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Building an accurate barometer (+/-0.035%) using a simple party balloon

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Bert Chenin
Bert Chenin

Building an accurate barometer (+/-0.035%!!) using a simple party balloon. Design, Construction, Analysis. Study of the complex physical behavior of a balloon using the Weinhaus/Merritt model.

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Building an accurate barometer (+/-0.035%) using a simple party balloon
Building an accurate barometer (+/-0.035%) using a simple party balloon
Building an accurate barometer (+/-0.035%) using a simple party balloon
MAIN CONCEPT Pressure Increases Diameter Decreases Pressure decreases Diameter Increases The Diameter of the Balloon is Directly Related to the Atmospheric Pressure
Atmospheric pressure at Mean Sea Level and 25C = 1,013mB A change of 1mB in atmospheric pressure is 0.1% If we assume that the variation in diameter is proportional to the variation of atmospheric pressure, For a balloon diameter of 300mm, a 0.1% variation is 0.3mm! In addition, measuring precisely the dimension of a balloon is very difficult as it has an odd shape, is soft and very lightweight CHALLENGES
Use a larger balloon Capture the balloon in a fixed position Make measurements at a fixed position on the balloon Measure without manipulating or touching the balloon Design a system that amplifies the variations in diameter SOLUTIONS
DESIGN-1
DESIGN-2 Shaft Counterweight Balloon Fishing line Wood Disk Glued to Balloon Wood Beam Ball Bearings Dial Indicator Hand Hub If the diameter of the balloon increases, then the counterweight goes down and the indicator hand moves to the right GREEN ARROWS If the diameter of the balloon decreases, then the counterweight goes up and the indicator hand moves to the left BLUE ARROWS
DESIGN-3 The diameter of the shaft is d. Therefore, the circumference of the shaft is d. Assuming that the thickness of the fishing line is negligible, if we pull a length of fishing line equal to d from the shaft, then the shaft will rotate by 1 turn. If we pull a length equal to z, the shaft will rotate by a fraction of 1 turn equal to z/d. = z/d turn 1 turn = 360属 Therefore, = 360 x z/d (属)
EXPERIMENTAL PROTOCOL - DATA Time Date Humidity (%) Temperature (0F) Atmospheric Pressure (in-Hg) Angle (degrees)
ANGLE 陸 AND LOCAL ATMOSPHERIC PRESSURE 80 100 120 140 160 180 200 996 1,000 1,004 1,008 1,012 1,016 1,020 0 1 2 3 4 PHI(deg.) mBar Elapsed Time (Days) Measured
LOCAL ATMOSPHERIC PRESSURE VS. ANGLE 陸 y = 0.1355x + 997.48 R族 = 0.9758 1,005 1,007 1,009 1,011 1,013 1,015 1,017 1,019 75 85 95 105 115 125 135 145 155 P(mbar) PHI (deg.) P(MSL)
CALCULATED PRESSURE VS. MEASURED PRESSURE 1,005 1,010 1,015 1,020 0 1 2 3 4 (MillibarMSL) Elapsed Time (days) P (Least Square) Measured-Local
We have assumed a linear relationship between the balloon diameter and the atmospheric pressure. Is this correct? When we inflate a balloon by mouth, we notice the following At first, it requires a lot of pressure to inflate the balloon. Then, it becomes easier to inflate the balloon as its diameter increases. From these observation, it becomes apparent that the balloon does not behave in a linear fashion. The behavior of a balloon is quite complex. Merritt and Weinhaus have proposed in 1978, a simplified mathematical model of this behavior. BALLOON THEORY-1
