Sky Elevator
This activity allows students to compare orders of magnitude of vertical speeds in different technological contexts. It develops the ability to analyze GPS data and perform speed calculations.
Visão geral da atividade:
During a plane flight, the student uses the FizziQ GPS to measure and record the altitude during the climb phase over a period of 30 seconds. By analyzing this data, he calculates the ascending speed of the device and compares it to that of the fastest elevator in the world (Shanghai Tower, 20 m/s). The student then thinks about the technical differences between these two vertical transport systems.
Nível:
Autor:
High school
FizziQ
Duração (minutos):
20
O que os alunos farão:
- Measure the altitude change during an aircraft's initial climb phase using GPS
- Calculate the aircraft's vertical speed (rate of climb) from the altitude data
- Compare the aircraft's climb rate with the speed of the world's fastest elevator
- Understand the physical differences between aerodynamic lift and elevator cable systems
- Develop skills in GPS data analysis and unit conversion
Conceitos científicos:
- Vertical speed
- GPS altitude measurement
- Average speed calculation
- Atmospheric pressure and pressurization
- Forces involved in vertical movements
Sensores:
- GPS (altitude measurement)
- Barometer (atmospheric pressure for altitude cross-check)
Materiais necessários:
- Smartphone with the FizziQ application and GPS reception
- A plane flight
- FizziQ experience book
Procedimento experimental:
Before the flight, open FizziQ and select the GPS Altitude sensor. If available, also select the Barometer (atmospheric pressure) in Duo mode for a cross-check.
Ensure GPS reception is working (preferably by a window seat). Note that airplane mode may need to be temporarily disabled for GPS lock, then re-enabled with GPS remaining active on some phones.
Once the aircraft begins its takeoff roll, start recording in FizziQ.
Record continuously for the first 5-10 minutes of flight, covering the initial climb phase.
After the seatbelt sign indicates stable flight, you may stop recording.
Examine the altitude-versus-time graph. Identify the linear climb phase where altitude increases steadily.
Select a 30-second interval during the steepest climb. Record the altitude at the start and end of this interval.
Calculate the rate of climb: vertical speed = (altitude change) / (time interval) in m/s.
Convert to other units: km/h (multiply by 3.6) and feet per minute (multiply by 196.85).
Compare your measured rate of climb with the Shanghai Tower elevator speed: 20.5 m/s (74 km/h).
If barometer data is available, cross-check the altitude using the barometric formula: Δh ≈ (P_ground - P_flight) × 8.5 m/hPa.
Discuss the fundamental physics differences between lift-based flight and cable-based elevator systems.
Resultados esperados:
A typical commercial aircraft climbs at 7-15 m/s (1500-3000 feet per minute) during the initial climb phase. This is comparable to, but often less than, the Shanghai Tower elevator speed of 20.5 m/s. GPS altitude measurements have typical precision of ±5-10 meters, which over a 30-second interval translates to a rate-of-climb uncertainty of about ±0.5 m/s. The barometer provides a more precise altitude measurement (±1 m) if properly calibrated. Students should observe that the climb rate decreases as the aircraft gains altitude, due to decreasing air density reducing engine performance and lift. The aircraft's horizontal speed (typically 200-300 km/h) vastly exceeds the elevator's speed, even though the vertical component may be slower.
Questões científicas:
- Is the plane climbing faster or slower than the world's fastest elevator? Does the answer surprise you?
- What is the fundamental physical difference between how an airplane and an elevator gain altitude?
- Why does the rate of climb decrease as the aircraft reaches higher altitudes?
- What forces must be overcome for an airplane to climb? For an elevator?
- Why is the horizontal speed of the aircraft much greater than its vertical speed?
- How do pilots control the rate of climb during flight?
Explicações científicas:
The ascent speed of an airliner in the initial climb phase is generally between 7 and 10 m/s (approximately 1500-2000 feet/minute), sometimes reaching 15-18 m/s. This speed is determined by factors such as engine thrust, wing lift, aircraft mass and atmospheric conditions.
For comparison, the Shanghai Tower elevator reaches 20.5 m/s (74 km/h), making it the fastest in the world. The fundamental difference between these two systems lies in their operation: the elevator uses electric motors and counterweights, while the plane exploits the aerodynamic lift and thrust of its engines.
A crucial aspect concerns pressurization: in an elevator, the pressure remains constant because the system is open to the atmosphere, whereas airplanes maintain an artificial cabin pressure, because atmospheric pressure decreases with altitude (approximately -1 hPa every 8.5 m).
Atividades de extensão:
- Is the plane climbing faster or slower than the world's fastest elevator? Does the answer surprise you?
- What is the fundamental physical difference between how an airplane and an elevator gain altitude?
- Why does the rate of climb decrease as the aircraft reaches higher altitudes?
- What forces must be overcome for an airplane to climb? For an elevator?
- Why is the horizontal speed of the aircraft much greater than its vertical speed?
- How do pilots control the rate of climb during flight?
Perguntas frequentes:
Q: GPS does not seem to work during the flight. How can I get data?
R: Many phones can receive GPS signals even in airplane mode if GPS is separately enabled in settings. Sit by a window for the best reception. If GPS is unavailable, use the barometer alone to measure altitude changes.
Q: The altitude readings are very noisy. Is the GPS accurate enough?
R: GPS altitude is less precise than horizontal position, with typical errors of ±5-10 m. Use longer averaging intervals (30-60 seconds) to smooth out the noise and get a reliable rate of climb.
Q: Can I do this experiment without taking a flight?
R: You can adapt it for an elevator ride in a tall building, comparing the elevator speed with published aircraft climb rates. The barometer gives excellent results for measuring elevator speed.
Q: The aircraft seems to climb faster right after takeoff. Is this real?
R: Yes, aircraft typically climb most steeply just after takeoff when they are at full thrust and low altitude (dense air provides more lift and engine power). The climb rate gradually decreases at higher altitudes.