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.

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 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

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

7. DESIGN-1

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 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 (°)

10. EXPERIMENTAL PROTOCOL - DATA
Time
Date
Humidity (%)
Temperature (0F)
Atmospheric
Pressure (in-Hg)
Angle φ (degrees)

11. 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

12. 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)

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.
• 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

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
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

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” 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

21. 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

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.