Pin is the pressure inside the balloon and Pout is the atmospheric pressure. Merritt and Weinhaus proposed the following relationship between Pin , Pout and the balloon diameter R. 倹 倹 is proportional to 告 告 with R0 the original diameter of the balloon. With = 告 this equation becomes = 告 BALLOON THEORY-2
BALLOON THEORY-3 (PIN-POUT VS. X=R/RO) Max, 1.383, 0.620 0.0 0.2 0.4 0.6 1.0 2.0 3.0 4.0 5.0 6.0 Y=Pin-Pout x=R/Ro Y=Pin-Pout Max
BALLOON THEORY-4 (3 < R/R0 < 3.02 OR A 10mB VARIATION) 0.0000% 0.0002% 0.0004% 0.0006% 0.0008% 0.0010% 0.0012% 0.3305 0.3310 0.3315 0.3320 0.3325 0.3330 3.000 3.004 3.008 3.012 3.016 3.020 % P R/Ro P as a function of R/R0 P P Linear dP/d(R/R0) Therefore, assuming a linear relationship between diameter and pressure is correct.
BALLOON THEORY-5 = 告 + = 告 1 0.52 0 1 2 3 4 5 2 3 4 5 6 mB/mm mm/mB R/R0=3 R/Ro=3 +176% +275% 1 The device becomes more sensitive when the balloon is inflated to a larger diameter
LONG-TERM DATA y = 0.1355x + 997.48 1,005 1,007 1,009 1,011 1,013 1,015 1,017 1,019 75 85 95 105 115 125 135 145 155 165 P(mbar) PHI (deg.) Additional Data (up to 9 days)
1. It appears that our device drifts over time. 2. We suspect that our balloon is slowly leaking. 3. To study this drift, we calculated from the observed atmospheric pressure the theoretical for each data point using the linear regression y = 0.1355x + 997.48 4. Then, we plot the difference between the theoretical and the observed as a function time. LONG-TERM DATA
LONG-TERM DATA y = 1.3477x R族 = 0.2830 0 5 10 15 0 2 4 6 8 10 DeltaPHI DAYS PHI versus T y = 0.0941x R族 = 0.2830 0 1 1 0 2 4 6 8 10 DeltaZ DAYS Z versus T The diameter of the balloon is reduced by one tenth of a millimeter per day
LONG-TERM DATA (TIME CORRECTED RESULTS) 1,008 1,012 1,016 1,020 0 2 4 6 8 AtmosphericPressure(MillibarMSL) Elapsed Time (days) Barometric Pressure (mBar MSL) Calculated P uncorrected Measured-Local Calculated P corrected for drift Not Corrected TIME CORRECTED MEASURED
1. With a large party balloon, we have designed and built an accurate barometer using simple and readily available parts and material. CONCLUSION 2. Over a 4-day period, our barometer provided local atmospheric pressure measurements with an accuracy of +/-0.35mB or 0.035%! 3. The analysis of the data suggested a linear relationship between diameter and pressure. This was confirmed by studying the model of balloon behavior proposed by Merritt and Weinhaus. In addition, this model indicated that the sensitivity of our experimental device could be increased by inflating the balloon to a larger diameter. 4. Over a longer period of time, the recorded data did not fit our earlier model. 5. We did not have enough data to diagnose with certitude the nature of the problem. However, a preliminary analysis of the data indicated that the balloon was slowly leaking and we proposed a methodology to correct for the slow leakage of the balloon.
Building an accurate barometer (+/-0.035%) using a simple party balloon
Building an accurate barometer (+/-0.035%) using a simple party balloon

