building an accurate barometer (+/-0.035%) using a simple party balloon
Post on 06-May-2015
64 Views
Preview:
DESCRIPTION
TRANSCRIPT
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%
ENDEND
top related