The physics of rowing

The Physics of Crew

This is a non calculus based review for students entering AP Physics this spring. Complete the worksheet and turn it in to room 25. Answers will be posted in class.

Setting the stage

Imagine a long and narrow row boat. A row boat designed for rowers and a coxswain. In unison they pull all eight oars forward, each just inches above the water. Suddenly the oars twist and drop into the icy waters. As the crew pulls the oars backwards through the waters the boat lunges forward. The crew members are seated on a sliding seats. The seats slide forward as the crew members pull backwards on the oars. At the end of the stroke, all oars lift several inches out of the water, blades are feathered. The blades start swinging forwards. Incredibly as the oars swing forward the boat seems to lift up in the water and gains even more speed. As quickly as it sped up the boat slows down as it coasts. Then once again, in unison the oars twist and drop into the icy waters. The process repeats, stroke after stroke, over a 2,000 meter long course.

Questions of Speed

For the purposes of this worksheet we will be looking at Olympic caliber men's and women's racing over 2,000 meter courses. At the Atlanta Olympics, the men's heavyweight time was 5 minutes and 37 seconds. That for the women's heavyweight crew was 6 minutes and 16 seconds. Assuming that each crew travels at a roughly constant speed, fill out the table below.

Notice that while the men's speed is greater than that of the women's, it is only greater by about 11 percent. We will be making comparisons between the two races as we proceed.

Questions of Drag

As any experienced crew member will tell, a racing boat will rapidly decelerate the minute the crew stops rowing. This is because at racing speeds almost all of the crew's energy is used to overcome the forces of drag that work against the boat. It turns out that the force of drag is proportional to the square of the speed of the boat.

In the equation above, force "F" is measured in Newtons and velocity "v" in meters per second. The constant "k" is similar to the coefficient of friction for sliding objects. It is determined by many factors including boat length and shape, water temperature, salinity, etc. For a racing eight, "k" is about 19.02 kg/m. Find the average force of drag experienced by each crew.

Notice that while the men's speed is only about 11 percent greater than that of the women's, this increased speed was at the expense of over a 24% increase in drag.

Questions of Power

Power is the measurement of the rate that energy is converted from one form to another. It is measured in Joules per second or Watts. There are two simple equations for the measurement of power.

And for situations where velocity is constant

In this second equation force is the needed force to maintain speed against the effects of wind resistance, viscous drag, wave drag, and other forms of drag. For crew, this force is overwhelmingly due to viscous drag of the water against the hull of the boat. Remember that the force of drag is given by a constant times velocity squared.

Let us return to the two racing crews and calculate the total power each must produce.

Note that while the men are traveling at only 11 percent greater speed they must produce over 40 percent more power to do so. Since there are 8 persons at the oars, each person only has to produce one eighth the total power. How much power is needed per person?

In the English system of measurements we are used to measuring power in terms of horsepower. One horsepower is equal to 746 Watts. How many horsepower must the average crew members produce over the course of the race?

Questions of momentum

The question arises, how does the boat get its speed. The answer lies in the law of conservation of momentum. Remember that momentum is what Newton called the quantity of an object's motion and it was equal to the product of its mass and its velocity.

The law of conservation of momentum states that in a closed system, the total momentum in a system before an event must equal the total momentum in the system after the event.

Before = After

Consider a boat at rest in calm water before the oars of the boat are pulled backwards. The total momentum of the system is zero. After pulling on the oars the boat is moving forward. This is because a portion of the water surrounding the boat is now moving backwards. Notice that the size of the oar blades has an effect on how much water will move and consequently, how fast the boat will now move. Larger blades will move more water. They do not have to move as fast as smaller oar blades to give the boat the same increase in speed.

The question arises, is it better to have larger blades or smaller blades? Or, does it matter at all? To answer this question we will consider the situation where a 900 kg boat (mass includes crew) gains a speed of 1.1 m/sec after the first stroke. Assume we have two sets of oars, a big bladed set of eight oars which are capable of grabbing a total of 330 kg of water and a small bladed set of eight which are capable of grabbing a total of only 165 kg of water. Find the speed of the water in each case after the stroke.

It makes sense that the smaller oars will be moving at twice the velocity of the larger oars because they move only half of the quantity of water. It also is reasonable that the water in each case must be moving backwards at a speed much greater than the boat's speed forward because the boat has much more mass. But momentum is only a portion of the question. Power is related to energy output. Which set of oars will give you the gain in boat speed using the least amount of energy? To find this let us look at the amount of energy gained in each instance in the chart above. Remember that we are looking at kinetic energy.

The first thing you will probably notice from the table above is that the smaller oar blades require about twice the energy to accomplish their task as the larger blades. Many years ago crews used blades that were long and narrow. Though they were able to slice through the water relatively quickly they were not very efficient at propelling the boat. Over the years blade size has increased substantially to take advantage of the efficiencies gained.

The second thing you will probably notice is that the larger sample blades are still only about 36 percent efficient during that first stroke. In a short paragraph explain where the lost energy went.

Based on our results one would be lead to believe that the optimal blade would be large enough to move a quantity of water exactly equal to the total mass of the boat. However this is only the case for a boat just starting out. Can you explain why the optimal size blades decreases as the boat speeds up?

Remember in the introductory paragraph it was stated that the boat continued to speed up as the oars were lifted out of the water? Why is this so? I will give you a hint. The center of mass of the boat continues at it's original speed even though the boat itself gains speed. The equation for a system's center of mass is given below where "r" is displacement and "m" is mass.

In our case this expands to look like

If we are looking at this over a short period we can divide both sides of the equation by time. However, disp/time = vel

Let us assume that total mass of the boat and crew is 900 kg while the mass of the 8 rowing crew members is 720 kg and that the boat has a speed of 5 m/sec. If the crew members are sliding backwards at a speed of 1.5 m/sec relative to the boat, what is the change in the boat's speed? Show your work.

New speed of boat = original speed + __________________________

Actually this answer is overly optimistic. This is because we have neglected to take into account several factors. Can you think of what they might include?

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