Simply put, power is related to time. How much work can be done in the lest amount of time. If I run for 45 min. my power output is low compared to throwing a baseball. Time to complete the task. Work is basically applying force over a distance. Like moving a barbell from the ground to hips (deadlift) or from ground to shoulders (clean).
In comparing a deadlift and clean we can directly compare the power output of two top level lifters. This comes from Pat O'Shea's book Quantum Fitness II page 92.
Kenady (deadlift)
140kg (body mass)
405kg (mass lifted)
.40m (distance)
2 sec. to execute
work=Force X Distance
For Kenady the work =1587.6
Power = Work/time to execute lift
Kenaday's power output was 793.8 watts
793.8 watts /140 kg = 5.67 watts/kg body mass
Pisarenko (clean):
120kg body mass
265kg mass lifted
.90m distance
.9 sec time to execute
Work for Pisarenko is 2337.3
power is 2597 watts
or 21.63 watts/kg body mass
Directly Kenady is putting out 5.67 watts/kg while Pisarenko is putting out 21.64 watts/kg
This is a massive difference. The biggest component to power output, again, is time. It takes Kenady 2 seconds while Pisarenko moves it further and in only .9 seconds!
Power can be seen in other ways too. "Cardiovasular power," like the 100m dash, or 50m freestyle swim. The 100m is 10 seconds or so and the 50yrd swim is 19 or so. Obviously the run is significantly higher output, the mass is moving further and faster!
Power can be trained by focusing on a couple different areas. Explosive lifts (olympic lifting), plyometrics or "shock training," and sprints. The key thing is, like strength training, intensity must exceed 80-85% of maximum "speed." This can only be done a couple times a week so dosing it is again key.
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