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# 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. 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

1. 1. MAIN CONCEPT Pressure Increases Diameter Decreases Pressure decreases Diameter Increases The Diameter of the Balloon is Directly Related to the Atmospheric Pressure
2. 2. • Atmospheric pressure at Mean Sea Level and 25◦C = 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
3. 3. • 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
4. 4. DESIGN-1
5. 5. 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
6. 6. DESIGN-3 The diameter of the shaft is d. Therefore, the circumference of the shaft is πd. Assuming that the thickness of the fishing line is negligible, if we pull a length of fishing line equal to πd 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/πd. φ = z/πd turn 1 turn = 360° Therefore, φ = 360 x z/πd (°)
7. 7. EXPERIMENTAL PROTOCOL - DATA Time Date Humidity (%) Temperature (0F) Atmospheric Pressure (in-Hg) Angle φ (degrees)
8. 8. ANGLE Φ 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 φ
9. 9. LOCAL ATMOSPHERIC PRESSURE VS. ANGLE Φ y = 0.1355x + 997.48 R² = 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)
10. 10. 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
11. 11. • 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
12. 12. • 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. • 𝑷𝒊𝒏 − 𝑷𝒐𝒖𝒕 is proportional to 𝑪 𝑹𝟎 𝟐 𝟏 𝑹 𝟏 − 𝑹𝟎 𝑹 𝟔 with R0 the original diameter of the balloon. • With 𝒙 = 𝑹 𝑹𝟎 this equation becomes 𝒚 = 𝑪 𝑹𝟎 𝟑 𝟏− 𝟏 𝒙 𝟔 𝒙 BALLOON THEORY-2
13. 13. 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
14. 14. 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.
15. 15. BALLOON THEORY-5 𝒅𝑷 𝒅𝑿 = 𝑪 𝑹𝟎 𝟑 𝟕 𝑿 𝟔+𝟏 𝑿 𝟐 𝒘𝒊𝒕𝒉 𝑿 = 𝑹 𝑹𝟎 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% 𝒅𝑷 𝒅𝑿 𝒅𝑷 𝒅𝑿 −1 The device becomes more sensitive when the balloon is inflated to a larger diameter
16. 16. 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)
17. 17. 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” φ for each data point using the linear regression y = 0.1355x + 997.48 4. Then, we plot the difference between the “theoretical” φ and the observed φ as a function time. LONG-TERM DATA
18. 18. LONG-TERM DATA y = 1.3477x R² = 0.2830 0 5 10 15 0 2 4 6 8 10 DeltaPHI DAYS Δ PHI versus T y = 0.0941x R² = 0.2830 0 1 1 0 2 4 6 8 10 DeltaZ DAYS Δ Z versus T The diameter of the balloon is reduced by one tenth of a millimeter per day
19. 19. 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
20. 20. 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.