CrossFit Performance rest day.  I thought this post from Jon Gilson was relevant with comparisons being made of big numbers being lifted by our athletes this week.

Enjoy a magnificient Sunday
I didn’t care too much about my weight.

Until Sunday.

That afternoon, I got an applied lesson in power-to-weight ratios. Rock climbing.

We often refer to the weight we lift in relation to our bodyweight. 1 x bodyweight bench press. 1 x bodyweight clean. 2 x bodyweight deadlift. When we do this, we’re implicitly refering to a power-to-weight ratio.

You’ll recall that power is a measure of work done per unit time. The equation for work is displayed below. Don’t worry about the math–we’re after conceptual understanding here. If you’d like to see this calculation in action, check out “A Physics Lesson”, posted earlier this month.

Work = Force (Newtons) * Displacement (Meters) * Cosine of Theta (Angle between F and D)

Power is simply Work divided by Time.

When we have two athletes performing the same lift, in the same amount of time, using the same range of motion, we can say that they have done the same amount of work and exhibited the same amount of power. A problem arises when we attempt to rank these athletes. How do we determine which one is the better athlete?

We’ve determined that both athletes have the same power output. Neither is explicitly more powerful than the other. Still, we must take the athlete into consideration.

If our athletes have different bodyweights, one has performed the lift with greater efficiency than the other. The lighter athlete produced the same amount of power with a smaller frame. This athlete has a higher power-to-weight ratio than his/her competitor, and is therefore the stronger athlete.

In rock climbing, athletes strive to have a high power-to-weight ratio. The want to be extremely light, yet possess enough strength to haul themselves up a rock wall as fast as possible. In this scenario, the weight is no longer an external object. It is the athlete himself.

Therefore, the athlete benefits from low bodyweight. The less he/she weighs, the less work he or she has to do to get up the rock.

Let’s take two hypothetical athletes, both climbing the same 50m cliff. Athlete A weighs 170 pounds (77.27 kilos), and Athlete B weighs 130 pounds (59.09 kilos).

Athlete A (work) = 77.27 kgs (9.8 m/s/s) * 50m * Cosine 0
= 757.25 N * 50m * 1
= 37852.5 N/m

Athlete B (work) = 59.09 kgs (9.8 m/s/s) * 50m * Cosine 0
= 570.08 N * 50m * 1
= 28504.00 N/m

Athlete B has to perform less work to climb the rock. Now, let’s examine power output. We’ll assume that each athlete climbs the rock in 15 minutes (900 seconds).

Athlete A (power) = 37852.5 N/m / 900 seconds
= 42.06 watts

Athlete B (power) = 28504.0 N/m / 900 seconds
= 31.67 watts

Athlete B has to produce less absolute power to scale the rock. However, if we examine power output per kilogram of bodyweight, the numbers tell a different story.

Athlete A (power/weight) = 42.06 watts / 77.27 kgs
= 0.54 watts/kg

Athlete B (power/weight) = 31.67 watts / 59.09 kgs
= 0.54 watts/kg

These athletes have an equivalent power-to-weight ratio, even though Athlete B is significantly smaller than Athlete A.

Light bodyweight confers an advantage: less work and less absolute power output is needed to exhibit the same power-to-weight ratio as a heavier athlete.

The advantage only holds if we assume that the two athletes climb the rock in the same amount of time. If Athlete A climbs in 12 minutes, and Athlete B climbs in 15, we get the following:

Athlete A (power/weight) = 0.68 watts/kg
Athlete B (power/weight) = 0.54 watts/kg

In the rock climbing scenario, the highest power-to-weight ratio belongs to the athlete who scales the rock the fastest, regardless of bodyweight. As in weightlifting, the power-to-weight ratio is a good way to rank different-sized athletes.

In the case of rock climbing, it is indicative of time. A higher power-to-weight ratio indicates a faster time up the wall. In weightlifting, it is indicative of moving a lot of weight with a small frame. Time is not a huge factor, because it won’t vary much between athletes on any given rep.

Hopefully, this post will give you a new appreciation for smaller trainees. Next time you see someone move less weight than you, remember that their power-to-weight ratio may be significantly better than yours.

When you see a light rock climber fly up a wall in half your time, remember that they just produced a higher power-to-weight ratio than you.

Absolute strength is important, but it is not necessarily the correct way to rank athletes. Make sure you take factors such as time, bodyweight, and overall power output into consideration. One variable may not be adequate to benchmark athletic ability.