The formula to calculate the Speed (S) is:
\[ S = \sqrt{\frac{2 \cdot P}{C_d \cdot A \cdot \rho}} \]
Where:
The relationship between watts and speed is determined by the power required to overcome the aerodynamic drag force that opposes an object's motion through air. The power output (in watts) is the rate at which work is done to maintain the speed against this drag force. The drag force itself is a function of the drag coefficient, frontal area, and air density. As power increases, the speed at which an object can travel also increases, assuming other factors remain constant.
Let's say the power output (P) is 400 watts, the drag coefficient (Cd) is 0.3, the frontal area (A) is 0.5 m², and the air density (ρ) is 1.225 kg/m³. Using the formula:
\[ S = \sqrt{\frac{2 \cdot 400}{0.3 \cdot 0.5 \cdot 1.225}} \approx 23.32 \text{ m/s} \]
So, the Speed (S) is approximately 23.32 m/s.