 yields 155 feet.
https://www.strava.com/activities/35926 ... /1568/1628
(Kinetic energy at the start) + (riders input "physiological") = (Kinetic energy at the end) + (Potential energy gained by the end) + (Losses due to friction)
It was interesting doing the pre-ride because with a hill that steep it's so hard to hold low power. There's a lower limit on functional cadence (50rpm? 40?) and even at that low cadence I was still doing 350+ watts. For the actual full gas attempt it was essentially the same torque (because same gradient) but at a much higher cadence (100rpm-ish). If you look close you can actually see in my cadence plot 2 distinct events -- at about 25 seconds in I switched from seated to standing and there was a momentary cadence hiccup. Then towards the end when crossing a road it leveled out slightly so my cadence went up to keep power output.djming wrote: ↑Wed Jun 10, 2020 2:32 pm So what was your gearing and cadence Chris?
And if speed upon entry "only" accounts for ~10% that still is a significant number (ya know, my FTP w/kg is only 10% lower than (some strong cat 1 guy))
I've held off on attempting one other hill that is steeper and more consistent as it's a slight uphill left turn entry. The only other approach is a flat but 90 degree right turn which is probably worse.
I think you're right, the lack of inclusion of air resistance in the calculations was offset by the fact that I didn't start from speed=0. The "theoretical max" would have been higher (probably by about 10% based on the ratio of the physiological to kinetic energy) so instead of 159.4 feet let's call it something like 175 feet (~10% higher than 159.4 feet), of which I attained 155, the difference of 20 probably due to friction/drag.remad wrote: ↑Wed Jun 10, 2020 2:40 pm
You can use conservation of energy to see how much energy went to friction. I would have expected to lose more than 3.4 feet worth of potential energy from friction. Plus you didn't include the Kinetic energy at the end of your attempt in the equation (or maybe you did and your post was already long enough haha)
Nevermind. I have decided that while as a crit fan I am willing to risk paralysis for some socks I'm leery of spending 3/4 of my two hours weekend riding time driving to Worcester in order to find out I suck now
There is actually a 3rd street on the same hill that AJ and Pare used in Arlington — School St. You could also try Pine Hill across from Walden Pond in Concord.peterkuhn wrote: ↑Thu Jun 11, 2020 11:51 amNevermind. I have decided that while as a crit fan I am willing to risk paralysis for some socks I'm leery of spending 3/4 of my two hours weekend riding time driving to Worcester in order to find out I suck now
Fixed for ya PJ (figured I'd take pity on you after the "Dad Legs" comment ). You actually got 148PJ McQuade wrote: ↑Sat Jun 13, 2020 4:15 pm https://www.strava.com/activities/3609874642/laps
Last minute entry. Gave it a shot up Uxbridge Road (south) in Sutton. Pretty good wall. Unfortunately the segment didn't register,so there's no segment showing but I did hit the lap button for 60 seconds and picked up 146 feet of elev. The link above is the my Strava lap page showing the attempt. Not sure if it will suffice.
146 ft - 5 ft/ Cat 3 penalty +4 35plus bonus = 145 feet.
Also - the Master's bonus is nice, but there should totally be a Dad legs bonus, 2 points for every child w/ extra points for kids under 5
+ 10ft for every sub-5 child. Dads who know, know.PJ McQuade wrote: ↑Sat Jun 13, 2020 4:15 pm
Also - the Master's bonus is nice, but there should totally be a Dad legs bonus, 2 points for every child w/ extra points for kids under 5