Altimeter
This experiment allows students to understand the relationship between atmospheric pressure and altitude. It develops the ability to establish mathematical models from experimental data.
Evangelista Torricelli, Blaise Pascal, and the early barometric scientists of the 17th century discovered that atmospheric pressure decreases with altitude, a principle that remains central to aviation and meteorology today. Every commercial aircraft uses barometric altimeters to determine its flight altitude by measuring the surrounding air pressure. The same principle is at work in modern smartphones, which contain precision barometric sensors originally included to improve GPS accuracy in urban environments. These tiny sensors can detect pressure changes equivalent to less than one meter of altitude difference. By climbing a staircase or a hillside with a smartphone, students can directly observe the relationship between pressure and altitude and develop a mathematical model from their own data. This experiment bridges historical physics, atmospheric science, and modern sensor technology, providing a concrete example of how a physical law translates into a practical measuring instrument.
Learning objectives:
The student uses the FizziQ atmospheric pressure sensor to take measurements at different heights, such as the floors of a building or on a hill. For each level, it records the pressure and estimated altitude, then analyzes the relationship between these values to determine how pressure decreases with altitude. From this data, the student develops a formula to calculate altitude from pressure.
Level:
Middle and high school
FizziQ
Author:
Duration (minutes) :
30
What students will do :
- Measure atmospheric pressure at different altitudes using the smartphone barometer
- Establish the relationship between pressure change and altitude difference
- Develop a simplified barometric formula from experimental data
- Calculate altitude from pressure measurements and evaluate accuracy
- Understand the physical reasons for the decrease of atmospheric pressure with altitude
Scientific concepts:
- Atmospheric pressure, Relationship between pressure and altitude, Mathematical modeling, Terrestrial atmosphere, Calibration of measuring instruments
Sensors:
- Barometer (atmospheric pressure sensor)
What is required:
- Smartphone with FizziQ (iPhone or Android with external sensor), Access to a multi-storey building or a hill, Tape measure, Experience book
Experimental procedure:
Open the FizziQ application and select the Atmospheric Pressure sensor. Verify that it displays a value close to 1013 hPa (may vary with weather conditions and local altitude).
Choose a building with at least 4 accessible floors (ideally more). If possible, determine the height of each floor (typically 3 to 3.5 meters between floors).
Stand on the ground floor and record the pressure reading. Note it as your reference measurement (P₀). Wait at least 10 seconds for the sensor to stabilize.
Walk up to the first floor and wait 15 seconds for the pressure to stabilize. Record the new pressure value.
Repeat this measurement on each successive floor, always waiting for stabilization before recording.
For each floor, calculate the pressure difference ΔP = P₀ - P relative to the ground floor.
If you know the height of each floor, plot a graph of pressure difference versus altitude in your FizziQ notebook.
From your graph, determine the approximate rate of pressure change per meter of altitude (should be around 0.12 hPa/m or equivalently about 1 hPa per 8.5 m).
Use your data to derive a simplified formula: Δh ≈ (P₀ - P) × 8.5 where Δh is in meters and pressures are in hPa.
Test your formula by predicting the pressure at a known altitude (e.g., the top of a nearby hill) and comparing with the measured value.
Investigate the effect of opening and closing doors or turning on heating/ventilation on the pressure reading.
Expected results:
Students should observe a consistent decrease in atmospheric pressure of approximately 0.10-0.12 hPa per meter of altitude gain. For a typical building with 3-meter floors, the pressure drop between consecutive floors should be about 0.3-0.4 hPa. The graph of pressure difference versus altitude should be approximately linear over the range of a few floors (up to about 30-50 meters). The derived conversion factor should be close to 8.5 m/hPa. Measurement precision with a smartphone barometer is typically ±0.1 hPa, corresponding to approximately ±1 meter of altitude uncertainty. Students may notice small pressure fluctuations due to wind, opening doors, or HVAC systems, which can introduce errors of 0.1-0.3 hPa.
Scientific questions:
- Why does atmospheric pressure decrease with altitude?
- Is the relationship between pressure and altitude perfectly linear? Why or why not?
- What factors other than altitude could cause the barometer reading to change?
- How do weather changes affect the accuracy of a barometric altimeter?
- Why do aircraft altimeters need to be regularly recalibrated during flight?
- Could you use this technique to measure the height of a mountain? What limitations would you encounter?
Scientific explanations:
Atmospheric pressure decreases with altitude in an approximately exponential relationship. At sea level, the standard pressure is about 1013.25 hPa, but it decreases by about 1 hPa every 8.5 meters at low altitudes.
This relationship is not perfectly linear over large variations in altitude, because air is compressible and its density also decreases with altitude. For small altitude variations (a few hundred meters), we can use the simplified barometric approximation: Δh ≈ (P₀ - P) × 8.5, where Δh is the altitude difference (in meters), P₀ the pressure at the reference point and P the pressure at the measurement point (in hPa).
For more precise calculations over large amplitudes, the complete barometric formula takes temperature into account. Modern smartphones incorporate precision barometers (±0.1 hPa, equivalent to approximately ±1 meter of altitude) to improve GPS positioning and other functions.
Extension activities:
- Why does atmospheric pressure decrease with altitude?
- Is the relationship between pressure and altitude perfectly linear? Why or why not?
- What factors other than altitude could cause the barometer reading to change?
- How do weather changes affect the accuracy of a barometric altimeter?
- Why do aircraft altimeters need to be regularly recalibrated during flight?
- Could you use this technique to measure the height of a mountain? What limitations would you encounter?
Frequently asked questions:
Q: The pressure reading fluctuates constantly. How do I get a stable measurement?
R: Wait at least 15 seconds after reaching each floor for the sensor to stabilize. Avoid taking measurements near open windows, doors, or HVAC vents, as air currents can cause temporary pressure fluctuations. Take the average of several readings over 10 seconds.
Q: My measurements do not show a consistent pressure decrease between floors. What could be the cause?
R: Ensure you are waiting long enough for stabilization. Check that doors to stairwells are closed, as pressure differences between areas of a building can be affected by ventilation systems. Very windy conditions can also create pressure variations.
Q: The calculated altitude does not match the known building height. Why?
R: The simplified formula Δh ≈ (P₀ - P) × 8.5 is an approximation valid for small altitude changes near sea level at standard temperature. Temperature variations, weather changes between measurements, and sensor calibration differences can introduce errors of several percent.
Q: Does this work on all smartphones?
R: Most modern smartphones contain a barometric pressure sensor, but some budget models may not. iPhones from iPhone 6 onward and most Android phones from 2014 onward include this sensor. FizziQ will indicate if the sensor is unavailable.