Panel Power

Panel Power is used to measure the power of a rotating device such as a Powered Wheel, mechanical engine or steam engine. In order to measure shaft power in Pp one must employ a drag shaft.

Procedure

A drag shaft consists of a single line of Wooden Blocks attached to the device's output, with Wing Panels attached so as to cause the greatest air resistance as shown. The panels can be placed directly on the block line at the discretion of the tester, as long as the shaft remains balanced with respect to the axis of rotation and a suitable number of panels is chosen. That is, too many panels and the machine to be tested may fail to turn over, too few (so as not to cause a noticeable decrease in shaft speed) may result in a poor calculation.

At the other end of the shaft, two Unpowered Wheels are placed on top of each other, the last one to be placed being pinned and having a camera placed on it in turn.

The camera is set to a height of zero, and smoothness zero in order to ensure it is looking directly down the axis of the drag shaft. Also to increase accuracy, is the use of unpowered wheels as this aids in taking the measurement of the time taken for the shaft to complete a single revolution.

The machine is started with the drag shaft attached (or it could be on a clutch mechanism which connects it to the device's output when it is up to speed), when the system's speed has stabilized, the timescale of the game may now be decreased in order to make an accurate measurement of the drag shaft's rotation speed.

The speed of rotation must be given in seconds per single revolution in 100% timescale in order for the following calculations to be made correctly so division of the time of revolution is necessary if the measurement was taken at a timescale lower than 100%.

Calculation

$Pp = \left ( \frac{r \times 2\pi}{t} \right )^3 \times \frac{n}{1000}$

• $r$ is the average distance of the centre of the drag shaft to the central hubs of the wing panels, measured in block lengths (or metres). This is always 2 metres as the panels must be placed directly on the axle - unless testing for the "multiplier law" (see below).
• $t$ is the time in seconds at 100% timescale for the drag shaft to make one revolution.
• $n$ is the number of wing panels.

Derivation

This formula comes from the power required to overcome aerodynamic drag equation which predominantly states that the power required to overcome drag is half the cube of the object's velocity multiplied with the object's surface area in the direction of motion.

The air's density, coefficient of drag and the halving can be ignored since they will remain constant for wing panels moving in the game and what is needed is a method of power comparison.

$r \times 2\pi$ is the distance the wing panel travels in one revolution (the circumference of a circle from its radius).

This, divided by the time taken for the wing panel to make one revolution, is the speed of the wing panel relative to the air (as speed is distance over time).

The multiplication by the number of wing panels is to take into account the total active surface area of the drag shaft, it's division by 1000 is arbitrary but is there to prevent Pp values getting too high. For example, a device consisting of a small wood block placed on and below the drag shaft with a flying block attached to the side of these, as displayed in the image, has a power of approximately 2.4 Pp after the division.

Accuracy

The equation cannot be exploited to its full potential due to the fact that for unknown reasons, it functions unpredictably if the panels are placed on each other's end to make the arms of the drag shaft longer: It seems that a multiplier equal to the number of wing panels on each arm is needed to get the correct value for Pp. However, if not all arms of the drag shaft are the same length, and the mean length of the arms is used as a multiplier, then even this rule appears to break down.

Further testing is required to verify or disprove the multiplier rule.