IPhO 2027 Round 1 Teorica

Problem — Aircraft take-off (accompanying graph)

This single-page document contains only the measurement graph for the “Aircraft take-off” problem of Round 1 of the selection competition for the IPhO 2027. The complete problem text is found in the main booklet (IPhO_2027_Aufgabenblatt_Rund1.pdf).

A smartphone was secured on board during an aircraft take-off and, using its accelerometer-sensor app, recorded the three spatial components of the acceleration $a$ as a function of time $t$. The measurement data are available in the accompanying CSV file (IPhO_2027_flugzeugstart_accelerometer_data.csv) with the columns nr; time; ax; ay; az (all accelerations in $\mathrm{m}{\mathrm{s}}^{-2}$, time in $\mathrm{s}$).

The graph shows three data series over the time range $t=0$ to $t\approx 92,5\mathrm{s}$:

• Vertical component $a_z$ (brown series, top): Initially fluctuates around $\approx 9,81\mathrm{m}{\mathrm{s}}^{-2}$ (gravitational acceleration at rest). During the rotation at $t\approx 60$–$63\mathrm{s}$ it rises to $\approx 13\mathrm{m}{\mathrm{s}}^{-2}$ (lift-off). In the climb it then drops to $\approx 8,2\mathrm{m}{\mathrm{s}}^{-2}$, which corresponds to the component of gravity reduced by the climb angle.

• Longitudinal component $a_y$ (green series, middle): Stays near zero until $t\approx 6,5\mathrm{s}$ (standstill). It then rises continuously to a plateau of $\approx 3\mathrm{m}{\mathrm{s}}^{-2}$ (engine acceleration on the runway). It reaches a maximum of $\approx 4\mathrm{m}{\mathrm{s}}^{-2}$ at $t\approx 60$–$63\mathrm{s}$ (rotation). In the climb it stabilises at $\approx 2,9\mathrm{m}{\mathrm{s}}^{-2}$.

• Transverse component $a_x$ (blue series, bottom): Remains near zero throughout the entire measurement.

From the graph, the phases of the aircraft take-off (taxiing, accelerating, rotation, lift-off, climb) can be identified and physical quantities such as the runway acceleration, the take-off speed and the climb angle can be determined.

Acceleration components ax ay az during aircraft take-off

Topic: Newtonian Mechanics, Order-of-Magnitude Estimation Metodi: Kinematic Equations, Experimental Data Analysis, Free-Body Diagram Competenze: Experimental Data Analysis, Graph Linearization, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.1

Problema — Decollo di un aereo (grafico allegato)

Questo documento di una sola pagina contiene soltanto il grafico delle misure per il problema «Decollo di un aereo» del primo turno della selezione per le IPhO 2027. Il testo completo del problema si trova nel fascicolo principale (IPhO_2027_Aufgabenblatt_Rund1.pdf).

Uno smartphone è stato fissato a bordo durante il decollo di un aereo e, con un’app per il sensore accelerometrico, ha registrato le tre componenti spaziali dell’accelerazione $a$ in funzione del tempo $t$. I dati di misura sono disponibili nel file CSV allegato (IPhO_2027_flugzeugstart_accelerometer_data.csv) con le colonne nr; time; ax; ay; az (tutte le accelerazioni in $\mathrm{m}{\mathrm{s}}^{-2}$, il tempo in $\mathrm{s}$).

Il grafico mostra tre serie di dati nell’intervallo di tempo da $t=0$ a $t\approx 92,5\mathrm{s}$:

• Componente verticale $a_z$ (serie marrone, in alto): inizialmente oscilla intorno a $\approx 9,81\mathrm{m}{\mathrm{s}}^{-2}$ (accelerazione di gravità a riposo). Durante la rotazione, a $t\approx 60$–$63\mathrm{s}$, sale a $\approx 13\mathrm{m}{\mathrm{s}}^{-2}$ (distacco da terra). Nella salita scende poi a $\approx 8,2\mathrm{m}{\mathrm{s}}^{-2}$, che corrisponde alla componente della gravità ridotta dall’angolo di salita.

