Auxiliary Tidal Force Effects
Transcript of Auxiliary Tidal Force Effects
![Page 1: Auxiliary Tidal Force Effects](https://reader030.fdocuments.us/reader030/viewer/2022020705/61fb77572e268c58cd5e7fe7/html5/thumbnails/1.jpg)
Auxiliary Tidal
Force Effects [AUTHOR(S) OMITTED FOR WEB POSTING]
h
![Page 2: Auxiliary Tidal Force Effects](https://reader030.fdocuments.us/reader030/viewer/2022020705/61fb77572e268c58cd5e7fe7/html5/thumbnails/2.jpg)
Background Tides
Gravity
Celestial bodies
Constructive Gravitational Forces Tidal Phases
![Page 3: Auxiliary Tidal Force Effects](https://reader030.fdocuments.us/reader030/viewer/2022020705/61fb77572e268c58cd5e7fe7/html5/thumbnails/3.jpg)
Outline Problem Scenario
Assumptions
Mathematical Development and Solution
Results and Conclusion
Extensions
![Page 4: Auxiliary Tidal Force Effects](https://reader030.fdocuments.us/reader030/viewer/2022020705/61fb77572e268c58cd5e7fe7/html5/thumbnails/4.jpg)
Problem Scenario The Sun’s size is increasing.
What are the tidal effects?
Compare tidal shift to the RMS Titanic.
![Page 5: Auxiliary Tidal Force Effects](https://reader030.fdocuments.us/reader030/viewer/2022020705/61fb77572e268c58cd5e7fe7/html5/thumbnails/5.jpg)
Assumptions 1. Considering only 3 bodies: The Earth, Sun, and Moon
2. Neap Tide Position
3. These bodies are stationary
4. Sun’s size increases, all other sizes remain constant
5. Each body possesses uniform density
6. As the Sun grows, it will continually have uniform density
7. Traveling momentum of the Titanic is negated
![Page 6: Auxiliary Tidal Force Effects](https://reader030.fdocuments.us/reader030/viewer/2022020705/61fb77572e268c58cd5e7fe7/html5/thumbnails/6.jpg)
Mathematical Development 1: Modeling Tides
Newton’s Law of Universal Gravitation:
A New Formula:
![Page 7: Auxiliary Tidal Force Effects](https://reader030.fdocuments.us/reader030/viewer/2022020705/61fb77572e268c58cd5e7fe7/html5/thumbnails/7.jpg)
center of mass (G)
center of buoyancy (B) (the center of the submerged
volume of the boat).
metacenter (M)
Mathematical Development 2: Capsizing Vessels and GZ Curves
![Page 8: Auxiliary Tidal Force Effects](https://reader030.fdocuments.us/reader030/viewer/2022020705/61fb77572e268c58cd5e7fe7/html5/thumbnails/8.jpg)
Righting Arm (GZ length)
Mathematical Development 2: Capsizing Vessels and GZ Curves
![Page 9: Auxiliary Tidal Force Effects](https://reader030.fdocuments.us/reader030/viewer/2022020705/61fb77572e268c58cd5e7fe7/html5/thumbnails/9.jpg)
Solution Assume time variable, and assume initial Lunar
displacement
Find a path from increasing Sun mass to Solar tidal
displacement by use of formulae:
Sun’s Mass(t) ⇒
Volume ⇒
Radius ⇒
Distance from Sun to Earth ⇒
Ratio of Sun's gravitational force to the Moon's ⇒
Solar Tidal Displacement
![Page 10: Auxiliary Tidal Force Effects](https://reader030.fdocuments.us/reader030/viewer/2022020705/61fb77572e268c58cd5e7fe7/html5/thumbnails/10.jpg)
Results Refer to Excel Tables
Table with Mass*e^(t)
t = 6
t = 17
y = 0.2419e1.0224x R² = 0.9999
0
500
1000
1500
2000
2500
3000
0 5 10
Dis
pla
cem
en
t (m
)
Time t
Tidal Displacement
Expon.…
![Page 11: Auxiliary Tidal Force Effects](https://reader030.fdocuments.us/reader030/viewer/2022020705/61fb77572e268c58cd5e7fe7/html5/thumbnails/11.jpg)
Conclusions 1. At t = 7, Tidal displacement exceeds record wave
height
2. At t = 17, Sun engulfs Earth (negative distance)
3. With the Sun tripled in size, tidal displacement is not
very significant
The Titanic has fallen
![Page 12: Auxiliary Tidal Force Effects](https://reader030.fdocuments.us/reader030/viewer/2022020705/61fb77572e268c58cd5e7fe7/html5/thumbnails/12.jpg)
Extensions
Measure danger of capsizing due to size waves and length
of righting arm:
Formula for relating size of waves to a vessel’s GZ curve
and righting arm
Probability of recovering from capsizing