Drag still has an exponential relationship to speed. The power needed to push your body through a medium such as air increases with the cube of velocity. The power required to go from 6 min mile to 5 minute mile increase exponentially and not linearly.
There's a legitimate question in here somewhere. Traveling at a faster constant velocity on a level track should not take any more energy from a purely physical standpoint. If our legs were wheels (i.e. your bicycle analogy) the energetic difference between 5 min pace and 6 min pace is only the difference in wind resistance (which is slight at running speeds.)
The energetic costs of running from a purely mechanical standpoint have to do with the specific costs around propulsion with legs. One way to think about "the most efficient form" would be to have a leg motion that is most similar to a wheel. It's because running is a series of leaps that require force that the energy costs increase as velocity increases according to the power equation someone talked about earlier in the thread: P = F * v.
If you break it down really simply, moving yourself forward at a constant speed required constant input of energy, almost all of which goes towards starting and stopping the legs every cycle. It's obvious once you think about it: With each step, your foot needs to reach zero velocity (in contact with the ground) and accelerate to more than double your running speed to get to the front. Just standing there and swinging your leg faster is harder than swinging it slower, largely the same thing when you're running.
There's another can of worms in regard to stride length and how much of that distance is covered in the air vs/ in ground contact, but that probably goes beyond the scope of this discussion.
I would like to know more about this from a biomechanical standpoint. You are right that the foot must be accelerated, but there is a lot of elasticity in the leg that conserves the energy put into each foot strike to create and preserve this motion.
You are correct that it takes a lot of energy to swing your leg around in the air without striking the ground -- a lot more, actually, than it does while running (try swinging your leg around for an hour in the air!) But when running, much of that energy is conserved and recovered in the muscle and tendon elasticity. Perhaps a simple analogy is a pendulum, which is constantly accelerating but in ideal conditions will swing forever. Our legs when running work much more like this, allowing us to use most of the force that we put into the ground towards the small "leap" of running.
(Also, in physics, it's always sketchy to talk of a "zero velocity" point without determining your frame of reference. While the foot is in contact with the ground, it is definitely moving quickly in relation to the runner. I think you get a much clearer picture of the biomechanics of the legs if you set the "zero" of the foot velocity at the runner center of mass as the feet move around that point, not around the road.)
If you break it down really simply, moving yourself forward at a constant speed required constant input of energy, almost all of which goes towards starting and stopping the legs every cycle. It's obvious once you think about it: With each step, your foot needs to reach zero velocity (in contact with the ground) and accelerate to more than double your running speed to get to the front. Just standing there and swinging your leg faster is harder than swinging it slower, largely the same thing when you're running.
There's another can of worms in regard to stride length and how much of that distance is covered in the air vs/ in ground contact, but that probably goes beyond the scope of this discussion.
I would like to know more about this from a biomechanical standpoint. You are right that the foot must be accelerated, but there is a lot of elasticity in the leg that conserves the energy put into each foot strike to create and preserve this motion.
You are correct that it takes a lot of energy to swing your leg around in the air without striking the ground -- a lot more, actually, than it does while running (try swinging your leg around for an hour in the air!) But when running, much of that energy is conserved and recovered in the muscle and tendon elasticity. Perhaps a simple analogy is a pendulum, which is constantly accelerating but in ideal conditions will swing forever. Our legs when running work much more like this, allowing us to use most of the force that we put into the ground towards the small "leap" of running.
(Also, in physics, it's always sketchy to talk of a "zero velocity" point without determining your frame of reference. While the foot is in contact with the ground, it is definitely moving quickly in relation to the runner. I think you get a much clearer picture of the biomechanics of the legs if you set the "zero" of the foot velocity at the runner center of mass as the feet move around that point, not around the road.)
You are starting to touch on it here but I feel like you guys are discounting the enormous amount of energy needed to combat vertical forces…gravity. Most everything can be explained using Newton’s three laws.
Taking a runner at full speed is a good way to explain things.
If you use an elite sprinter as an example horizontal forces are large out of the blocks and drive phase. At max velocity horizontal forces are at near zero while vertical forces remain constant from start to finish. The non elite sprinter tires from the verticals forces sooner than an elite sprinter and reaches that low horizontal force value sooner in the race.
