BALLOON BAROMETER

3BALLOON

BAROMETER

MAIN CONCEPT

Pressure IncreasesDiameter Decreases

Pressure decreasesDiameter Increases

The Diameter of the Balloon is Directly Related to the Atmospheric Pressure

• 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

• 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 DiskGlued to Balloon

Wood Beam

Ball Bearings

Dial

IndicatorHand

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-3The 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 turn1 turn = 360°Therefore,

φ = 360 x z/πd (°)

EXPERIMENTAL PROTOCOL - DATA

Time

Date

Humidity (%)

Temperature (0F)

AtmosphericPressure (in-Hg)Angle φ

(degrees)

ANGLE Φ AND LOCAL ATMOSPHERIC PRESSURE

0 1 2 3 4996

1,000

1,004

1,008

1,012

1,016

1,020

80

100

120

140

160

180

200

Measured φ

Elapsed Time (Days)

mB

ar

PH

I (d

eg.)

LOCAL ATMOSPHERIC PRESSURE VS. ANGLE Φ

75 85 95 105 115 125 135 145 1551,005

1,007

1,009

1,011

1,013

1,015

1,017

1,019

f(x) = 0.135461673206544 x + 997.479210513376R² = 0.975829797727714

P(MSL)

PHI (deg.)

P (

mb

ar)

CALCULATED PRESSURE VS. MEASURED PRESSURE

0 1 2 3 41,005

1,010

1,015

1,020

P (Least Square)

Measured-Local

Elapsed Time (days)

(Mil

lib

ar M

SL

)

• 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.

• is proportional to with R0 the original diameter of the balloon.

• With this equation becomes

BALLOON THEORY-2

BALLOON THEORY-3 (PIN-POUT VS. X=R/RO)

1.0 2.0 3.0 4.0 5.0 6.00.0

0.2

0.4

0.6

Series1, Max, 0.620Y=Pin-Pout

Max

x=R/Ro

Y=

Pin

-Po

ut

BALLOON THEORY-4 (3 < R/R0 < 3.02 OR A 10mB VARIATION)

3.000 3.004 3.008 3.012 3.016 3.0200.3295

0.3300

0.3305

0.3310

0.3315

0.3320

0.3325

0.3330

0.3335

0.0000%

0.0002%

0.0004%

0.0006%

0.0008%

0.0010%

0.0012%

P as a function of R/R0

PP LineardP/d(R/R0)

R/Ro

P

%

Therefore, assuming a linear relationship between diameter and pressure is correct.

BALLOON THEORY-5

2 3 4 5 60

1

2

3

0.52

1.94

mB/mm

mm/mB

R/R0=3

R/Ro=3

+176%

+275%

𝒅𝑷𝒅𝑿

( 𝒅𝑷𝒅𝑿 )−1

The device becomes more sensitive when the balloon is inflated to a larger diameter

LONG-TERM DATA

75 85 95 105 115 125 135 145 155 1651,005

1,007

1,009

1,011

1,013

1,015

1,017

1,019

f(x) = 0.135461673206544 x + 997.479210513376R² = 0.975829797727714

PHI (deg.)

P (

mb

ar)

Additional Data (up to 9 days) do not fit our earlier model

The new data does not fit the original regression

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

LONG-TERM DATA

0 2 4 6 8 100

5

10

15f(x) = NaN xR² = 0

Δ PHI versus T

DAYS

Del

ta P

HI

0 2 4 6 8 100

1

1f(x) = NaN xR² = 0

Δ Z versus T

DAYS

Delt

a Z

The diameter of the bal-loon is reduced by one tenth of a millimeter per day

The new data does not fit the original regression

The balloon appears to be leaking slowly….

LONG-TERM DATA (TIME CORRECTED RESULTS)

0 2 4 6 81,008

1,012

1,016

1,020Barometric Pressure (mBar MSL)

Calculated P uncorrected

Measured-Local

Calculated P corrected for drift

Elapsed Time (days)

Atm

osp

her

ic P

ress

ure

(M

illib

ar M

SL

)

Not Corrected

TIME CORRECTEDMEASURED

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.

ΔP/P < 0.035%

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