Note: This is part of my ongoing attack of ESPN's show Sport Science. Really, I am continuing to look at the episode where they calculate a football player can produce 57,000 Watts by pulling some stuff. Wait...I don't want to limit my stuff to Sport Science. I see this stuff all the time. The problem is that people confuse the force needed to move something with its weight.
So, you want me to pull something? Great, I am a physics guy. I could probably pull maybe 100 pounds. That seems reasonable? But wait! I will increase it to 500 pounds! That is like two huge football players. Pulled by me! No, I will crank it up. 1000 pounds! 3000 pounds! How about OVER 3500 POUNDS! I am going to try it. Here it is:
That is not a fake video. It is real. I pulled a Mazda 5 with some kids and a grown woman inside.
Now on to the real stuff. Yes, it is true. I did not exert a force of 3500 pounds. Here is a force diagram for the car.
So let me pretend like I want to pull the car at a constant speed. In this case, I would have to pull with a tension equal in magnitude to the frictional force - not equal to the weight of the car. Sure, often the frictional force is related to the weight. However, just because the weight is large this does not mean the frictional force is too large. What if I want to get it moving? In this case, I just need to pull a little harder than friction and the car will accelerate. Really, it is not that hard. Here is my 6 year-old daughter moving the car (she had trouble pulling it the whole 5-yards, so I won't use her for the calculations below). Also note: it looks like the driveway is at an incline - that is because of the camera. This is Louisiana, everything is pretty much flat.
Calculating the power - the wrong way
I still never figured out how Sport Science calculated a power of 57,000 Watts. My guess was that they assumed the force was the weight of the tires and the sled (which it wouldn't be). This still gave me a value that was too small. Anyway, I am going to calculate my power doing it the wrong way and see what I get. Here is what I am starting with:
- I pulled a Mazda 5 - weight of about 3500 lbs (11,000 Newtons)
- The distance the car was pulled was 5 yards (4.6 meters) - just like in the Sport Science
- The time it took me to go 5 yards was about 9 seconds.
Using my same calculations as before and the weight of the car as the force, I get:
I failed to get the 57,000 watts, but I am better than an elite bike sprinter (2000 watts).
The correct way
If I wanted to do this the correct way, I would need to measure the force I exert on the car (which is NOT the weight). I did not measure this, but I am sure my actual power is significantly less than 5000 watts.
Cycling is something where power output is pretty easy to measure, and people who are into performance based cycling are obsessive about different aspects of their power output (average, peak, how long they can sustain an above average output, etc.).
A world-class cyclist can produce over 1000 W in a sprint, that is for a short time period. Some track cyclists have cracked 2000 W for a few seconds, as you mentioned. Sustained output is usually more in the 300 - 400 W range. A fit amateur will usually be in the 200 - 250 W area.
My guess is that a pro-football player is somewhere between 400 and 1000 W when pulling the kind of stunts Sport Science has them do. Nothing to sneeze at when you consider a horsepower is 745 W.
I agree that the numbers from sport science are baloney, and liked the video of you and your daughter pulling the car.
If you're looking for maximum human power output for a short duration, I'm sure football players can crank out a lot more than cyclists: if you're considering short-duration output, it'll be limited more by muscle mass than by the aerobic system, and cyclists tend to be relatively low mass athletes.
From the split times of the fastest man on earth (http://speedendurance.com/2008/08/22/usain-bolt-100m-10-meter-splits-an…) and his ~85 kg mass I would estimate his peak power output is over 4 kW, merely from the rate at which he increases his kinetic energy (not counting inefficiencies in running).
If you're looking for "instantaneous power", my guess is that heavyweight olympic lifters (or football players pulling optimally loaded sleds) can put up even higher numbers.
Working on a dock we used to move ships weighing literal thousands of tons by having three or four of the guys climb out on the spring lines. Kind of neat to do it. You climb out and just hang. Letting your weight do all the work. Don't slip and fall in. At first, often for several minutes, nothing seems to happen. But then, very slowly, the ship starts inching toward you.
I wish I had a huge ship like that. It would make a great video.
Hah! I'm a semi-sedentary, small, 68 year old woman with a heart problem, and I can push a loaded car out of a snowbank. I can rock it back and forth until it climbs out of a deep rut in packed snow and ice. No strength needed, just a bit of planning and a little more persistence.
I have been looking for an excuse to try video analysis in Logger Pro, so I had a go at estimating your power output:
Thanks for the great videos and posts!