Eric Murray's Erg Record

Of Numbers and Physics

How much do sliders help?

Yeah, I got this: a look at the physics behind Eric Murray's record 5k erg test.

There are a few basic concepts of physics necessary to understand the difference between the mechanics of a "static" rowing machine (like a Concept2 Model D/E) and one that runs on a slide (or sliders, in the case of the C2).

If you sit on a static erg and push your legs towards the footplate, you move backwards with respect to a fixed point by a distance that is equal to the length of your legs (minus a few inches due to physiology, ergonomic limitations, etc.).

On a dynamic erg, if you sit down and push the legs toward the footstretcher, you move backward by a distance equal to only about 20% compared to the distance on a static erg. The remainder of the movement, or 80%, is made by the erg as it moves away from us.

The Third law of Newton

This movement is the result of the principle of action and reaction, known as the Third law of Newton. The force applied by the legs will similarly act on the mass of the rower as well as on the rowing machine, with the relative proportions of speed and distance based on the differing masses of each object.

In the case of the static erg, we can consider the rowing machine actually connected to the whole planet, so it does not move, because we accept that mass is infinite and the speed of the machine will be zero. Namely: the erg is stopped. In the case of the dynamic erg, the mass of the rowing machine is much lighter (one third), and moves away from the athlete when pressure is applied to the footboards.

In addition to the differences in the relative motions, in the case of a static rowing machine we are performing more work to accelerate the athlete's body weight compared to a dynamic erg (ergometer with floating mass), in which the work is divided between the displacement of the rowing machine and the body of athlete in opposite directions.

A dynamic rowing machine dynamic, such as the C2 Dynamic erg or RowPerfect, tries to simulate the effect of reaction, moving the footstretcher and/or the flywheel. This occurs on an erg placed on sliders as well; by reducing the inertia of the mass we reduce the waste of energy that occurs when we have to move the athlete.

Hoping to have been sufficiently clear, we move on to an example. Thanks to erg tests that NZ Olympic rower Eric Murray performed in 2014 on a static rowing machine (6000 meters in 18:16), and one a C2 on sliders performed in November 2015 (5000 meters in 14:56), we can do a few calculations and apply the theory mentioned above.

Murray has mass "Ma" and is sitting on the rowing machine, which is mass "Me". Initially, the system of athlete and rowing machine are still. Then, by separating its center of mass by a distance "s" (length of the stroke) in a time "t" with a constant acceleration, (using the principle of conservation of momentum and the third law described previously), Murray will have velocity "Va" while the erg has velocity "Ve" (travelling in opposite directions) so that:

Ma * Va = Me * Ve

Considering length traversed s in a time t, with constant acceleration, then:

Va + Ve = s / t

By calculating the total kinetic energy Et system in the final state we have:

E = ½ Ma Va2 + ½ Me Ve2 = ½ Ma Va2 + 1/2 (Ma Va) (s / t - Va) = ½ Ma Va (s / t)

Now we must make the necessary considerations about the difference between dynamic and static. The overall length of the drive phase is shorter on the dynamic, (sd < s) because we do not have any help from inertia to reach the catch position, and the length at the front end is reduced.

On the Dynamic erg or on sliders it will be easier to increase the rate of striking, because you don't need to accelerate the body of the athlete. Furthermore, we can consider the performance of the stroke at the change of rate to be a constant.

With the data found on worldrowing.com that Eric Murray has a weight/mass of 95kg, so Ma = 95 kg. And we know that in 2014 he did 6000 meters with an average rating R = 34 strokes per minute, and time t = 0.885 sec, with distance s = 1 meter.

In case of the static erg, Me is de facto infinite and Ve = 0, so we will have a Va = 1.13 m/s, as result the dissipated kinetic energy will be:

Et = 95 x 1.13 x 1.13 x 0.5 = 61 J/s (joule per stroke)

In case of the dynamic erg or erg on sliders, we have a Me = 26 kg, so in Murray's most recent 5000 meters test:

R = 36 s/min, Me = Ma /3.65 and 0.9

Ve = 3.65 Va

Ve + Va = 1.08

So with the two equations, having considered a stroke length that is 10 cm shorter than that of on a static erg, we have:

Va = 0.23 m/s and Vc = 0.85 m/s

which will give us a value of Dissipated Energy:

Ed = 0.5 * 95 * (12:23) 2 0.5 * 26 * (0.85) ^ 2 = 36.71 J/s (joule per stroke)

The difference between the dynamic test and the static test is 24.29 J/s, where P=Et/t equals a power loss of 26.24 watts. So, the power "wasted" to move the athlete's body mass on the static erg, or 26.24 watts, will actually be actually converted to power on the dynamic erg.

During the test on the static erg we recorded a time of 18:16 for a distance of 6000 meters, which converts to an output of 459.4 watts.

On the Concept2 rowing power P is:

P=2.8*V3

If we consider that the additional 26.24 watts is converted to power by rowing on the dynamic erg; so we will have a higher power output on the slide, or 459.4 + 26.24 = 485.64 Watts, which will allow us to predict a time for a 5000 meters test of 14:56.58, or perfectly in line with the time recorded in the November 2015 test by Murray.

In conclusion, this theory tells us that the 26 watts added by the sliders allowed Murray to lower his time in those 20 seconds, allowing him to break Pinsent's record. But we must add that for these added watts to contribute to an athletes performance it is critical that the athlete has mastered the differing feel of the dynamic erg, the stroke length and the increased number of strokes. The search for efficiency in rowing is a path along which we must consider all the variables, but we'll talk about in a future article.

This article was taken from the website Volevo Essere Un Canottiere ("I wanted to become a rower") and was written by Vincenzo Triunfo.

Vincenzo Triunfo Is a mechanical engineer and rower of the "C.N. Posillipo". He is one of the Directors at "+39 Energy" and he is interested in "Mechanical Efficiency and Renewables" and improvement of environmental performance of several industrial sites. You can contact Vincenzo via Twitter (https://twitter.com/v_triunfo)

Translated from the original Italian by Marco Bovo. The original version of this article can be found here.