Eldron Posted February 7, 2019 Posted February 7, 2019 If they had the same velocity at the end, the heavy dude would simply have double the KE of the light dude (assuming 100kg vs 50kg) due to the difference in mass. KE = 1/2 MV^2 Even if they were the same weight, and one climbed faster than teh other, the other would need to descend faster than the one to get to the end at the same time. It's a simple case of calculating the required avg speed in order to complete the distance in the same time. Nothing to do with potential / kinetic energy. If they end at the same speed, at some point the gap between them is constant, and he will never catch the light guy. If the heavier rider never goes faster than the lighter rider, then he will never catch up on the descent. If they both reach max speed as soon as they start descending, heavy rider will STILL be behind the light rider by the same amount of time they were apart at the top of the hill. Right - let's start this over. We have a million riders - all different weights all doing the same speed in a row across the road as they cross a line. The get to a hill - they all climb the hill at the same power. Lightest is fastest to the top - heaviest is slowest to the top. They all go around a beacon and descend the same hill. Slowly but surely the heaviest rider catches the lightest rider and at the bottom they're all doing exactly the same speed in exactly the same line as they cross exactly the same line. All this depends on wind and rolling resistance being removed of course. Do you agree now?
Captain Fastbastard Mayhem Posted February 7, 2019 Posted February 7, 2019 Right - let's start this over. We have a million riders - all different weights all doing the same speed in a row across the road as they cross a line. The get to a hill - they all climb the hill at the same power. Lightest is fastest to the top - heaviest is slowest to the top. They all go around a beacon and descend the same hill. Slowly but surely the heaviest rider catches the lightest rider and at the bottom they're all doing exactly the same speed in exactly the same line as they cross exactly the same line. All this depends on wind and rolling resistance being removed of course. Do you agree now?No. Because the gap would still need to close. More potential energy doesn't mean they magically close the gap. It just means that for any given period, he has a higher Energy value due to the extra weight. Different KE / PE values also have no bearing on the time taken to complete a course. The Velocity does. If they're all doing the same speed in the same line, then the bigger rider would have had to catch up to the smaller rider - which means going faster than him. It's a simple distance over time calculation, nothing to do with kinetic energy or potential energy. If there was no wind resistance or friction, and they STARTED descending at the same time, then your assertion would be true. If they all had the same power to weight ratio, and climbed at the same speed, reaching the top of the hill and then starting the descent together, your assertion would be true. But as soon as you introduce a time / speed differential, the person who is behind needs to go faster than the person who is in front, in order to finish at the same time. A differential in potential energy at the top of the hill doesn't allow for that, neither does a difference in Kinetic Energy at the bottom. All it allows for is a difference in mass. If there's no resistance, and there's zero input (pedalling) anywhere down the hill (IE Equal power) then whoever started the descent first will finish first.
Jehosefat Posted February 7, 2019 Posted February 7, 2019 Right - let's start this over. We have a million riders - all different weights all doing the same speed in a row across the road as they cross a line. The get to a hill - they all climb the hill at the same power. Lightest is fastest to the top - heaviest is slowest to the top. They all go around a beacon and descend the same hill. Slowly but surely the heaviest rider catches the lightest rider and at the bottom they're all doing exactly the same speed in exactly the same line as they cross exactly the same line. All this depends on wind and rolling resistance being removed of course. Do you agree now? They can't be doing the same speed and crossing the line at the same time. It must be 1 or the other. The heavier riders will be slower on the way up the hill therefore in order for them to get back to the line at the same time they must be faster on the downhill.
Captain Fastbastard Mayhem Posted February 7, 2019 Posted February 7, 2019 They can't be doing the same speed and crossing the line at the same time. It must be 1 or the other. The heavier riders will be slower on the way up the hill therefore in order for them to get back to the line at the same time they must be faster on the downhill.Correct. And that has boggerall to do with KE / PE. It just has to do with average speed. It's being made more complicated than it needs to be, and thus confusing people.
DieselnDust Posted February 7, 2019 Posted February 7, 2019 Right - let's start this over. We have a million riders - all different weights all doing the same speed in a row across the road as they cross a line. The get to a hill - they all climb the hill at the same power.to weight ratio...(they can't do the same speed at the same power if their masses are different) P=f xv Lightest is fastest to the top - heaviest is slowest to the top. They all go around a beacon and descend the same hill. Slowly but surely the heaviest rider catches the lightest rider and at the bottom they're all doing exactly the same speed in exactly the same line as they cross exactly the same line. All this depends on wind and rolling resistance being removed of course. Do you agree now?
Jehosefat Posted February 7, 2019 Posted February 7, 2019 But Eldron's point was that they must climb at the same power, not power-to-weight. otherwise his next sentence is moot because if they all climb at the same power-to-weight then they would all reach the top at the same time, the lightest rider would not reach the top first and the heaviest would not be last.
