## Monday, December 4, 2017

### Physics of Rowing

Rowing is a pretty niche sport. For those who know nothing about it, it might seem pretty simple. However, there is a lot that goes into a stroke that is often never noticed. The physics of the entire system are a bit complicated so I will only go over the physics of the stroke itself.

When a rower takes a stroke there are two phases.

Phase one is the power phase, which is where the rower is actually taking the stroke. In this movement, a few things are happening. 1. The rower has their arms fully extended 2. Legs bent 3. Back leaning forward.

Phase two is the resting phase, which happens after the rower has finished taking the stroke, and is moving up to get back into position to take the next stroke. In this phase, the rower has to 1. Move their legs into position 2. Lean their back forward 3. Curl their arms and 4. Roll up the slide. "The slide" refers to track the seat goes up and down on. The seat in a boat has wheels, that are meant to add some resistance while going up the slide and make it easy to roll when one is taking the stroke.

A typical crew race is 2000 meters (a 2k). The world record for an olympic 2k in a men’s eight is 5:18.68 minutes, or 318.68 seconds.  In a men’s eight several weights have to accounted for: the rowers, the coxswain (the person who animates the rowers and also steers the boat), the hull (the boat itself), the speakers and other miscellaneous electronics, the rigors (they hold the oars), and the oars themselves. Olympic rowers typically will weigh around 180 lb (82 kg), meaning that in a men’s eight, the rowers total weight is about 719 kg. Vespoli (a rowing company) estimates that the weight of the hull, coxswain, electronics, rigors, and oars weigh about 899 kg. So a full boat with everything included weighs about 1618 kg.

The average speed of the world record holding boat during their race is (2000m/318.68s) 6.276 m/s. Stroke rate is the amount of strokes one takes per minute. During a race, the average stroke rate is about 40 strokes per minute. Meaning that in the world record, the crew took about

[(40 strokes/1 minute) * (1 minute/60 seconds) * 318.68s = 212.45 strokes

Meaning that each stroke made them travel an average distance of:

2000m/212.45 strokes = 9.41 m/stroke

If the boat were to accelerate to this velocity within the first stroke, then the acceleration when Vf= 6.276 m/s, Vo=0 m/s, ΔX=9.41 m would be a=.33 m/s^2. The amount of force that it takes to accelerate the boat to this speed then would be

F=ma= (1618 kg) (.33 m/s^2) = 533.94 N -- 66.7 N per rower.

If the power phase takes about .7s in a 3s stroke (20 strokes/minute) then the power phase when the stroke rate is 40 stroke/min is about .35s and the full stroke takes about 1.5s. That means that in the power phase, the boat travels 2.196 m, and during the resting phase, the boat travels 7.214m.

If the average rower is 6ft (1.83m), then the torso of the rower is about 3ft (.915m). So by leaning forward, bending their legs, and extending their arms, the rowers are increasing the amount of distance that they can move the oar by about (.915m/2.196 * 100) 42%.

It is often said that rowing is 70% legs, 20% back, and 10% arms. If the total amount of force needed is 66.7 N per rower, then the total work over the course of a 2,000 meter race is  (66.7 N)(2,000 m) = 133,400 J. That means that over the course of the world record 2k, the rower's legs did (133,400*.7)= 93,380 J, their back did 26,680 J, and their arms did 13,340 J.

The back of the rower moves about 20 degrees throughout the entire stroke, meaning that the force that the back puts on the oar is angular. If an average rower is about 1.83 m (or 6 feet), then that means that the radius of the movement is .915 m. If the back of the rower (in this case)  is doing a total of 17.34N, then the amount of torque on the rower's back is

T=(.915m)(17.34N)sin(20)=5.43 N*m.

This also means that if the rower is taller then the amount of torque the rower can exert on their back increases, thus increasing their contribution to the movement of the boat. Longer arms, also means that the amount of work done by their arm increases. By extension, one might think that if a rower is more flexible then the torque would increase and thus the boat should move faster, but when a rower moves too much on a boat (in particular their torso), the boat tends to fall to one side or another -- thus making it harder to move the oars to even catch the next stroke.

So yeah, thats pretty fun. This analysis of the stroke is also not including the buoyancy of the shell itself, the material the shell is made of, flexibility of the oars, flexibility of the boat, steering of the boat, surface tension of the water, wind, or the entering or exiting of the oars in the water.

Boy, those engineers sure are smart.

Here' s a video of some pretty good rowers at it.