• Componente longitudinale $a_y$ (serie verde, al centro): resta vicina a zero fino a $t\approx 6,5\mathrm{s}$ (aereo fermo). Poi cresce con continuità fino a un plateau di $\approx 3\mathrm{m}{\mathrm{s}}^{-2}$ (accelerazione dei motori sulla pista). Raggiunge un massimo di $\approx 4\mathrm{m}{\mathrm{s}}^{-2}$ a $t\approx 60$–$63\mathrm{s}$ (rotazione). Nella salita si stabilizza a $\approx 2,9\mathrm{m}{\mathrm{s}}^{-2}$.

• Componente trasversale $a_x$ (serie blu, in basso): resta vicina a zero per tutta la durata della misura.

Dal grafico si possono riconoscere le fasi del decollo (rullaggio, accelerazione, rotazione, distacco da terra, salita) e determinare grandezze fisiche come l’accelerazione sulla pista, la velocità di decollo e l’angolo di salita.

Componenti dell’accelerazione ax ay az durante il decollo dell’aereo

Topic: Newtonian Mechanics, Order-of-Magnitude Estimation Metodi: Kinematic Equations, Experimental Data Analysis, Free-Body Diagram Competenze: Experimental Data Analysis, Graph Linearization, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.1

The following is the list of aircraft that have been involved in the flight:

This single-page document contains only the measurement graph for the “Aircraft take-off” problem of Round 1 of the selection competition for the IPhO 2027. The complete problem text is found in the main booklet (IPhO_2027_task sheet_Rund1.pdf).

A smartphone was secured on board during an aircraft take-off and, using its accelerometer sensor app, recorded the three spatial components of the acceleration $a$ as a function of time $t$. The measurement data are available in the accompanying CSV file (IPhO_2027_aircraftstart_accelerometer_data.csv) with the columns nr; time; ax; ay; az (all accelerations in $\mathrm{m}{\mathrm{s}}^{-2}$, time in $\mathrm{s}$).

The graph shows three data series over the time range $t=0$ to $t\approx 92,5\mathrm{s}$:

• Vertical component $a_z$ (brown series, top): Initially fluctuates around $\approx 9,81\mathrm{m}{\mathrm{s}}^{-2}$ (gravitational acceleration at rest). During the rotation at $t\approx 60$–$63\mathrm{s}$ it rises to $\approx 13\mathrm{m}{\mathrm{s}}^{-2}$ (lift-off). In the climb it then drops to $\approx 8,2\mathrm{m}{\mathrm{s}}^{-2}$, which corresponds to the component of gravity reduced by the climb angle.

• Longitudinal component $a_y$ (green series, middle): Stays near zero until $t\approx 6,5\mathrm{s}$ (standstill). It then rises continuously to a plateau of $\approx 3\mathrm{m}{\mathrm{s}}^{-2}$ (engine acceleration on the runway). It reaches a maximum of $\approx 4\mathrm{m}{\mathrm{s}}^{-2}$ at $t\approx 60$–$63\mathrm{s}$ (rotation). In the climb it stabilizes at $\approx 2,9\mathrm{m}{\mathrm{s}}^{-2}$.

• Transverse component $a_x$ (blue series, bottom): Remains near zero throughout the entire measurement.

From the graph, the phases of the aircraft takeoff (taxiing, accelerating, rotation, lift-off, climb) can be identified and physical quantities such as the runway acceleration, the takeoff speed and the climb angle can be determined.

Acceleration components during aircraft take-off

Topic: Newtonian Mechanics, Order-of-Magnitude Estimation Metodi: Kinematic Equations, Experimental Data Analysis, Free-Body Diagram Competenze: Experimental Data Analysis, Graph Linearization, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.1