From Ralph Mann’s book:
An elite sprinter’s ground contact time at max velocity is around .087. The amount of vertical force needed while traveling at 1 meter per second can be shown as:
Vertical force = 77.5*(1.0)/.087 = 890 Newtons (200) pounds
Assume the elite sprinter weighs 170 lbs or 760 Newtons.
The sprinter has to stop downward velocity and produce upward velocity. Each ground contact would be:
Total Vertical Force = 890+760 = 1650 Newtons (370 Pounds)
You are right that a runner utilizes the force put into the ground as part of this which is explained with Newtons Laws.
This is why I have such an issue with the carbon shoes. Just because it does not have a motor does not mean it is not using artificial energy. In this case elastic energy. So few people are willing or capable of understanding it at that level so it gets a pass.
If you break it down really simply, moving yourself forward at a constant speed required constant input of energy, almost all of which goes towards starting and stopping the legs every cycle. It's obvious once you think about it: With each step, your foot needs to reach zero velocity (in contact with the ground) and accelerate to more than double your running speed to get to the front. Just standing there and swinging your leg faster is harder than swinging it slower, largely the same thing when you're running.
There's another can of worms in regard to stride length and how much of that distance is covered in the air vs/ in ground contact, but that probably goes beyond the scope of this discussion.
I would like to know more about this from a biomechanical standpoint. You are right that the foot must be accelerated, but there is a lot of elasticity in the leg that conserves the energy put into each foot strike to create and preserve this motion.
You are correct that it takes a lot of energy to swing your leg around in the air without striking the ground -- a lot more, actually, than it does while running (try swinging your leg around for an hour in the air!) But when running, much of that energy is conserved and recovered in the muscle and tendon elasticity. Perhaps a simple analogy is a pendulum, which is constantly accelerating but in ideal conditions will swing forever. Our legs when running work much more like this, allowing us to use most of the force that we put into the ground towards the small "leap" of running.
(Also, in physics, it's always sketchy to talk of a "zero velocity" point without determining your frame of reference. While the foot is in contact with the ground, it is definitely moving quickly in relation to the runner. I think you get a much clearer picture of the biomechanics of the legs if you set the "zero" of the foot velocity at the runner center of mass as the feet move around that point, not around the road.)
You are correct that some energy is conserved and recovered from tissue elasticity in a running stride, but not anywhere near 100%. Even if you recover half of the energy, you still have half that you're putting out as effort, and therefore need more energy output to go faster. Even if you recover 99% of the energy, it's still going to be harder to go faster due to the remaining 1% input.
I'm inclined to believe that the majority of the 'energy return' from tissue and/or supershoes primarily applies to vertical movement. The force vector from ground to foot begins pointing up and back (as anyone who heel strikes can feel) and eventually pointing up and forward. I have to think that competent runners have intuitively optimized the energy return balance between upward motion, forward motion, and leg swing motion based on practice and feel.
(You are also correct about the specific frame of reference, but for the purposes of an running forum I just winged it. Probably the easiest frame for analysis is the runner's COG, but for illustrative purposes I think the ground may be better)
You can’t think of minuets as linear. A 10 min mile to a 9 min mile is a 10% decrease. But a 6 min mile to a 5 min mile is closer to 18%. As minuets smaller the percentage of each miner gets bigger. That’s why it is much easier to go from a 30 minuet 5k down to a 27, then a 20 minute to an 17 minute. Same time difference but the percentage increase goes way up.
Ah, so that’s how percentages work! But what does that have to do with dancing?
Why is running at 5 min/mile pace so much harder than 6 min/mile? Do we just run that much less efficiently as we speed up? Biking at 12 mph vs 10 mph isn't that much more difficult. What's the scientific explanation?
"As an object approaches the speed of light, the object's mass becomes infinite and so does the energy required to move it."
5-minute mile is closer to the speed of light than 6-minute mile.
Drag still has an exponential relationship to speed. The power needed to push your body through a medium such as air increases with the cube of velocity. The power required to go from 6 min mile to 5 minute mile increase exponentially and not linearly.
