# Physics behind the Rowperfect advantage

The Rowperfect has been designed to simulate as closely as possible a light racing shell in all its aspects. This also holds for the relation between Power generated, the weight of the rower, and the calculated virtual boat speed.

## Power calculation

The calculation of the power dissipated by the rower is based on sound engineering principles, is self-calibrating, and has the moment of inertia of the flywheel as a basis.

The mechanical design of the fan and its cage, and the system of adjusting the resistance factor of the fan by using central disks, ensure that the fan is operating under conditions of virtually undisturbed flow at the inlet side of the fan. This causes the power P dissipated by the fan to be proportional to the cube of its rotational speed N. For the ROWPERFECT fan arrangement this proportionality has been verified over the whole range of rotational speeds and of resistance factors envisaged in rowing.

The amount of energy dissipated by the rower for a given stroke is the sum of the following components:

**1. The amount of energy dissipated by friction of the fan during the stroke.**

During each and every recovery, over every 90 degree turn of the flywheel, the deceleration of the flywheel with known moment of inertia, is measured. From this deceleration and the moment of inertia, the resistance factor is calculated. This resistance factor then is used during the next stroke to calculate the amount of energy dissipated by friction during each ¼th of a turn of the flywheel. This then is integrated over the whole number of turns of the flywheel to give (E1).

**2. The incremental amount of kinetic energy in the flywheel due to its increase in rotational speed.**

The kinetic energy content of the fan is the product of its moment of inertia and the square of its rotational speed. The increase in kinetic energy content of the fan during the stroke is calculated from the difference in rotational speed of the flywheel at the end and at the beginning of the stroke (E2).

**3. The amount of energy taken up by the shock cord due to its elongation during the stroke.**

From the size of the sprocket used, and from the number of ¼ turns of the flywheel during the stroke, the stroke length, actually made by the rower, is calculated. This in combination with the force/length characteristic of the shock cord gives the amount of energy absorbed by the shock cord during the stroke (E3).

The total amount of energy dissipated by the rower during the stroke then is:

Estroke = E1 + E2 + E3 [Joules]

Dividing Estroke by the total cycle time for stroke plus recovery in seconds gives the Power P produced by the rower, in watts.

## Virtual boat speed

Because a rowing simulator is not a boat, relating the Power, generated by the rower on a rowing simulator, to a virtual boat speed, is inevitably arbitrary to some extent. In the Rowperfect system utmost care has been taken to keep the degree of arbitrariness to an absolute minimum, so as to provide the most realistic calculated speeds possible. As a result of this effort, the Rowperfect system features a weight corrected calculated speed that, for each type of racing shell, and for the whole range of crew weights, gives results generally within some seconds of the results actually obtained on the water under ideal conditions and with a near to perfect rowing technique.

From literature it is known that for rowing boats the relation between Power P and boat speed V and is given by the following formula:

P = K x V^b

whereby drag factor K and power b are boat dependent factors. Values found for b in literature for racing shells range from 2.95 to 3.05. The ROWPERFECT software uses 3.0.

The virtual boat speed as a function of the Power P is therefore given by the formula:

V = (1/K)^(1/3) * P ^ (1/3)

## Weight correction factor

For long slender boats such as racing shells, at a given speed, the influence of a change in weight of the rower or crew mainly the affects friction between the boat and the water; variation in wind resistance or wave resistance as a function of crew weight is minimal. Therefore, with a good approximation, it can be stated that the drag factor K is directly proportional to the wetted surface of the boat, and the proportionality factor A is boat type dependant. For racing shells with a semicircular wetted cross section it can be derived that the wetted surface Sw is proportional to the square root of the total displacement mass Mtot , whereby

Mtot = Mcrew + Mboat + Moars

Calculated per individual, for most racing shells the sum of Mboat + Moars is around 17,5 kgs. Taking this value for a single, the influence of the rowers weight on the drag factor is

K = A * (Mrower + 17,5) ^(1/2)

The proportionality factor A can be expressed as a boat speed constant B with

B = A^(-1/3)

Inserting this expression for K and the boat speed constant B into expression (I) results in the expression used in the ROWPERFECT software to account for the influence of the rower's weight on boat speed:

V = B *(Mrower + 17,5)^ (-1/6)*P^(1/3)

For the single scull mode of the software, the boat speed constant B has been derived empirically by calibrating the rowing simulator performance against the on-water performance of top class male and female scullers with weights ranging from 59 to 95 kgs. Speed constants for other boats have been derived thereof.

The system has proven to give reliable weight corrected virtual boat speeds. For technically highly skilled rowers the calculated times are generally within some seconds of the actual on-water performance.