**Physik | Technik**

## Timo Eugster, 2002 | Solothurn, SO

**In this project, I tried to take a closer look at a now relatively common air vehicle, the quadrocopter. With the help of 3D models and fluid dynamic simulations, I calculated and modelled certain flight characteristics of the quadrocopter. Of interest was the static thrust, the vertical velocity and the horizontal velocity. Simultaneously, I conducted measurements with a self-built quadrocopter, so that the calculations and measurements could be compared later. The results showed that even without any professional equipment, acceptable results can be produced. For the velocity calculations for example, the error was only about 9%, which is relatively close to the actual measurements, especially when taking into consideration the many uncertainties that come up while working with aerodynamic processes.**

#### Fragestellung

Small quadrocopters have been gaining a lot of popularity in the last couple of years. Most of them are consumer drones, but some could have more specific applications such as deliveries of important goods and so on. It is therefore important to know, what the limits of such quadrocopters are and how they could be calculated. This project explores how these flight characteristics can be calculated and examines how accurate these methods are by comparing them to measurements. The flight characteristics that were of subject are the static thrust of the quadrocopter, the maximum vertical velocity and the maximum horizontal velocity. Furthermore, the drag of the quadrocopter was studied in more detail with fluid dynamic simulations.

#### Methodik

Firstly, the quadrocopter was built, so that the individual components of the quadrocopter and its physical properties were clear. This then allowed for the calculations to be made. For that, I derived the formulas for the flight characteristics of interest. Additionally, a 3D-model of the quadrocopter was drawn in a CAD software, with which several fluid dynamic simulations were done. The results of these simulations included the drag coefficient, which is a property that describes the aerodynamic resistance of the quadrocopter. This drag coefficient was then implemented into the formulas so that the calculations would be as accurate as possible. After rigorous testing of the quadrocopter on an open field, I was then able to examine all the data and compare my findings.

#### Ergebnisse

– The thrust calculations initially did not include any energy losses, so the effectiveness of the quadrocopter system was calculated by comparing the calculations with the measurements. This yielded a rotor thrust constant of 0.110328. The maximum thrust was measured at 28.567N (2.913kg) which is in line with different sources.

– The difference between the calculations and the measurements of the vertical velocity at different battery voltages was about 8.4%. The velocities were slightly lower than in the calculations with a maximum speed of 29.64m/s (~107km/h).

– For the horizontal velocity, the calculations were around 9.3% higher than the measurements. The highest measured velocity was 34.72m/s (~125km/h).

#### Diskussion

I was really pleased with the results of both the calculations and the measurements. It was good to see that the difference between the two were rather small. Therefore, I can say that all the goals that were set for this project were achieved. However, I was really surprised by how low the degree of effectiveness of the quadrocopter actually is, even though the thrust was about the same as in the sources I read. The differences between the velocity calculations can also be explained rather easily. The most apparent reason is that the 3D-model in the simulations is not completely accurate when compared to the actual quadrocopter. This means that there was more drag induced than was accounted for in the calculations.

#### Schlussfolgerungen

This project shows that it is possible to calculate various flight characteristics of modern quadrocopters. The results of said calculations are a good approximation of the actual values. Of course, in order to receive the most accurate data, nothing is better than actual measurements. These calculations could for example be used to evaluate whether a project involving a quadrocopter could even be feasible. For further improvements of the calculations, it would be helpful to investigate the relationship between the pitch of the quadrocopter and the dynamic thrust, as this was still rather unclear. Furthermore, it would be interesting to analyse how different propellers affect the calculations and measurements.

#### Würdigung durch den Experten

Michael Pantic

Timo Eugster charakterisiert in seiner Arbeit die Flugeigenschaften eines selbst gebauten Quadrokopters. Dazu kombiniert er kreativ und sorgfältig eine breite Auswahl an theoretischen und praktischen Methoden.

Physikalische Berechnungen, numerische Simulationen und Flugexperimente mit GPS und Waage werden durchgeführt und verglichen. Besonders der geschickte und wissenschaftliche Einsatz der zur Verfügung stehenden Messmethoden sticht hervor. Die Arbeit überzeugt durch die genaue Dokumentation und Durchführung der Experimente sowie durch die kritische Diskussion der Resultate.

#### Prädikat:

hervorragend

Sonderpreis Metrohm – Summer School of Science

**Kantonsschule Solothurn
**Lehrer: Niklaus Baltisberger