P = 1/2 pv^3 CdA
hence not exponential according to your own definition
I'll just add one more interesting thing from a physical standpoint is that the total energy required to run a certain distance is (mostly) independent of the speed that you run that distance. It takes the same amount of energy for a runner to run 8 miles at 8:00 pace as it does to run 8 miles at 6:00 pace. The only difference is the rate at which energy is expended (the power.)
Source? I've heard this before but haven't seen data to confirm.
I'll just add one more interesting thing from a physical standpoint is that the total energy required to run a certain distance is (mostly) independent of the speed that you run that distance. It takes the same amount of energy for a runner to run 8 miles at 8:00 pace as it does to run 8 miles at 6:00 pace. The only difference is the rate at which energy is expended (the power.)
Source? I've heard this before but haven't seen data to confirm.
W = F * d
d = v*t
W = F*(v*t) <-- as v increases, t decreases proportionally (v*t is a constant = to the distance.)
The amount of energy would be different if the amount of force into the ground changed with velocity. The force of the foot plant is more of a function of the runner's weight as the purpose of the force is to propel the body upwards. I think this is what otter was talking about.
Here's an article that talks about how modeling the leg as a massless spring working as a pendulum actually proves to predict most of the things about foot strike, stride length, etc. In this model, the force of each foot strike is *only* dependent on the weight of the runner.
Full disclosure, I am not a scientist or bioengineer or anything like that. Just a physics teacher. I'm sure there are folks on this board with a lot more knowledge of this.
For those of you who don't know, Dr. Kram is truly a subject area expert on running economy and the energetics of running. Also, I noticed that US Olympian Shalaya Kipp is the lead author on this paper.
I'll just add one more interesting thing from a physical standpoint is that the total energy required to run a certain distance is (mostly) independent of the speed that you run that distance. It takes the same amount of energy for a runner to run 8 miles at 8:00 pace as it does to run 8 miles at 6:00 pace. The only difference is the rate at which energy is expended (the power.)
Source? I've heard this before but haven't seen data to confirm.
I would like to know more about this from a biomechanical standpoint. You are right that the foot must be accelerated, but there is a lot of elasticity in the leg that conserves the energy put into each foot strike to create and preserve this motion.
You are correct that it takes a lot of energy to swing your leg around in the air without striking the ground -- a lot more, actually, than it does while running (try swinging your leg around for an hour in the air!) But when running, much of that energy is conserved and recovered in the muscle and tendon elasticity. Perhaps a simple analogy is a pendulum, which is constantly accelerating but in ideal conditions will swing forever. Our legs when running work much more like this, allowing us to use most of the force that we put into the ground towards the small "leap" of running.
(Also, in physics, it's always sketchy to talk of a "zero velocity" point without determining your frame of reference. While the foot is in contact with the ground, it is definitely moving quickly in relation to the runner. I think you get a much clearer picture of the biomechanics of the legs if you set the "zero" of the foot velocity at the runner center of mass as the feet move around that point, not around the road.)
Yes, this is the factor that makes runners more or less efficient, and why forefoot fad was prone to failure. The most efficient 'usually' have minimal vertical oscillation (at hip), but high backlift, long air time and short contact.
The pendulum is being helped by energy return from contact, via tendon elasticity etc....same as a kangaroo uses their tail. The original energy input still has to come from the runner, no one else. So the shoe argument , instead of looking at 'the shoe enables the pendulum to swing', it is simply that the shoe - vs say a sponge sole- 'loses less' of your own energy input.
I have no problem with 'super' shoes, there is no external force applied.
I would like to know more about this from a biomechanical standpoint. You are right that the foot must be accelerated, but there is a lot of elasticity in the leg that conserves the energy put into each foot strike to create and preserve this motion.
You are correct that it takes a lot of energy to swing your leg around in the air without striking the ground -- a lot more, actually, than it does while running (try swinging your leg around for an hour in the air!) But when running, much of that energy is conserved and recovered in the muscle and tendon elasticity. Perhaps a simple analogy is a pendulum, which is constantly accelerating but in ideal conditions will swing forever. Our legs when running work much more like this, allowing us to use most of the force that we put into the ground towards the small "leap" of running.
