Resources to learn about scaling arguments

In summary: AND THE UNIVERSALITY OF THE FALLING RATE OF ...In summary, the conversation discusses the topic of scaling arguments and the search for resources to better understand it. The main focus is on the lecture by Walter Lewin from MIT, where he performs a scaling argument with femurs based on Galileo's assumption. The conversation suggests revisiting the lecture and using dimensional analysis as a starting point for understanding scaling. A resource for further reading is also provided.
  • #1
jonander
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TL;DR Summary
Good resources to learn to make scaling arguments
Hi everybody,

After watching the first lecture by Walter Lewin from MIT, I'm finding hard to follow the part in what he talks about scaling arguments. I've been watching around the Internet for resources to get my head around it but I couldn't find much or maybe I'm not using the right keywords.

Does anybody know good resources and exercise where I can get a clearer picture of how to make scaling arguments?

Thanks
 
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  • #2
Google "dimensional analysis"
 
  • #3
Hi Chester, thanks for replying. I know that in the lecture Walter performs a dimensional analysis, but that's after the scaling argument with the femur.
 
  • #4
Maybe you can provide more context? Are you talking about scale-up of a system (or scale-down)?
 
  • #5
Sorry, I don't understand what you mean with the "scale-up"

In the lecture, he performs a scaling argument with femurs based on a Galileo's assumption. He makes several operations involving proportionality with the mass and lengths of the femurs. These kinds of analysis and the procedure are what I'm looking for.
 
  • #6
My experience is that scaling typically starts with dimensional analysis. Maybe someone else can give you a better answer.
 
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  • #7
jonander said:
but that's after the scaling argument with the femur.
Having heard the scaling argument, perhaps you could revisit the earlier parts of the lecture. I agree with @Chestermiller that dimensional analysis is probably the key here.
 
  • #8
jonander said:
In the lecture, he performs a scaling argument with femurs based on a Galileo's assumption. He makes several operations involving proportionality with the mass and lengths of the femurs. These kinds of analysis and the procedure are what I'm looking for.

"Galileo realized that simple geometric scaling does not work when the mechanical strength of structures is taken into account."
Have a look at:
[PDF]SCALING - GALILEO
 
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FAQ: Resources to learn about scaling arguments

1. What are scaling arguments and why are they important?

Scaling arguments are mathematical tools used to understand how a system or phenomenon changes as its size or other variables change. They are important because they allow scientists to make predictions and draw conclusions about systems that are too complex to fully understand through direct observation or experimentation.

2. Where can I find resources to learn about scaling arguments?

There are many resources available to learn about scaling arguments, including textbooks, online articles and tutorials, and scientific journals. Some universities also offer courses or workshops on the topic. Additionally, there are online communities and forums where scientists discuss and share information about scaling arguments.

3. How can I apply scaling arguments in my research?

Scaling arguments can be applied in various fields of science, such as physics, biology, and economics. To apply scaling arguments in your research, you first need to identify the relevant variables and their relationships in your system. Then, you can use mathematical equations and principles to analyze how these variables scale and make predictions about the behavior of the system.

4. Are there any limitations to using scaling arguments?

While scaling arguments can be a powerful tool, they also have limitations. They are based on simplifications and assumptions, so they may not always accurately represent complex systems. Additionally, scaling arguments may not be applicable to all types of systems, and their predictions may only hold true within certain ranges of variables.

5. How can I improve my understanding of scaling arguments?

One way to improve your understanding of scaling arguments is to practice using them in different contexts and with different types of systems. You can also read and study examples of scaling arguments in scientific literature. Collaborating with other scientists who have experience with scaling arguments can also help deepen your understanding of the topic.

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