# Minimizing action of falling maple seed.

• Maple
• Spinnor
In summary, the maple tree seed falls to the ground, then surges upward and floats before eventually landing.

#### Spinnor

Gold Member
In the following link is a slow motion video of a maple tree seed falling (you have to wait till the 7th second).

From the Wiki article on Action

http://en.wikipedia.org/wiki/Action_(physics)

"In physics, action is an attribute of the dynamics of a physical system. It is a mathematical functional which takes the trajectory, also called path or history, of the system as its argument and has a real number as its result. Action has the dimension of energy × time, and its unit is joule-seconds in the International System of Units (SI). Generally, the action takes different values for different paths. Classical mechanics postulates that the path actually followed by a physical system is that for which the action is minimized, or, more strictly, is stationary."

If we consider the falling seed and the air through which it falls as the dynamical system how can we use the above quote to help explain how the seed falls in the above video?

Thanks for any help!

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I haven't actually seen a Lagrangian treatment for rigid body motion. The Newtonian treatment is much simpler I think when it comes to rigid bodies.

The maple tree seed spins because it interacts with the air. The air flows around it in a highly complex, non-static, non-rigid way. If you dropped the seed in a vacuum with no initial spin, it would not spin. To use the action principle, you would have to model all the possible ways (possible mathematically, not necessarily physically) that the air can flow around it - this is the action - then minimize your expression to get the actual physical air flow - this is the least action. It's simple in concept, but would be difficult in practice to use a least action approach quantitatively to solve for fluid flow. If I remember right, the least action approach is useful in practice if there are very few degrees of freedom in the system (a bead on a hoop, a weight on a plane, etc.). For a fluid, each molecule is somewhat free, so your system would have a huge number of degrees of freedom.

If you want to try to conceptualize the least action principle for a twirling maple seed, you could say that its twirling leads to the least amount of drag and least amount of air turbulence, because the air encounters its knife edge when it twirls instead of it's broad face. This similar to a simple paper airplane. If you simply drop a paper airplane, it will not fall straight down, but instead will glide at an angle, in the direction where the drag is minimized.

I think what he is pointing to is that the seed falls, then surges upward, then floats or maintains its elevation... as if the seed's airfoil suddenly gets a better grip on the air, speeds up its rotation, then somehow "overspins" to lift the seed...

That floating at the very end of the video must be a very subtle effect or be just the camera getting bumped. I have watched a lot of real maple seeds fall in my life time and I have never seen one stop falling suddenly.

chrisbaird said:
That floating at the very end of the video must be a very subtle effect or be just the camera getting bumped. I have watched a lot of real maple seeds fall in my life time and I have never seen one stop falling suddenly.

I think what happens at the end of the video is the seed lands on a table that can't be seen.

Thanks for help in understanding this!

## 1. How does the shape of a maple seed affect its falling motion?

The shape of a maple seed, also known as a samara, is designed to minimize its air resistance and slow down its falling speed. The shape of the seed creates a higher pressure below the seed, causing an upward force that counteracts the force of gravity.

## 2. What is the role of air resistance in the falling motion of a maple seed?

Air resistance plays a crucial role in the falling motion of a maple seed. As the seed falls, it encounters air resistance, which slows it down and causes it to spin around its center of mass. This spinning motion creates a stable and slow falling motion, giving the seed a better chance of landing in an ideal location for germination.

## 3. How does the angle of the wings on a maple seed affect its falling motion?

The angle of the wings on a maple seed, known as the wing pitch angle, is crucial in minimizing its falling action. A smaller wing pitch angle creates a larger surface area for air to push against, resulting in a slower falling speed. However, if the wings are too flat, the seed may not have enough lift to slow down its descent and may fall too quickly.

## 4. Can the weight of a maple seed affect its falling motion?

Yes, the weight of a maple seed can affect its falling motion. A heavier seed will fall faster due to the increased force of gravity. This is why maple seeds have a low density and are lightweight, allowing them to fall slowly and have a better chance of landing in an ideal location for germination.

## 5. How does the size of a maple seed impact its falling motion?

The size of a maple seed can impact its falling motion in two ways. Firstly, a larger seed will have more mass, making it fall faster due to the increased force of gravity. Secondly, a larger seed will have a larger surface area, which can increase air resistance and help slow down its descent. Ultimately, the size of a maple seed must be balanced with its weight and shape to achieve the optimal falling motion.