(Also, in physics, it's always sketchy to talk of a "zero velocity" point without determining your frame of reference. While the foot is in contact with the ground, it is definitely moving quickly in relation to the runner. I think you get a much clearer picture of the biomechanics of the legs if you set the "zero" of the foot velocity at the runner center of mass as the feet move around that point, not around the road.)
Yes, this is the factor that makes runners more or less efficient, and why forefoot fad was prone to failure. The most efficient 'usually' have minimal vertical oscillation (at hip), but high backlift, long air time and short contact.
The pendulum is being helped by energy return from contact, via tendon elasticity etc....same as a kangaroo uses their tail. The original energy input still has to come from the runner, no one else. So the shoe argument , instead of looking at 'the shoe enables the pendulum to swing', it is simply that the shoe - vs say a sponge sole- 'loses less' of your own energy input.
I have no problem with 'super' shoes, there is no external force applied.
The plate in then shoe bends as the athlete applies weight in the regular cycle of running (basically landing due to gravity and not force applied by the athlete) but resists and then retains its original shape on takeoff providing elastic energy NOT produced by the athlete. This happens roughly 180 times per minute while racing.
I allow my athletes to wear the shoes otherwise they will not be able to compete with those that are, but I stop short comparing their times to past athletes that did not have the same benefits.
There’s a maximum amount of oxygen uptake. There’s a limited number of mitochondria for energy production. There’s limited amount of hemoglobin to carry that oxygen. There’s a maximum amount of blood your heat can pump. There’s a maximum force your muscles can apply with each stride. There’s increased lactate production as you increase speed, which inhibits muscle contraction. The list goes on and on… …
Yes, this is the factor that makes runners more or less efficient, and why forefoot fad was prone to failure. The most efficient 'usually' have minimal vertical oscillation (at hip), but high backlift, long air time and short contact.
The pendulum is being helped by energy return from contact, via tendon elasticity etc....same as a kangaroo uses their tail. The original energy input still has to come from the runner, no one else. So the shoe argument , instead of looking at 'the shoe enables the pendulum to swing', it is simply that the shoe - vs say a sponge sole- 'loses less' of your own energy input.
I have no problem with 'super' shoes, there is no external force applied.
The plate in then shoe bends as the athlete applies weight in the regular cycle of running (basically landing due to gravity and not force applied by the athlete) but resists and then retains its original shape on takeoff providing elastic energy NOT produced by the athlete. This happens roughly 180 times per minute while racing.
I allow my athletes to wear the shoes otherwise they will not be able to compete with those that are, but I stop short comparing their times to past athletes that did not have the same benefits.
I hate the shoes, but we are stuck with them.
This is no different, but more efficient than, the flexing of your tendons etc.
I joked at school physics above, but simply energy is not 'created' but simply converted. The gravitational force you refer to comes from what? The potential energy at the highest point of the cycle is due to 'you' the runner lifting your feet back up. The fact is that you may require less energy as opposed to not wearing the shoes to do that because you are returning more of that gravitational potential energy back to kinetic energy.
I see it as no more of an advancement than that over softer shoes. In fact 'old' runners have always known that the dunlop volleys, or the stiff squash playing shoes I had in my first marathon were 'faster' but with too much shock resulting in damage and pain. We moved to waffle, then combined to cushioning and control for the masses. The new shoes are returning energy in the best way possible, with the least shock transfer.
To add to the analogy at its extremes, when you stand at the start line , idly, those shoes do what? Absolutely zero. It will not 'lift' your foot up, start the pendulum, until you lift it up, bring it down and get that pendulum swinging, and keep feeding energy in to replace that which is lost. The less you lose the better.
Drag still has an exponential relationship to speed. The power needed to push your body through a medium such as air increases with the cube of velocity. The power required to go from 6 min mile to 5 minute mile increase exponentially and not linearly.
P = 1/2 pv^3 CdA
How can drag have an exponential relationship to speed while being proportional to the cube of the speed?
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