## 3 Results  
Before the performance tests were conducted, the diameter of the propeller was measured and the finished prototype was weighted. In addition, the static and rolling friction forces were calculated (Tables 1 and 2). \begin{table}
\begin{tabular}{l l l} \hline \hline
**Category** & **Calculated Results** & **Units** \\ \hline Friction Force (Static) & 1.582–4.474 & N \\ Friction Force (Rolling) & 0.00949 & N \\ Actual Velocity & 0.558 & m/s \\ Acceleration & 0.409 & m/s\({}^{2}\) \\ Actual Efficiency & 18.55 & \% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calculated Results (1). In the first test, the RPM of the propeller was measured by using a handheld tachometer (Figure 2a). The measurements were taken at the propeller's maximum RPM and at the minimum RPM needed to start the vehicle in motion. The results of the tests gave a range of 8000 to 13,000 RPMs. With these results, the range of efficiency was determined. In the second test, the velocity of the vehicle was measured (Figure 2b). Using a stopwatch and a measuring tape, the amount of time needed for the vehicle to travel five feet (1.524 m) is recorded, and the velocity can be easily calculated. Two tests were performed on the linoleum floor and three tests on a wooden tabletop. The average time was 2.73 s, giving a speed of 0.558 m/s (Table 3). The third test was done in SolidWorks Motion, which is a 3-D CAD program that allows us to simulate the design's motion (Figure 3). A constant force was applied to the motor to represent the force that the propeller would normally provide. With each test, the force that was applied to the motor was changed, and we found the corresponding velocity of the vehicle at 2.73 s. With these results, the velocity change with respect to efficiency can be compared to that given by hand calculations (Table 4). The efficiency and thrust of the propeller system determines the velocity of the vehicle. To better understand the relationship between the efficiency of the propeller system, thrust of the propeller system and velocity of the vehicle, Figure 4a,b have been created. The maximum efficiency of the propeller system is assumed to be 100%. By setting the efficiency of the propeller system into eight efficiency levels within the range of 0% to 100%, the corresponding values of the thrust can be calculated from Equation (4). The average error was 12.02% when comparing the velocity between the experimental result and the one from the simulation using SolidWorks. The results suggest that using SolidWorks Motion is an alternative way to find the velocity of a vehicle. \begin{table}
\begin{tabular}{l l} \hline \hline
**Trial** & **Time (sec)** \\ \hline
1 & 2.49 \\
2 & 2.81 \\
3 & 2.72 \\
4 & 2.93 \\
5 & 2.71 \\ Average & 2.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Time Needed to Travel the 5 ft (1.524 m) Distance. Figure 2: (a) Revolutions per minute (RPM) Measurements by Tachometer; (b) Speed testing of the vehicle. As calculated in Table 2, the actual velocity is 0.558 m/s. As shown in Figure 2, the calculated velocity is approximately equal to the actual velocity. As shown in Figure 4c, the velocity of the vehicle is directly proportional to the thrust of the propeller system. Therefore, with more thrust of the propeller system, the velocity of the prototype will increase. The highest discrepancy between the two results was obtained at the low velocities of the vehicle. At low velocities, the static friction plays a major role in motion. That is the reason for a high error percentage between the SolidWorks Motion results and those theoretical velocity calculations in the beginning (error = 41.6%). As the velocity increased, the error percentage between SolidWorks Motion and theoretical Calculations decreased significantly, because the static friction is changed to rolling friction (error = 3.5%). Figure 4 contains the calculated velocity of the vehicle and SolidWorks Motion velocity, and shows a close relationship between calculated and simulated results.