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Building an accurate barometer (+/-0.035%) using a simple party balloon

  • 4. MAIN CONCEPT Pressure Increases Diameter Decreases Pressure decreases Diameter Increases The Diameter of the Balloon is Directly Related to the Atmospheric Pressure
  • 5. Atmospheric pressure at Mean Sea Level and 25C = 1,013mB A change of 1mB in atmospheric pressure is 0.1% If we assume that the variation in diameter is proportional to the variation of atmospheric pressure, For a balloon diameter of 300mm, a 0.1% variation is 0.3mm! In addition, measuring precisely the dimension of a balloon is very difficult as it has an odd shape, is soft and very lightweight CHALLENGES
  • 6. Use a larger balloon Capture the balloon in a fixed position Make measurements at a fixed position on the balloon Measure without manipulating or touching the balloon Design a system that amplifies the variations in diameter SOLUTIONS
  • 8. DESIGN-2 Shaft Counterweight Balloon Fishing line Wood Disk Glued to Balloon Wood Beam Ball Bearings Dial Indicator Hand Hub If the diameter of the balloon increases, then the counterweight goes down and the indicator hand moves to the right GREEN ARROWS If the diameter of the balloon decreases, then the counterweight goes up and the indicator hand moves to the left BLUE ARROWS
  • 9. DESIGN-3 The diameter of the shaft is d. Therefore, the circumference of the shaft is d. Assuming that the thickness of the fishing line is negligible, if we pull a length of fishing line equal to d from the shaft, then the shaft will rotate by 1 turn. If we pull a length equal to z, the shaft will rotate by a fraction of 1 turn equal to z/d. = z/d turn 1 turn = 360属 Therefore, = 360 x z/d (属)
  • 10. EXPERIMENTAL PROTOCOL - DATA Time Date Humidity (%) Temperature (0F) Atmospheric Pressure (in-Hg) Angle (degrees)
  • 11. ANGLE 陸 AND LOCAL ATMOSPHERIC PRESSURE 80 100 120 140 160 180 200 996 1,000 1,004 1,008 1,012 1,016 1,020 0 1 2 3 4 PHI(deg.) mBar Elapsed Time (Days) Measured
  • 12. LOCAL ATMOSPHERIC PRESSURE VS. ANGLE 陸 y = 0.1355x + 997.48 R族 = 0.9758 1,005 1,007 1,009 1,011 1,013 1,015 1,017 1,019 75 85 95 105 115 125 135 145 155 P(mbar) PHI (deg.) P(MSL)
  • 13. CALCULATED PRESSURE VS. MEASURED PRESSURE 1,005 1,010 1,015 1,020 0 1 2 3 4 (MillibarMSL) Elapsed Time (days) P (Least Square) Measured-Local
  • 14. We have assumed a linear relationship between the balloon diameter and the atmospheric pressure. Is this correct? When we inflate a balloon by mouth, we notice the following At first, it requires a lot of pressure to inflate the balloon. Then, it becomes easier to inflate the balloon as its diameter increases. From these observation, it becomes apparent that the balloon does not behave in a linear fashion. The behavior of a balloon is quite complex. Merritt and Weinhaus have proposed in 1978, a simplified mathematical model of this behavior. BALLOON THEORY-1
  • 15. Pin is the pressure inside the balloon and Pout is the atmospheric pressure. Merritt and Weinhaus proposed the following relationship between Pin , Pout and the balloon diameter R. 倹 倹 is proportional to 告 告 with R0 the original diameter of the balloon. With = 告 this equation becomes = 告 BALLOON THEORY-2
  • 16. BALLOON THEORY-3 (PIN-POUT VS. X=R/RO) Max, 1.383, 0.620 0.0 0.2 0.4 0.6 1.0 2.0 3.0 4.0 5.0 6.0 Y=Pin-Pout x=R/Ro Y=Pin-Pout Max
  • 17. BALLOON THEORY-4 (3 < R/R0 < 3.02 OR A 10mB VARIATION) 0.0000% 0.0002% 0.0004% 0.0006% 0.0008% 0.0010% 0.0012% 0.3305 0.3310 0.3315 0.3320 0.3325 0.3330 3.000 3.004 3.008 3.012 3.016 3.020 % P R/Ro P as a function of R/R0 P P Linear dP/d(R/R0) Therefore, assuming a linear relationship between diameter and pressure is correct.
  • 18. BALLOON THEORY-5 = 告 + = 告 1 0.52 0 1 2 3 4 5 2 3 4 5 6 mB/mm mm/mB R/R0=3 R/Ro=3 +176% +275% 1 The device becomes more sensitive when the balloon is inflated to a larger diameter
  • 19. LONG-TERM DATA y = 0.1355x + 997.48 1,005 1,007 1,009 1,011 1,013 1,015 1,017 1,019 75 85 95 105 115 125 135 145 155 165 P(mbar) PHI (deg.) Additional Data (up to 9 days)
  • 20. 1. It appears that our device drifts over time. 2. We suspect that our balloon is slowly leaking. 3. To study this drift, we calculated from the observed atmospheric pressure the theoretical for each data point using the linear regression y = 0.1355x + 997.48 4. Then, we plot the difference between the theoretical and the observed as a function time. LONG-TERM DATA
  • 21. LONG-TERM DATA y = 1.3477x R族 = 0.2830 0 5 10 15 0 2 4 6 8 10 DeltaPHI DAYS PHI versus T y = 0.0941x R族 = 0.2830 0 1 1 0 2 4 6 8 10 DeltaZ DAYS Z versus T The diameter of the balloon is reduced by one tenth of a millimeter per day
  • 22. LONG-TERM DATA (TIME CORRECTED RESULTS) 1,008 1,012 1,016 1,020 0 2 4 6 8 AtmosphericPressure(MillibarMSL) Elapsed Time (days) Barometric Pressure (mBar MSL) Calculated P uncorrected Measured-Local Calculated P corrected for drift Not Corrected TIME CORRECTED MEASURED
  • 23. 1. With a large party balloon, we have designed and built an accurate barometer using simple and readily available parts and material. CONCLUSION 2. Over a 4-day period, our barometer provided local atmospheric pressure measurements with an accuracy of +/-0.35mB or 0.035%! 3. The analysis of the data suggested a linear relationship between diameter and pressure. This was confirmed by studying the model of balloon behavior proposed by Merritt and Weinhaus. In addition, this model indicated that the sensitivity of our experimental device could be increased by inflating the balloon to a larger diameter. 4. Over a longer period of time, the recorded data did not fit our earlier model. 5. We did not have enough data to diagnose with certitude the nature of the problem. However, a preliminary analysis of the data indicated that the balloon was slowly leaking and we proposed a methodology to correct for the slow leakage of the balloon.