Captain Fastbastard Mayhem Posted February 7, 2019 Posted February 7, 2019 Right - let's start this over. We have a million riders - all different weights all doing the same speed in a row across the road as they cross a line. The get to a hill - they all climb the hill at the same power. Lightest is fastest to the top - heaviest is slowest to the top. They all go around a beacon and descend the same hill. Slowly but surely the heaviest rider catches the lightest rider and at the bottom they're all doing exactly the same speed in exactly the same line as they cross exactly the same line. All this depends on wind and rolling resistance being removed of course. Do you agree now?Okay, let's switch this around. We have all the riders in a row, starting the climb. In order to get to the top, and due to the effect of GRAVITY on the heavier riders, they need to put out more power than the lighter riders in order to maintain power/weight parity and reach the top of the hill at the same time. Regardless of the time it takes to get to the top, the heavier riders will have more PE than the lighter riders, purely due to the extra weight. Then, there has to be no wind resistance and no friction and zero power input on the pedals, in order to reach the bottom of the hill at the same time and the same speed.
Jehosefat Posted February 7, 2019 Posted February 7, 2019 They all go around a beacon and descend the same hill. Slowly but surely the heaviest rider catches the lightest rider and at the bottom they're all doing exactly the same speed in exactly the same line as they cross exactly the same line. All this depends on wind and rolling resistance being removed of course. Do you agree now? The heaviest rider would only be faster on the downhill if we include the effects of air resistance. If we exclude it then all riders would travel down the hill in exactly the same time since their acceleration due to gravity would be the same all the way down.
Captain Fastbastard Mayhem Posted February 7, 2019 Posted February 7, 2019 But Eldron's point was that they must climb at the same power, not power-to-weight. otherwise his next sentence is moot because if they all climb at the same power-to-weight then they would all reach the top at the same time, the lightest rider would not reach the top first and the heaviest would not be last.Yes, but the fact is as you & I stated earlier. Unless the heavier rider goes fast enough down the hill to overcome the time differential he had at the top of the hill, there's no chance of them finishing at the same time and the same speed. This still has nothing to do with the differences in potential energy at the top of the hill, or the differences in kinetic energy at the bottom. If you asked "at what velocity would a 100kg person have the same kinetic energy as a 50kg person" the answer is simply at SQRT ((v^2)/2) where v is the velocity of the 50kg person.
Captain Fastbastard Mayhem Posted February 7, 2019 Posted February 7, 2019 The heaviest rider would only be faster on the downhill if we include the effects of air resistance. If we exclude it then all riders would travel down the hill in exactly the same time since their acceleration due to gravity would be the same all the way down.and... if there was a gap at the top, there'd be a gap at the bottom.
Captain Fastbastard Mayhem Posted February 7, 2019 Posted February 7, 2019 anyway. IMO bike weight is less important than rider weight. I say this, owning a bike that weighs more than 15kg and I would have a LOT of justification to do before I spent more on it to reduce the weight. Justifying ME losing weight, and the effect it'll have on my riding, is easy to do.
Eldron Posted February 7, 2019 Posted February 7, 2019 The heaviest rider would only be faster on the downhill if we include the effects of air resistance. If we exclude it then all riders would travel down the hill in exactly the same time since their acceleration due to gravity would be the same all the way down. Well screw me sideways with a 10 day old rusty nail - never do science posts on thehub when you're busy with something else. I've just had a fun delve into gravity, wind resistance, angular momentum and velocity. Sadly I cant find the article I based my model on but doing a combination of napkin calcs, scouring my memory - if wind resistance were linear then my proposed model would work. All riders use the same power to get up the hill but the heavier riders use that same power for longer so they've used more energy to get up the hill - that energy is then returned on the downhill and they end up same speed and same place because the wind resistance slows then down unequally. Have at it science boffs :-)
blondeonabike Posted February 7, 2019 Posted February 7, 2019 and then go riding with a 3L camelbak....I know some crazy okes that train for freedom with an old camelbak filled with sand. Around 8kg...And then go ride 100km with over 2000m climbing.
DieselnDust Posted February 7, 2019 Posted February 7, 2019 Well screw me sideways with a 10 day old rusty nail - never do science posts on thehub when you're busy with something else. I've just had a fun delve into gravity, wind resistance, angular momentum and velocity. Sadly I cant find the article I based my model on but doing a combination of napkin calcs, scouring my memory - if wind resistance were linear then my proposed model would work. All riders use the same power to get up the hill but the heavier riders use that same power for longer so they've used more energy to get up the hill - that energy is then returned on the downhill and they end up same speed and same place because the wind resistance slows then down unequally. Have at it science boffs :-) uuummmmm i'm confused. So we're not ignoring losses now? or are we?
NotSoBigBen Posted February 7, 2019 Posted February 7, 2019 uuummmmm i'm confused. So we're not ignoring losses now? or are we?Does anyone besides the two of you actually understand it or care? Okay maybe the Captain .... [emoji6]
DieselnDust Posted February 7, 2019 Posted February 7, 2019 Does anyone besides the two of you actually understand it or care? Okay maybe the Captain .... [emoji6] I hear crickets
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